Category Archives: digital harmony

The rolling-down-a-hill of backpropagation with gradient descent has proven enormously powerful. The process of identifying chords in a ternary harmony system is curiously similar, though the loss function is far more naïve and transparent. Instead of using derivatives, the algorithm simply derives the smallest earth-moving distance, at bit level. It’s rather prosaic. But what this […]

One advantage of this ternary system is that a lot of the crazy folds and skips of scales and arpeggios – even in quite advanced tonalities – turn out to be pretty simply algorithmic. Here, for example, is what you get when you take every second bit in the F-to-B group of bits, starting on […]

Up to now, I’ve been showing these bit-groups in black and white, like a piano. But doesn’t do justice to the differences within the 12-bit bandwidth. An octave makes a sort of spectrum. To begin, here is the circle fifths, visible and audible. This serves as a kind of identity matrix, serving specifically to mark […]

Just as an experiment, here are a few chord progressions given as shepard tones. I was curious to see/hear how they would affect the perception of voice leading. (The intonation is just: powers of 3, sequential.) C Major: ii-V-I C minor ii-V-i: A harmonic minor ii-V-i: It begins to introduce questions of voice leading and […]

A few simple patterns within the ternary harmony system can yield a surprising wealth of familiar diatonic chord progressions with close to zero computational effort. To keep things simple, I’m going to do just one sequence, reachable with only a bit shift operation. All the major/minor folds of thirds fall naturally into the right place. […]

This is a theory, but it works in practise, and yields surprisingly specific and rich musical results. We know that binary numbers represent the presence or absence of powers of two: We might also use binary numbers to represent the presence or absence of powers of three: Using threes in these positions is a step […]

I would post this as ‘blues’ only because I know it’s not blues and never should be categorised as such. It’s just some sort of tightened symbolic rendering, some mathemagical/numerological shadow. But here in our digital igloos, before our computers, respecting our ‘social distance’, we play with dots and waves, alone. Perhaps, at least, there […]

These days, we musicians are left with a question: what is left? What is left when everything is audio? What can performance mean in this infinite, icy context? What can be the message from our fingers, our own digits, our own breath, when touch seems at best superfluous and at worst outright dangerous? Even as […]

The question that keeps appearing before me is about what changing keys does to your memory. I’d like to build a framework to seek a more particular answer. long-term and medium-term tonal memory: ii vs. V/V To begin down this path, I’m going to start with the vi-ii-V-I sequence I’ve been going on about in […]

harmonypartition works simply and cleanly with MIDI files. Using the music21 package, harmonypartition is able to analyze a MIDI file in exactly the same way it analyzes an audio file. Results from MIDI are cleaner than those from audio – though not necessarily better, since resonance and continuity play such a key role in analysis, […]