Category Archives: Just Intonation

Shorts #42: Lacewing


This piece was commissioned and titled by Tim Walters.

This piece has two instruments – one uses the Ringz Ugen in SuperCollider and the other is a Sine wave which is phase modulated by another sine wave where both are tuned to the same frequency. It is in harmonic minor, tuned with the default just tuning.

Harmonic minor is known as “Mogen Ovos” to klezmer musicians. Rather than apply western harmony practice (except for the final cadence), every player is picking notes independently. The just tuning helps hold the notes in a key centre.


Wacky Kings

[play] Wacky Kings (2015)

If you enjoyed this piece of music, please consider donating to Mermaids. Mermaids is an organisation that provides support to trans children and their families.

The sound generation is based on a synthdef by Rukano (which is based on a meme, which is based on Eurovision). I modified sound to use slightly different envelopes for every partial, to sharpen the attack and to have the sound gradually decrease in amplitude over time. From the sound, I generated a dissonance curve and from that, generated a 12-tone just scale.

For the melody, I generated Markov chains from a MIDI version of We Three Kings. I slowed the result down, added legato and mapped it to my derived scale. The overlapping tails of notes ends up obscuring the brass sound and makes it sound more like a pipe organ or bells.

This track is part of a larger project, ’12 days of Crimbo’, which will raise funds for homeless and/or LGBT charities.


Ask Not for Whom the Bell Carols

[play] Ask Not for Whom the Bell Carols (2015)

If you enjoyed this piece of music, please consider donating to the Albert Kennedy Trust, who work with homeless LGBT young people.

For this piece, I used Risset bells with a long decay. I used a Dissonance-curve style analysis of the partials to generate a tuning based on the timbre. Rather than use the method outlined by Bill Sethares, I compared the partials to look for good just tuning ratios. I then picked the 8 most in-tune partials (using a moving window system, so make sure they weren’t all next to each other). This is part of my TuningLib quark, which is available to SuperCollider users. (See the justScale method for DissonanceCurve)

Then I used an mp3 of the Bell Carol, but very slowly. I also adjusted the tuning of every partial by up to 10Hz and delayed all attacks by up to 60 milliseconds. This creates weird beating effects, as two identical bells are just slightly out of tune with each other. Their attacks are also often just a bit too far apart to be simultaneous.

I have ambitions to generalise harmony in terms of dissonance, so that it’s applicable to bespoke tuning systems, but ended up not applying that to this piece. This track is part of a larger project, ’12 days of Crimbo’, which will raise funds for homeless and/or LGBT charities.


Blake’s 9 – draft

[play]Blake’s 9 (2008)

This piece has changed significantly since I first posted it and a newer version has since been posted.

I recently watched the entirety of the TV series Blake’s 7. Like all BBC science fiction productions of it’s era, the incidental music and sound effects are outstanding. The background hums, the computer whirrs and the ominous notes create a mood and a sense of place that is alien. After watching several of the episodes, I went home and created a patch on my MOTM synthesizer which seemed to perfectly capture a progression of mood as it might appear in an episode with Avon creeping along with a ray gun, infiltrating a Federation base.

However, as nice as patch was, with it’s 4 minute long loop, it wasn’t a piece. And there wasn’t an obvious way to make it become one. It was too complex and had too much character to mix, but not enough to stand on it’s own. I let it sit for weeks and thought about other things, specifically, a beat generation algorithm that was going nowhere. And then I met a poet who is obsessed with divisions / groups of 9.

I set my beat maker to 9, and then I thought of using it as a an organizational principle for cutting, rather than a way to make cheesy drum loops. I used it to cut my loop to sections and then into grains. Then I played back the grains in groups of 9, to make measures of 9 beats. In order to add some pitch variety, I changed the speed of playback of the grains, with rates of 1, 27/25, 9/7, 7/9, 25/27, a few intervals in a just version of the Bohlen Pierce scale. This scale uses 3’s instead of octaves, so the ratios have multiples of 3 where you would expect powers of two for more traditional scales.

This is a work in progress and may go on to be an installation or gain additional movements or neither or both.




This piece moves through undertones of (2^x)/y. It starts with 32/21 and then adds in 32/19 and then 32/17 to create a triad. Then 32/21 drops out and 16/15 enters. As the farthest out note finishes, a closer one comes in so that the piece migrates from 32/21 to 2/2, always playing a triad.

These triads are AM modulated by low frequency pulse waves, starting at 2 Hz. As the piece progresses, faster pulse waves are added to modify new pitches. The pulse introduced are the base pulse times 2, then 3, then 4, then 5 and finally 6. They do not reach the audio range, although they flirt with the idea. The hard cutoffs of the pulse create interference patterns of clicking.


Bell Tolls

Bell Tolls

This piece plays triads with a sound that resembles wind chimes. It uses a spatialization algorithm so that each “chime” sounds like it is coming from a different location. The pitch of each new set of chimes is based on the pitch of the chimes that precede it. The pitches come from a 21-limit tuning table.

I wrote this piece while going through a divorce. It was intended to sound angry, but instead seems sad.

Des triades des cloches fausses.


Morpheus’ Snare

Morpehus’ Snare

In this piece, I have detuned the left and the right channels. As the piece starts, the detuning falls randomly in between 2 Hz and 20Hz. As it progresses, the range narrows until the left and the right always differ by 10Hz. Alpha brain waves are generally around 10Hz. There are rumors that listening to pitches detuned between the left and right ear at 10Hz will make the listener sleepy and cause them to enter an alpha state.

Dans cette pièce la droite et la gauche ne sont pas en accord. Au début, il y a un écart de 2 à 20 Hz d’accord. Dans la conclusion, l’écart est toujours de 10 Hz, la même fréquence des ondes alpha dans le cerveau.