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JavaScript
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144// counterpoint.mjs — first-species counterpoint after Fux's// "Gradus ad Parnassum" (note-against-note, two voices).//// checkFirstSpecies(cantus, counter, opts) -> { ok, violations, warnings }// generateFirstSpecies(cantus, opts) -> counter[] | null//// All pitches are MIDI note numbers. The counterpoint sits ABOVE the// cantus firmus. `cantus` and `counter` are equal-length arrays, one// counter note per cantus note.//// ref: archive.org/details/imslp-ad-parnassum-fux-johann-joseph
// Harmonic-interval classes (semitones mod octave).const CONSONANT = new Set([0, 3, 4, 7, 8, 9]); // P1 m3 M3 P5 m6 M6const PERFECT = new Set([0, 7]); // P1/P8 and P5
const ic = (semis) => ((semis % 12) + 12) % 12;export const isConsonant = (semis) => CONSONANT.has(ic(semis));export const isPerfect = (semis) => PERFECT.has(ic(semis));
// ── checker ───────────────────────────────────────────────────────────// Hard rules → `violations`; stylistic preferences → `warnings`.// `ok` is true when there are no violations.export function checkFirstSpecies(cantus, counter) { const violations = [], warnings = []; const n = Math.min(cantus.length, counter.length); if (cantus.length !== counter.length) violations.push({ index: -1, rule: "length", detail: "voices differ in length" });
const V = (index, rule, detail) => violations.push({ index, rule, detail }); const W = (index, rule, detail) => warnings.push({ index, rule, detail });
let parallelImperfect = 0; for (let i = 0; i < n; i++) { const iv = counter[i] - cantus[i];
if (iv < 0) V(i, "voice-crossing", "counterpoint falls below the cantus"); else if (iv === 0 && i !== 0 && i !== n - 1) W(i, "unison", "interior unison — weak");
if (!isConsonant(iv)) V(i, "dissonance", `dissonant interval (${iv} st) — first species is all consonances`);
if ((i === 0 || i === n - 1) && !isPerfect(iv)) V(i, "imperfect-bound", `${i === 0 ? "first" : "last"} interval must be a perfect consonance`);
if (i > 0) { const prev = counter[i - 1] - cantus[i - 1]; const cantusMoved = cantus[i] !== cantus[i - 1]; const counterMoved = counter[i] !== counter[i - 1]; const dirC = Math.sign(cantus[i] - cantus[i - 1]); const dirP = Math.sign(counter[i] - counter[i - 1]);
// parallel perfect consonances if (isPerfect(iv) && isPerfect(prev) && ic(iv) === ic(prev) && (cantusMoved || counterMoved)) V(i, "parallel-perfect", `parallel ${ic(iv) === 0 ? "octaves/unisons" : "fifths"}`);
// hidden/direct perfect — similar motion into a perfect interval if (isPerfect(iv) && !isPerfect(prev) && dirC !== 0 && dirC === dirP) W(i, "direct-perfect", "perfect consonance approached by similar motion");
// melodic leaps in the counterpoint const leap = Math.abs(counter[i] - counter[i - 1]); if (leap > 12) V(i, "leap", `counterpoint leaps ${leap} st (> octave)`); else if (leap > 7) W(i, "wide-leap", `counterpoint leaps ${leap} st`);
// run of parallel imperfect consonances if (!isPerfect(iv) && isConsonant(iv) && ic(iv) === ic(prev) && cantusMoved) { parallelImperfect++; if (parallelImperfect >= 4) W(i, "parallel-run", "4+ parallel thirds/sixths in a row"); } else parallelImperfect = 0; } } return { ok: violations.length === 0, violations, warnings };}
// ── generator ─────────────────────────────────────────────────────────// Backtracking search for a valid first-species line above `cantus`.// Candidates are notes of the given key/scale within a range above each// cantus note. Returns the counterpoint array, or null if none found.//// opts: {// tonic: MIDI pitch class 0..11 (default = cantus[0] % 12)// scale: semitone degrees (default natural minor)// minAbove, maxAbove: search band over each cantus note (default 2 .. 16)// }export function generateFirstSpecies(cantus, opts = {}) { const n = cantus.length; if (n === 0) return []; const tonic = opts.tonic ?? (cantus[0] % 12); const scale = opts.scale ?? [0, 2, 3, 5, 7, 8, 10]; // natural minor const scaleSet = new Set(scale.map((d) => (d + tonic) % 12)); const minAbove = opts.minAbove ?? 2; const maxAbove = opts.maxAbove ?? 16;
// candidate pitches for position i, ordered to prefer imperfect // consonances and contrary motion vs the previous note. const candidatesFor = (i, prev) => { const cands = []; for (let p = cantus[i] + minAbove; p <= cantus[i] + maxAbove; p++) { if (!scaleSet.has(p % 12)) continue; const iv = p - cantus[i]; if (!isConsonant(iv)) continue; if (i === 0 || i === n - 1) { if (!isPerfect(iv)) continue; } cands.push(p); } return cands.sort((a, b) => { const score = (p) => { let s = 0; if (isPerfect(p - cantus[i])) s += 3; // prefer imperfect inside if (prev != null) { const dirC = Math.sign(cantus[i] - cantus[i - 1]); const dirP = Math.sign(p - prev); if (dirC !== 0 && dirP === -dirC) s -= 2; // reward contrary motion s += Math.abs(p - prev) * 0.3; // reward small steps } return s; }; return score(a) - score(b); }); };
const counter = new Array(n); const solve = (i) => { if (i === n) return checkFirstSpecies(cantus, counter).ok; for (const p of candidatesFor(i, i > 0 ? counter[i - 1] : null)) { counter[i] = p; // prune: the partial line must already be violation-free const partial = checkFirstSpecies(cantus.slice(0, i + 1), counter.slice(0, i + 1)); const onlyBoundary = partial.violations.every( (v) => v.rule === "imperfect-bound" && v.index === i && i !== n - 1, ); if (partial.ok || onlyBoundary) { if (solve(i + 1)) return true; } } counter[i] = undefined; return false; };
return solve(0) ? counter : null;}