design+data+people nerd ❦ previously partner at IDEO, co-founded Datascope
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Dec 2, 2023
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function makeModes(nWholesteps, nPitchesPerOctave = 12) {
const nHalfsteps = nPitchesPerOctave - 2 * nWholesteps;
const nPitches = nWholesteps + nHalfsteps;
if (nHalfsteps < 0) {
return [];
} else if (nHalfsteps === 0) {
return [new Array(nPitches).fill(2)];
}
const range = new Array(nPitches).fill().map((_, i) => i);
return _.combinations(range, nHalfsteps).map((indexes) => {
let result = new Array(nPitches).fill(2);
indexes.forEach((i) => (result[i] = 1));
return result;
});
}
makeModes(0)
makeModes(4)
nTotal = nModes(0) + // chromatic (12 notes)
nModes(1) +
nModes(2) +
nModes(3) +
nModes(4) +
nModes(5) + // ionian mode, dorian mode, etc in here (5 whole steps, 2 half steps)
nModes(6) // whole tone scale (6 notes)
// abbreviating frequencies to "freqs" because I keep spelling frequencies wrong
function equalTemperedFreqs(
nPitchesPerOctave = 12,
startFrequency = 261.6255653, // start at C4, where A4=440Hz
nOctaves = 5
) {
const n = nPitchesPerOctave;
const logs = _.range(nOctaves * n + 1).map(
(i) => Math.log2(startFrequency) + i / n
);
return logs.map((d) => 2 ** d);
}
function modeToFreqs(
intervals,
nPitchesPerOctave = 12,
startFrequency = 261.6255653 // start at C4, where A4=440Hz
) {
const notes = equalTemperedFreqs(nPitchesPerOctave, startFrequency);
const result = [];
let index = 0;
result.push(notes[index]);
intervals.forEach((interval) => {
index += interval;
result.push(notes[index]);
});
return result;
}
wholeToneFrequencies = modeToFreqs(makeModes(6)[0])
function playFreqs(
freqs,
duration = 0.25,
playDescending = false,
arpeggiate = true
) {
const synth = new Tone.PolySynth(Tone.Synth).toDestination();
const now = Tone.now();
const n = freqs.length;
if (arpeggiate) {
freqs.forEach((f, i) => {
const dDown = (2 * duration) / 3;
synth.triggerAttackRelease(f, dDown, now + i * duration);
if (playDescending && i !== n - 1) {
let j = 2 * (n - 1) - i;
synth.triggerAttackRelease(f, dDown, now + j * duration);
}
});
} else {
freqs.forEach((f, i) => {
if (i !== freqs.length - 1) {
synth.triggerAttackRelease(f, duration, now);
}
});
}
}
function playButton(label, f, ...params) {
const button = Inputs.button(label);
button.oninput = () => {
f(...params);
};
return button;
}
playButton(
"⏵ Ionian Mode (Major Scale)",
playFreqs,
modeToFreqs([2, 2, 1, 2, 2, 2, 1])
)
constellationPlot([2, 2, 1, 2, 2, 2, 1])
function* allRotations(array) {
for (let i = 0; i < array.length; i++) {
yield [...array];
//array.unshift(array.pop()); // take the last element and move to front
array.push(array.shift()); // take the first element and move to end (will do this way because it’s how it was in the sketch above
}
}
[...allRotations([1, 2, 3])]
function groupRotations(scales) {
// this currently looks at every rotation of every scale that
// is passed in, which I’m pretty sure is not necessary. It could
// be made more efficient, but it will do for now.
// keys of incomplete are string
let incomplete = new Map(scales.map((d) => [d.toString(), d]));
// choose any key as the "focus" to start
let focus = incomplete.keys().next().value;
let group = [];
let result = [];
while (true) {
// group together all the scales that are rotations of the focus (and remove from incomplete)
for (let rotation of allRotations(incomplete.get(focus))) {
const found = incomplete.delete(rotation.toString());
if (found) {
group.push(rotation);
}
}
result.push(group);
// choose any key as the next focus, until incomplete is empty
focus = incomplete.keys().next().value;
group = [];
if (focus === undefined) {
break;
}
}
return result;
}
groupRotations([
[1, 1, 2],
[2, 1, 1], // same as first, rotated
[1, 1, 1] // different
])
sevenPitchRotationGroups = groupRotations(makeModes(5, 12))
eightPitchRotationGroups = groupRotations(makeModes(4, 12)).map((d) => d[0])
nTotalTNE = _.sum(_.range(0, 7).map((nWhole) => nTNE(nWhole)))
function makeAllScales(n) {
const allSequences = new Set();
function* divide(...seq) {
yield seq;
allSequences.add(seq.toString());
for (let [i, n] of seq.entries()) {
for (let m = 1; m < n; m++) {
const sub = seq
.slice(0, i)
.concat([m, n - m])
.concat(seq.slice(i + 1));
if (!allSequences.has(sub.toString())) {
yield* divide(...sub);
}
}
}
}
return [...divide(n)];
}
allScales = makeAllScales(12)
function* makeAllScalesBinary(n) {
for (let i = 0; i < 2 ** (n - 1); i++) {
yield i
.toString(2) // convert to binary (I’m sure there’s a better way of doing this than casting to string, but 🤷🏻)
.padStart(n - 1, "0") // pad to the correct length
.split("") // convert back to array
.map((d) => +d) // convert back to numbers
.map((d, i) => (d ? i + 1 : null)) // convert to pitch class indexes
.filter((d) => d !== null) // remove empties
.concat([n]) // add next octave index
.map((d, i, a) => d - (i - 1 >= 0 ? a[i - 1] : 0)); // subtract consecutive indexes to get steps
}
}
allScales2 = [...makeAllScalesBinary(12)]
allScales.filter((scale) => !scale.some((step) => step > 2))
allScales2.filter((scale) => !scale.some((step) => step > 2))
eightNoteScales = allScales.filter((d) => d.length === 8)
transpositionallyNonEquivalentEightNoteScales = groupRotations(eightNoteScales)
totalShapes = groupRotations(allScales)
sixNoteScales = allScales
.filter((scale) => !scale.some((step) => step > 3))
.filter((scale) => scale.length < 6)
//.filter((scale) => intervalsToIndexes(scale).includes(7)) // only include those that have a major fifth
_ = require("lodash", "lodash.combinations")
Tone = require("tone")
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