The 2nd International Guitar Research Centre Conference (March 18-23, 2016) has attracted speakers and performers from every continent, and guitar style. It’s a fantastic line-up, and timetable shaping up.
The fabulous Alexia Coley, for whom its an honour to work has a video out for her great soul tune: Drive Me Wild
The most succinct analysis I can make of Arvo Pärt’s Spiegel Im Spiegel (a stunning and elegant work). Listen here: https://open.spotify.com/track/3rlqTqUOzu0zDwQFJe44gk
I’ve had this insight about palindromic scales, modes, modal groups, and the Euclidean (and sometimes maximally even) distributions of 7 notes in a one octave scale. This is what it looks like in my head. I really like that the ‘central’ scale of a group is not the traditional figurehead (Ionian, melodic minor etc.) but the palindromic parent. Nice to see the patterns emerge diagrammatically, and I will aim to use Melodic Phrygian and its modes in composing/improvising!
A real pleasure to appear with my sister Alex to talk about the Bloodlines project (and data sonification in general) on BBC Radio 4’s Midweek on Wednesday 28th October hosted by the quite brilliant Libby Purves. Fellow guests included the delightful and inspirational Peggy Seeger and Amati’s James Buchanan.
The next in the series of Hidden Music data sonification works. Data sonification is a long term interest/project/passion of mine, which involves the systematic translation of ‘non-musical’ data into music.
Here I’ve taken Kandinsky’s beautiful 1926 painting Several Circles and translated it systematically into sound. Colour and vertical position are translated into timbre and pitch respectively, as the red cursor scans the image horizontally.
Whether Kandinsky was a synaesthete or not is disputed, but his fusion of music and visual art metaphor, working process and concept is well documented. From the link:
“Our response to his work should mirror our appreciation of music and should come from within, not from its likenesses to the visible world: “Colour is the keyboard. The eye is the hammer. The soul is the piano with its many strings.”
Kandinsky achieved pure abstraction by replacing the castles and hilltop towers of his early landscapes with stabs of paint or, as he saw them, musical notes and chords that would visually “sing” together. In this way, his swirling compositions were painted with polyphonic swathes of warm, high-pitched yellow that he might balance with a patch of cold, sonorous blue or a silent, black void.”
Thanks as ever to Anna Tanczos for the visuals.
Here’s the first in a long series of data sonification experiments. This Hidden Music series is a long term interest/project/passion of mine, which involves the systematic translation of ‘non-musical’ data into music. Here’s a simple example, the orbital periods of the planets of the solar system translated into pitch and rhythm. The rhythms are simply created by speeding up the actual orbital periods by 25 octaves (doubling the speed 25 times), and the pitches are created by transposing them up 37 octaves. I haven’t quantized pitch or rhythm, so its both microtonal to the nearest cent (100th of a semitone) and microtemporal (to the nearest millisecond), but I hear a clockwork beauty in this irrational/chaotic collection of ratios nonetheless. Stay tuned for some even more distant harmony from some ex-planets. I recommend a sub-bass speaker to really feel Uranus and Neptune’s drones. Thanks to Rob Scott for his space science brain, and my long term partner-in-nerd Anna Tanczos for the visuals.
The next international conference of the International Guitar Research Centre has been announced. It will take place 18th to 23rd March 2016. The call for papers, keynote speakers and headline concert artists can be found here. The deadline for proposals is midnight GMT on Friday 9th October 2015.
The IGRC has no stylistic or conceptual prejudice, if you are doing work that is innovative, creative and related to the guitar, we are interested. For further info
It’s hard (for me at least) to start talking about any aspect of musical theory without talking for an hour or writing several thousand words and/or producing many diagrams. So I’m going to try and just provide some vignette posts, little moments of insight in a hugely complex field of study.
Here let’s look at the harmonic series (the pitches that emerge by multiplying a frequency by the set of integers (1,2,3,4 …) and its relationship to 12-tone equal temperament (the ‘standard’ division of the octave into 12 equal divisions).
The following diagram courtesy of the incredible programmer Dean McNamee (and Mathematica) shows how the pitches generated through the harmonic series differ from 12-tone equal temperament.
The X-axis names the harmonic number (ending at the 20th harmonic) and the Y-axis is the deviation from the nearest even-tempered note (where for example -0.2 is 20% of a semitone flatter than equal temperament). If you look carefully, you’ll see that the fundamental and all the octave equivalents (harmonic numbers 1,2,4,8, 16 etc.) align perfectly with the even-tempered equivalents. In fact these powers of 2 are the only point where the harmonic series meets up (exactly) with 12-TET. These points are circled in red below.
The ‘non-octave’ harmonics are indicated with different coloured arrows (showing in which way they differ from equal temperament). The 3rd harmonic (indicated in orange) is about 2 cents (a mere 2% of a semitone) sharper than the equal tempered equivalent (a perfect 5th), and so of course are its octave equivalents the 6th, 12th, 24th etc. The 9th harmonic is about 4 cents sharper (as it is ‘affected’ by two 3rd harmonics), and is indicated with 2 orange arrows. This ‘stacking’ (and unstacking) of the 3rd harmonic is what is used to create the Pythagorean scale, also known as a 3-limit scale, since we only allow the 3rd (and 2nd) harmonic as tools to reach musical notes.
The 5th harmonic is significantly flatter than the 12-TET equivalent (and the cause of the many historical temperaments that have emerged in polyphonic music. The 10th harmonic has the same ≈14 cents discrepancy. The 15th ends up about being 12 cents flatter, since 15 = 3*5, it uses the 3rd harmonic (which makes it ≈2 cents sharper than 12-TET) and the 5th harmonic (≈14 cents flatter) resulting in an overall drop of about 12 cents (note the contrary orange and yellow arrows). Incidentally, the use of the 3rd and 5th harmonic (together with the trivial 2nd harmonic), creates the 5-limit system of tuning, with its extensive and beautiful use in Hindustani music.
You’ll see that the other prime-numbered harmonics get their own coloured arrows (7th=green, 11th = blue, 13th = purple etc.). The 11th is about as far from 12-TET that is possible, which is why Harry Partch stops there in his 11-limit 43-note universe. Since the primes never end so the harmonic pathways of tuning are (theoretically) endless.
Another way to see the relationship between the harmonic series and 12-TET is to visualise the harmonics resting at points on an infinitely expanding spiral. Each sweep of the spiral represents an octave, and the 12 equally spaced slices of the octave pizza represent each 12-tone slice. This has the advantage of indicating where in the octave each harmonic lies, as well as the octave relationships between sets of harmonics (e.g. between the 3rd ,6th, 12th and 24th harmonics etc.). Here’s a beautiful rendering by Skye Lofander (whose website musicpatterns.dk has many awesome visualitions of musical concepts and is highly recommended).
You’ll notice that the harmonics get closer and closer together, and essentially ‘sweep’ through the 12-TET discrepancy in an ever (but never completely) flattening upward slope. Here’s Dean’s rendering which shows the same phenomenon emerging with the first 500 harmonics:
So along the way the 12-TET and harmonic series will get ‘close enough’ most certainly for human perception (which is a couple of cents on a good day) and acoustic instruments (which waver considerably in temperature and human execution). Even a slight head-turn will invoke enough doppler shift to make fractions of a cent meaningless in real terms.
So which is ‘better’ 12-TET or tuning derived from the harmonic series (also known as just (i.e. ‘true’) intonation)? And what incantation of the harmonic series is more ‘pure’? Is 4 jumps up the 3rd harmonic more ‘natural’ than one jump up the 5th harmonic? They both roughly approximate the major 3rd (the first a ‘Pythagorean third’ ≈8 cents sharper than 12-TET, the second a ‘just 3rd’ at ≈14 cents flatter). Some have attempted a measure of harmonicity (see Vals and Monzos), but its relationship to subjective experience is sketchy at best. Can one think of 12-TET as existing way, way up the harmonic series (so still harmonic), is it a ‘good enough fit’, or wholly incompatible with the harmonic series? What’s inate and wha’t encultered? Why 12 equal divisions and why not some other number?
Just intonation enthusiasts can get heated about its superiority to 12-TET, but there is no doubt that the limiting of notes to 12, close-to, or exactly evenly-spaced has led to the creation of countless, otherwise impossible, musical creations and activities.
The best answer is that they are different, and both available to every composer, get over it, embrace and enjoy.
P.S. this was 3 times longer than planned. Apologies.