A short, deep dive into harmonic consonance and dissonance and an understanding of harmonic flavour and spiciness. Dissonance curves, interval classes, vectors, All-interval tetrachords and introducing the Harmonic Scoville (or Scofield?) Scale.
This video reveals the beautifully interconnected symmetry of the diatonic modes, three entwined cycle of rotation, brightness and reflection in a single compass. Further Reading/Sources: Touissaint’s original Euclidean paper (concerning rhythms but relevant here): http://cgm.cs.mcgill.ca/~godfried/pub… Persichetti’s quite awesome and insightful ’20th century harmony’: https://www.academia.edu/38883692/Vin…
Every chord in the (12TET) Universe – a gentle introduction to Pitch-class Set Theory.
To download the Mr. PC patches (for Max/MSP standalone and Max for Live click below. Note: 1) they both need the excellent and free Bach package by A. Agostini & D. Ghisi (installable in Max’s Package manager) consider donating (to them). 2) For Apple Silicon computers, Max needs to be running under Rosetta. 3) These are good enough tools for teaching and music adventure – use at your own theoretical risk.
A cosmic view of the earthly and unassuming diatonic scale.
It’s privilege to present the Keynote for the Guitar Foundation of America convention this year.
The event runs June 26, 2022,5 PM – 9:30 PM UTC+01 on Zoom (register to join)You are warmly invited to join us for a series of discussions with scholars from Brazil, the United States, Switzerland, and England. Attendees will have the opportunity to speak informally with the presenters or simply listen. Registration is required. Abstract below:
Diamonds, Abaci, and Hexagrams: Exploring the Pitch Surface of the Guitar Fretboard
In this presentation, I will analyze the idiosyncrasies, challenges, limits, and affordances of the guitar’s “pitch surface”: its fretboard and tuning. Whatever the context—staff notation, music theory, improvisation, performance, and other arenas of guitar activity—the layout of the fretboard exerts a profound influence on how guitarists learn, play, and compose. Inspired by De Souza, Goodrick, and Martino, I will also explore the benefits of creative constraints: scordatura, capo, MIDI tools, and other ways of remapping the guitar’s pitch matrix. These constraints can be used to break the guitarist’s tight auditory-motor link, revitalizing the fretboard as a primary musical space and insightful musical “abacus.”
It was fun putting together this article with Chris Bird for Total Guitar (Feb 2022), and using the whole BoomerBendGate as an opportunity for some bendological research. In so doing discovered some ridiculously killer zoomer players in Tim Henson, Mateus Asato, Wes Hauch, Ichiko Nito, Plini and all.
And is now published online in Guitar World
My article on the remarkable John Mayer’s Blues techniques is the cover feature of Guitar Techniques GT328. Read it and (make your guitar) weep.
Total Guitar (Issue 345) has published an article on what Eurovision teaches us about music listening, and (guitar) performance. Some sample images below on rhythmic, perception, tempo and modulation respectively.
My article providing practical insights into the music and playing of the late, great Allan Holdsworth is now available for public free consumption on MusicRadar (including notation & audio). A teaser below.
A breakdown of the musical science of the Sea Shanty in Total Guitar Issue 344
Engaging directly with time-feel and micro-timing on the electric guitar with specific exercises and style studies. This is for many levels of player who wants to draw focus to the elements of groove which are often excluded, glossed over or mythologized in the learning process.
Soundboard Scholar (No.6) features my paper. “Monitored Freedom: Swing Rhythm in the Jazz Arrangements of Roland Dyens” examines the time-feel in the performances and scores of Roland Dyens, in particular reference to his arrangement of Nuages – and Django’s performances of this piece. Working with the genius Jonathan Leathwood is always a privilege and joy, and I am very grateful that my illustration is used as the cover image to the journal. Available here.
A pleasure to indulge in full-tilt nerdery about micro-timing with the annoyingly talented and annoyingly nice hosts of The Guitar Hour Podcast. \m/ \m/
By (heavily belated) popular demand here’s a stab at ‘common-practice’ chord progressions in major and now minor keys!
Am looking forward to this event and the opportunity to do something different and fun with the excellent Ensemble Montage.
What does the skyline of New York sound like? How can you make a composition from your sleep patterns or blood cells? Music can be made from anything we find around us, from our names or birth dates to our cells, from atoms to stars. Composer and guitarist Milton Mermikides presents the fascinating origins and history of data sonification – the translation of information or patterns into sound and music – as well as a selection of his own compositions derived from sleep cycles, viruses, paintings, exoplanetary moons, traffic patterns and other ‘non-musical’ data. In addition, a string trio of the Ensemble Montage will demonstrate how these data sound and perform a new composition based on ‘the hidden music’ of Noorderzon Performing Arts Festival. Discover how music can reveal the patterns in the natural world, and give us both a theoretical and aesthetic appreciation of everything around us.
For students and subscribers of Studium Generale tickets are € 5,-
An audio sampling rate is the frequency at which an audio signal has been captured. You can think of it like the frame rate in movies, capturing a series of photographs from which a seemingly smooth film can be generated. The sampling rate for CDs is 44.1kHz (that’s 44,100 samples per second between you and me), but other sampling rates exist 48kHz, 96Kz, 192Khz etc. It’s a contentious issue – beyond the scope of this wee post – about how high is high enough and why that may be the case but it is vital to ensure that whatever rate an audio file is recorded at, that’s the rate that it should be played back (unless you want the speed and pitch of the original recording to change of course). Essentially its like a record player and a record. A record may have been produced at 33rpm, and to ensure you hear the intended pitch and speed the record player has to spin at the same speed. Simple.
So what happens if we spin a record (or playback a digital audio file) at a higher rate than it was recorded? Well it’s pitch becomes higher and its speed increases. Play back at a slower rate and its lower in pitch and, well, slower.
What’s more, if we play a file (or record) at twice its intended rate (a 44.1kHz file at 88.2kHz), its duration is halved (of course) and its pitch goes up an octave. In contrast, a file played back at half of its recorded rate drops an octave (you can hear this used musically in loop pedals).
An octave (derived from halving or doubling a frequency) has a kind of musical equivalence. (It’s called the Law of Octave Equivalence no less), but what of other frequency relationships? Here things get a bit complicated. Our experience of pitch is logarithmic, so that the multiplication of a frequency produces a particular musical interval. Double a frequency it goes up an octave, halve it it goes down an octave, multiply by ≈1.059463 and the pitch goes up one (equal-tempered) semitone. This catchy number is actually the 12th root of 2, which makes sense if you think about it. Multiply it by itself 12 times and it reaches 2, because there are 12 ‘equal’ jumps between in each octave in the 12-tone equal-tempered system.
To help us understand this, let’s imagine an octave as a physical vertical object, then we can slice it into a number of equal slices (say a tower block with a number of equal storeys). Again, I say ‘equal’ because each slice is the same musical interval but that in fact means that it is the same multiplication every time (that’s the whole logarithmic thing). The convention is to divide the octave into 1200 cents. Why are they called cents if there are 1200 of them? It makes no cents HAHA – well because often the octave is divided in 12 big slices (known as semitones or half steps) and each of them has 100 cents. So 100 cents is a semitone (in the US half-step), 200 cents is a tone (whole-step), 700 cents is a perfect 5th and so on.
So how can we calculate the resulting musical interval from a dispcrepancy in sampling rates?
We use this equation.
cents = 1200 × log2 (f2 / f1)
So, imagine an audio file was recorded at 44.1kHz (f1) and played back at 48kHz (f2), the cents difference would be
1200 × log2 (48000 / 44100)
This comes to ≈146.7 cents, which is just shy of one and a half semitones. A no-person’s land in most musical situations, and if you were trying to play along on the guitar you could go up one fret (one semitone) and still be a quarter tone flat, but 2 frets would be over a quarter tone sharp. Most ears forgive a few cents here and there, and a keen musician can bend into a few cents more but a 46.7 (or 53.2) cent differential is about as cold sweat nightmare of a musical situation imaginable. A bass player would face the same problems, and a keyboardist would have to resort to Herbie Hancock style pitch bends, or embark on a desperate hunt for the operating manual to readjust the tuning reference. Failing that they could run away at just the right speed to allow the doppler effect to drop the pitch.
Would you like to know what it sounds and feels like? Just ask Van Halen and their audience, who suffered this exact ordeal when a backing track (or keyboard triggered sample) recorded at 44.1kHz played back at 48kHz during a live performance of ‘Jump’ – not the most obscure of their tunes. Eddie desperately tries to adjust by shifting frets but is cursed by the mathematics.
Funny or painful, you decide. The jump that EVH desperately offers at 2:02 is fraught with all the tragedy of the human condition. But at the very least, this remains an important lesson in the importance of sampling rates, logarithmic scales and their relation to musical intervals. Thanks Van Halen!