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/**
* Builds the MiniZinc CSP for Step 3:
* assigns one note per active sub-beat and voice.
* Encodes T1-T3, R4, R9, H12, H19, M1, M9, M14 from the Thesis.
* @param {Object} parameters - Step-3 form params plus chord progression and tempo; see {@link Step3Notes#schema}.
* @param {{subdivision: number, subBeatsPerBar: number, numSubBeats: number, activeBeats: Set<number>[]}} time
* R4+R9: Time-grid built by Step 3: subdivision (tau), T, per-voice onset sets (omicron).
* @return {string} MiniZinc source.
*/
export function modelNotes(parameters, time) {
const pitch = pitchGrid(parameters, time);
return [
'include "globals.mzn";',
...varDecls(parameters, time, pitch.varDomains),
...dissonanceConstraints(parameters, time, pitch),
...range(parameters.voices).flatMap((s) =>
seedOneVoice(parameters, time, pitch, s),
),
...forbidUnisons(parameters, time),
...restsBudget(parameters, time),
...melodicConstraints(parameters, time),
...forbidParallels(parameters, time),
`solve :: ${searchAnnotation(time)} satisfy;`,
].join("\n");
}
/** @private 0..n-1 index range. */
const range = (n) => Array.from({ length: n }, (_, i) => i);
/**
* @private T1+T2+T3 + H19 setup: pitch domain per (s,t) within ambitus [alpha, beta];
* chord/scale tones from gamma_t; dissonance set.
*/
function pitchGrid(parameters, time) {
const { voice, voices, mode, key, chords } = parameters;
const { numSubBeats, activeBeats, subBeatsPerBar } = time;
const chordTones = { ...CHORDS.major, ...CHORDS.minor };
const scaleTones = new Set(
(mode === "major" ? [0, 2, 4, 5, 7, 9, 11] : [0, 2, 3, 5, 7, 8, 10]).map(
(p) => (p + key) % 12,
),
);
const tonesPerBeat = range(numSubBeats).map((t) => {
const base = chordTones[chords[Math.floor(t / subBeatsPerBar)]];
return base ? new Set(base.map((p) => (p + key) % 12)) : scaleTones;
});
const withRest = parameters.rest_pct > 0;
const varDomains = Object.fromEntries(
range(numSubBeats).flatMap((t) =>
voice.slice(0, voices).flatMap((v, s) => {
if (!activeBeats[s].has(t)) {
return [];
}
const allowed =
v.chord_tones === "chord" || v.chord_tones === true
? tonesPerBeat[t]
: v.chord_tones === "scale"
? scaleTones
: null;
const ps = range(v.max_pitch - v.min_pitch + 1)
.map((k) => v.min_pitch + k)
.filter((p) => !allowed || allowed.has(p % 12));
return [[`note_${s}_${t}`, withRest ? [-2, ...ps] : ps]];
}),
),
);
return {
varDomains,
dissAllowedSet: dissSet(parameters.dissonance, voices),
seededValues: {},
};
}
/** @private H19 setup: dissonance-cost array (chi) thresholded by phi; null = no H19. */
function dissSet(dissonance, voices) {
if (dissonance === 0.5 || voices <= 1) {
return null;
}
const cost = [0, 4, 2, 1, 1, 0, 3, 0, 1, 1, 2, 4];
const cons = dissonance < 0.5;
const th = cons ? (dissonance <= 0.2 ? 1 : 2) : dissonance >= 0.8 ? 3 : 2;
return new Set(
cost.flatMap((c, i) => ((cons ? c <= th : c >= th) ? [i] : [])),
);
}
/** @private Build var declarations note_s_t (varDomains already has hold sentinel when restsEnabled). */
function varDecls(parameters, time, varDomains) {
const { numSubBeats, activeBeats } = time;
const withRest = parameters.rest_pct > 0;
return range(numSubBeats).flatMap((t) =>
activeBeats.map((set, s) => {
const n = `note_${s}_${t}`;
if (!set.has(t)) {
return `var int: ${n} = -2;`;
}
const dom = withRest ? [-1, ...varDomains[n]] : varDomains[n];
return `var {${dom.join(",")}}: ${n};`;
}),
);
}
/** @private H19: per voice-pair, per sub-beat, interval class must be in allowed set. */
function dissonanceConstraints(parameters, time, pitch) {
const { dissAllowedSet, varDomains } = pitch;
if (dissAllowedSet === null) {
return [];
}
const setLit = `{${[...dissAllowedSet].join(",")}}`;
const real = (k, t) => realPitches(varDomains[`note_${k}_${t}`]);
const pairs = voicePairs(parameters.voices);
return [
...range(time.numSubBeats).flatMap((t) =>
pairs.flatMap(([a, b]) => {
const rA = real(a, t);
const rB = real(b, t);
if (!rA.length || !rB.length || !anyAllowed(rA, rB, dissAllowedSet)) {
return [];
}
const na = `note_${a}_${t}`;
const nb = `note_${b}_${t}`;
const body = `(abs(${na} - ${nb}) mod 12) in ${setLit}`;
return [guarded(parameters, na, nb, body)];
}),
),
];
}
/** @private Real-pitch subset of a domain (drops -1/-2 sentinels). */
const realPitches = (domain) => (domain || []).filter((p) => p >= 0);
/** @private Unordered voice index pairs (a < b). */
const voicePairs = (voices) =>
range(voices).flatMap((a) =>
range(voices - a - 1).map((k) => [a, a + 1 + k]),
);
/** @private True iff some pair (x in xs, y in ys) has interval class in allowed set. */
const anyAllowed = (xs, ys, allowed) =>
xs.some((x) => ys.some((y) => allowed.has(Math.abs(x - y) % 12)));
/** @private Wrap MZN body with rest/hold sentinel guard when rest_pct > 0. */
const guarded = (parameters, a, b, body) =>
parameters.rest_pct > 0
? `constraint (${a} >= 0 /\\ ${b} >= 0) -> ${body};`
: `constraint ${body};`;
/** @private Seed xi-percent of voice s; emits constraints and mutates pitch.seededValues for cross-voice filtering. */
function seedOneVoice(parameters, time, pitch, s) {
const active = [...time.activeBeats[s]].sort((a, b) => a - b);
const pct = parameters.seed_pct;
const numSeeds =
pct > 0 ? Math.max(1, Math.floor((active.length * pct) / 100)) : 0;
const spacing = Math.max(
1,
Math.floor(active.length / Math.max(1, numSeeds)),
);
const positions = new Set(
range(numSeeds).map(
(k) => active[Math.min(k * spacing, active.length - 1)],
),
);
const seedOrder = [];
return active.flatMap((t) => {
if (!positions.has(t)) {
return [];
}
const ps = pitch.varDomains[`note_${s}_${t}`];
if (ps.length < 3) {
return [];
}
const used = pitch.seededValues[t] || {};
let cs = ps.filter((p) => !Object.values(used).includes(p));
if (pitch.dissAllowedSet !== null) {
cs = filterByDissonance(time, pitch, cs, { s, t });
}
if (seedOrder.length > 0) {
const prev = seedOrder.at(-1)[1];
cs = cs.filter((p) => Math.abs(p - prev) <= parameters.max_interval);
}
if (seedOrder.length > 1) {
const prevPrev = seedOrder.at(-2)[1];
cs = cs.filter((p) => p !== prevPrev);
}
if (cs.length === 0) {
return [];
}
const pick = cs[Math.floor(Math.random() * cs.length)];
seedOrder.push([t, pick]);
(pitch.seededValues[t] ||= {})[s] = pick;
return [`constraint note_${s}_${t} = ${pick};`];
});
}
/** @private H19-aware filter: drop candidates whose interval class to other voices is forbidden at sub-beat (s, t). */
function filterByDissonance(time, pitch, candidates, subbeat) {
const { s, t } = subbeat;
return range(time.activeBeats.length)
.filter((k) => k !== s && time.activeBeats[k].has(t))
.reduce((acc, k) => {
const seeded = pitch.seededValues[t]?.[k];
const others = realPitches(
seeded !== undefined ? [seeded] : pitch.varDomains[`note_${k}_${t}`],
);
if (others.length === 0) {
return acc;
}
return acc.filter(
(p) =>
p < 0 ||
others.some((q) => pitch.dissAllowedSet.has(Math.abs(p - q) % 12)),
);
}, candidates);
}
/** @private H12: pairwise note_a_t != note_b_t for real pitches (skip holds/rests). */
function forbidUnisons(parameters, time) {
if (!parameters.forbid_unisons || parameters.voices <= 1) {
return [];
}
const { numSubBeats, activeBeats } = time;
const pairs = voicePairs(parameters.voices);
return range(numSubBeats)
.filter((t) => everyVoiceActive(activeBeats, t))
.flatMap((t) =>
pairs.map(([a, b]) => {
const na = `note_${a}_${t}`;
const nb = `note_${b}_${t}`;
return guarded(parameters, na, nb, `${na} != ${nb}`);
}),
);
}
/** @private True iff every voice is active at sub-beat t. */
const everyVoiceActive = (activeBeats, t) =>
activeBeats.every((set) => set.has(t));
/** @private Per-voice holds/rests budget (rest_pct, UI-driven; not a chapter4 constraint). */
function restsBudget(parameters, time) {
const pct = parameters.rest_pct;
if (pct <= 0) {
return [];
}
const sb = time.subBeatsPerBar;
const term = (s, t) =>
`bool2int(note_${s}_${t} == -1) + bool2int(note_${s}_${t} == -2)`;
return range(parameters.voices).flatMap((s) => {
const active = [...time.activeBeats[s]].sort((a, b) => a - b);
const maxHR = Math.max(1, Math.floor((active.length * pct) / 100));
const terms = active.map((t) => term(s, t)).join(" + ");
const out = [`constraint ${terms} <= ${maxHR};`];
const downbeats = active.filter((t) => t % sb === 0);
if (downbeats.length >= 2 && active.length - downbeats.length >= maxHR) {
const maxDB = Math.max(1, Math.floor(downbeats.length / 4));
const dbTerms = downbeats.map((t) => term(s, t)).join(" + ");
out.push(`constraint ${dbTerms} <= ${maxDB};`);
}
return out;
});
}
/** @private M1 (max semitone jump delta) + M9 (per-voice no immediate repetition) per voice. */
function melodicConstraints(parameters, time) {
const max = parameters.max_interval;
return range(time.activeBeats.length).flatMap((s) => {
const active = [...time.activeBeats[s]].sort((a, b) => a - b);
const noRep = !parameters.voice[s].allow_repetitions;
const transitions = active.slice(1).map((t2, k) => [active[k], t2]);
return transitions.flatMap(([t1, t2]) => {
const prev = `note_${s}_${t1}`;
const curr = `note_${s}_${t2}`;
const m1 = guarded(
parameters,
prev,
curr,
`abs(${prev} - ${curr}) <= ${max}`,
);
const m9 = guarded(parameters, prev, curr, `${prev} != ${curr}`);
return noRep ? [m1, m9] : [m1];
});
});
}
/** @private M14: forbid parallel fifths and octaves between consecutive shared-active beats. */
function forbidParallels(parameters, time) {
if (!parameters.forbid_parallels || parameters.voices <= 1) {
return [];
}
const { numSubBeats, activeBeats } = time;
const shared = range(numSubBeats).filter((t) =>
everyVoiceActive(activeBeats, t),
);
const pairs = voicePairs(parameters.voices);
const transitions = shared.slice(1).map((t2, k) => [shared[k], t2]);
const n = (v, t) => `note_${v}_${t}`;
const line = ({ a, b, t1, t2 }, i) =>
`constraint not (abs(${n(a, t1)} - ${n(b, t1)}) mod 12 == ${i} /\\ abs(${n(a, t2)} - ${n(b, t2)}) mod 12 == ${i} /\\ (${n(a, t2)} - ${n(a, t1)}) * (${n(b, t2)} - ${n(b, t1)}) > 0);`;
return transitions.flatMap(([t1, t2]) =>
pairs.flatMap(([a, b]) => [7, 0].map((i) => line({ a, b, t1, t2 }, i))),
);
}
/** @private Fisher-Yates-shuffled int_search annotation over all active note vars. */
function searchAnnotation(time) {
const allVars = range(time.numSubBeats).flatMap((t) =>
time.activeBeats.flatMap((set, s) =>
set.has(t) ? [`note_${s}_${t}`] : [],
),
);
for (let i = allVars.length - 1; i > 0; i--) {
const j = Math.floor(Math.random() * (i + 1));
[allVars[i], allVars[j]] = [allVars[j], allVars[i]];
}
return `int_search([${allVars.join(", ")}], input_order, indomain_min)`;
}
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