This is my first ever finished musical composition, let alone a first microtonal!

Huygens' Clock is a contemporary instrumental in 31-tone equal temperament and 7/8 time: sixty-four bars, every one counted 2+2+3. It is generated procedurally, by a program written in Microtone's own music language, to show what the 31-TET grid can do; the last paragraph of this note says where to find it.

The title is two inventions of one man. Christiaan Huygens built the first pendulum clock in 1656, and in 1691 he proposed dividing the octave into 31 equal steps. The marimba figure that opens the piece and closes it is the clock, fourteen sixteenths to the bar, ticking in sevens. Everything else is the tuning.

A step of 31-TET is 38.7 cents, a little less than a quarter tone. Its major third is within a cent of the pure 5/4, and its harmonic seventh within about a cent of 7/4, the seventh that barbershop singers lean into and a piano cannot play. Between the minor and the major third it has a neutral third (close to 11/9), and outside them a subminor (7/6) and a supermajor (9/7) third. The piece is built from exactly those.

Bars 1–8: the clock alone, then the band arriving.

Bars 9–16: the theme, on a septimal blues pentatonic: D, F half-flat (7/6), G, A, C half-flat (7/4). The tonic chord is 12:14:18:21. The dominant and the chord before it are both harmonic seventh chords (4:5:6:7); in 31-TET a German sixth is exactly that chord, which is why the turnaround slides home so smoothly.

Bars 17–24: a synth solo over the same loop. Listen for bends of a single step.

Bars 25–40: major chords climbing by neutral thirds: B flat, D half-flat, F, A half-flat, C, E half-flat, G, B half-flat. Two neutral thirds make a perfect fifth, so every other chord lands on the circle of fifths and the ones between sit exactly halfway. Two notes of each chord move by a single step and the third by a neutral second; the pad and the strings glide into each chord instead of striking it, and the flute's long notes bend by one step as the harmony turns under them.

Bars 41–48: over a D pedal, the third climbs one step a bar through all five thirds 31-TET has (subminor, minor, neutral, major, supermajor), and then the harmonic series assembles itself: the seventh, the ninth, the eleventh.

Bars 49–56: the theme again, its third raised from 7/6 to 5/4, over a 4:5:6:7 tonic.

Bars 57–64: German sixth and dominant once more, then the harmonic series on D (4:5:6:7:9:11) while the clock runs down.

Every note sits on the 31-TET grid, and the Timeline is set to 31-TET notation, so the names you read are the notes you hear: D, Dt and Dp are D, D half-sharp and D half-flat. The beat bands are set for 7/8, a line every eighth and a bar every fourteen rows.

The instruments are General MIDI patches from the GeneralUser GS soundfont by S. Christian Collins, the one Microtone bundles. Its samples are tuned for twelve-tone music, a few cents either way, and up to eight on the pad: nothing in a piano, but a fifth of a step here. So the script measures where every zone the song plays really sounds and re-tunes it onto the 31-TET grid, to within about a cent. The corrections are ordinary per-zone detune: open the Instruments view to see them.

The master is Microtone's own chain, saved with the project: a 25 Hz high-pass, four bands of EQ, a 2:1 compressor, stereo width at 130% and a limiter holding −0.2 dB, for about −14 LUFS. Bypass it in the Mastering view to hear the mix underneath.

Nothing in this project was played or placed by hand. The notes, the instrument bank, the re-tuning, the mix and the master are all computed by a program in Taud Motif Language, and this project is its output: the same program always builds the same song. The program travels inside the project. Open the Motif view to read it, change it and build the song again. You can still edit the project like any other, but a rebuild starts again from the program.

Created using Microtone tracker (https://microtone.cc), also available as Microtone's demo project.