Hertz So Good? 432Hz Examined.

Guitar Waves

 

Hertz so Good?

The resonating delusion of the 432Hz movement

Milton Mermikides ©2014
@miltonline

 

[tl;dr Kindly read at least the following 5 points before commenting:
1) I am pro-choice in terms of music, and actively encourage experimentation and challenge of the status quo in music, both in my practice and my teaching. I am also well-versed (but always learning) in terms of the science, history and multicultural practice of music.
2) This article examines all the various ‘scientific’, ‘historical’ and ‘cosmic’ arguments I have found for the superiority of the 432Hz over 440Hz tuning reference, and find them to be fallacious, contradictory, misinformed and/or unevidenced. I also see no evidence for 440Hz superiority to 432Hz (or any other over any other for that matter).
3) While there are some subtle physical world differences of 432Hz to 440Hz, I suggest that it is not a very significant musical argument to have, and there are many far better music areas of development and cultural shift (including temperament, microtiming etc.)
4) I use different tuning references, I’m very happy for anyone to do so (or anything they want to musically of course), I just am yet to find any good argument or evidence for 432Hz superiority.
5) Despite accusations to the contrary, I am not a shill of some shadowy musical establishment, Illumaniti or lizards to challenge 432Hz. Believe it or not, I’m not being paid to write this. Heaven forbid.

I welcome any critical feedback, but please keep it civil, and threats and insults to me and my family will not be tolerated. I can’t believe I have to write this about a music theory post. ]

There’s been a recent musical movement by a small but impassioned group of people advocating a change from 440Hz to 432Hz musical tuning. Proponents claim that tuning music to this frequency results in a more sonorous and ‘natural’ sound which will ultimately make every one of us happier, peaceful and healthy. Tips of how to retune music libraries and instruments abound and the benefits of the adjustment are zealously extolled by advocates. These recommendations are often accompanied by claims that the prevailing 440Hz standardization has negative effects, as well as links to Nazi Germany. The Illumaniti have also been implicated (presumably in the guise of a political powerful and wealthy musical academia) who are hiding this ‘musical truth’ which ‘they don’t want you to know”. Any popular interest in musical analysis – the enquiry into the complex and beautiful mechanics which make music work – is rare and welcome, and new ideas, subversions and revolutions are the lifeblood of musical progress. All music traditions however fossilised today are built upon revolutionary ideas of the time, so this – as any other – movement which challenges the homogeneity in musical practice, wherever they arise deserves serious consideration.

But in order to understand the effects of such a move, some basics of frequency and pitch need to be discussed, so here’s a very succinct introduction.

Frequency and Pitch

An instrument, voice – or any ‘excited’ object – will disturb the molecules in the air surrounding it, and as that object vibrates – imagine the oscillating prongs of a struck tuning fork – the molecules in the surrounding air (or whatever medium) oscillate sympathetically. Thus a wave of changing pressure propagates from the object, spreading its energy out in the surrounding air, perhaps to fall on some local ear drums (or microphone diaphragms) which in turn oscillate sympathetically. The amount the molecules are displaced is known as the amplitude and is related to our experience of volume, but here we are more concerned with the frequency of the waves: the time for each vibration cycle of the object to be completed (for example how often the prongs of our tuning fork move from their rightmost extent, bounce back and forth and return to the rightmost extent). The frequency of this oscillation is usually measured in Hertz (Hz.) the number of these cycles per second (or kHz for 1000s of cycles per second) and when these fall in the approximate range of 20Hz-20kHz we humans experience them as sound, with the frequency value correlating to pitch. The lower the frequency, the lower the pitch, the higher frequencies are heard as higher pitches. Crucially, this frequency is continuous – we can have theoretically create any frequency (and pitch) at whatever increment (440Hz, 440.02Hz, 893.3482Hz whatever) it is not stepped – although there is a perceptual limit to fine difference. It’s also important to understand that our experience of frequency is logarithmic, we hear multiplications and divisions (rather than additions and subtractions) of frequency as similar musical intervals. For example, a doubling (or halving) of a frequency creates a musical interval known as an octave, which has a sense of musical equivalence (this phenomenon is sometimes referred to as the Law of Octave Equivalence). Incidentally, doubling (or halving) a frequency is equivalent to halving (or doubling) a string length and that’s why for example you’ll find an octave exactly halfway along a guitar string.

Almost all musical cultures share the concept of the octave and give the same note names to pitches whose frequencies are multiples (or divisions) of 2. So if concert A is at 440Hz, we’ll find an infinite number of theoretical As (although only 10 or so audible ones) at 880Hz, 1.76kHz, 3.52kHz etc. above and 220Hz, 110Hz, 55.5Hz etc. below.

Slicing the Octave

So by halving or doubling we can create octaves, but other musical intervals can also be created by multiplying (or dividing) by numbers other than 2. In fact by multiplying a frequency by various frequency ratios the octave itself can be sliced into any number of subdivisions. How an octave is divided in music theory and practice is hugely interesting, complex and musically relevant with an early history that includes Ancient Babylon, Pythagoras and the Arabic world resulting in a staggering number of systems from the 22 Hindustani shrutis, 55-division Classical tuning, Javanese Slendro and Pelog, the 15(+) divisions of the Arabic maqam, Blues microtones, Harry Partch’s 43-note universe and innumerable other intuited or theoretically grounded systems.

The system many of us have inherited – at least conceptually – divides the octave into 12 equal parts (that is, each increment is based on a fixed multiplication of a reference pitch). In this 12 tone equal tempered (12-TET) system we can calculate the 12 notes by multiplying a reference pitch (usually 440Hz) by this fixed frequency ratio (the 12th root of 2 ≈1.059463) to create a series of pitches (see below). Incidentally these fixed multiplications are associated with corresponding fixed divisions of a wavelength, and that is why you’ll notice the frets of a standard guitar fretboard get closer together as you progress up the string – each fret is placed at about 5.95% of the remaining string – not at fixed distances throughout.  The resulting pitches can be repeated at any number of octaves above (or below) by doubling (or halving) the relevant frequencies.

 

12-TET

Frequency (Hz)

440Hz Reference

Frequency relationship

to reference (440Hz)

A

440

1

A# or Bb

466.16376

1.05946

B

493.88330

1.12246

C

523.25113

1.18921

C# or Db

554.36526

1.25992

D

587.32954

1.33484

D# or Eb

622.25397

1.41421

E

659.25511

1.49831

F

698.45646

1.58740

F# or Gb

739.98885

1.68179

G

783.99087

1.78180

G# or Ab

830.60940

1.88775

A’

880

2

Table 1: Absolute frequencies (and frequency relationships) of 12-TET (Concert A to the octave above) in 440Hz. All numbers approximated to 5 decimal places.

12-TET has some specific merits and many shortfalls, simplistically it excels at providing a simple system for handling complex chords and changing keys and hence became standard in the transition from Classical to Romantic music and its ultimate – and perhaps inevitable – ascent (some say descent) into 12-tone serialism. However, 12-TET ignores the spectrum of alternative divisions of the octave including those based on ‘just’ or ‘pure’ frequency ratios such as 3/2, 5/4 (as favoured in the monophonic drone based Hindustani music for example). In fact 12-TET is just one of many possible tuning systems available which have been, are, or could be put into musical practice. It is rarely questioned and many people (including musicians) blindly accept this method of octave division, wholly unaware either that other systems exist or that 12-TET is relatively new in the history of Western Art music, for example we know that Mozart considered enharmonics such as G# and Ab (which are equivalent in 12-TET) to be differently pitched notes. If one is looking for a cultural blindspot against which to rail, 12-TET is the perfect candidate. Other tuning systems are theoretically beautifully, historically and stylistically diverse and startlingly effective and relevant. If you are into a ‘revolution of consciousness’ (as the 432Hz movement purport to offer) then engage with music which eschews 12-TET: the tuning of Hindustani ragas (based on simple ‘pure’ frequency ratios of 3/2, 5/4, 6/5 and the like), the harmonic series exploitation in Tuvan throat singing, Javanese Gamelan, Murail’s spectralism, Lucy tuning’s ‘squaring the circle’ approach to 5ths and 3rds, Partch’s 11-limit universe, Taiwanese 7-TET flute and stretched octave tuning for starters.

So what ‘musical truth’ are the 432Hz proponents offering?

A New Reference

The 432Hz proponents suggest that the A reference point (often called concert A, the A above middle C on the piano, and the familiar orchestral tuning note) should be tuned not to 440Hz but to 432Hz. It’s about 31.8% on its way down to the next equal-tempered chromatic note (about 32 cents in music tuning jargon – around one third of a semitone). When one ‘tunes to 432Hz’ all the other pitches move down. So for example, the A above concert A which was previously at 880Hz (double of 440Hz, creating the octave above) now moves down to 864Hz, as do all the other 12 notes in every octave (in a 12-tone per octave system). In fact the whole network of relationships, the spectrum of frequency relationships to that reference pitch moves down.

 

12-TET

Frequency (Hz.)

440Hz Ref

Frequency relationship to reference (440Hz)

Frequency (Hz.)

432Hz Ref

Frequency relationship to reference (432Hz)

A

440

 1

432

1

Bb

466.16376

1.05946

457.68806

1.05946

B

493.88330

1.12246

484.90360

1.12246

C

523.25113

1.18921

513.73747

1.18921

C#

554.36526

1.25992

544.28589

1.25992

D

587.32954

1.33484

576.65082

1.33484

D#

622.25397

1.41421

610.94026

1.41421

E

659.25511

1.49831

647.26866

1.49831

F

698.45646

1.58740

685.75725

1.58740

F#

739.98885

1.68179

726.53450

1.68179

G

783.99087

1.78180

769.73649

1.78180

G#

830.60940

1.88775

815.50741

1.88775

A

880

2

864

2

Table 2: Comparison of Frequencies and their relationships of 440Hz and 432Hz tuning. All numbers approximated to 5 decimal places.

This is an important point to make – and one many 432ruthers do not seem to understand – everything moves along with the frequency relationships. It’s like moving a Rembrandt painting a fraction of an inch down a wall and claiming an improvement. All the notes have moved, but the frequency relationships between them are identical (Table 2). [Another – perhaps better – analogy might be a small uniform decrease in the saturation of all colours in a painting]. Even though some buzz words concerning tuning systems (temperance, pure 5ths, cycles and spirals of 5ths, fundamental, just intonation etc.) appear in the word-salad of 432Hz proponent sites and posts, few show an understanding of the concept, let alone offer relevant alternatives to 12-TET tuning systems. Certainly transposing everything down to 432Hz alone will not alter any internal frequency relationships – the essence of tuning. Changing a tuning system is significant, changing a reference pitch is not necessarily so. One could argue that a reference pitch (as opposed to a tuning system or temperament) is more about the arbitrary naming of pitches, than the more pertinent interrelationship between them. The 432Hz movement lay claim to a musical enlightenment yet ironically, many accept without the question the highly conventional (and mainly ‘Western’) 12 tone division and 7 note names, and erroneously conflate a poor grasp of tuning systems with that of reference frequencies. And crucially, even when 432Hz recommend ‘just’ intonation or other alternatives to 12-TET, one must remember that 432Hz has no monopoly on these systems, which may (and are) implemented with any other reference frequency (including 440Hz).

The Arguments for 432Hz Examined

So what difference will changing a reference pitch make, and why is 432Hz specifically promoted? Let’s take some of the key arguments in turn.

1) 432Hz sounds more relaxed/seated/centered/peaceful etc. than 440Hz

Play any higher tone followed by a slightly lower one and you can convince yourself and others that the second is more relaxed and resolved, and less ‘harsh’. This is simply a trick of associating negative connotations to higher pitches and positive ones to lower pitches. A higher pitch could be described as harsh, cerebral, brash, brittle and sterile (as opposed to soft, spiritual, peaceful, relaxed and warm) or strong, thoughtful, brave, optimistic and bright (as opposed to weak, thoughtless, cowardly, pessimistic and dull). Our expectations do the rest. If you value anecdotes, then consider this: I’ve discussed the 440Hz/432Hz issue and played the two tones to an audience, almost all agree that the latter sounds more ‘relaxed’ and ‘peaceful’.  However it’s then revealed that what was actually heard was 432Hz followed by a 424.15Hz tone (a drop in pitch proportional to 440Hz-432Hz).

2) Frequency is important and 432Hz is a special number of cosmic significance

This is the most common argument for the shift to 432Hz but fails to acknowledge some basic errors of judgment. Firstly although frequency is central to musical pitch (as well as rhythm and timbre of course) it is no more important in a 432Hz than a 440Hz setting (or with any other reference point you wish to choose). Secondly, although frequency as a concept is vital, the measuring system we use (Hz: cycles per second) is entirely arbitrary, based on the various measurements available for the Earth’s – not entirely consistent -rotation period. Most recently a specific number of radiation periods of a particular atom at a specific temperature is used as the calculation. There is nothing natural or axiomatic about the number of periods, or the atom and temperature chosen. In addition 432ruthers show a complete obsession with integers, when the decimal numbering system we use is neither natural nor cosmic. Pi and Phi (as ‘naturally occurring’ numbers as one can hope to find) don’t conform to such rational niceties. The onus is on the 432Hz proponent to demonstrate any reason to accept this number over any other and have yet to come close to evidence. Embarrassing arguments about Saturn’s 864 ‘year’ (432×2) procession are approximate, data-mined and irrelevant. Saturn is argued to be the Solar System’s (and hence the Universe’s presumably) time-keeper as it is the furthest planet from the Sun. Which it is of course, not. Links of 432Hz to the ‘Earth frequency’ are examined later.

3) 432Hz is a ‘good’ frequency and tuning to 432Hz makes all the related notes ‘better’

If we accept that 432Hz is somehow better a frequency than 440Hz, then let’s look more critically at what would result from such an adjustment. 432Hz would only be the frequency of the (arbitrarily named) concert A, the other notes would be (presumably 12-TET) multiplications of that frequency, are these special also?

The argument sometimes touted that 432Hz produces more integer frequencies than 440Hz, is patently untrue (see the table above) and irrelevant even if it did. If we are so generous as to suggest that proponents mean that more integers are produced when using the 22-Shruti ‘just intonation’ tuning system, 432Hz fares a little better than 440Hz (12 of 22 vs 10 of 22 integers) but worse than other reference notes like 400Hz, 600Hz or even 622.08kHz the latter of which has all divisions as integers.

It gets worse. Just because we use a 432Hz reference doesn’t mean that that frequency is prominently represented in a piece of music. A piece entirely in the keys of B major, F# major, Eb major, Ab major, Db major among others will have no A notes in them, and other keys will have more prominent frequencies than 432Hz (and its octave equivalents).

And it gets worse still. When a note is played we hear the fundamental pitch, together with a pattern of higher harmonics above it (an electronically generate sine wave is the only instrument which doesn’t exhibit this property) and that contributes to how we say, differentiate a C played on a flute to the same note on a piano. These harmonics are found at clearly differentiated and ordered intervals on melodic instruments, and more smeared across a range of frequencies in percussive instruments and ‘noisier’ sounds. The upshot of this is the following: In reference systems other than 432Hz (including the evil 440Hz), the specific frequency of 432Hz (and associated multiplications) will be heard repeatedly, presumably making it better. Conversely all those nasty frequencies found in a 440Hz reference system will be amply represented in 432Hz tuned music. Most inconvenient. Comparing a piece of music tuned from 440Hz to 432Hz (Figure 1) shows little difference in harmonic content or prominence of the ‘magic’ frequencies.

Harmonic spectra

Figure 1: If you look closely you can probably tell which of these identical pieces of music is in 440Hz and which is in 432Hz. Are there any salient differences in harmonic spectrum?

4) 432Hz links to other auspicious frequencies

Claims that a 432Hz system produces the precise magic integer of 256Hz in a C below, are false. It’s close but that’s not good enough if you want to make the argument from exact integers, which is baseless anyway.

The argument from the ‘cosmological significant’ 108Hz (2 octaves below 432Hz) collapses quickly. Here’s the argument: 108 is cosmological significant because it is the distance of the Earth to the Sun divided by the Sun’s diameter (actually it’s 107.5) and also the distance of the Moon to the Earth divided by the Moon’s diameter (a way off at 110.63), so therefore 432Hz is cosmologically better. Four problems
1) The maths is wrong – or so approximate that you could make the same argument for 430.2Hz (or 442.5Hz)
2) Those 2 very provincial celestial bodies are no more cosmologically significant than the billions of others from which to choose, and the equation arbitrary
3) There’s no reason why a distance/diameter ratio – which would seem to be about gravity and relative density – should have bearing on the arbitrary time-slicing of the Hz.
4) Even if problems 1-3 somehow disappeared, there’s no reason for that number to make better music.

Don’t look behind the curtain.

Another argument – which is perhaps the most interesting – is that 432Hz produces a C# two octaves below at precisely 136.1Hz (very close but not exactly, you’d need a reference frequency of about 432.09Hz for that in 12-TET- more on that later). Why 136.1Hz? Well this is the ‘Earth frequency’  found in the Om tuning fork and is used to tune the drone note of a Sitar in Hindustani music. It is derived from the (first decimal approximation) of the frequency of the earth’s rotation around the Sun scaled up by 32 octaves (let’s not mention the complexities and competing systems of calculating a year). Rather beautiful – it doesn’t employ the fallacy of integers (only the fallacy of single decimal points) or the trappings of manufactured time units. If a reference point is arbitrary you may as well think big. It’s a rather localized geo/heliocentric view of the Universe (we could just as well use the frequency of star formations, galactic spin, cometary orbits and so forth), but if it gives one a layer of awe while engaged with music that’s all good. The implication is that it resonates in harmony (read ‘simple frequency ratio’) with the Earth’s orbit.

But there is a serious issue which arises when attempting to link it with 432Hz tuning.

Remember that there is an ethos here of harmonic rational relationships, from the Earth’s orbit to 136.1Hz. However let’s look at the relationship between 136.1Hz and the proposed 432Hz reference. Sure it’s very close to a 12-TET C# in 432Hz tuning, but this yields a wholly unwieldy 1.26018518518519 ratio (adjusting for octaves) a wasteland – or tenuous approximation – of a ‘pure’ frequency ratio. If we accept that sort of level of harmonic elegance then there are countless other reference points we might choose, and many far better. So 432Hz is linked is 136.1Hz only via the standardized ‘western’ 12-TET system, hardly a claim to an ancient harmonic truth. It’s a henna tattoo of a claim to authenticity. Sure one could use a 432hz reference and 12-TET to ‘find’ a close approximation to 136.1Hz on a C# but then if you wanted to make pure intervals from that fundamental, 432Hz would not be one of those ‘pure’ related intervals. In fact the equal-tempered major 3rd (the interval found between A and C#) is a fundamental problem with 12-TET and why musicians and theorists have for years worked on ways to make 3rds sonorous with a limited set of pitches. As it stands the 12-TET major 3rd is way sharper than the pure third (5/4) which is implemented in musical performance where pitches can be freely altered (Indian classical music, string ensemble, vocal choirs etc.) and flatter than the ‘Pythagorean third’ of 81/64. In short 432Hz and 136.1Hz may be crowbarred together, but it’s a significantly nonharmonic crowbar.

If we’re after sympathetic and harmonic resonance with 136.1Hz (and thus the Earth’s orbit) we could use that (or its octave equivalents) as a tuning reference (as the Sitar does) or if we want something closer to conventional concert A: 408.3Hz (3/1), 435.52Hz (16/5) 453.66..Hz (10/3) are all more elegant – and consistent with claims to harmonic resonance – than 432Hz.  Not that I am advocating any of these, there is as yet no evidence that 136.1Hz is experientially special, nor has it lived up to any of its claims such as healing, being immune to mechanical noise or the like.

But if you enjoy the idea of being in harmonic resonance with the Earth’s orbit (or any Jupiter’s or Io’s or the 49 Bus schedule for that matter) you should at least be consistent in your aims.

5) Instruments and voices sound better when tuned down to 432Hz

This is the only argument which has real world relevance, though still unconvincing. Acoustic instruments are physical objects, and the tension imparted on their structure has a contribution to the nature of their sound – their timbre – so changing the reference frequency will alter somewhat the timbre of the instrument. The timbre will be different, not necessarily better. For example some guitarists like to ‘downtune’ their instruments for the sound it produces and the looser string feel it provides, but there is no reason for this adjustment to be exactly down to (the impossible to achieve with complete accuracy) 32-odd cent differential. Many adjustments are used, and tuning the guitar all the way down to the next chromatic note in 440Hz tuning was favoured by the not un-cosmic Jimi Hendrix. Note that instruments are designed to sound as good as possible, but they are always adjusted to suit the desires of a player or particular style, and there’s no good argument the changes made by this specific change are in any way better than any other tweak, and there’s no reason to think that – given a 432Hz reference – musicians would suddenly stop making tuning adjustments. Some singers prefer lower tuning systems for the relative ease of vocal production, particularly true when repertoire written for lower systems is tuned to modern concert pitch. However in most circumstances transposing music to lower keys (within a 440Hz reference system) can solve any performance range issues, and still there is no significant relevance or benefit to tuning down by those particular 32ish fractions of a semitone

Now adjusting the tuning by this small amount to synthesizers will create no significant timbral change, and adjusting your music library will in no way make the music more ‘natural’: the timbres will not change, save for perhaps some wholly unnatural artefacts of the adjustment process, and any internal tuning system relationships (for better or worse) will remain identical. If you want to do that to all your music, go for it (you could even play your 33 1/3 LP records at about 32.73 rpm) but rest assured you’re not adjusting the music in any meaningfully significant manner, and any perceived improvements are the results of placebo listening. We humans are hugely suggestible and music is an ideal environment to let those biases run riot.

6) It was an ancient practice from a wiser time

The Earth frequency has been discussed, but there is argument from antiquity based on the claim that 432Hz was previously universally employed Western standard, and presumably superseded by an unwise or malicious musical domination. So here’s a very concise (and far more accurate) history: Prior to the 19th Century, people made music with no specific – or highly localized – reference pitches. These varied wildly and frequencies given for concert A, as low as around 380Hz and way higher than today’s 440Hz. So much for ancient universal truth. In fact there was a general rise in pitch forged by instrument builder’s arms race – and perhaps deteriorating (and thus shortening) church organ pipes. But as the demand for a shared music practice grew – and singers complained of this pitch inflation – various attempts at standardization arose. Dozens were proposed in the 19th and 20th centuries (which varied with region, repertoire and even temperature measurement). Among these were the mid 19th century ‘Verdi tuning’ of 432Hz (suggested by the composer as a flattening of the prevailing 435Hz French system), and the fairly close to 432Hz ‘scientific tuning’ of C=256Hz (A≈430.54Hz) with its ‘scientific’ basis of C=2^8Hz but these were not particularly favoured among several others. 440Hz itself was formally proposed as early as 1859, so much for the embarrassing Hitler associations (presumably based around a 1939 tuning conference, for which we have no evidence of his association). Even if he happened to like it (for which let’s repeat there is no evidence) there is as much an argument for associating vegetarianism with the Nazis than tuning forks. 440Hz still took till the 1970s for general acceptance, but is still no means universal: Boston Symphony Orchestra use 442Hz, many German and Austrian symphonies use 443Hz and when playing Baroque music, and many ensembles favour the superlow 415Hz. Even rock and pop music – for technological (intended or otherwise) or ad hoc reasons – vary from 440Hz, although less so these days particular with the use of the music technology’s default of 440Hz. However any decent sequencing software and electronic instrument include the ability to deviate from 440Hz (including 432Hz), so those Illuminati need to work harder.

Illuminati fail

 

Figure 2: Illuminati Fail. I can set my tuning on NWO’s Logic Pro X to 432Hz, and also dial in any temperament. No-one stopped me.

In short as regards reference frequency, there was never an ancient truth, just a glorious diversity (including useful standardisations) which still continues today.

7) The argument from pretty patterns

Many 432Hz proponents claim that cymatics – the vibration patterns of a liquid (usually water) driven by a frequency – lends support to 432Hz superiority over 440Hz (and other) tuning frequencies. Stunning videos of the glaring differences, and the aesthetically more pleasing resulting patterns which 432Hz creates. Here’s the fatal flaw. The patterns produced are dependent on the driving frequency AND the geometry of the container. So some containers will have prettier patterns with a 432Hz rather than a 440Hz, and others might have quite the opposite. The differing wavelengths of 432Hz, 440Hz (and any other frequency) will behave differently in various containers. No 432Hz proponent shows a container that responds well to a 440Hz (although they exist just as readily as ‘432Hz-tuned’ bowls) because that doesn’t fit the a priori conclusion. It’s like arguing that a particular shoe size is perfect by showing a video of  one individual happily walking with one pair, and struggling to put on a different size. Shoes for feet. Horses for courses. Bowls for frequencies.

The Accuracy Issue

There remains a significant pale proboscidea in the room of ‘harmonic’ arguments: There must be some element of acceptable deviation from the harmonic truths, otherwise any microtonal deviation from the pure ratios by unintended human inaccuracy, or intended expression, or even the doppler shift from a slight turn of the listeners head – or temperature fluctuation – will deviate a tuning from harmonic perfection (if ever attainable) of say 3/2 to some crazily irrational proportion ever so slightly higher or lower. I’m a strong advocate of microtonal considerations in music, but I must admit that with a trained musician’s limitation (even in ideal listening conditions) of not much less that 1 cent, along with the laws of physics, means we must take a moderated view to the field. And if one has to make a host of arm-waving concessions to harmonic music, it further undermines any fundamentalist argumentation for the superiority of an arbitrary tuning reference.

In Sum

There’s no particular detriment to moving all music to 432Hz (or any other) tuning, but it’s also entirely possible to engage with music with a variety of tuning reference points, in fact a quick analysis of my music library finds a host of non-440Hz music including pop (Michael Jackson, Beatles), Classical, Renaissance, Jazz, Folk etc. Why advocate the arbitrary homogeneity of 432Hz  when one could have a broad and colourful diversity? Although it’s probable that some advocates are simply tuning all their music down 32-odd cents without checking whether all of it is actually in 440Hz first, making the farce all the more farcical. Most of the claims of the 432-truthers are dubious or fallacious particularly in reference to any superiority or a Musical Truth. If you want to retune your music libraries and instruments go for it, although time is probably better spent investigating any of the many other more pertinent musical dimensions (including – most relevantly – tuning systems).

Musical experience is subjective so if one enjoys 432Hz for whatever reason (even through the placebo effect), that’s fine. But to make real world claims about what is true and what ought to be in music should invite healthy critique and critical thinking and not gullible acceptance and credulous resharing. Speaking of which, if there is a demand, there are a series of controlled listening tests that I am happy to build to investigating any claims of 432Hz superiority while minimizing cognitive biases.

It’s refreshing to see any sort of popular foray into musical analysis, rather than the usual interest in the particular gyratory behaviour of some artist, or the tortured journalism of some sub-sub-sub-genre as a ‘stunning’ revolution. Unfortunately, even with the most generous spirit there’s practically nothing of substance to be found in the 432-truther movement. It seems the only thing discovered is yet another branch of musical pseudoscience, alongside extortionate speaker cables, crystals on speakers and the brown note.

Bonus

As a reward for making it through this post, I offer you some alternatives to 440Hz and 432Hz, feel free to tune your music to any of them (and select whether A, C, C# or whatever note name you invent is the most cosmic) and then start a Facebook group (alongside any manufactured history) to advocate its use.

Pi-tuning 402.1Hz

7 octaves up from Pi, this will add a very rounded and cyclical feel to your music, rather than the square 432Hz and irregular 440Hz

Phi-tuning 414.2Hz

8 octaves above Phi, this is a very balanced tuning, unlike the very disjointed 432Hz and 440Hz.

Selfie Tuning

Perhaps the most personal tuning, simply take the reciprocal of your age in seconds, and multiply it up to a sensible pitch for tuning. For example on your 21st birthday, tune to 414Hz. This results in far more subjective, present music than the materialism of 432Hz and 440Hz. Warning, this will rise, and be prepared to sing like Mariah Carey in your eighties.

Olympic Tuning 272.2Hz

272.2Hz is based on the frequency of the Olympic Games, this produces a more triumphant tuning than 432Hz, with a greater sense of unity than the Earth Frequency.

Galactic Tuning 254.2Hz

65 octaves above the age of the Milky Way, 254.2Hz is way more cosmic than the provincial 432Hz.

Universal Tuning 338.1Hz

67 octaves above the age of the Universe, 338.1Hz is the best tuning reference you can use, and if you don’t agree you must be some kind of Nazi.

I’ll Be Back Tuning 332.7Hz

At 332.7Hz this is 33 octaves above the frequency of Arnold Schwarzenegger movies/per year over the last quarter century. More powerful that 432Hz, and works well with accents.

Bloody Cat Frequency 436.9Hz

This is the most irritating of tuning references: 436.9Hz, a mere 21 octaves above the frequency of my cat waking everyone up in the middle night just to tell us that it’s still raining or that the carpet is in the same position on the floor.

Additional Reading

Benade, Arthur H (1976). Fundamentals of Musical Acoustics. New York: Oxford University Press.

Danielou, Alain (1968). The Ragas of Northern Indian Music. Barrie & Rockliff, London.

Danielou, Alain (1995). Music and the Power of Sound: The Influence of Tuning and Interval on Consciousness. Inner Traditions; Rep Sub edition.

Duffin, R. (2008) How Equal Temperament Ruined Harmony: And Why You Should Care. Paperback edition. Norton.

Fabian D, Timmers R and Schubert E (eds) (2014) Expressiveness in Music Performance: Empirical Approaches Across Styles and Cultures (Oxford University Press)

Fonville, John (1991) “Ben Johnston’s Extended Just Intonation: A Guide for Interpreters”, p.121. Perspectives of New Music 29, no. 2 (Summer): 106–37.

Gann, K (2016) An Introduction to Historical Tunings. http://www.kylegann.com/histune.html

Hans, J. (2001) Cymatics: A Study of Wave Phenomena & Vibration (3rd ed.).

Raichel, D. (2006) The Science and Applications of Acoustics, second edition (Springer).

Skudrzyk, E. (1971) The Foundations of Acoustics: Basic Mathematics and Basic Acoustics (Springer)

Stephens, R. & Bate, A. (1966) Acoustics and Vibrational Physics (2nd ed.). London: Edward Arnold.

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216 Responses to Hertz So Good? 432Hz Examined.

  1. Great stuff Milton. Although like so many of these things, I worry that the people who could benefit most would be the least likely to read it.

    • miltonline says:

      Thanks. I actually like that people are taking more of an interest in the mechanics of music and a less passive consumerist stance. And down tuning instruments is all well and good (although I don’t buy 32 cents as special). Retuning preexisting music is I think just silly.

      • kelly says:

        32 is 8 times 4! Half the numéro of chromosomes in a zygote !!!

      • youri says:

        it is a lot of number to deal with something related to perception….i don’t find it relevant….maybe if you took some physiological measures of test subject we could have a deeper talk about that but for now i just see haters and lovers of these 440 vs 432 hz stuff without ever considering the body response to those tuning….without these data all related to these talks are pure opinion
        have a good day mate

        • miltonline says:

          I agree, a blinded, well-conducted test of 432 over other reference points would be one valid way of analysing claims of 432 superiority. None have been offered yet.

      • What was the logic of choosing 440Hz back in 1939 at the international conference in germany???. I know that orchesters before had tuned this high or even higher to make the orchesters sound brighter and louder..

        The Old Diapason normal (A4=435Hz) from 1859 was a cure to fix the inflation in pitch that was seen in the years prior to 1859. Opera singers were not pleased with the inflation in pitch…

        1859 A=435Hz, Karlsruhe, Germany. Pitch at the German opera. Kapellmeister Jos. Strauss felt that this pitch fatigued his singers the least and was the best pitch for the performance of operas from all periods. Strauss’ fork became the pitch standard for the French Commission’s Diapason Normal.

        Personally I have sung for 20 years and there has been something not right with 440Hz for my Voice,, my upper range and passaggio simply do not like that pitch.. I tried 435Hz (20 cents down) and boy that solved my year long issue with 440Hz… I was stunned that such as mall different in pitch could matter so much….My leadsinger has tried 435Hz too and his voice also prefers 435Hz by a large margin…

        I hate the retardness of people never questioning standards such as the 440Hz.. For relaxing smooth music 432Hz is great… One women commented that her students (hyperactive children or people with autism spectre who had concentration difficulties responded very positively to music played at 432Hz compared to music played at 440Hz)… So there is no question about it. 432Hz works for relaxing and meditative music…

        • miltonline says:

          Dear Anders,Actually the 1834 Stuttgart conference predates the 1939 conference. There have been many, many more tuning standards than you mentioned, with much (still standing) regional differences.Even this year For a project in Holland I tuned to 442Hz (their standard).
          Your points:
          “So there is no question about it. 432Hz works for relaxing and meditative music…” – so long as you take one anecdote over evidence. How do we not know that another tuning standard is better? Or that it makes no difference? Or that;s it different for each person? Your singer prefers 435Hz after all. It sounds like you aren’t interested in questioning that standard…
          “I hate the retardness of people never questioning standards such as the 440Hz..” Well leaving aside the objectionable ‘retardness’ term, this post does exactly that -it questions the pitch reference standard including the claims of the 432Hz community. In case you missed it in your response, I start and end by advocating the use of a range of pitch references. So we are on the same page in that regard.

  2. Brigham Bartol says:

    I’m all for questioning convention, but the 432 Hz phenomenon is nothing but illuminati/Nazi conspiracy nonsense. If you want to tune to something other than 440Hz go ahead, but don’t do it for stupid reasons.

    I commend you for actually taking the time to write about this in detail. Hopefully some of the 432ers will actually read it!

    • miltonline says:

      Thank you, and thanks for reading.

    • kevx says:

      just beginning to study the mechanics of sound. This i do know, gimmick shockers tuned specifically to 440hz are harsher than any other frequency in the 100hz-1khz range. Im pretty sure that 440hz is one of the ‘sharpest’ sensations in shocks. To your point on pitch resonance – it is definitely directly proportional to density, then certainly the precise frequency is of importance and differing frequency responses would be the expected outcome in any tuned circuit (ok – based on Q). I can only guess that applies to any resonant cavity as well unless there is some sort of scalar phenomenon at work here.huh.. or is it the Q im thinking of here – ah is the Q of the resonant admittance, determined by the fundamental frequency – that is the Thevinin of the tuning connection – i see thank you! so basically in terms of a bass resonant sound its the difference between stabbing me with a broad sword compared to hitting me with that old battle hammer. Or the amount of torture (goose bumps, chalk board sounds) Im going to endure in any given song – then of course specific freq matters. – No Tesla pun to gravity there;} The problem with theory is that it doesnt understand that im emotionally listening to this dribble, so its the resonant moments that matter – thats the drop in the rave, the synthesizer in Floyd, the Cello in orchestra, it may be too late for you. (teasing, peace)oh this is my visualization of your team: https://www.youtube.com/watch?v=VTnuGkZgaMc&list=PL5B4dgb9Bh2wFtACO_gIVj8XHgKla0bu7

    • Elie Wiesel says:

      “illuminati/Nazi conspiracy nonsense.” — You mean like the Holohoax?

  3. Paice93 says:

    I tune my guitar to A432Hz and I agree with your article.

    I don’t have even the slightest notion where some of the above-mentioned ‘evidence’ comes from – especially since some of it is proved wrong simply by double-checking the math yourself…

    This is the reason why I play in A432Hz: In my opinion and to my ears (and this could be a placebo effect or down to the physical properties of my particular guitar – I do not deny either) it simply sounds better. My guitar is more resonant and open-sounding – good for the music that I play.
    I get roughly one more second of sustain on a note or chord compared to A440 tuning.

    Interesting… This is not to say that I would not get an extra 2 seconds (for example) sustain if I were to tune to A424Hz (440 -> 432 is a difference of -8Hz. 432 -> 424 is a difference of -8Hz). I should try this.

    Good article. Placing aside all of the crazy claims and evidence presented in support of A432 tuning, what are your opinions on the actual sonic differences between 440 and 432? I ask this since, in music, it’s really the sound that matters above and beyond all evidence that could possibly be presented both for and against a case.

    Peace

    • miltonline says:

      Thanks for reading. Yes, down tuning acoustic instruments has a perceptible sonic difference. And that’s what music is about tweaking various parameters for emotive (or other) effect. But one must remember that the instrument was built for a 440hz and what one is doing is ‘hacking’ it to induce the downtune effect. If the instrument was built for 432hz, there’s no reason to think that people wouldn’t enjoy that instrument for a similar effect. In other words the standardisation needs to exist against which to down tune. In short changing instrumental tuning (in all sorts of directions and wats) is pertinent and relevant but I don’t see any reason to see the target of 432hz to be in any way superior to any other. As for sonic inferiority of 440hz vs 432hz, I don’t buy it at all (for all the reasons above). I will put together controlled tests sometime! Peace out.

      • Harry says:

        Yeah that’s spot on I’ve been thinking the same thing about all this. How are you going to get a more organic sound by pitch shifting the few cents. The instrument must be built for A=432 I wonder if old church organs are tuned to 432. I’m surprised there aren’t more results on google for guitars tailored to it.

        • miltonline says:

          It’s an interesting point. An instrument is designed for a certain tuning reference but can be ‘hacked’ and it sound changed by tuning to a different reference and thereby not just altering the pitch but the timbre. Downturning guitars is a case in point. An instrument ‘designed’ for 440Hz will sound different at 432Hz than one designed for 420Hz for instance.

          • K Mike Savoy says:

            I am just blown away at the amount of good information this post contains!

            I have played music for years without training. I’ve experimented with down-tuning, and adjust it mainly to match my natural singing tones. Lol
            But the science was never once shown to me or pursued…..

            …..so…. thank you. For the lesson, and more importantly a new outlet for my scholarly nature. Haha!

      • Jim Rosgen says:

        We own a 1909 Steinway piano, which would have been built for 432 Hz, so in effect it has been hacked to play at 440 hz. My wife has retuned her cello to 432, and prefers it. She is considering retuning the piano to 432 as well, and I look forward to hearing if there is a noticeable difference.

    • kelly says:

      Or something

      But.

      27 is 3 times 9 😉

      Youre right, everything seems to be based on the 12 système.. Why is this??? Zodiac, time etc.. Who said à second could be à second ?????

      • Jerzy says:

        Hi Milton

        Thank you for taking the time to shed more light on this fascinating subject and providing a lot of good, in-depth information with some good laughs along the way. I read the whole blog including the comments and still think that calling the advocates of using 432 Hz as a concert pitch delusional is somewhat presumptuous. Time will tell… personally I find 432 amazingly “sweet” and resonant and would never go back to 440.
        Here are two contributions I’d like to make to the subject:
        1. http://www.interferencetheory.com/HarmonicTheory/HarmonicEvolution/page8.html
        2. http://thegatekeeperxix.nl.eu.org/post/55525998900/metatronic-flower-of-life-tree-of-life#.VMFiyij4_vb

        In the second link please find the comparison of Kathara grid math and spiral with Fibbonaci’s math and spiral.

        Looking forward to reading about your blind test results when you get it done.

        Greetings from Canada

        Jerzy

        • miltonline says:

          Hi Jerzy,

          Thanks for the kind and polite feedback, they are quite rare at the moment from people who see me as an enemy.
          Yes I use the word delusion, and that will upset some people. But a definition of delusion as “an idiosyncratic belief or impression maintained despite being contradicted by reality or rational argument” and I think it’s fairly sound here. Everyone (including me of course) is deluded about something at some point: the prospects of their local team, the amount of time it takes to do admin, calorie intake etc. etc. I’d like to think that if someone pointed out how I had misleaded myself I’d be accepting (if not grateful). I happen to really care about what is true, and about music education and was compelled to write this article after encountering some of the 432Hz proponent sites. If anyone points out any inaccuracy (or where I am wrong/deluded) I will fix it, and change my view accordingly.
          So on to your points: You say you prefer 432Hz over 440Hz, but would you say you could tell the difference between them and other frequencies without being told which is which? Would you care to find out? You may even find that you prefer other tuning frequencies over 432Hz, or you may find that you have no clear preference. When I find time I’m going to put together a controlled test (and one which I have no chance of influencing the outcome) to see if there’s is in fact a preference among people. Let me know if you’d like to take part. So far no 432 proponents have come forward so it would be good to have a range of people.

          As for your links, they are both about harmonic ratios. I love harmonic ratios in music, use them in my music and could talk your ears blue (or some appropriate colour) about the history, theory, practice of harmonic tuning.(You can even look up my video on the maths behind music on this site) But harmonics are about ratios *between* frequencies and not the arbitrary naming of any one frequency. We can engage with harmonic tuning with *any* tuning reference and 432Hz has no superiority in that regard. Furthermore people tuning their equal tempered music down to 432Hz are making no changes (let alone improvements) in harmonic relationships. As explained in great detail Hz (frequency per second) is arbitrary as the second is an arbitrary time unit. It’s based on (an approximation) of a (changing) orbit of one particular planet among billions of billions. A highly provincial and localised view of the universe. Hence my offerings of other equally arbitrary tuning references. Your sources claim harmonics are important, I agree with them in that regard (but also understand the power and usefulness of non-harmonic ratios like the twelfth root of 2), but there is nothing in harmonic theory that prejudices 432Hz over any other tuning reference.
          And yes I’m happy to await further evidence, rational discussion, but in the meantime I’ll embrace all frequencies without prejudice.
          All best
          Milton

    • Freqrider says:

      Honestly, I find my guitars have better harmonics tuned to 440hz. But I like making weird sounds with different techniques.

  4. Eric says:

    I never did pay any attention to all the conspiracy theories or even the math. I just like the way it sounds. Some of us aren’t all nutty about it. We just prefer it.
    I tried tuning my J45 down to 432 just for kicks and enjoyed the resonance. Since I play harmonica a lot, I had a G harp dropped just to try it out. I really really like it, and am having a full set of harps tuned to 432. As a solo artist I don’t need to worry about being in tune with other musicians.

    Thanks for all the hard work here.
    – Cheers.

    • miltonline says:

      That’s all cool. Although I suggest you wouldn’t really mind if it was 432.3hz, 429.06hz or a whole fractional spectrum of slight downtune. I suggest you like floppier resonating strings (for which ironically one needs the instrument built for a higher tuning). You may one day acclimatise and enjoy drifting further down, or back up. It’s all cool. Enjoy.

    • Drew says:

      Hey Eric,
      Where did you send your harps off to get retuned and about how much does it cost per harp?

      Cheers thanks,
      Drew

    • kelly says:

      What about 456 – 16hz above??

  5. philip guterez says:

    One of the things that convinced me of the validity to the 432hz was watching cymatics videos and having a korg tuner calibrated to 432 and always matching when the paterns were most solid.

    • Miltonline says:

      Thanks Philip for the comment, and you remind me to update the article to address the cymatics argument. I’m actually entirely unconvinced by these videos for 3 reasons.
      1) cymatics depends on the geometry of the container, the temperature and viscosity of the liquid. 432hz may make prettier shapes than 440hz in one environment and less pretty shapes in another. So the videos are an exercise in cherry picking.
      2) if one frequency makes subjectively prettier patterns in certain conditions than another (I don’t happen to accept 432hz is better than any other incidentally) – then it still doesn’t follow that it translates into better sounding or more salubrious music. Deaf tests of patterns in a range of environments coupled with blind tests of listening examples (which I might provide) are what are needed to answer that question at all. So far there’s no evidence whatsoever to suggest the link.
      3) see points 3 & 4 of the article. Even if one is to argue for the superiority of a 432hz tuning reference it doesn’t necessarily follow that the music produced represents that frequency (or its rational relationships) significantly more than alternative reference points.
      You said cymatics was ‘one of the things’ that convinced you. What were the others may I ask?

      • philip guterez says:

        The first thing was the way it made me feel. One of the big reasons is finding random world music tuned to 432hz. Discovering 432hz was like discovering music all over again. Then there is the factor 9 argument. I suggest watching the short documentary called sonic geometry. 432 in a lower octave is 108. 108 is a cosmicly significant number for many reason for example. The distance of the sun from the earth is 108 times the diameter of the sun, same story with the moon. Cheap wooden flutes are more often tuned to 432 than 440. In my chorale days before i knew about 432. I got my first korg chromatic tuner and i was practice by singing the melody first to see if was in perfect pitch but i was always flat unless i heard the 440 tone first. Call me delusional if you must but i’ve had too many synchronicities to confirm to me that im on the right tract. And i know about the limitations of equal temperament. But i like equal temprament because of the simplicities that arize from it. There is no perfection. Only the illusion of perfection being the ever ellusive goal that keeps the spiral dance going

        • miltonline says:

          Hi Philip, Well of course I’m not in the business of stop people enjoying their music – quite the opposite actually. But I’m also into what is demonstrably true in music (including and beyond the subjective), and so want to examine the claims seriously:
          So for example the cosmological argument is addressed in my post, and I offer a range of ‘cosmologically significant’ tuning systems based n the life span of the universe and the galaxy or cometary orbits etc. But let’s look at the 108 claim.
          Distance of Sun to Earth 149,600,000 km
          Diameter of Sun 1,391,000 km
          Dist./Diam = 107.549
          Which would imply that 430.2Hz (not 432Hz) A significant 7cents difference.
          As for Moon to Earth: 384,400 km
          Diameter of moon: 3,474.8km
          Dist./Diam = 110.63
          Which would imply that 442.5Hz was cosmologically significant.
          So that particular argument is easily tested, and found to be invalid.
          Doesn’t mean 432Hz is bad it just means that argument is not sound.

          2) As for the argument from World Music. Well that’s testable, (and I do test) and have found no correlation to 432Hz. (I deal with the Earth frequency above) – I’d be interested to see the evidence that there is, but what I’ve found is a glorious diversity of tuning references.

          If (and when) I put a test together of tuning references, would you be so good as to take part? I’d be really interested to know whether 432 (or any other tuning reference) is superior in blind test. No obligation of course.

          • philip guterez says:

            You have to use feet and miles and not kilometers.

          • miltonline says:

            Erm, I’ll assume that’s not a joke…

            No matter what units you use (be it km, miles/feet, inches, furlongs, yards, mm or whatever) the ratio of distance and circumference will be identical, thus:

            Distance of Sun to Earth 149,600,000 km = 92,957,130.4 miles
            Diameter of Sun 1,391,000 km = 864,327.328 miles
            Dist./Diam = 107.549 (to 3 decimal places) for both

            Distance of Moon to Earth: 384,400 km = 238,855.086 miles
            Diameter of moon: 3,474.8km = 2,159.14062
            Dist./Diam = 110.625 (to 3 decimals places) for both

            Neither of which are in octave relation to 432Hz, nor does it bear up to claiming 108 as “cosmologically significant”.

            Where did you find such a claim might I ask?

        • Roel says:

          The “factor 9” grid in the short documentary called sonic geometry in their video is not calculated right. There are actually tones missing in the grid. The “Factor 9” concept generates a 15-tone system, not a 13-tone system as they have setup their grid.

          I have mentioned this to the authors about a year ago, but they don’t seem to care enough to fix it … and that’s bad – to leave flawed info as it is when notified about it – if you are serious about your work.

          Personally I think it does not look well if you are making an “educational” mini docu about geometry (math) and you fail to calculate yourself properly. 😉

          Anyway, I have explained this mistake in my blog, feel free to check it out: http://www.roelhollander.eu/en/432-tuning/432-the-factor-9-15-tone-temperament/

  6. Ronald Bushnell says:

    Thank you for the comprehensive information. I am convinced of what I already intuitively suspected (egocentric association), that those with perfect pitch utilize interval relationships from an infinitude of frequencies; where the “memorized” reference frequency is arbitrary at the point of memorization. It would also seem that a “resonant” frequency could be found in any object such as petrified dinosaur excrement. As always my mind remain open, but I will be continuing to use my 440 tuning fork that my Martin D-28 like just fine.

    • Miltonline says:

      Thanks for the comment, Yes all evidence and reason suggests that perfect pitch is learned relative to the prevailing reference frequency. (The idea that a human is born ‘pre-tuned’ is wholly unsupported). I would however probably support moving to a dinosaur poo tuning system.

  7. Theodor says:

    Thank you sir for this small speciment of reason and logic between all this internet Middle Age mentality

  8. Ben Goerner says:

    I played in a bar band for years tuned to 435 (cause that’s as low as my tuner went). Not because I wanted a sedate crowd. Only because it seemed to make it slightly easier to pull off lead vocals on guns n roses, zeppelin and ac/dc. The crowds went wild and we worked hard. I did feel the difference in the sound of the guitar in the example provided by Guy Wood (I think it was) and I appreciate your explanation of the effect.

    • miltonline says:

      Thanks for the message. Did you consider tuning down to Eb (as Guns and Roses often do?) In effect this is equivalent to ‘tuning to’ 415.3Hz as far as the guitar is concerned and contributes to the distinctive guitar tone. Strangely I’ve notice that some AC/DC tracks are tuned sharper than 440Hz although I suspect this might be a tape speed effect – perhaps intentional to create a more brighter tempo (and maybe timbre).

    • Anders says:

      That sounds like a great idea…

      I play leadguitar in a band and the leadsinger who also play guitar struggels a bit singing two hours straight… We got like 60 songs in the cover catalog,, and instead of learning say half the material in new handpositions due to be lowered a half key, we tried downtuning the bass and guitar a half step to E-flat and play the entire material a half key lower… Personally I think some songs got out of our leadsigners sweet spot… A more moderate downtune to the suggested Verdi Pitch at A4=432Hz would work wonders for him….
      Both the bassplayer and us guitarist have TC polytunes and could try a downtune to 435Hz (lowest setting),, THat would be really interesting to see if he would notice a difference….
      The other suggestion I have is that we calibrate to 445Hz before we tune to E-flat. That way we go from 415Hz (G#4) to 420Hz (G#4) which to my surprise and ears sounds much better when strumming those open E and open A,, In regular E-flat the timbre seems a bit to dark for those chords in relation to the singers “sweet spot”:..

  9. Molola says:

    This has nothing to do with mathematics. It’s about Harmonics.
    Are speakers made for only 44.100? 🙂

    • miltonline says:

      1) Please define what you mean by ‘harmonics’ precisely and clearly without using mathematical terms. ‘Harmonics’ are mathematical relationships, so you must have a different definition.
      2) Speakers cover a frequency range (depending on design) and can handle all manner of tuning references. For the reasons described above they are no more suited to 440Hz than 432Hx than 438.275Hz. So I’m not sure the point of your (presumably rhetorical) question. Please explain. Also when you say “44,100” (or did you mean to say 440Hz?) you presumably are referring to the sample rate of digital audio, as in 44.1kHz, which means that due to the Nyquist Theorem frequencies up to 22.05kHz can theoretically be captured. I’m not sure why this relates to the issue. However if you can clarify your questions, I’d be happy to respond.

    • Roel says:

      44100Hz is the “sampling frequency” (or sample rate) of standard CDs. The “sampling frequency” has NOTHING to do with Pitch, you are “mixing” things up.

      • miltonline says:

        I know what pitch is and what sampling rates are. I’m just asking what you mean by “Are speakers made for only 44.100?”

  10. Skye says:

    Thanks a lot!
    I also found it necessary to summarize most of the same arguments in an article: http://goo.gl/31m1gg
    Your article is more comprehensive and detailed. Congratulations!
    There are just some details I have to lead your attention to:
    – In the argument about the distance between Earth and the other celestial bodies: As their orbits are not described by perfect circles, the values that both the 432ruthers and you are using are mean distances.
    – I doubt your assumption that 12-TET had a leading part in classical composition. As far as I know its dominance did not emerge for keyboard instruments before well up into the 19th century. Many students don’t distinguish between well tempered tunings and 12TET.
    I only make these comments because I get the impression that you may extend and elaborate your article further.
    It is also worth to mention that 440 Hz has been used as a standard before the 1939 conference:
    – Stuttgart conference 1834 http://en.wikipedia.org/wiki/Concert_pitch
    – American Standard Pitch 1926 http://en.wikipedia.org/wiki/A440_(pitch_standard)
    Keep up the good work!

    • miltonline says:

      Excellent post and blog, and good points. I was (trying!) to be succinct and inevitably I had to simplify (or leave out) some points. Yes mean distances, and there are also issues with even defining a year which compromises the ‘Earth frequency’ hypothesis. And indeed 12-TET is indeed relatively recent, split key keyboards and fingerboard diagrams (with different notes for say G# and Ab are found well into the 19th Century), and many of the Classical composers understood temperament and its implications extremely. Have you seen Mozart’s notes to his student Thomas Atwood on the difference between a ‘major semitone’ (e.g. E to F) and a ‘minor semitone’ (E to Fb). Fascinating. Yes there were 440Hz standards in the 19th century I did mention this ” 440Hz itself was formally proposed as early as 1859, so much for the embarrassing Hitler associations”.
      You keep up the good work, I will follow your blog with interest (although with a hefty use of google translate I confess), and thanks for reading mine.

  11. VST says:

    Bravo Milton! Very thorough and thoughtful.

  12. Perica Šuran says:

    Thank you, sir, great article! I find this 432 Hz new-age mumbo jumbo quite annoying.

  13. Mark Borghardt says:

    Awesome.

  14. Andrej says:

    Nice thoughts overall but….

    In an extensive written text like this one, you’re missing two most important information regarding frequencies and pitch, one is related to your tables and 2nd is related to your 7th point.

    a) Bach wrote The Well-Tempered Clavier which is, to quote, “…is generally regarded as being among the most influential works in the history of Western classical music.”

    Quote is from: http://en.wikipedia.org/wiki/Well-Tempered_Clavier

    Why would Bach wrote this with the collaboration of the actual top class (best at his time) physicist which helped him find the best HZ to tune piano – in 432 Hz?

    432 Hz is far from perfect yet it is way better then 440 Hz but to see that from both of your tables is impossible. Reason for that is in fact that, to get A0 from A1 yes, you do cut the Hz in half but the more you go down (or up in that matter) you CANNOT divide in in half each time and assume it will be perfect. It will not because of the range of the HZ human ears can hear (its not linear, its progressive).

    Bach knew that. Any sound expert that has a diploma in his hands regarding History of the sound (I am lucky to know one) knows this. How come that after all your research which you did, you fail to even mention important data like this?

    Scr*w Bach and what he wrote and what he scientifically researched & published regarding tuning the piano, what does HE knows right? Who is Bach, anyway?

    b) Wanted to write something here but I had too much trouble struggling with my English with point a) (lol) so I’ll just leave it to this. I’ll just write that, just from an additional personal observation, I cannot pinpoint exactly where does sound comes from (my speakers) when listening to music at 432Hz. With standard Hz, I have no problem regarding that, what so ever.

    To conclude:

    Each of you, out there, do what you want. Listen to music @432Hz or not, your choice.

    I thought of several tests and performed them all – music @ 432hz… to ME… just feels better and sounds better.

    Its your choice. I know mine.

    Thank you for reading.

    Andrej

  15. miltonline says:

    Dear Andrej,

    Thanks for reading, but I find your arguments nonsensical, perhaps you can clarify.
    a) Believe it or not I do know Bach’s Well-Tempered Clavier very well . I even know what the ‘well’ and the ‘tempered’ bits mean as well including Lehman’s et al interpretations of the loops on the inscription page. Can you please provide a reference to show that J.S.Bach in 1722 deemed 432Hz as the reference pitch? I await.
    Then you say “you CANNOT divide in in half each time and assume it will be perfect.” Please explain what you mean by ‘perfect’ in the sense of doubling and halving frequencies without using the fallacy of integers (which is dealt with comprehensively in the text). Why would 432Hz be better than 440Hz or any other reference frequency without invoking special pleading?
    b) So you are claiming that localisation is inferior to you when down tuning from 440Hz to 432Hz? Not sure why that is an endorsement if it is indeed true.
    And on that matter, would you be interested in taking part in a blind test to see if you actually do prefer 432Hz over other reference frequencies in a controlled study?

  16. Gregory Thomas says:

    Interesting article, very informative after reading a pro-432 article someone posted on Facebook.

    I am going to nit-pick about something else entirely, though.

    “It’s like moving a Rembrandt painting a fraction of an inch down a wall and claiming an improvement.”
    While it wouldn’t improve the painting, as composition (it’s physicality, literally the paint on canvas) it could change how we experience it. It sounds trivial, but sometimes art can be hung too high or too low and it can actually consciously be distracting. This doesn’t change if the artwork is good or not, but it’s optimal from an artists point of view to have it hanging in such a fashion that you’re not distracted from the work itself, either by being crooked or at a wrong height.
    But then you get artists who create work and deliberately hang it differently to make it part of the artwork, so it’s not a hard and fast rule. But there’s a reason why ‘1.5 (metres) to the centre of the work’ is a thing. It falls apart a bit when you consider everyone is of different height, but generally, it’s a sound rule.

    So shifting it an inch down could change how you experience an artwork, but wouldn’t change the quality of Rembrandts work, which is what you may have meant, but it being the internet I found some room for misinterpretation…

    • miltonline says:

      Thanks for the comment. Actually it would probably be more accurate to say fractions of millimetre of movement (although the analogy is not ideal anyway). The 1/3 of a semitone proposed motion is arbitrary in the sense that it can be absorbed by acclimatisation similar to a fractional readjustment of a physical object.

      • James True says:

        Hi! Your analogy of the painting is flawed by moving the canvas at all. Your article technically argues analogously that changing all of the hues of each color in the painting a few notches would create the same painting and shouldn’t matter. This analogy is weak and flawed since art like music is both felt and sensed. I really enjoyed the science in this article. You did gloss over as quickly
        as possible what happens when sound is amplified over a medium. You poked holes in water as the medium but completely ignored sand and the effects of resonance on sand over a flat surface. It’s truly stunning to watch. I was hoping this article would save me from having to consider tuning my piano to 432 but you missed the boat bc I still wonder. Thanks for the great attempt and for all of the logic you applied. Very thorough otherwise. Cheers

        • miltonline says:

          Dear James, Thanks for the comment. Well the painting was indeed an incomplete analogy (and by no means the crux of the argument). A more accurate analogy might be a uniform (and very slight) decrease of luminosity of all the colours equally and claiming that would be an improvement to all pictures everywhere, which I don’t accept as valid. As for a medium (as mentioned in the article) the principle holds regardless of the resonating medium. Frequency, speed of sound through the medium, and dimensions/architecture of the cavity predicts accrately the wave interference. It’s a well established field that doesn’t favour 432Hz (and its equal tempered or harmonic ratios) over any other reference. But of course, tune to what you like, that’s my point entirely – I just don’t find good evidence for 432Hz (or 440Hz or any other reference) intrinsic superiority. Thanks.

  17. Wish it was true says:

    Thank you for a well written piece Milton.

    Re cymatics, here is a video with a tonoscope that has a plate not a bowl http://youtu.be/1zw0uWCNsyw It shows that 432 and 440 produce equally beautiful and interesting patterns. Who knows how different frequencies can effect us.

    Sure there’s a bit of placebo going on with this too. I really liked the idea of instruments tuned to a ref note the same frequency as the earth and sad to find out there’s no solid evidence. I like 432. Could be because it sounds like my guitar which is only tuned to concert pitch every couple of months. Ha ha. I think it is important people tune to what makes them happy so they are resonating positively and having a positive presence in our society. Whether that is 440 or 432 doesn’t make a big difference to me.

    • Skye says:

      What brings forth the patterns of sand/ lycopedium/ flour etc on vibrating plates is the distribution of nodes and antinodes. So you have to consider one thing: These patterns will not only change when change the frequency but also if the plate was replaced with one which is thicker or thinner or of a different material.

      Cymatics are compelling, but you have to realize that the plate is actually a filter: It only expresses what happens to that particular material, dimensions and shape, not what happens in air nor to the human body nor anything ‘universal’!

    • Mackenzie says:

      Actually, I look at that video and I see that the patterns created are in fact much clearer and defined with a 432hz tuning. Our bodies are susceptible to vibrations; think of therapeutic ultrasound or brainwave entrainment, these are just examples that are known to be beneficial, and even though this article made me question I still feel like this is a massive indicator as to the purity of the vibration. Forgive me if i just missed it but I didn’t see an argument against the correlation of geometric shapes and Pythagorean tuning, which are essentially what cymatics is interpretating.

      Call me a loony if you will, I am someone who believes that the world is run on psychopathic behaviour, stemming down from the big cheese onto a society that is so distracted by consumerism and day to day stresses that they don’t realise life is meant to be more than this. So yes I am prone to believing in a disharmonious state created by the manipulation of frequencies we hear, along with other forms of brainwashing so clearly imposed on us. When allowed, our experiences in life dictate our perception of the world around us, and manifest into our actions and belief system. I’ve seen it in myself and in others, without a strong perspective from all different angles you can’t know your own truth and we make decisions wholly on our limited experience. We CAN be controlled, and the past actions and current agenda being shown by those who control all the wealth show me that making sure of being conditioned to think a certain way is something to be extremely aware of. Very few want to break out of their cage, as they don’t understand that they are in a cage of their own minds, and this is due to the conditioning of society that says you must be successful, you must make money, you must look good whilst you’re doing it. Money is fictitious and binds you to a life of enslavement; There’s way too much money in the world for there to be any poverty whatsoever, for every bit of money that is hoarded by the elite is directly responsible for the poverty stricken streets in London, I won’t even go into 3rd world countries. We are in a society that is conditioned to divide and conquer, and feel completely desensitised to the fact that in everything that capitalism has shat itself over, there is a necessity for someone else to suffer for you to succeed.

      Life is meant to be about living for each other, so we can all grow with the help of others, connection with other people is a wonderful thing that can’t be quantified in any way, and I genuinely believe with the percentage of people that don’t realise this simple yet revolutionary understanding, there’s gotta be something causing a hindrance. Whether tuning to 440hz is a part of that is beyond me, I truly don’t know, I will forever remain a skeptic until I have definitive proof one way or the other. My intuition tells me there is something more to life than meets than what we look at with our two eyes, and when we start to see with the one that we have forgotten how to use, things begin to make a lot more sense.

      I think the Sumerians are very interesting, as the first civilisation that has a recorded history of using music. They are also very strongly connected to the Pythagorean tuning; something to look into if you wanna research ‘the loony side’

      • miltonline says:

        Sumerians are very interesting, I’ve studied them quite closely, and actually Babylonian ‘god-numbers’ predate (and possibly are the foundation of) Pythagorean tuning. Remember however that Pythgorean tuning (the relative ratios between pitches) is different from 432vs440vs437vs441 etc. Hz (which is the abritrary naming of a specific pitch relative to an abritrary time unit). THis is what seems to be lost to many 432Hz advocates, which is a pity because the truth and reality is far more interesting than the myth. And just to repeat what I’ve said both in the article and in the comments I’m totally interested – in fact passionate about – alternative/universal/primal tuning systems, i advocate and use them. I simply find the common arguments for 432Hz superiority entirely without foundation.

  18. drew hempel says:

    Milton, an excellent expose/debunking article on 432. Thank you! All those who know a bit of music theory on the planet are in gratitude. Nevertheless, although I completely agree with you about 432, I do think there are some secrets to what sound can do when it is understood as an open infinite spiral of fifths, not as measured by irrational magnitudes.

    • miltonline says:

      Thanks for reading. Actually, I find the spiral of fifths beautiful and important (as are the rarely mentioned spirals of 3rds and 7ths etc.). However, there are no compelling reason to imagine why the concept of infinite spirals would favour any reference frequency (in particular why 432Hz is better than 440Hz). If we are to engage honestly with the concept of an infinite microtonal universe, then reference frequencies are only for naming convenience and do not change in any way the constituent harmonic relationships, or available frequencies within that musical world.

    • Skye says:

      An illustration of a spiral of perfect fifths and just major thirds:
      https://flic.kr/p/kqJdbP

  19. drew hempel says:

    Milton – I’m talking about this article specifically. Thanks http://t.co/D7fcFqK7L6

  20. Jeff says:

    Interesting article, although i find all this 432hzvs440hz very complicated;) but i love it….Look, I found a 432 player, so you can play music directly in 432 hz (I think some songs are ruined when doing so, especially if there are vocals..here it is:: https://itunes.apple.com/us/app/432-player/id633600716?mt=8
    I have produced a electronica album at 432hz and all track are at 72bpm. Its like a sound healing experiment. Lots of magic melodies…I hope you will enjoy it and please share http://alford.bandcamp.com/ Thank you

    • anders says:

      I find 432Hz too deep on some songs. Som vocals sound too deep when the singers note are in their chest register.
      But I did a lot of Audacity conversions and could not find any song i preferred at 440Hz in relation to a version of that song tuned down -15 cents or 436.2Hz. Vocals sound more natural, less like they were straining which is weird as it is the same recording.
      I especially found the middle and head register of those singers to sound far more balanced..
      I did a lot of testing on my own voice, and its hates the 440-441Hz tuning. Its so much better when it gets down to 436Hz. 435Hz is also nice and very easy to balance the shift from middle to head resonance. (bridging the passaggio). Down at 432Hz it starts loosing the dynamics for rock and pop and my chest notes sits to far down in a band mix…

  21. Greg Ely says:

    Interesting stuff, I have been playing my Martin tuned down a semi-tone for years now, not for any of these reasons, but simply because I like the deeper bass notes. Oh well……

  22. Andy says:

    One this that has been missed by both the 432ers and the sane people is that orchestras tune to the Oboe and “Concert pitch” is a falecy in an actual concert. Sure the oboe is built to aim for 440 but it might be a hot day.

  23. James Reid says:

    Just for fun, here’s something else. Years ago I became interested in fragrances and perfume. I ran across a very old book– I believe it was from around 1850, but its been so long, I can’t remember. I think a friend of mine still has it these days.

    Anyway, in that book, by, I think the fellow’s name was Charles Piesse, consulate, if memory serves, to Nice, France. So Mssr. Piesse put forth the proposition that fragrances had “velocities.” These he measured by opening a fragrance in a still room at a particular distance from him and measuring the amount of time that it took for him to be able to sense the fragrance. He then prepared a table of frequencies and related these to musical notes. Based on this, he put forth the theory that one could prepare perfume blends that would have the same affect on persons exposed to them as their correspondent musical chords. In other words, by building a fragrance in which the velocities of the components bore the same relationship to one another as the notes in a C major chord, one would, according to Mssr. Piesse, arrive at a perfume which would impart a happy, bright feeling– just like a C major chord. The same would hold true for, say, an F minor chord– that is, a perfume constructed proportionally to the chord’s notes would result in a melancholy, rueful, slightly sad fragrance. I’ve not tested his theory, but it is, to my mind, as intriguing as it is likely dubious.

  24. Gerry Hundt says:

    Great article! My experience has been thus… I’ve started playing solo acoustic gigs at A=432Hz and I’m digging it. Specifically, I like the increased resonance of the guitar’s mid-range and the reduction of the harmonica’s jagged highs – to my ear, both sound more sonorous this way. I find it easier to sing too. The conspiracy theories are titillating to some folks but as for me, the proof is in the sound – I like the sound better, so I play better, enjoy the gig more, and entertain better as a result. Thanks again, and I look forward to many re-reads and shares!

  25. jorri says:

    The origins of 432Hz actually was because you can divide by ratios easily to create a just scale resulting in rational numbers. Someone must have read up a book about tuning systems and gotten completely confused by this, resulting in some myth about it. It doesn’t help that ‘432Hz music’ does not always contain an A note. And that they haven’t bothered to explore just intoning that (or would that resonate too much?!).
    Instead there are interesting things about Phi in music…swing quavers for example seem to fall around this, it also creates rhythms in a ratio that has the most variance of any number etc. There are also tuning qualities that could be improved such as microtonal notes in blues–like neutral thirds, 7ths and just minor sevenths in the 1/7th, guitarists/singers actually reguarly bend to these notes roughly as quarter tones.
    Or tuning drums to actual notes

    …or to avoid resonances in certain object as they can cause buzz and other nasty wolftones…

    ALso….does 432Hz mean we are not allowed to use vibrato either??? name a song without vibrato

  26. Rick Henderson says:

    Dear sir, a mind-boggling display of current and historic musical perspectives. Your mastery of intervalic mathematics is enough to make me swoon. And, the adroit and witty way you debunk the 432ruthers (that’s classic itself) is long overdue. When a friend of mine tried to feed me this snake oil I replied that the great Indian musician Ali Akbar Khan (my teacher) produced an inordinate supply of cosmic music with his sarode (often) tuned to the standard C of 440hz reference. And, indeed, his ethereal command of the Hindustani shrutis would be equally mesmerizing at a slightly varied reference frequency bot not TOO low lest the crisp bol tans turn to mush. Being a mathematical weakling I will accept your tour de force as valid and worthy. Thank you for this precise and delightful article.

  27. Jon says:

    Very interesting article.
    I’m on the fence about 432hz.
    There are indeed a number of claims that just seem ridiculous.

    Then there are other things that really make me wonder about the powers of frequency such as Coral Castle. It’s creator claims it was created by finding the resonant frequency of coral and reversing the polarity in order to completely change matter. It’s an interesting story if you haven’t checked it out.

    Stories like that certainly make me contemplate the power of certain frequencies. This 432hz comes up again and again from so many people that I wonder if there is more to it than just the oddball stories behind it. It doesn’t seem as though anyone has actually tested this in a controlled scientific environment to verify any possible physical or psychological benefits to 432hz.

    You did mention some things about the history of music that I was curious about. “Prior to the 19th Century, people made music with no specific – or highly localized – reference pitche”.
    I was wondering what your references are on this? I would like to read some more on this specifically.
    Well thanks again for the article.

  28. Albert says:

    Thank you for this thorough and concise piece. I enjoyed reading it: a lot of it I already knew, some of it was new to me. When you are setting up for audio tests, please let me know: I’ll be happy to participate!

  29. Frank Verhoef says:

    Hi Milton, as a Onemanband i combine the guitar/singing with both feet playin’ a different set of basspedals. By tuning my right foot a little bit lower than the left there’s a warm, smooth feeling comin’ over me. Musical greetings, Frank.

  30. Tikki says:

    surely there must have been a change in the original order of harmony as you can see in astrology where the first sign is Aries in march april… the first month of the year is January, its 2 steps shift. september is the number 7, sept in french translation.
    and its the 9th month as been teached in the west.
    Oktober is from OKT from Octo, 8 instead of 10th month
    November is Neuf 9 nuevo
    december is 10 Dix
    so january would be 11
    February 12
    the same can be seen in the notes on the piano
    where is been told that the first note of a scale and the middle of the piano is C
    while we all know that the first letter of the alpha,Beth(a) is A
    from A to C in the major keys is also 2 steps, so seems like the same shift is made in astrology as well, as in the musical structure. also the days of the week are different in other cultures who have different day on the beginning of the week , seems like also the shift in the week order has been made somehow. and also in the chakra system where now all the information that is found says that C is the note of the Root chakra.
    if someone makes music with the idea to touch the emotion of the root chakra and uses C for this , will actually make music for the Solar plexus.
    music made for the heart in western F would be D in the ancient theory
    i beleave its more likely and logic that this is the way the energy centers ( chakras) are linked to the notes
    A Root , B Sacral , C Solar plexus , D heart , E Throat, F 3d eye , G Crown
    just wanted to share also this insight , possibility.
    grtz

  31. Bo says:

    Congratulations for this excellent article, Milton! I kind of empathize with the advocates of 432, simply because Western music theory is so counterintuitive and unaccessible. We tell our children that tonality and equal temperament are the definition of music, the pinnacle of musical evolution, when in fact they are just contrivances excogitated by medieval thought, which reflect medieval technical limitations. Then we rant on about sharps and flats, call the 2nd harmonic “8ve” and the 3rd one “5th”, we hide the entire harmonic series behind cents, and never mention that equal temperament is dissonant and out of tune.

    It is of course very clear why innocent music lovers are mislead into deifying a frequency – at least they can understand that the ratios used for building pyramids are the same for making music, but it’s very hard to explain in a few lines what the harmonic series really is, and that those are harmonics and not frequencies.

    Besides the obvious points, mainly:
    1. choosing as standard the 10th tone from a 12-tone system is completely arbitrary;
    2. the tuning system itself – the abstract ladder of sounds defining a series of mathematical relationships between the tones’ frequencies – is completely overlooked. Even if mentioned, “Pythagorean” tuning is never used in practice but equal temperament is used instead;
    3. the unit of measurement Hertz is based on the arbitrary second of time;
    4. different units of measurement have no common scaling factor, so equating 432 Hz with the Kali Yuga from Hindu cosmology for example, having 432.000 years is ridiculous, just like linking it to the side of the Great Pyramid of Giza which nobody can prove that it is 432 Earth Units (51,49 cm) at its sea level foundation, and to the radius of the Sun in miles (approx. 432.450). How can an arbitrary association between different units of measure for time, distance and frequency can be taken seriously? Even if the Yugas did refer to actual Earth years, how can 432.000 years be linked to 432 vibrations per second when there are 31.556.925,975456 seconds in one year?
    5. the equal tempered association with “The Frequency of an Earth Year” at 136,102207779696… Hz
    6. the attributions of 432 to the crystallization of Scared Geometry in space, its “inherent harmonic alignment” with the creation of the Universe, and other delusional statements that can’t be demonstrated, like: “432hz vibrates on the principals of the golden mean PHI and unifies the properties of light, time, space, matter, gravity and magnetism with biology, the DNA code and consciousness.”
    7. there are many others, but…
    Innocent music lovers have no clue about tuning and the inner workings of music, so any concept is good as long as it promises salvation. If tuning to 432 Hz will make them ascend toward illumination, then let’s re-tune the entire musical collection, play it, and wait to ascend to the Heavens.

    Notice the inescapable ambiguity of nomenclature: “tuning” refers both to a set of related numbers defining the individual tones of a system, and to the reference frequency of that system.

    But the most overlooked aspect, even among musicians, is the (true) ancient math using pebbles in the form of a tetraktys, representing multiplication and division tables – much like the Lambdoma. This is thoroughly explained in Ernest G. McClain’s book “The Myth of Invariance”. The process is simple, and turns any system of ratios (tuning) into a series of integers by finding the least common denominator. Conversely, such a series can be written as ratios by dividing every member by the first and simplifying the fractions.

    As a definitive example, the tuning 1/1 – 9/8 – 32/27 – 4/3 – 3/2 – 27/16 – 16/9 – 2/1 can only be written as 432 – 486 – 512 – 576 – 648 – 729 – 768 – 864 using the smallest integers. There are no whole numbers smaller than these that can accommodate the above tuning without using ratios. Call this “Pythagorean”, “Dorian”, “Just Intonation”, “Ancient Mesopotamian”, “Diatonic” or whatever (most of these names are misnomers and inaccuracies), the simple fact is that those are not frequencies expressed in Hertz, but harmonics of the harmonic series. It is indeed a coincidence that the 10th note of a certain system has the same value, and the number 432 is definitely not the Hertz rate of the 10th member of a twelve-tone system, but a harmonic/ratio from the harmonic series.

    There maybe are temples and pyramids built using, among many others, this ratio, but this has absolutely nothing to do with its value in Hertz. The above set of numbers can be easily reproduced by knowing the limits of the system 432:864, and the rules of getting the other members (“cycles of fifths”).This is what 432 really is: 1/1 in a tuning of spiraling intervals of the 2nd and 3rd harmonics.

    432 was introduced by Maria Renold in her book “Intervals, Scales, Tones and the Concert Pitch C = 128 HZ” first published in 1985. As the very title of the book says, she advocated 256 Hz (the double or “octave” of 128) as the fundamental frequency – the first note, and not the 10th, used in conjunction with a scale called “The Scale of Twelve True Fifths”. In this scale, just like in “Pythagorean” tuning (a scale attributed to Pythagoras on which Maria Renold based her scale), the 10th note A is 27/16.

    Maria Renold conducted very simple experiments over the course of 20 years and with many people, the participants preferring 256 (and its 10th of 432) even if 440 was the familiar tone. Because she showed that humans preferred 256 but didn’t explain why, the results of her experiments were taken on, and escalated to our present day into the madness called “tuning to 432” and the absurd explanations linking to unrelated phenomena and New Age numerology.

    • miltonline says:

      Hi Bo,
      Apologies for the delay in response.
      Some points
      1) Actually equal temperament is not medieval, but is a relatively modern concept.
      2) Tuning systems and tonality are entirely separate concepts from reference tones (e.g. 432Hz vs other systems). So all talk of just intonation (which I heartily endorse) is wholly irrelevant to arbitrary tuning reference. i.e. just as valid in 440,432 or any other reference tone one might invent.
      In short, the conflation of 432Hz with temperament is highly fallacious, and yet every 432Hz proponent site does it. Simply, they don’t know what they are talking about.
      Happy to talk about tuning systems all day (and by the way some people in music academia (like me) engage with it completely)
      All best

  32. Great encapsulation. One paragraph that you must add especially over the last 10 years is that of recordings. Master tapes and then tape recorders and cassette audio tapes. The pitch and frequency depends on the RPM and the dust in your house after af few years. So to the bands of your turntable trying hard to keep it going at 33.3 RPM. As a guitarist with no youtube and internet learning from tapes and LPs posed challenges of frequency UN-imaginable to a non-musicians. Then come guitars made in India with Indian strings. Never at full tension as your guitar would turn into a boat-shape quickly. That’s where we musicians learnt that the pitch and key does not matter at all. Just play it. (A bit like Nike just done it).

  33. Thanks for this comprehensive article, Milton. As you point out, ll the reasons for shifting to A-432 are pretty bogus, based on equations that look like math, but which are based on arbitrary measurements in arbitrary units. Sometimes, you want to smack some of these people over the head with Sensations Of Tone (Helmholtz/Ellis) and Genesis of a Music (Partch).
    So, make your music with whatever pitches you like. Harry Partch liked G-196 (which puts a 9/8 at A-440). I have written some fun and extensive tools for you harmonically inclined folks to experiment with , namely my apps Droneo, Tondo and my little online tone spiral http://jhhl.net/tonespiral.html .

    But, here’s what I think: the reasons for basing your music system on 432 specifically are completely wrong, but conceiving a piece of music that actually HAS psychoacoustic properties based on the specific pitches it uses is worth investigating. The phenomena I refer to are resonances in a listener’s body and ears, which would mean each performance – or generated rendition of the piece – would be customized for the specific listener. There’s already a kind of precedent for this in Head Related Transform Filters, which give a “3D” effect to what would otherwise be stereo audio but simulating the filtering and phasing effects of the listener’s head and ears and probably cochlea. While filtering for an “average” person does provide some significant effects, actually generating the audio for the specific listener would probably be phenomenal.

    Music (physically) is fluctuating air pressure (isn’t that romantic?). So what I propose is a class of music that resonates a particular listener’s performer’s body’s resonant spaces. That is, that relates to the speed of sound at body temperature and pressure in the lungs, in the head, in the heart, in the bones. You can similarly compose pieces for specific resonant spaces that causes them to add their own harmonic reinforcement – and this has been done repeatedly!

    And guess what? This whole forum, devoted in great part to harmonic chanting, is in a way, devoted to finding those harmonies that resonate with the singer’s body! If you are left on your own to find pitches to chant on, you’re sure to find some that literally feel engaged with your body! And, thanks to the physics of harmonics, the whole progression of pitches will ALSO stimulate those same resonances!

    Here’s a little abstract that gives you an idea of the range of cranial resonances in humans: http://www.ncbi.nlm.nih.gov/pubmed/8176050
    the tl;dr is : there’s about a variation of more than 500 cents BETWEEN INDIVIDUALS in their cranial resonances, so even using my very plausible basis for finding a new concert pitch shows how ludicrous it would be to pretend there is a perfect or even a good one that could be generally used.
    Also, remember what concert pitch and the 12-TET system are about: getting large numbers of fixed-pitch instruments to play something like the same notes. That might not be what music is about.

  34. Thank you for trying to straighten all of this 432 Hz business out. I had been blissfully unaware, and will now return to tuning my harpsichords in a way that actually facilitates playing with instruments of more or less fixed pitch. We have made our compromises with the universe and they work pretty well. But I do love the Bloody Cat Tuning the best!
    Sandra

  35. Salem Beats says:

    I really liked the “selfie tuning” part – I thought it was funny. 😀

  36. louis says:

    please sir, is there a Fibonacci tuning… and does this all mean the notes stay the same diference apart???

    • miltonline says:

      Well, I offer a Fibonacci ‘reference’ tuning, which is a silly and abitrary way of what to call ‘A’ (as is the case with 440Hz and 432Hz), but if you are talking about the distance between notes, then no, I’ve not heard of that specifically. If it means you multiply each frequency by the successive members of the fibonacci series then no, they won’t be the same distance apart. Tuning with notes the same difference apart is called equal temperament, and you can have any number of notes dividing the octave in equal parts, includes 12 as in 12-tone equal temperament which we all know and sometimes love.

  37. Skye says:

    I just added this paragraph to my blog article about 432 Hz:

    “If you – like the 432-proponents – choose to focus on the frequency aspect of a tone, you actually miss half of the picture and end up with something amputated. The identity of a tone is actually a totality composed by a time aspect, frequency, and a space aspect, wavelength. The two are inseparable parts of the analysis as indicated by the formula λ x f = v (wavelength x frequency = velocity of sound in the medium, mostly air, 343 m/s at 20°C). This also means, that if you move an A4 organ pipe from an unheated church in Greenland to Bali the frequency will rise much more than the 8 Hz difference between 432 and 440 Hz. The tone equation is dependant on temperature and density of air!”

    Table of the relationship between velocity of sound and temperature can be found at Wikipedia:
    http://en.wikipedia.org/wiki/Speed_of_sound#Tables

    • miltonline says:

      Very interesting! Thanks. Also one could calculate the velocity needed to travel away from the listener to produce a pitch drop from 440 to 432Hz tuning.

  38. Alistair Thomson says:

    Bookmarked. I despair at the mental processes of some people. Vibrations on a metal plate proving a theory regarding nature’s resonance? Gobbledegook.

    Thank goodness for this sensible post. And thank goodness that 440Hz is currently well enough established, providing sufficient resistance to that flighty impetuosity which calls for frivolous change. Some day, there may be some sense in the musical establishment, once the 12-TET accommodation is gone from the Western musical landscape, but that won’t happen any time soon.

    • miltonline says:

      Thanks for the message, Alistair! I actually love 12-TET, but I also love [insert 100s of static and dynamic temperament systems].

  39. Robin says:

    Thanks for the brilliant article. As a sound engineer I am constantly battling against nonsensical audiophile claims that seem to spread in the pulic domain (and belief systems) like wildfire. Trying to bring a minimum of rationality to the debate can be tough and does not make you popular at parties 🙂

    On a side note, I am very fond of the ukulele and frequently tune my guitar up to experience some of the galactic brilliance, clarity and joy that only those little fellas can produce. It’s all 580Hz for me (at least)… 😉

    • miltonline says:

      Thanks for the positive feedback, Robin. What is frustrating is that the reality is far more interesting and beautiful than the myths. Oh well.

  40. Jimbo Jones says:

    I must admit that watching a 432 Hz Music blah blah video on YouTube too late the other night did have me, say, 74.432% convinced? I’m glad I’ve found this document, it was very informative and pretty funny once i accepted that 432 is ridiculous, mostly. However there are two things i would like answers to if someone with the knowledge would reply.

    Question One
    I’m curious to find out why so many cultures chose A-432 Hz as an optimum note
    (I guess 432 would be used as a drone, i.e singing bowl etc because 12TET isn’t used)
    one video claimed there are 432 Buddha statues at some place, and Indians call it *something* etc. if thats true, maybe 432 Hz does have an effect on the brain?
    Any information would be very interesting.

    Question Two
    Like the examples of alternatives above, what would be a relevant method of producing a #Hz for the A in a 12 note scale, to co-inside with celestial bodies etc. OR
    How would i produce a Hz in representation of our Sun? or Moon etc?
    This is just for my personal interests and admiration of the cosmos and physics, as a guitarist.

  41. Jester says:

    That was a very interesting dialogue so far. I thank you all.
    I fully agree with Milton. There is no reason to fight over something so subjective.
    Play in whatever frequency you like.
    My question is this, if everything is frequency and frequencies react with each other. Then how do different frequencies affect each other? If we want to know that then we first need a way to catalogue frequencies of matter? Then, we must find a way to see their reaction to each other.
    Point being: I’m started to get really curious if we could measure the frequency of everything. Lol… big question there, but why hold back eh?
    If everything is a wave, then how do we make harmony?
    I imagine a cosmic concert.
    Anyway.. I digress.
    You, good sir, seems to be in need of a challenge. Or do you want to keep spending your apparent intellect on bickering with the uninformed populous? It must be possible to capture the frequencies of matter. We can measure it for atoms and we can capture it from light that comes from far away galaxies.
    And we, the uninformed populous, are in need of an insight in the frequencies around us. So we extend this challenge to all who are in love with frequencies. Find a way to measure and catalogue the different vibrations around us.
    And if you laugh, and say: “Impossible”, then don’t. Theory is one thing. Reality is another. The basics are simple, everything is vibration. Some resonate, some don’t and some are in harmony while others are not. That’s the playground. Your missions, should you choose to accept it, is to create a falsifiable method of finding the frequency of everything. Now go play, and have fun.

  42. pako says:

    A complete RUBBISH biased piece of journalism PAID UP by someone interested in having us out of tune.
    All I see is a total attack to what many people have well researched and tested to be true in a 432 hz frequency being just desmantled by someone, I presume a shill, with contradictory arguments, nonesense and charlatan-like gibberish with no proof whatsoever of anything (s)he says about the subject.
    Therefore very unconvincing. 440 is very very BAD for your health. Period. 432 is still the RIGHT way to go forward.

    • miltonline says:

      Please tell me which arguments are contradictory, nonsensical or gibberish. If they are, I will fix them.

      • Roel says:

        I don’t think you need to change what you’ve written.

        Some people so much wish to believe in something, that they close themselves off and do no longer listen to reason. You – and for that matter I as well with some of my blog articles – disrupt their “dream”, reality can really hurt sometimes. 😉

        Don’t waist your time and energy on those who do not wish to receive it.

      • Scott says:

        From one paid shill to another: when are we finally getting paid? The Illuminati, the Nazis, the Rockefellers, and the Reptilians all just keep telling me “the check is in the mail”.

        Very nice work, Milton. I’ve used most of your arguments, but you’ve put them in a very comprehensive and understandable form here, a real service to those of us promoting the reality-informed picture.

        cheers from a fellow temperament freak, musician, and instrument builder in Vienna, Scott

        • miltonline says:

          Read the ‘argument from pretty patterns’ above. Cymatics deoends on a) the driver frequency b) the size/shape of the resonating body/material.

  43. Thank you for this very well-written and thorough article. I’ve spent far too much time debunking this 432Hz nonsense on social media over the last few years, utilizing the same examples and arguments as you but it’s nice to have it all in once place.

    From a musician and piano tuner, I salute you!

  44. Rudy Nunes says:

    Well Milton, I think you opinion is valid but I see all the data and your explanations as simply a point of view, not bad not good, but limited tough. I’ve seen many many people which had a good testimony after they change their music to 432Hz and they cannot be ignored just because it’s not written in the primer of science. Throughout the years I’ve found out that science is a human point of view not a ultimate truth. Since human beings are very problematic creatures many conclusions humans take are very problematic too. Science is a money oriented discipline, things are taken serious mainly based on profit, paradigms and power. I used to love mainstream science until I notice its problems which are many.

    Today science and religion are not that different anymore. Religions have their doctrines, their traditions and their masters. If you question the bases of their beliefs you will be rejected. In the past they banned or killed you if they decided so. Science has followed the same line of thinking. If you dare to have a position which defies the establishment you are ridiculed and banned before you finish your speech. They tell you what you must believe and what you can’t. Isn’t that what religions do with their followers?

    I’ve seen things which defies modern science and they are absolutely real, things that scientists in their laboratories do not know how to handle and they prefer not to talk about them. When something is mysterious and uncomfortable enough for scientists to handle usually they ridicule it and don’t talk about it anymore because their careers are at risk if they do so.

    Did you know all diseases can be cured without treatments or medicines? Well, science doesn’t accept that however I saw it happens many times before my eyes.

    I wish you all the best,

    My best regards.

    • miltonline says:

      “I think you opinion is valid but I see all the data and your explanations as simply a point of view,”
      Actually I’m presenting facts and logical arguments, if you think they are in any way incorrect way, please explain why, and I will fix.
      “I’ve seen many many people which had a good testimony after they change their music to 432Hz and they cannot be ignored just because it’s not written in the primer of science. ”
      Confirmation bias, suggestibility and wishful thinking are well established among humans, however intelligent or well-intentioned. The concept of a “primer of science” is silly.
      “Science is a money oriented discipline, things are taken serious mainly based on profit, paradigms and power”
      Science is a process by which we arrive closer to the truth, based on systemic testing, reconsideration and refining of hypotheses. Your claim that it is money-oriented is an unsupported opinion.
      “Today science and religion are not that different anymore. Religions have their doctrines, their traditions and their masters. If you question the bases of their beliefs you will be rejected. In the past they banned or killed you if they decided so. ”
      Not true at all. If you can successfully revolutionise scientific thinking you are rewarded, the fact that you have to show evidence for claims is precisely the opposite to faith-based religion where counter-evidence is ignored.
      “When something is mysterious and uncomfortable enough for scientists to handle usually they ridicule it and don’t talk about it anymore because their careers are at risk if they do so.”
      Not true. Any scientific claims are subject to scrutiny, that’s the driving mechanism of scientific progress (which allows you to use the Internet for example). 432Hz advocates are making truth claims, and I’ve taken those claims seriously and examined them in turn, and find their arguments totally without merit. But I took them seriously.

      I’m wondering why you are so keen to accept the scientific claims of 432Hz advocates, yet are resistant to any thing which challenges that view. Odd.

  45. Dr Scoville says:

    Trust the old master composers, polyphonics and instrument builders.
    http://www.schillerinstitute.org/music/rev_tuning_hist.html

    • miltonline says:

      I’m not sure if this is meant to somehow advocate 432Hz tuning. If so then there’s some problems…
      1) The linked history is largely unreferenced and inaccurate. Here’s a better referenced, and more accurate account. The whole Mazi/440Hz is a myth perpetuated by those who like a good story but not overly interested in the truth.
      http://www.roelhollander.eu/en/tuning-frequency/goebbels-and-440/
      2) Even if your source was accurate about say Bach and scientific tuning, (halo effect and argument from tradition fallacies aside), this doesn’t support 432Hz tuning. With C-256Hz, concert A is 430.5389646099018Hz (not 432Hz)
      3) The fact is that orchestras are free to, and do, choose various tuning references (as I’ve outlined in the article).
      4) My article is completely neutral about tuning references, all are fine. It just fines no evidence for the superiority of 432Hz to any other (or inferiority of 440Hz to any other). That’s all. The fact that this is so upsetting to 432Hz advocates is interesting.
      You’ll also note that I’ve not been challenged on any fact or logical step in the article, although I welcome peer review openly. Is there anything I’ve got wrong?

  46. Roel says:

    I do like using a lower pitch for some of my work (for example 435Hz, 432Hz or 430.5Hz) I have become tired of coming across the same old myths and fairy tales over and over again. It’s refreshing to come across an article that goes deeper into this subject then the usual one liners and superficial copy ‘n paste content. The fact is that there isn’t as much scientific or historical “evidence” that supports 432Hz tuning. Mose “evidence” put on the table by most sites and blogs is “pseudo-scientific” or rather speculative and in general lacks proper references to sources.

    Using Concert Pitch 432Hz instead of 440Hz does not per definition make your music sound better or so. For some of my music I have used lower pitches and find the low end to sound more “cored” and the high end less “edgy”, but that does depend as well on the quality of the instruments used, when recording the hard- and software used, and of course the skills of the musicians and sound engineers.

    To me the subject of Temperaments is more important then Concert Pitch. The relationship between the tones of a tuning system is key. The closer you can approach the pure intervals (found in the harmonic series), the closer you get to nature, and thus perfection.

    For some music styles it does not seem to be very beneficial, for some it does. In particular for music made with acoustic instruments a pitch change could be beneficial. Music that is more “punchy” or requires a more “aggression” sound it seems that raising the pitch above 440Hz might actually be more rewarding.

    Anyway …

  47. michael says:

    You speak in this article mostly about intangible numbers. It’s the vibration that’s being argued as relevant.

    Heat is a form of vibration.

    You’re basically telling people there would be no noticeable difference in reaction between touching a warm biscuit or sticking your hand in the flame of a stove.

    This example is extreme I know but shows there is a tangible difference in REACTION to different vibrations.

    However small the change in vibration, the effect on molecules changes. Do you know for a fact 440hz is healthy? Do you know for a fact 432hz doesn’t produce a more positive reaction in molecules.

    What about sound weapons used to control riots? What about vibrational heat weapons used in those same riots? Should we tune our instruments to these frequencies? Why not?

    Because the reaction would be undesirable.

    Write a blog when you have tangible info.

    • miltonline says:

      “You speak in this article mostly about intangible numbers. It’s the vibration that’s being argued as relevant.”
      The argument of the 432Hz movement is about frequencies of vibrations, so those ‘intangible numbers’ are very much part of their (and your) argument.
      “You’re basically telling people there would be no noticeable difference in reaction between touching a warm biscuit or sticking your hand in the flame of a stove.”
      Arbitrary analogy. One could make an analogy with 440Hz as touching a warm biscuit and 432Hz as dipping one’s hand in liquid nitrogen, with no less logic (or nor more lack of logic). And again, you’re using those intangible numbers…
      “This example is extreme I know but shows there is a tangible difference in REACTION to different vibrations.”
      Yes that’s what matters, and I see no evidence that a blinded test shows an improvement of 432Hz over 440Hz, (or any tuning reference to any other for that matter).
      “However small the change in vibration, the effect on molecules changes. Do you know for a fact 440hz is healthy? Do you know for a fact 432hz doesn’t produce a more positive reaction in molecules.”
      I’m not claiming the superiority of any tuning reference to any other, in fact I repeatedly advocate the use of any tuning reference. It’s the 432Hz who are making the claim of 432Hz superiority and yet to provide good argument or evidence in its support. Furthermore, 440Hz tuned music will include many instances of 432Hz frequencies and its harmonic vibrational relationships. Also 432Hz tuning referenced music doesn’t necessarily include a prominent use of that frequency. A diatonic piece in 432Hz in the key of B or A-flat will have no significant use of 432Hz relationships.
      “What about sound weapons used to control riots? What about vibrational heat weapons used in those same riots? Should we tune our instruments to these frequencies? Why not?”
      Now you are getting confused, mixing up amplitude with frequency, harmonic overtones with tuning references. You are basically arguing that sound weapons (presumably based on 440Hz tuning references) are more pleasant a third of a semitone lower.

      “Write a blog when you have tangible info.”
      Loads of tangible info above, and far more than the 432Hz-proponent sites. Now would you be up to putting yourself up to blinded test? Ie listening to a range of sound examples and identifying your preference, as you say it’s about the “REACTION to different vibrations.”
      Now please if you have any ‘tangible info’ and sound argumentation for the superiority of 432Hz over 440Hz or any other tuning reference, then please present it. I’ve shown above how the common arguments for 432Hz superiority (actually ANY tuning reference superiority) are without substance, so the onus is on you and other 432Hz proponents to show otherwise. Good luck.

  48. Sean Wolfe says:

    Thank you so much for writing this article. I had come across the 432 nuts as I was doing my usual browsing of synthesizer modules and clips. And every single thing they spout just made me… Angry. I know I shouldn’t care, but music and sound is a very special realm to me, and to have it all muddied up with this trash is just annoying. I understand that today, many people seem completely ignorant or unwilling to accept real scientific and rational modes of thought. And music and musical experiences aren’t always rational. But I’d just leave that up to personal experiences, and not equate it to some sort of hocus pocus.

    More irritating is how much of the ‘evidence’ they reveal are simply just wrong. Like the bad math and not understanding different tuning interval systems, or our arbitrary measurement on a time based phenomenon. It goes on and on. But your article knocks out all of these myths very well, and well written.

    But I guess it would probably be much simpler, and a lot less waste of time to just say to them, to quote Ben Goldacre “I think you’ll find it’s a bit more complicated than that.”

  49. Martin says:

    I am a chant leader, singer and multi-musician. I have started to tune in 432, and I experience more united and heartfelt sessions than ever before. It may or may not have any esoteric explanation, simply being the lower frequenzy, but in the end of it all, it works. Heck, even animals and children seem to be more hypnotized by the music, once I tune the A those 8hz down.

    But I’d like to make an observation upon your observation. I observe that you are lacking the faith to change this world into something better. It’s not really important what the truth is. If there is something that makes people believe in a more beautiful world, then don’t try and stop them. Or well, you can do as you want, I don’t want to resist your mind-trip neither. So take this not as a critizism, but merely as an observation, that even though you have the intellectual arguments, and even that they are very solid and convincing, it’s not always a reason in itself to put it out there. The 432 people are all peace activists, and they are trying generally to make music for peace. I think this aspect is much more important, especially to those of us who can understand the theory behind all of this. FOr us to let go of our intellectual mind trips, our judgements and just surrender to a vision of something more beautiful… this if faith, and especially this kind of faith, which has beauty as a vision, is the kind of faith that is helping our world and our people.

    Before I chose to start with the 432, I made a major study into it. And all the points you go through are more or less exactly what I came to as well. I couldn’t find any reason why 432 would be better, only the one that the pitch is lower than what we are used to. But once I started to experiment with myself, it really worked. Maybe one day, when we all are used to 432, we will get a musical revolution from the 424 movement 😉

    The human race is so mind tripping and neurotic. Maybe a lower musical pitch is really something of a peace project.

    Thank you for your insights. I completely agree with them and I will happily continue to change the world through my music made in 432.

    Love from Martin

    • miltonline says:

      Dear Martin,

      Thank you for the thoughtful comment.
      You touch on the three concepts I think are of value with the 432 ‘movement’
      1) People taking interest/ownership of music. Obviously I think it’s misguided, but the fact that people are engaged is a good thing (as I state in the post).
      2) Physical instruments playing at a different tuning sound different (as I state above), flatter makes some things easier (although if something is too low for your range…) and detuned guitars sound different. Different can often feel better, at least initially. However once has acclimatised.. A 30cent drop from 432 might feel equally welcome.
      3) Musical experience is of supreme importance to me (and me), and if through suggestibility (regardless of the validity of the claims) one has a better musical experience, then so be it. I do however have issues with this (see below).

      So for what it’s worth, here’s where I don’t (with all peaceful thoughts) don’t align with your position.

      ” Heck, even animals and children seem to be more hypnotized by the music, once I tune the A those 8hz down.”

      Placebo effect is one thing, and all well and good, but claiming that 432Hz music (independent of suggestibility) is more hypnotic/relaxing is a truth claim. I actually really care about what is true, and if 432 has a more relaxing effect on children and animals than any other tuning reference, then this can be tested, I remain open, but very skeptical.

      ” I observe that you are lacking the faith to change this world into something better. “

      If by faith, you mean desire, then you are wrong. If by faith, you mean blind belief without evidence, then possibly. I also see no reason to believe (good evidence from any source) that tuning music down 30-odd cents (as opposed to any other move) will improve the world. Liberation of women, greater education, scientific education and advancement in medicine and agriculture, greener energy, advancement of the arts, cultural growth, greater empathy, tolerance, equality etc. I see as valuable. Tuning down your music library by a fraction of a semitone, no so much. I see it as a very superficial claim on musical understanding. As I say above, if you want to engage with a hidden aspect of music that is of primary importance, engage with temperament. Unfortunately I’ve no seen a 432 proponent site with a solid understanding go temperament, and they often conflate it with tuning reference. Music is too complex, deep and beautiful to need fabrication.

      “…even though you have the intellectual arguments, and even that they are very solid and convincing, it’s not always a reason in itself to put it out there. The 432 people are all peace activists, and they are trying generally to make music for peace.”

      Here’s where we disagree again. I think there is something sinister behind blind faith in things that are untrue, and I am just examining what is likely to be true or not. Of course it’s not a major threat what people do with their music. And I’ll say it again (as I repeat above), I encourage the embrace of any and all tuning references (including but not limited to 432Hz), isn’t that a more open-minded and accepting position than advocating world wide adherence to just one tuning reference? By the way (as stated above) different ensembles of all styles, electronic musicians, music cultures already use a huge range of tuning references other than 440 (including adhoc ones). Having an agreed if arbitrary tuning reference is convenient, but I embrace diversity not conformity.
      Incidentally, I’ve received all manner of insults and accusations merely by writing this post e.g.
      “A complete RUBBISH biased piece of journalism PAID UP by someone interested in having us out of tune…I presume a shill, with contradictory arguments, nonesense and charlatan-like gibberish with no proof whatsoever of anything (s)he says about the subject. 440 is very very BAD for your health. Period. 432 is still the RIGHT way to go forward.”
      So if I don’t agree with this peace activist then I am corrupt and stupid. I politely invited this peace activist, to point out what was contradictory or nonsensical but no reply. I’m made the enemy by not agreeing. That’s the darker side of faith-based belief. Not enlightened, tolerant not open-minded. I’m not saying 432-believers are all like that (far from it), but it certainly doesn’t make one immune to that sort of divisive mode of thought.

      Finally, as I said before, I am very interested to learn what is true, independent of suggestibility, placebo effect and so on. Later this year I’m devising a controlled listening experiment to see if people do indeed report greater feelings of relaxation, or generally more positive experience with 432Hz over other tuning references (including 424 🙂 ). Please let me know if you would be interested in taking part.
      All best!
      Milton

      • Martin says:

        Hi Milton

        I see all your points. For sure you are well acquinted and rational about all details, and I also sense your sincerity.

        I guess what I was trying to say, was just that in you somewhere, there is a resistance towards something, that in this case is being manifested as a scientific attack on the 432 movement. An attack that you can only win, because you are obviously right in all that you say.

        For me myself I have dropped my resistance agains almost anything. Even stuff like war and killings, I honestly believe AND SEE that we are all one. I see my own face in any face passing me by, and so I do not judge people’s action from a seperated point of view. Furthermore I believe that we’re simply evolving through this phase of violence still, and there’s nothing wrong with people wanting violence, it’s just an expression of the totally natural consequense of our existence. So resisting anything real, is actually quite neurotic. Few people can truly understand this, so I don’t want to encourage any discussion about it. And I am neither saying that we shall not take any action in our lives. On the contrary I think everyone should do what they feel they really need to do, and hopefully they will do it with awareness, so they can learn and grow from it.

        I mention this my understanding, so you also can understand, why on earth I want to point out that you have a resistance in you. Because I am in you and you are in me brother, and I love you, and I hope you will let go of all your resistance against everything, so you may experience the universe vibrate with love and joy in full consciousness.

        But don’t force anything. Do what you feel you must do. I am very interested to see where your listening experiments will go. I am doing them all the time, because I often play with flutes or other woodwind instruments that forces me to go back to 440, and it is crystal clear to me, that the general human body, when engaging in heart songs and chants, are calmed down much more by A tuned to 432. But hey, calming down may not be the point of all kinds of music. So there’s no right or wrong here, simply one experience.

        Thank you brother 🙂 Love and light

        Martin

  50. Paul says:

    Another guy trying to be smart and rational but totally forgetting that music is about feeling, doh! I’m going to trust my feelings on tuning to 432Hz, been experimentin’ with this and 416 and this one sounds best. And yes I tried loads of tempermants.

    Wasted a lot of time being smarter then the others. There are no arguments, some stuff just feels right. Oh maybe you forgot the polygons and their degrees all fitting in 432 and Pythagoras tuning 😛

    • miltonline says:

      Thanks for the feedback, for what it was. I find it interesting that you claim that it’s about feeling and not about rationalism, but then attempt to justify your preference with a rational argument.
      The ‘polygon’ argument I find unconvincing due to the fallacy of integers and the arbitrariness and solipsistic obsession with the second.
      I also note that you conflate Pythagorean tuning (3-limit system for intervallic construction) with tuning reference. Entirely independent concepts, surprising you make this error given you’ve tried loads of different ‘tempermants’. So while you say it’s not about rational arguments but what feels right, I suggest that under controlled blinded conditions most 432hz would not express a preference. Do you disagree? A previous commenter suggested that it doesn’t matter, it’s all about blind faith regardless of its validity. Fair enough of that’s your position. Is it? Personally I’m more interested in what is true, not what we pretend to be so.

  51. Marcus says:

    Word To ya motha, Milton I agree with everything you said and I appreciate the debunking of the false claims. Some of them are so silly to begin with. I would like to add something that even advocates for 432 dont really understand. Different frequencies have different effects on the body in a quite literal sense. A loud high pitch noise will hurt your body in different places than a loud low pitch noise at the same db level. By the same process, different frequencies are better for meditation even though everyone is different. 99.9 percent of people would agree that the OM frequency is far more relaxing then say the frequency of nails on a chalkboard. That’s obviously a fact even though I don’t have any sources for that lol. Also if you play two sounds to a dog, one higher than humans can hear and one lower, the dog will usually go more bat shit crazy over the higher one. So to say that 432 is superior simply because it is easier to induce meditation is where all this confusion comes into play. Didferent strokes for different folks is what it comes down to. I suppose I can see how people can confuse a more relaxing frequency with a cosmic truth especially if your chanting or somerhing like that. I just want to make sure that you don’t think different frequencies don’t have different effects on the mind and body even if we still are figuring out what they are. Hell acupuncture has been around for a loooong time and just the other day I was reading an article that science proved why it works. Well millions of people already knew it was real even thought they couldn’t explain scientifically why. As for 432 being the “way to go”, well that truly is in the eye of the beholder. I myself like to be tuned down a half step with my guitar.

  52. steve syms says:

    Great article and discussion , Milton I wondered ad this question is a little left of field, any thoughts on 453hz and global scaling ? Are you aware of anyone using this as a refernce for tuning?

    I also wondered if you had any view of a lot of the focus being around c# @432 , with a push to align to 136.1 , do you feel there are any differences other than in a mathemaica sense around for example an F?

    Thanks

  53. Roger says:

    Lol, the typical skeptopath’s wall of text filled with snarky comments and muddling of waters. Unfortunately for you and your buddies, numbers have a “life of their own” so to speak, and point to metaphysical realities. Ask any really high-level mathematician and he will probably agree, if reluctantly.

    Putting aside all the stuff that seems to both prove and disprove your point and the one you’re trying to “debunk”, let’s come to the visual evidence: cymatics. You’re basically saying that people who do 432/440 comparisons with plates, calibrated their plates to make them produce better looking sand patterns at 432hz?
    This sounds like conspiracy theory to me…
    Are they selling 432hz in a bottle?

    But more important: why the hell do you care? do people who don’t like the color red or yellow write walls of texts on their blogs to say how wrong it is to use those colors? You sound to me like a buttmad creationist or atheist, locked in a useless confrontation with something he’s profoundly afraid of, for fear it might be true.

    And the fact that there are stupid arguments about 432hz doesn’t disprove anything. Hitler said UK is an island, so UK is not an island, I guess?

    Seems to me you’re one sad zeteticist getting irate that people are deviating from the “scientific” norm. Your kind is dogmatic and your beliefs are a religion for you, while you don’t even see it. That’s pretty pathetic but then again to each his own 😉

    • miltonline says:

      Thank you for the feedback. I’ll take your questions, criticisms (and insults) in turn:

      “Lol, the typical skeptopath’s wall of text filled with snarky comments and muddling of waters. “

      Please let me know which of my points are ‘muddling’ the waters, and I’ll clarify/adjust/delete accordingly.

      “Unfortunately for you and your buddies, numbers have a “life of their own” so to speak, and point to metaphysical realities. Ask any really high-level mathematician and he will probably agree, if reluctantly.”

      I’m (very) interested in music, and (very) interested in what’s true, so there is no fortunately/unfortunately about it. And this article has indeed already been vetted by a really high-level mathematician. But if you (or anyone) can point to anything here which is incorrect, or link to a high-level mathematician which calls into question any of the above, let me know, and I will adjust accordingly.

      “Putting aside all the stuff that seems to both prove and disprove your point and the one you’re trying to “debunk”””

      Which stuff disproves my point?

      “let’s come to the visual evidence: cymatics. You’re basically saying that people who do 432/440 comparisons with plates, calibrated their plates to make them produce better looking sand patterns at 432hz?
      This sounds like conspiracy theory to me…
      Are they selling 432hz in a bottle?”

      Cymatics is precisely about 1) driving frequencies and 2) resonating bodies. Patterns occur because of the wave reinforcement, interference and cancellation that occur with the relationship between the wavelength of the frequency (or frequencies) of the sound and the dimensions of the resonating body.
      So why do people choose to upload videos which confirm pre-existing beliefs? You’ll have to ask them. I suspect confirmation bias (unwitting or not). Only noticing things that confirm with pre-existing beliefs and ignoring the rest. I try to do the opposite, considering evidence even when (and especially when) it challenges pre-existing beliefs.
      Now since cymatics seems to you to be evidence of 432Hz superiority, would you change your views if you saw 432Hz pretty (or ugly) patterns reproduced in bowl of different dimensions with 440Hz (or any other frequency)? If you rather not lose faith in 432Hz that’s fine, but I’m just interested to know if you actually care about what’s true.

      “But more important: why the hell do you care?”

      Thanks so much for asking. I care (deeply) about music, music education, music experience, science and what is true. What is true about music is always more interesting than myths, and I see a lot of myths posited by the 432Hz movement. Now I’ll reiterate what is in the article (which you seem to have skimmed at best), I am not claiming the superiority of 440Hz over any other tuning reference, nor the inferiority of 432Hz over any other, and I advocate the embrace of any without prejudice. 432-proponents are claiming its superiority and I’m examining their common arguments in turn.
      Now why do you care if I do that? Why do you feel the need to respond to this post?

      “do people who don’t like the color red or yellow write walls of texts on their blogs to say how wrong it is to use those colors?”

      If they claimed that red or yellow caused poor health, had links to the Nazi party, or resonated poorly with the vibrations of the universe, then I think someone is perfectly justified in responding. As for subjective enjoyment, it’s a poor analogy, you literally can’t do blinded tests for colour. Most 432Hz aren’t just claiming that “music sounds better if you belief it’s tuned to a special frequency”, they are (among other things) claiming that music sounds better at 432Hz whether you don’t know it is so-tuned. I find this completely unevidenced (and 432 Hz proponents generally uninterested in testing that proposition). What are they afraid of?

      “You sound to me like a buttmad creationist or atheist, locked in a useless confrontation with something he’s profoundly afraid of, for fear it might be true.”

      I am not afraid of any frequencies or music (nor prejudiced against any, apart from some forms of Euro techno from the mid-90s). Right now, I am playing a 432Hz tone with upper partials at 5/4 3/2 and 15/8 ratios. Sound very nice (as it does at 402.3Hz and any other reference tone, and am feeling no fear.

      “And the fact that there are stupid arguments about 432hz doesn’t disprove anything. Hitler said UK is an island, so UK is not an island, I guess?”

      …or vegetarianism for that matter. Agreed, and that’s why I was careful to take each argument in turn and treat it entirely fairly and independently. Let me now where you think I haven’t done that. Your metaphor however is a tad ironic given that many 432hz sites imply that 440Hz is evil because of (fabricated) Nazi connections.

      “Seems to me you’re one sad zeteticist getting irate that people are deviating from the “scientific” norm. “

      I love the science of music and embrace new evidence (if valid), why on earth would I be angry about learning something new and true. I just haven’t (yet) heard such things from 432Hz proponents, even though I’ve been entirely fair and open-minded about the claims. Interestingly I see a lot of conformity with uncritical copy and pasting within the 432Hz movement, as well as appeals to science. p.s. not said, why do you say zeteticist, when later you accuse me of not wanting to deviate from the scientific norm. Get your insults sorted!

      “Your kind is dogmatic and your beliefs are a religion for you, while you don’t even see it. That’s pretty pathetic but then again to each his own ;)”

      I’ll assume this is simply intended as an insult. But no, I would say I’m the opposite of dogmatic or belief-driven when it comes to music (or most other things).
      And remember I use many tuning references, but I’m not making a claim for the superiority of any one of them (including 440Hz). So the only thing it seems you are upset about is that I don’t find the claims of 432Hz convincing.

      It’s odd that that would upset you so much, but then again to each his own 😉

  54. barry curran says:

    Wow…..thank you…..I don’t understand the maths behind the explanation,but the explanation itself is clear….
    Shut up about the difference,there is none….
    Magic!!!!

  55. Marcus says:

    Here I am trying to bring the conversation to the next level, trying to expand my mind and yours Milton, but I noticed you only respond to comments that induce futile arguments and you seem to be much happier disproving people’s beliefs than really getting to the heart of the problem. There is much more to frequencies even on a scientific level if not metaphysical, same thing with colors. So let’s get down to the bottom of it instead of saying who’s right and who’s wrong

    • miltonline says:

      Dear Marcus,

      Thanks for the feedback. Apologies, I didn’t realise a missed an opportunity to reply to you.
      Actually I’m interested in the truth and not ‘disproving people’s beliefs’. Sometimes the latter happens as a consequence of the former but it’s certainly not an objective.
      Yes very happy to get to the bottom of it. Here’s my position: All frequencies are ‘natural’, beautiful and cosmic. How they interact is sublimely wonderful (and to what I dedicate much of my life). The prejudice for or against certain frequencies is an impoverished view of nature and music. To claim superiority (or inferiority) of any frequency (or any colour for that matter) is to misunderstand the beauty of music and nature, and to unnecessarily vilify a group of musicians and music cultures. What’s your take?

      • miltonline says:

        Hi Marcus,
        Did you want to carry on the conversation? Very happy to…

        • miltonline says:

          Honestly, I’m very happy to discuss it and open both our minds.

          • awrhz says:

            And that’s a lie because you don’t publish messages that put you and your paradigm in a bad light :^)

            However we can see that the skeptopath bots are in full swing :DDDDD

          • miltonline says:

            I don’t automatically allow comments due to spam, but if you look through the comments you’ll see many who are allowed comments critical of the post. I don’t allow threats of harm to me or my family (which I receive), but I allow any healthy discussion on the topic. Your first of 3 posts came in at 4:54pm less than 30 minutes ago, so you may need to update your world-view subject to the evidence.

      • asgasfgh says:

        Did you really wrote that saying that some frequencies are more stable than others is prejudice?

        Absolute relativism is a monster Nietzsche was so fucking right

        • miltonline says:

          Please define “stability” in terms of frequencies and why 432hz is more stable than any other. That would be a good basis upon which to hold a discussion.

    • miltonline says:

      Still happy to discuss this.

      • Hallo says:

        But you aren’t as there are many comments you didn’t publish

        Not surprising: you are a devious individual, anybody with intuition understood it

        • miltonline says:

          Anonymous commenter, fake email address, baseless insult, no specific points to address. Anything in particular about 432Hz you’d like to address?

  56. george says:

    Milton, may I ask what instruments you play?

  57. Thanks for this article. I know many people who were trying to sell the 432-story to me and I was always asking the very questions you have answered. In the end it is about understanding how frequencies interact with each other that makes music, not to which frequency they are anchored. I personally disliked tuning down to 432 because the tension of my strings was off. it would mean I would have to re-investigate what strings to use etc…
    Honestly, if your music is good, it will move people. No amount of tuning will change that.
    Check my website if you want some good music at 440 🙂

  58. Miriam Erasmus says:

    Thank you dear Milton, what a beautiful reasoned article. I agree that music can be both Universal and scientific. I believe that it is not how the music is played, it is the intention of the performer that has far more power than the numbers. Love, Mim xx

  59. Pablo Donadelli says:

    Hell, this is such a good article. Amazing stuff Milton. My problem with 432 (or any other outside 438-442ish range) is it takes me some minutes to get used to, so when i start listening, i feel it’s all out of pitch.
    Anyways, good job. Keep doing this and maybe hippies would stop attacking rational (but not less spiritual) people.

  60. Ricardo says:

    Yall put numbers to a phisical phenomena to quantify something that it just have to be an experience only comprobable or verify through the observation method.. the number to identify is just referential to get with a aproximation frequency and doesnt put some very specifical number to get with the real deal that its the wave.. sound.. vibration.. produce.. from the numerical view 432 it just an accesible referential like any other just to get a common language! This phenomena that it claims to be trascendental.. universal.. natural.. espiritual or delusional in fact appeal to phisical problem of Pitagorad which occurs when several sound effect it produces by the total resonance of each note harmonic in a string.. besides that occurs to those notes ratios it generates geometrical forms some of their in a clear and more regular patterns and forms from the cymatics experiment.. i’m a musician since the 8 years old now i’m a 27 years old electric engineer and architecture student and in my experience playing string instruments is that intonation around the 432 hz it’s sound and feels way much better since ever.. there’s nothing solid about this or other argues cuz every of them are trying to explain something that it’s has been former contemporary restudied since relative recently.. for example the experiments token for the schiller institute of music or the various efforts to try to discover this intuning and not detuned approach like the sonic geometry documental what it claims to be delusional too.. and that almost every to claim the disguise and dismissed information and some number that doesnt do much more that identify some specific values instead the mechanical and even electromagnetical process of the sound.. theres a direct relation whit the properties of light.. time and space and it should be a integral form in all of them.. so it should it be some kind of law or rules about that process in despite there’s the string and the quantum energetic fields theory wherever it goes it has to be more important to stand and understad the esentia of the sound like a trigon senoidal functions where every number or result is given in periods.. angles and waves with a pi base numbers which occurs to result in majority by irrationalia like phi and euler constant in fact both of them with severeal trigon’s properties.. so it had to be taken a year a solar year like a period ratio and the distance values both equally important to thoses vagues calculations make by almost everybody even me.. for example the solar year value is 365,242 190 402 middle solar days , 365 d 5 h 48 m 45.25 s. plus one day every 4 years or the thirteen month’s lunar calendar.. the 13/12aves of a minute.. the fact that a meter is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second or that the light traveling in the vacuum of the space it bends or that the way it the sound travels in correlation of the light.. in so many other things to analize and it happens to be the start point of my clearly understood of this “musical revolution”.. but until i don’t get a rehearsal with all of the gigs.. guitar.. bass.. keyboard and even drums with this intonation i can’t understand what is all that crazy thing.. theres a lot ideas.. thinks and opinion out there but my personal criteria it’s that in despite isn’t all thruth there are a lot to study to do and more important and to experiment instead tryin to reprobe or aprobe if this bittersweet chocolate or stinky bullshit.. I even made an amplifier that it works with a different voltage and calibrate my guitar to it work in a diferent intonation.. my individual experience like others it’s positive.. let’s take to prove it right and then will see what it doesn’t work! P.D. Excuse for my english..

    • miltonline says:

      Thanks for the comment. I think I’ve got the general gist of your points and they are all addressed directly in the blog post. In essence there is no convincing argument that has been made for 432hz superiority over other reference tones. And I’m open to all ideas and treat them fairly.

  61. Mikesch says:

    After watching this video it persuaded me to the 432hz realm. I like the sound, works for me!

    https://www.youtube.com/watch?v=1zw0uWCNsyw

    • miltonline says:

      I’m glad 432Hz is working for you. Out of curiosity, do you think you’d prefer 432Hz over other tuning frequencies when ‘blinded’?
      Thanks for the video, but I personally find it unconvincing (and I deal with cymatics above). You would get the same patterns with 440Hz with a slight smaller plates. Similiarly a slighter larger plate would respond to say 412Hz ‘better’ than 432Hz. The experiemnt doesn’t show a universal truth but just how one specifically sized plate responds to specific frequencies. Music is substantially bigger than one frequency (or related set of frequencies) being ‘better’ than others. The entire frequency range is beautiful/relevant/available.

      • awrhz says:

        What point are you trying to make? the video clearly shows 432hz is more “stable” than 440hz.
        Unless you think this video is trickery, of course. Are you a conspiracy theorist?

        • miltonline says:

          Read the section of the post above “The argument from pretty patterns”. Come back with any specific questions.

  62. Dan Reyes says:

    Thanks for the dose of common sense. It’s amusing to read some of the “proof” put forth by these “432ruthers” (love that one, by the way!); At best, it’s ignorance about music, pitch, tuning systems, and acoustics and at worst, downright fabrications such as the belief in a previous universal standard of 432 Hz or a Nazi/Illuminati/Gluten connection. I’m a string player and whenever I play early music (baroque or earlier) I like to tune to an A of around 415-420 Hz. For stringed instruments like the violin, it does change the timbre of the instrument slightly, but the true difference is in the playing technique, not the arbitrary selection of an A. I would bet money that you can play any 2 A’s at an 8 Hz difference and convince the hearer that the second was somehow better or more mellow than the first.

    • awrhz says:

      Of course frequencies make no difference, that’s why blue and red are the same color for example

      • miltonline says:

        I never said frequencies “make no difference”, just pointing out how the oft-repeated arguments for 432Hz are flawed. Let me know how you think it’s mistaken, but you may need to actually read and understand the post first.

  63. BUILDER says:

    432Hz resonates with the frequency of 8Hz. On the musical scale where A has a frequency of 440Hz, the note C is at about 261.656 Hz. On the other hand, if we take 8Hz as our starting point and work upwards by five octaves (i.e. by the seven notes in the scale five times), we reach a frequency of 256Hz in whose scale the note A has a frequency of 432Hz.

    According to the harmonic principle by which any produced sound automatically resonates all the other multiples of that frequency, when we play C at 256 Hz, the C of all other octaves also begins to vibrate in “sympathy” and so, naturally, the frequency of 8Hz is also sounded. This is why (together with many other mathematical reasons) the musical pitch tuned to 432 oscillations per second is known as the “scientific tuning.”

    This tuning was unanimously approved at the Congress of Italian musicians in 1881 and recommended by the physicists Joseph Sauveur and Felix Savart as well as by the Italian scientist Bartolomeo Grassi Landi.

    In contrast, the frequency chosen in London in 1953 as the worldwide reference frequency and which all music today has been tuned to, has come to be defined as ‘disharmonic’ because it has no scientific relationship to the physical laws that govern our universe.

    [links removed]

    • miltonline says:

      I’ve seen this passage copy and pasted several times on 432Hz sites and comments. What’s remarkable (and very telling) is that I’ve dealt with every single one of these points in the post above, and the poster hasn’t made any adjustment whatsoever in order to respond or adapt the text accordingly. This shows a systematic unwillingness to engage with any valid criticism or comment. It’s just mindless (as well as close-minded) repetition characteristic of the 432Hz movement. But for the interest of completion, let’s analyse the text:

      432Hz resonates with the frequency of 8Hz.

      If you mean ‘resonates with’ as has a ‘simple harmonic ratio with’ then yes it’s at a 432/8 = 54 ratio. Multiplying an octave by 2 creates an octave but what is multiplying a frequency by 54 in terms of a musical interval. That’s 6 octaves an even tempered major 6th and some change. Or in terms of the harmonic series it uses the 3rd harmonic three times and then up an octave (3x3x3x2=54). If we bring it down to the same octave (using the law of octave equivalence) we have the ratio 27/16. That’s a Pythagorean major 6th I’ll have you know. Stacking up the 3rd harmonic then bringing down a few octaves. Is this the most elegant/simple way to get to a major 6th? Well it’s one way, and it’s lovely. I (and others) think 5/3 is a more elegant way to reach a major 6th (some theorists equate the size of the integers in the ration with harmonic simplicity). Regardless there are many at-least-as-harmonic rations as 27/16. But ok yes. Now why is that a good thing that 432Hz resonates with 8Hz. 27/16 may be a “good thing”. But 8hz is no more special than 7.3432Hz. Why? Because as explained in detail in the post, the second is an arbitrary (and only useful through universal agreement) unit of time. It’s not even accurately linked to our local cosmology, and we are just a wee speck in the universe. Let’s move on.

      On the musical scale where A has a frequency of 440Hz, the note C is at about 261.656 Hz. .

      Do you mean 261.63Hz? That’s what it would be for a C with A440 and 12-tone equal temperament, your figure comes in at 0.17 cents out from this and isn’t related to a just intonation I can glean. It may be an error, but it’s a bit accurate to be an approximation. I’ll assume you mean 12-TET and this is a simple error, let me know otherwise.

      On the other hand, if we take 8Hz as our starting point and work upwards by five octaves (i.e. by the seven notes in the scale five times), we reach a frequency of 256Hz in whose scale the note A has a frequency of 432Hz. .

      Well actually only with the Pythagorean tuning of 27/16, so not on a standardly fretted guitar or piano (yes even at 432Hz) or most common fingerings on acoustic instruments, and in fact as beautiful as it is, not in wide (read non-Western) music practice. If you used 12-tone equal temperament (as you used with 440Hz example), then it comes out at 430.1Hz. Oops.

      According to the harmonic principle by which any produced sound automatically resonates all the other multiples of that frequency, when we play C at 256 Hz, the C of all other octaves also begins to vibrate in “sympathy” and so, naturally, the frequency of 8Hz is also sounded. This is why (together with many other mathematical reasons) the musical pitch tuned to 432 oscillations per second is known as the “scientific tuning.” .

      Kinda. Scientific tuning is (an arbitrary) decision to use a binary system as a tuning reference. I quite like it, As arbitrary systems go, it’s neat. However, it needs a non-harmonic crowbar to link it to 432Hz. Oops.

      This tuning was unanimously approved at the Congress of Italian musicians in 1881 and recommended by the physicists Joseph Sauveur and Felix Savart as well as by the Italian scientist Bartolomeo Grassi Landi. .

      And other scientists, engineers and musicians have settled on other tuning references previously and more recently. So what.

      In contrast, the frequency chosen in London in 1953 as the worldwide reference frequency and which all music today has been tuned to, has come to be defined as ‘disharmonic’ because it has no scientific relationship to the physical laws that govern our universe.

      And there we have it, the made up nonsense. It’s hard to know where to start here but let’s try. Who calls it 440Hz ‘disharmonic’ (other than 432Hz proponents)? The implication (given the context) is that it’s ‘disharmonic’ because there is no harmonic relationship between 8hz and 440Hz but actually it has 55:1 ratio which is linked through the 5th and 11th harmonic series. And regardless, there is nothing special about Hz, and so there is nothing special about 8Hz. What matters in musical tuning is the relationship between frequencies and not an arbitrary naming system based on an arbitrary time unit.

  64. bleak says:

    This post has answered so many questions I have failed to find (accessible) answers for my self in relation to the general theory about musical notes. (Why is A 440Hz? How do the notes relate to each other, and why?) It seems it’s something one is expected to just accept at face value when attempting to learn music. (I only came across this 432Hz business around 20 minutes ago.)

    Thanks, a very enlightening post. 🙂

    • miltonline says:

      Thanks bleak,

      Thanks for the comment, and I’m glad you found it enlightening. When I can find time, I’ll comple a related reading bibliography at the end should you or others wish to further explore the (to me fascinating) field.

  65. daff says:

    Amazing trip there Milton! I’ve just spent more than an hour reading your article and all the posts in response. I came here after seeing some 432 post on fb. It all felt a bit wrrong!
    I should be asleep by now but I just wanted to thank you for your article. And moreso for your tireless logical deduction in replying to some of these posts.
    Incredible dediction man!

  66. Pete says:

    Nice one Milton!
    I was getting extremely frustrated with all the uninformed arguments littering my search engine. No evidence, just speculation, basic maths can debunk most of these pseudo scientists ‘discoveries’ (opinions based on big dreams of inter connectivity). Glad to see a thorough report based on some actual evidence and not just ignorant bs. If there really is a perfect scale for music then that ain’t it as far as I can see, and now your report has confirmed my suspicions. Why oh why do these morons think that lying about data and stating opinions as fact will ever help their argument. It’s also very amusing to see the naive still blindly following that video they saw posted on youtube or whatever, posted by no one of any significance. Some people just can’t recognise facts staring in their face, unfortunately its those kinds of people we have to blame for the world being the messed up way it is.
    Thanks again from one truth seeker to another!! Keep it real!!
    Pete

    • miltonline says:

      Thanks Pete I appreciate the comment. We are all subject to cognitive bias, wishful thinking and mistakes, so I try not to be too judgmental of 432 proponents. Nonetheless they are demonstrably and repeatedly wrong on most of their factual claims, and I find the truth more interesting than fantasy. Music (and science) requires no elaboration to be fascinating.
      Your band sounds great by the way!
      Milt

  67. Bryan Anthony says:

    Thank you so very much for this article! I am currently a musician and am also diving into the more New Age field of sound healing and have been wrestling with this notion of ideal frequency needed to be most potent in my practice. This article has reminded me that it’s the relationships that matter, not necessarily the notes themselves. I was a bit zealous about jointing the 432hz movement whenni first heard about it, but I had no basis of judgement other than what I thought I felt when I retuned. I ended up realizingn that tuning my guitar down a full half step allowed me a bit better range and still allowed me to tune with others.

    Thank you again for your hard work!

  68. Osbert Quimby says:

    Thank you for this injection of sanity; I think I might be a bit Asperger’s: there is something about untruths that profoundly physically upsets me (in my gut).
    I’ve been looking for 432 Hz truth on the Internet for the last few hours and finding few rational oases in the wasteland of hive mind falsehood. Dare I suggest that there are people talking about something that they aren’t qualified to talk about? A terrible thing to say, I know, in this egalitarian age. I’ve been playing music since 1968 and have a BSc. in Physics, and the very low standard of reasoning from the proponents of the 432 Hz camp has shocked me. For me it’s ludicrous that so many confuse the measurement of frequency, which is based on a man-made unit, the second, with numerical ratios. But, hey, we live in an age where people judge the truth of a proposition on how many up-votes or likes it gets. I like the motto of “The Straight Dope”: “Fighting ignorance since 1973; it’s taking longer than we thought”. Perhaps worst is that the Alternative, New Age Movement has encouraged a culture of blind acceptance of wacko ideas, rather than double-blind testing. Phew….thanks again.

  69. Harton Myers says:

    after playing “Heard it through the grapevine” in Em @ A = 440 Hz three times a week for 2 years straight at a residency gig. I found myself internally (in my head) singing the song to myself on my home whilst driving the car. I had been interested in the understanding of “perfect pitch” for some time, and wondered, how close my mental interpretation of the song was to the actual pitch of the guitar that usually played it on.
    I decided to check the accuracy of my mind, with the 440Hz tuning of the guitar so when i got home i got the guitar out and compared my brain with the Em chord on the guitar.
    Lo and behold, i was right on the money.
    I knew that i wasnt a candidate for perfect pitch, so i assumed that the constant gigging and playing of the song for such a long time repetetively had caused my brain to adjust its normally out of whack pitch, to that of perfect 440Hz. I found that at that precise moment, i could internally sing the intervals of Em – C and that my middle C was exactly as it should be.
    After a while, the gigging stopped and the band broke up. several months later, after having not played the song, i decided to do the experiment again, and by virtue of natural adjustment, supposedly i had reverted back to my original pitchyness. I found that i was internally singing the song in F#m
    I have concluded from this that my natural music / brain pitch is at worst 2 semi tones above 440Hz, and at best, like a pond of water, settled back to its natural state of resonating at F#.
    I like to refer to it as, ” the key in which i think”.
    Now…if every person, has a specific key in which they think, or better still, a specific resonance frequency, would it not be appropriate, to tune their instruments to the frequency in which the brain operates?

  70. it's all arbitrary says:

    Ok, first off, let me say all your points are valid and undeniable. I’m very refreshed to see a “debunking” that isn’t just trashing the people supporting the claims. The truth is, it’s all arbitrary. Nothing we do is truly right or wrong for any individual. No diet or tuning or any other such concept is universal because there is no “standard” human specimen. Other than mathematics, everything is arbitrary.

    However, I find one key factor missing from all (not just your) arguments and to me it plays a huge part in the 432 theory.

    Everything gives off a frequency. This much is common knowledge (I hope). Every atom of every person and object gives off a frequency. The human brain picks up ALL of these frequencies and does its best to interpret them. This is where the application of cymatics comes into play. Applying a frequency to a substance through a filter manipulates the substance in different ways. If frequency has any effect of liquid, it has an effect on us. THIS is the core of the 432 movement. Now many claim that it makes music better but that’s opinion and cannot be argued. But the claim that it has effects at the atomic level can’t be denied. Even a cursory looks into the effects of binaural beats and other applications of sound can prove this.

    Now, I don’t necessarily think it makes better music. Again, the “best” music or tuning can be argued until our extinction. However, your article here is more inconsequential than the tuning itself. It’s not about the notes relationship with each other, it’s about the notes relationship with us. There are extensive studies into how frequency affect our brain. Color and sound play enormous factors in brain activity and emotional responses. So for you to sit here and light heartedly jab at people who believe that 432 is better for them or others simply based on musical theory is a fallacy in and of itself. You have a vast knowledge of how music works but not how it applies to the human body.

    All in all, this entire post (including this comment) is moot. We have not yet found our true connection to this universe and how we can be better in tune with the world around us and until we do, no tuning change or argument about such will have any real basis in our lives.

    To any 432 supporters, do your thing. It’s not about being right, it’s about be happy. With your music and more importantly yourself.

    • miltonline says:

      All cool. Except…

      “Everything give off a frequency” – well several frequncies of different types of things. Radiation, reflected light, (sometimes) sound. However there is no good evidence that 432Hz music has a better/differenct effect on our bodies. If you have it, please share. I’ve seen nothing to support that assertion.
      Also, see this quote from the post. In short: If frequencies in 432Hz music is good for our bodies then so will many of the frequencies in 440Hz music. (And conversely if 440Hz music has ‘bad’ frequencies, so will 432Hz music). Any piece of music of any type of content has entire washes of frequency content. However I the entire premise that 432Hz is good for us and 440Hz is bad, is nowhere established.
      [from above]
      “When a note is played we hear the fundamental pitch, together with a pattern of higher harmonics above it (an electronically generate sine wave is the only instrument which doesn’t exhibit this property) and that contributes to how we say, differentiate a C played on a flute to the same note on a piano. These harmonics are found at clearly differentiated and ordered intervals on melodic instruments, and more smeared across a range of frequencies in percussive instruments and ‘noisier’ sounds. The upshot of this is the following: In reference systems other than 432Hz (including the evil 440Hz), the specific frequency of 432Hz (and associated multiplications) will be heard repeatedly, presumably making it better. Conversely all those nasty frequencies found in a 440Hz reference system will be amply represented in 432Hz tuned music. Most inconvenient. Comparing a piece of music tuned from 440Hz to 432Hz (Figure 1) shows little difference in harmonic content or prominence of the ‘magic’ frequencies.”

  71. David StarBear says:

    Firstly,
    Thank you for, as priorly mentioned, an ethical and honoring approach to balancing excessive hype in alternate tunings without being mean spirited or inflammatory, Bravo!
    Honest, True observation and evaluation that provokes compassionate and unbiased skepticism and contrast is vital to all of us.

    I have been an active part of evaluating and performing musical modalities and tunings for many years. I have watched the deplorable promotion of what should be an elevated concept of a musical potentials, like alternate tunings, turned into a self promoting garbage. I have also sat in front of 100 year old men from india and nepal who blew open my mind to amazing potentials in musical, vibration and sound to move us closer to unity. I have worked with many masters here in the states that work in these realms of sound as a bridges. I have spent years, aligning Pythagorean concepts, mayan calendars, indian mantras and yantras, solfeggio frequencies to find possible clues to creating healing or elevated music, sounds or the magical key to it all. Honestly i have found myself more fulfilled by eating a really good sandwich, while just loving making music. I have participated in recorded blind studies of alternate frequency work, and.. yada yada. It is not my intention to self promote my background, or validate my comments, only to create a container for what I feel is most fundamental, and that I believe you come from from your diligence in this article. And what I have learned in the decades of study, working with many musical and sound modalities can be distilled into one simple concept; Intention.

    As you and many folks state here, Yes, I too palpably feel certain sensations and emotions when I tune certain instruments differently. I tend to lean more towards the higher 442-444 tunings, and yet with some work in say Kirtan mantras, they seem to fit right into the pocket, “For Me” in 432. As music and sound in my opinion has the capacity to reach deeply into our bodies greatest propellant system, our emotions, I can say with full belief that I am moved emotionally by sounds, song and arrangements from every tuning. Even if it pisses me off, which some does. There in for me layers the validation of synaptic connections that we humans can use to create our own personalized alchemy and connections to transformation. Call it healing, call it shifting, call it potato soup if you like. By removing the judgment and division, and the constant white noise of needing to call something “better than”, or demonizing or creating illuminati bs to support it, we grow as a species. For as many agenda less, hopeful readings and work from genuine musical beings, I have also read reams of hard to digest, and unfortunately unconvincing articles of specific tunings carrying “THE ONE” healing vibration. And this from someone whom believes in sound and vibration intention intuitively. The downside of the internet is that it carries the capacity to over use the miraculous “cut and paste” feature that continues to perpetuate bad information. What I lean into, what i choose to believe, and what i have witnessed first hand as I encourage myself to use as a personal barometer. I have worked with death bed groups, whom sang songs that the receiver requested bring them peace in their passing. I have watched people in the hospitals and nursing homes change completely from sullen and lost to re-awakened and coherant by hearing an old nostalgic song from their youth. Both I might add, usually in 440 or 432 tuning. Science, as powerful as it can be, may help to create explanations within the realms of our current knowing, and, is not the end all to be all of truth either. So if we can balance the hokum out with truth from our own personal experience, feeling and observation, then we may all dine on hope. Terrance McKenna said once (and he may have been re-quoting) “Truth needs no science or belief to exist, only bullshit does”.

    In short ( if i can still say that after 4 paragraphs), just like with humans, our potentials are opened exponentially when we honor all perspectives, possibilites and diversities. Each and every tuning, when paired with specific intentions can be medicine or poison. The intention of love, compassion and unity can be sewn into all voices, all mediums, and in this case all frequencies, as they are all part of the same source. Sorry if thats too woo woo, for some, however I felt after reading every post that the scientific aspects have been covered quite well. Felt it needed some etheric balance from an old hippy musician. Thanks for a great thought provoking article! I appreciate the contrast.

  72. Don Naduriak says:

    Terrific, thanks. I enjoyed the whole thing comments and all.

  73. Martin says:

    Thank you for a most excellent and well thought out article. The most cursory inspection of the subject by anybody with a scientific background reveals the arbitrary definition of the second there at it’s root.

    But, there is one argument for, yes for, the 432 argument, that doesn’t appear anywhere in the 432 literature which does actually have a scientific basis.

    The music of today is universally tuned to 440 hz and is listened to frequently, and often at high volumes. Many of us have had the experience of ears ringing after a concert or club. This is due to damage to specific cilia in the ears, each detecting a specific tone. After a period of exposure I hypothesize that the frequency response of the ears may become desensitized to the frequencies found in the 440 scale. As a result is it not possible that music played in an alternative tuning, not necessarily 432 but any intermediate tuning, could be a breath of fresh air to the ears, as it were ?

    I don’t have evidence, but we are talking very subtle differences when it comes to the enjoyment of music. Have you heard of this argument before ?

    Once again, great article

  74. Jedediah Allen says:

    Ciao miltonline,

    Great article. If you wanted to geek out about the performance practice of historical tuning in western Europe, you should find a copy of Bruce Haynes’ book. Here’s a link to it on Amazon though, it’s a bit expensive so you might try searching for it in a library. http://www.amazon.com/History-Performing-Pitch-Story-ebook/dp/B009GIPBQK/ref=mt_kindle?_encoding=UTF8&me=

    Cheers!

  75. Yak says:

    Thanks for the article which I found while looking for something to substantiate my attempts to explain why arguing about one fixed pitch as more spiritual than another one is ridiculous.
    And I really enjoyed the Bonus part 😀

    However, I am afraid this cannot reach the brains that are eager to hear they any “esoteric” knowledge hidden to stupid scholars. It could, but the main body of the article requires higher understanding of music than most of them have. Anyone able to write an easier-to-digest digest of this?

    And one question: Are you really sure there is ONE PITCH used for tuning sitars?!
    Something new to me. I’ve been always told there’s no fixed pitch in raga music (whether Hindustani or Carnatic) and have never seen any traditional native instrumentalist, including sitar players, in the realm of South Asian “classical” music to use any reference point (definitely not a fork) for tuning.
    But I am a laymen and have not discussed this in detail with them.
    Am I getting it wrong. Any more referrences to the “tuning fork” for sitars???

    (Apologies, if I read too cursorily and misunderstood something)

  76. Dave Jackson says:

    one problem the A432 proponents don’t seem to address is now you’re supposed to retune instruments with fixed tuning – it’s possible to adjust the length of a saxophone a bit by moving the mouthpiece, but not enough to change the pitch that much and to retune a woodwind instrument properly you’d not only have to adjust the overall length but also the distance between the holes, Similarly, I can’t see how you’d lower the pitch of a marimba or vibraphone. I don’t see many woodwind players offering up their precious vintage instruments for the kind of expensive major surgery required to make them play in a different concert pitch. So if we’re going to play in tune with instruments that aren’t retunable, then we have to play in A440

  77. musictheorynerd says:

    An excellent article! Perhaps as a follow-up to this, would you consider examining the equally delusional claims of those promoting 528 hz as the love frequency and hijacking the history of solfege by equating it with the work of Guido of Arrezzo.

    http://www.somaenergetics.com/forgotten_in_time.php

  78. Ko says:

    Thank you for debunking this nonsense. Have you heard about the music that was apparently transmitted to Earth by distant space aliens, on behalf of another group of distant space aliens? It seems their favored tuning system is 13 tet (thirteen equal divisions of the octave) with some variations (13 equal divisions of the double-octave, and something called “complimentary intervals”. See my website for more info… http://www.beyondtheeventhorizon.org. I received a cassette in the mail along with the text that’s now on the main page of my site, with no return address. I’d be happy to make and send a copy to you if you are interested.

  79. Karen says:

    Hi Milton,

    Thank you so much for this fabulous article. I was whooping and punching the air in unrepentant joy at your infallible and thorough research. Finally, the article to end all articles (dis)regarding 432. The trick is, getting the hive-mind to actually READ it. Not skim, not assume, not disregard without careful consideration, but to really read it.

    When this nonsense started doing the rounds on social media, my first thought went something like this: ‘…really? One note, one frequency, that appears in everyday sonic environments anyway is… magical? A432, that can be found in a plethora of places, from harmonic partials, to an a note within a ‘chord’ produced by the exhaust pipe of a truck on the expressway somehow aligns with the universe?’ I would have followed this thought with a loud scoff and a severely furrowed brow. I remember, upon first hearing of the A432 conspiracy, being very concerned for the mental capacities of those subscribing to it.

    I’m not a maths girl, but I followed your article easily because it was well written, so bravo. I am an orchestral musician who plays in loads of different tunings. Mostly, as per the European standard, it’s A442. Sometimes A443, A441, A439, A438 and on a cold day, I would not be surprised if my clarinet gets down to A432 and below. No one, literally NO ONE has told me or the rest of the orchestra off when we deviate from A440. I mean, apart from the one time the Illuminati Nazis wrote us an angry letter because we played a concert with loads of microtones.

    Anyway, I read all the comments for this article, checked out some of the ‘references’ and allowed myself to be ‘opened up to truth’, but when one is cognisant of the omnipresence of this particular frequency (my fridge is making it right now, actually) and soooo many others, it is difficult to really feel that there is a conspiracy in the world denying us of our right to A432.

    In the spirit of thorough investigation though, I once played a concert A at 432Hz, and didn’t feel a damn thing.

  80. Jayson says:

    I haven’t finished reading yet but I am curious, is there any possible way to re-tune your VST’s to 432 rather than the default?

    • miltonline says:

      Yes. For example, In Logic Pro X: Project Settings/Tuning/Tuning Reference – should adjust all MIDI and VST. Otherwise, it’s just a case of detuning samples by 31cents (or at 98.2% of the speed).

  81. James Tuttle says:

    So I started tuning to A432 about a year and a half ago because I was curious about it and found that I enjoyed it so I stuck with it. Since then I’ve had more people come up to me after a performance and tell me that they had never heard music like that before and I’ve seen more people come to tears after my performance then ever before. I also don’t usually mention the tuning because it just flies past most people’s level of comprehension. Even if it’s just on a subconscious level I sound slightly different from the multitude of musicians using A440 this gives me an edge. Anything that makes you stand out in the music world is generally a good thing. So pseudoscience and mysticism aside I will be sticking with A432. I also do mess around with micro tonality. Finally if Hendrix were alive today I bet he would tune to A432 just because he was a hip individual and into the whole cosmic thing anyways I did enjoy your article.

    • miltonline says:

      Thanks for the comment and I’m glad you are enjoying your music (although I happen to never think about having an ‘edge’ in music – rather deepen my experience and develop my craft rather than compete). Like I say, whatever makes you experience music better is valuable and interesting. However I’m dealing here with the factual claims for 432 superiority made by some of its advocates and find them wanting. Incidentally one could perceive Hendrix as tuning to 415.3Hz…

  82. AL says:

    Top article, well-written and presented. For me 432 is the quintessential example of the old adage ‘why let the truth get in the way of a good story?’

  83. Jim says:

    True… but missing the one fabulous element to this great mystery:
    Both Einstein as well as other great mathematicians and physicists spent a great deal of time trying to figure out why certain ‘primes’ in existence operate at a different quality than other numbers. They too stated that since it is all relational, that it SHOULD be the same effect no matter what number they started from. What they concluded was that they had NO idea why or how, but that it was clear that primes operated differently. They gave up on this project since they could not conclude why to such an outrageous finding. Not really having much opinion, since i’ve been playing all instruments at 440 my whole life, but in a way I’d like to shift the whole world back to 432Hz… and see if it changes something non-physical in everyone. 🙂

    Seeing how physics is only 1/9th of our manifestation, perhaps there are things we don’t see that are affected by this shift.

    • miltonline says:

      Thanks for the comment, but what do primes have to do with 432Hz (which isn’t prime)? Pythagorean tuning is not the only prime based tuning (as noted in the post)and 432Hz has no monopoly on its usage or benefits. Prime maths is fascinating and beautiful (and I’m very interested in it) but not sure what you mean by ‘operate at a different quality’ or ‘what number they started from’. Also, much has been learned – and continues to be used and learned about primes – so mathematics have in no way “given up” on learning about primes. But still not sure why it is relevant to a discussion of the purported merits of 432Hz. Cheers!

  84. Willy Wonka says:

    Every time you tune to 432, A dead Nazi rolls over in their mass grave.

    WWII never ended, it just started getting people to start tuning sharp.

    Although this article is indeed interesting, it totally missed the fact that 440 didn’t exist until the Jews started the myth of the holocaust.

    Read a book people.

  85. davide severi says:

    Milton, thanks for your effort.
    I always loved music and numbers, and science. i think there are many levels on which all the energies (be them vibrational/acoustic, or magnetic) work and interact. i love the research and i don’t like to be fooled by false myths, as indeed i love a lot of mythologies.

    I had my piano tuned to 432hz when i was 19, in 1996, to the curiosity of the piano tuner. I did so because i like numbers and thought 432 could reserve something, with all the mathematical properties the number has. Didn’t expect to levitate or anything.

    I was also very much intrigued on how and why all these ancient cultures used such numbers as 72, 108, 144, and of course 432 (just to name a few: Tibetan buddhism, Hinduism, Chinese martial arts, acupuncture, architecture; all rely on the use of 108 points, or steps, or figures, or “something” to create a unity). I researched a lot afterwards; some years later, the 432Hz frenzy started.
    It’s not about “being there before it was cool”; i’m just trying to explain my point.

    I am not deluded at all of having spent all that time trying. That was the start of my whole research that still forages my music. I am absolutely happy and grateful for studies like yours to come out, to clear the mist and state the facts. Thanks again.

    The thing i was intrigued with was the use of these numbers. They are part of a whole, and they are “wholes” in themselves; they represent harmony. in fact the relationships of the subdivisions of 432 (or of 72, for that matter: 9/8 of 432 is 486, 9/8 of 72 is 81; 5/4 gives 540 and 90 respectively, and so on) are “harmonic” to each other in the same way the frequencies of the notes in Pure Tuning are. They represent the harmonics; it’s the “as above, so below” riddle perpetrated in various myths to teach us about harmony on all levels.

    As it has been stated elsewhere, if you tune to 432 and then use Pythagorean or Pure tuning you end up with integer numbers (btw, they are all factors of the powers of 2 and 3).
    This is very important, but not because of the frequency of reference; just because it SHOWS the harmonic relationships between the parts.

    When two frequencies are harmonic to each other (4:3, 7:8, 3:2) they create overharmonics, so high that can hardly be heard but can be perceived because of the “ghost” frequencies they create. This can only happen in pure tuning. Everything else (12-TET, that makes 99.9% of the music we listen) is only a near-consonance that can create no over-harmonics (actually, i think it to be quite dissonant). Whoever listens to pure consonances can spot them right away against the popular 12-TET ratios (i have been studying harpsichord and baroque music and had many examples of this).

    It has to be made clear that this “432 revolution” everybody is raving about should not be about the frequency of reference – it should be about the intercurring relationships between the actual players, the notes.

    I find it very annoying to have such an important topic put in bad light by people who don’t really have the time or patience to understand what is the real magic of music, or at least some basic rules of harmony and acoustics. Everybody is posting images of Cymatics claiming it’s this or that frequency – not true. Cymatics, like Lissajous figures, or the plates of Chadni – involves the relation between two players: the sound wave, and the resonating medium. When the two are in harmony, energy is amplified: this is the effect of sympathetic resonance.

    This is the meaning of the phrase “the whole that is greater of the sum of its parts”.

    The rest is dissonance.

    All we people, in love with the 432 concept, let’s bear in mind that we’re just missing the point. Frequencies may vary. Relationships is what counts: that is what music is made of. Blame the 12-TET, not 440hz; that one is destroying our perception of harmony.

    And please stop pitching down any music to 432hz, that is just plain silly.

    Sorry for the long post, and sorry if i made some mistakes or inaccuracies, English is not my mother language.

    Congrats on how you manage all this feedback, too.

    • miltonline says:

      Dear Davide, Thanks for your comment! I agree with (almost) all your comments, and my post aims to reveal all these harmonic possibilities (and beauty). Indeed, I advocate experimentation (or downright occupation) away from 12-TET (although I love both). However I have 2 points of contention with your comment:
      1) Pythagorean as the only valid non-12-TET system
      2) Fixation with frequencies (as opposed to frequency ratios) as integers

      THere seems to be an obsession with pythagorean (3-limit) tuning among 432-advocates. (You too seem to conflate ‘pythagorean’ with ‘pure’). Maybe they stop at the 3rd harmonic, because it maintains the (I say unnecessary) fixation with the frequencies becoming whole integers. (However E.g. multiplying 432Hz by 6/5 or 8/5 is perfectly ‘harmonic’ (and fundamental to Indian classical music) but not an integer). Stopping at the 3rd harmonic is of course fine, but Indian classical music is generally 5-limit (no 432 advocate suggests that hindustani music ‘gets it wrong’), Tibetan/Tuvan music can employ up the 37th harmonic and beyond!
      Time is not arbitrary, frequency ratios are not arbitrary but the time unit of the second is, and so is the decimal system, so the need for the resulting absolute frequencies to be integers is misguided and limited. Although I like you do also like the elegance of ‘seeing’ some of these relations in 432Hz (and other reference points), I still contest that it is the ratios not the absolute frequencies that matter most (of which 432Hz has no monopoly) AND Pythagorean 3-limit tuning is by no way the final word in harmonic tuning. (5/4 is as (or more) valid a ‘major 3rd’ than 81/64).
      Then there is the no small matter of the ‘accuracy’ issue above.
      Cheers!

  86. Todd says:

    typical gatekeeping disinfo… adding lies to truth. 432 is the ancient way. the correct way. wake up people.

    • miltonline says:

      Hey Todd!
      Thanks for reading (if you did of course) and the comment.
      I’m very keen that the post on s accurate so please identify where exactly you feel it is inaccurate.
      Also please provide evidence that 432hz is an ‘ancient’ tuning. Many thanks.

  87. Bruckner8 says:

    Thank you for the rational approach, debunking the modern mysticism cropping up with this 432 nonsense! I have used similar arguments for years, but now I just link to this page.

  88. Yesss. Some logic and sound reasoning. This is all simple high school math, if that, so am surprised at the depths of misunderstanding that some display. Is this 2016 or 1016? (maybe the latter, considering the antivaxers, homeopathists, and astrologers I see all around.

    Keep up the good work.

  89. Dmach says:

    When I tune my piano by 5ths I start by tuning the middle octave in equal temperament referenced to A4 at 440Hz. However because of how piano strings resonate, it is necessary to “stretch” the octaves above and below the middle one by sharping each note in the upper octaves and flatting each note in the lower ones .As a result, instrument tuning is not as mathematically scientific as these discussions would have you believe. The real problem with abandoning a A440 reference in favor of A432, or any other frequency, is that now other instruments are out of tune with respect to each other.

  90. Dave Jackson says:

    I love this. My favourite reason for choosing non-standard tunings is that it messes with the heads of those with absolute pitch.

  91. Juan says:

    This is a great article. Thank you very much for your insights; just one question. For your personal taste and knowledge on the subject matter, what would be the best frequency to tune an instrument? Thanks a lot in advance.

    • miltonline says:

      Well there is no perfect tuning for all instruments, and so much is subjective. But for a stringed instrument, I’d start with where it was designed and head down (not up) for safety reasons, until you are happy. There are many guitarists (including Hendrix) who favoured tuning a semitone low (and many got a tone or more, particularly just on the 6th string). Up to you and the laws of physices (and the practicality of making music with other people) 🙂

  92. SonicMancer says:

    The most amazing thing about using A=432 hz is to get of 12ET tunning and come in Just Intonation tunning, if u use computers to record or create music u must think in highly composite numbers… My friend Derrick made a book about this ”mathemagical music”’
    a part of that:

    If you work with a computer, you may have noticed that when you enter Hz frequencies or BPMS in any software, you will have a limit on the amount of decimals or numbers you can enter after a comma. Most music software has a limit of between one and four decimal places. So, while a number like 128 or even 128.28 will be fine to enter, a number like 128,47366747 will not.

    ***I dont read all comments maybe someone sayd the same

  93. Vergil says:

    Milton, you’re the man. A sound knowledge base, accuracy of argument, and humour are a potent combination. Thanks for that!

  94. Dr. Mermikides-

    Thank you so much for the time and care that you gave to writing this wonderfully cogent essay. What a pleasure to read! (And thank you also for so thoughtfully responding to your commenters here for, it appears, more than 2 years! You’re an internet hero.)

    I am of course convinced by your argument, and so see no reason to prefer any particular reference frequency. However, after experimenting with several tunings for my guitar, I was informed telepathically by my cat (a nazi, no denying it) that from now on ONLY a 436.9Hz A is permitted in my house! She says that 440 sounds “lonely,” and “too much like Sarah’s (my ex) ugly nasal laugh,” whereas 436.9 is more grimalkin and also helps her catnip-trips come up more visually. So now I’m in a very difficult position. I want to go back to 440 so that I can jam with my human friends, but she won’t let me. She says she’ll turn me over to the illuminati lizard gestapo if I ever play “that Sarah frequency” again. Even once! Help me, if you can – any advice is welcome. Considering drastic measures. (perhaps having her euthanized and adopting a small or medium-sized dog? What do you think?)

    Kidding, of course (I love my little kitty-kins!) … But I do have a serious question for you. I’m afraid it’s not related to your subject or your field, but rather to the (rather bizarre, I thought at first) request at the top: “please keep it civil, and threats and insults to me and my family will not be tolerated.”

    This fascinates me, grotesquely. Has your article REALLY provoked hateful, insulting, and threatening messages?? (From HIPPIES!? Can there really be a guerrilla movement of new-agey, crystal-swinging, nag-champa-smoking, yoga-class-going-to, chakra-tuning, motherfucking HIPPIES trolling on the internet? In support of a frequency? Sending hate-mail?? To a music-theory scholar???

    Oh my god. I cannot express the degree to which this idea excites me. I am trembling as hard as my cat will allow. Please say it’s so.

    I realize that this may be a very odd request, but if there is any possibility that you could share some of the comments that you’ve had to actually exclude or remove from the above dialogue… I would be so very happy.

    With kind regards,
    Namaste,

    Christopher

    • miltonline says:

      Many thanks for the kind supportive comment. I won’t include the hate mail because the (particularly one individual), started referencing/contacting my work and family, so it wasn’t worth it for me to engage any more. I leave all other comments up for posterity. All best to you and your cat.

  95. one full rotation of Earth about its axis is 23hours 56minutes 4seconds, (rounded),
    about 4 minutes shorter than what we call a “day”.

    so a “special” frequency could be one that is in harmony with the rotation of the earth.

    23 hours 56 minutes and 4 seconds = 86164 seconds

    so 1 rotation of earth is 86164 seconds

    or 0.00001160577503 hz (aka 1/86164)

    so start multiplying by octaves (*2*2*2*2*2*etc)

    and we find that 97.356297hz could be said to be in tune with the spinning of the planet

    so put that into your tuning field new age nerds

    thanks for your interesting article
    and please feel free to rip my napkin math to shreds if justified.

    • musictheorynerd says:

      I agree totally. It’s a G. Now multiply by 1.122843 (a whole tone in 12tet) then raise two octaves equals 437.114999, a logical tuning standard related the earth and close enough to 440 to be practical.

  96. Mark jenkins says:

    No one has mentioned my questions like do you meet to make strings tensioned for the 432 tuning and also have the frets specific to the tuning as well?

  97. mark says:

    does it matter for frequencies when we move into the visible light spectrum?
    Yes, there are pure colours and mixed ones.
    red is the 42nd octave above 432hz and green is the 43rd above 256hz
    we could look the other way also (lower octaves)

    • miltonline says:

      Red light covers a range from 400–484 THz, green light from 526–606 THz. Note that:

      1) its a range not exact (440 is likely to fall in these ranges also at some octave), and why are these particulalr colours important, and important to sound
      2) 432X2^42 does not fall in this range (by my quick caluclation correct me if I’m wrong)
      3) Why is 256Hz introduced here?

  98. PresentTenseLP9 says:

    I love you – how un-440Hz of me to say that! So many things you mentioned here I kind of concluded just logically already but you summed it all up into an amazing article. The biggest thing for me is the whole measurement system of seconds, as in Hz = Cycles per SECOND. The very essence of the second as we know it is only used by humans. In another planet on another solar system, those beings “second” as a unit of measurement of time can be something else – If you change our measurement of the “second”, then that changes what 440, 432 and every other frequency is because we are simply assigning numbers in relation to what our accepted measurement of seconds is.

    So lets say that this other planet’s second is only a small deviation form ours, then possibly our measurement of 440 could be actually be 432 on their planet, which means that our 432 would be 424 for them (I think).

    Using that logic the whole relationship between numbers, ratios and everything else changes, so if I were an all-in 432 guy looking to make hippie friends in this other planet, those hippies would turn me down saying “you are in 424 man, that’s negative,” where as a Nazi in 440 would be a mega-hippie on that planet.

    See what I mean? Am I thinking of this correctly? If not please correct me or present another scenario.

    thanks

    • miltonline says:

      I love you too.
      Yes you are exactly right (I think), the specific time unit is (pretty much) arbitrary, which is what makes a claim for 432Hz (or any) superiority implausible. Even with that there is a major accuracy issue. If 432Hz is sublime, what about 432.003Hz? A slight temperature change or subtle head move even with electronically genreated tones makes all tuning approximate.

      Good day!

  99. Chris says:

    if people want to use 432 then let them, say enjoy it, and be on your way.

    Why since you use Pythagorean math all day long, do you seem to ignore this aspect of his work. If it was not for him, you wouldn’t be playing anything.

    More interestingly…

    Why do all the 440’s have so much hate?
    Why do all the 440’s feel they have to debunk and destroy everyone else?

    Strangely you don’t get that “Attitude” from 432 people.

    And maybe therein lays the answer.. 🙂

    • miltonline says:

      It doesn’t sound like you’ve bothered reading the article, as all the responses to your comments are therein, but anyway here goes…

      “if people want to use 432 then let them, say enjoy it, and be on your way.”

      Agreed. I totally encourage (am passionate about) musical experimentation/unconventional/alterative engagement. I am just responsing to claims that 432Hz is superior to 440 and other tuning frequencies – and that 440Hz is somehow ‘bad’, which for the numerous reasons listed above, I don’t buy. As I say in the post, I advocate the use of any and many tuning frequencies (as I happen to)

      Why since you use Pythagorean math all day long, do you seem to ignore this aspect of his work. If it was not for him, you wouldn’t be playing anything.

      I’m not sure what you mean by ‘pythagorean math’, or how I’m “ignoring this aspect of his work”, if you are talking ratio-based tuning, I’ve engaged and appreciated this fully. Pythagorus didn’t use 432Hz (partly because the tuning fork nor the second had been invented at that time). I in fact totally love and understand pythagorus’s contribution (just not invented ones).

      More interestingly…

      Why do all the 440’s have so much hate?
      Why do all the 440’s feel they have to debunk and destroy everyone else?
      Strangely you don’t get that “Attitude” from 432 people.

      I wouldn’t know the answer to this (or the veracity of the claim). I’m not a ‘440’ (like I said I advocate the use of, and love music in, many tuning reference 432, 440 and others included)
      I have however witnessed 432 advocates accuse others of being sheeple, nazis and willfully destructive.

      So to recap (which I will flatter myself in assuming you are actually reading this) – I’m in no way “anti-432” (or pythagorus which is a barely related concept), in fact I encourage its experimentation/engagement (but think it’s less important than temperament – Pythagorus’ actual contribution incidentally), just offering some critical response to the myths of 432 (as I would if anyone used the same arguments to claim 440Hz was superior).

      Why would anyone have a problem with this? And maybe therein lays the answer.. 🙂

  100. SkyCharger001 says:

    I’ve only come across one case where 432 was factually better than 440 and that was for counter-detuning an FM-patch. (base-frequency of 440 created an output-frequency of 448.148148…, base-frequency of 432 created an output-frequency of 440(which was the reference for the real instruments))

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