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d09f52e | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 | """A probabilistic functional-harmony grammar.
Rather than a fixed list of textbook progressions, this assembles phrases from
functional zones — opening (tonic) -> predominant -> dominant -> cadence — with
weighted choices at each step, plus sevenths, inversions, cadential 6-4s, and
secondary dominants. It is a Markov-style generative grammar constrained to
common-practice syntax, so every phrase is musically shaped, cadence-terminated
(key-pinning), and — by construction — labelled correctly.
All chord specs are drawn from a set pre-verified against the gold gate, so the
grammar never emits a chord whose Roman-numeral label disagrees with its pitches.
Deterministic under a seed.
"""
from __future__ import annotations
import random
from typing import Optional
from .vocabulary import Analysis
# Each option is (list-of-specs, weight). Specs are compact DCML labels parsed by
# Analysis.parse. An empty predominant list yields direct I-V-I motion.
_CONFIG = {
"major": {
"tonic": "I",
"submediant": "vi",
"openings": [
(["I"], 6), (["I", "I6"], 1), (["I", "vi"], 2),
(["I", "iii", "vi"], 1), (["I", "V6", "I"], 1), (["I6"], 1),
],
"predominants": [
([], 2), (["IV"], 4), (["ii"], 3), (["ii7"], 3), (["ii6"], 2), (["ii65"], 2),
(["IV", "ii6"], 1), (["vi", "ii7"], 1), (["vi", "IV"], 1), (["I6", "IV"], 1),
(["V7/V"], 1), (["V7/ii", "ii7"], 1), (["V7/IV", "IV"], 1), (["V7/vi", "vi", "ii7"], 1),
],
"dominants": [
(["V"], 2), (["V7"], 4), (["V65"], 1), (["I64", "V7"], 2), (["I64", "V"], 1),
(["viio6", "V7"], 1), (["V7/V", "V7"], 1),
],
# half cadences end on a V *triad*; deceptive resolutions need the
# dominant in root position (see cadence.py) — hence the separate lists.
"dominants_half": [(["V"], 4), (["I64", "V"], 2), (["V7/V", "V"], 1)],
"dominants_deceptive": [(["V7"], 4), (["V"], 2), (["I64", "V7"], 2), (["viio6", "V7"], 1)],
"plagal_predominants": [(["IV"], 3), (["ii6", "IV"], 1), (["I6", "IV"], 1)],
"resolutions": [(["I"], 6), (["I6"], 1)],
},
"minor": {
"tonic": "i",
"submediant": "VI",
"openings": [
(["i"], 6), (["i", "i6"], 1), (["i", "VI"], 2), (["i", "III"], 1), (["i6"], 1),
],
"predominants": [
([], 2), (["iv"], 4), (["iio6"], 3), (["ii%7"], 2), (["iv6"], 2),
(["VI", "iv"], 1), (["iv", "iio6"], 1), (["III", "iv"], 1),
(["V7/V"], 1), (["V7/iv", "iv"], 1), (["V7/VI", "VI", "iio6"], 1),
],
"dominants": [
(["V"], 2), (["V7"], 4), (["V65"], 1), (["i64", "V7"], 2), (["i64", "V"], 1),
(["viio6", "V7"], 1), (["V7/V", "V7"], 1),
],
"dominants_half": [(["V"], 4), (["i64", "V"], 2), (["V7/V", "V"], 1)],
"dominants_deceptive": [(["V7"], 4), (["V"], 2), (["i64", "V7"], 2), (["viio6", "V7"], 1)],
"plagal_predominants": [(["iv"], 3), (["iio6", "iv"], 1), (["VI", "iv"], 1)],
"resolutions": [(["i"], 6), (["i6"], 1)],
},
}
_KINDS = [("authentic", 5), ("half", 2), ("deceptive", 2), ("plagal", 1)]
def _pick(rng: random.Random, options: list[tuple[list, int]]) -> list:
seqs = [o for o, _ in options]
weights = [w for _, w in options]
return list(rng.choices(seqs, weights=weights, k=1)[0])
def _assemble(cfg: dict, rng: random.Random) -> list[str]:
kind = rng.choices([k for k, _ in _KINDS], weights=[w for _, w in _KINDS], k=1)[0]
specs = _pick(rng, cfg["openings"])
if kind == "plagal":
specs += _pick(rng, cfg["plagal_predominants"])
specs += [cfg["tonic"]]
else:
specs += _pick(rng, cfg["predominants"])
if kind == "half":
specs += _pick(rng, cfg["dominants_half"])
elif kind == "deceptive":
specs += _pick(rng, cfg["dominants_deceptive"])
specs += [cfg["submediant"]]
else:
specs += _pick(rng, cfg["dominants"])
specs += _pick(rng, cfg["resolutions"])
return specs
def generate_phrases(mode: str, n: int, seed: int = 0) -> list[list[Analysis]]:
"""Return up to ``n`` distinct, cadence-terminated phrases for the mode."""
cfg = _CONFIG[mode]
rng = random.Random(seed)
out: list[list[Analysis]] = []
seen: set[tuple[str, ...]] = set()
cap = max(500, n * 80)
for _ in range(cap):
if len(out) >= n:
break
specs = _assemble(cfg, rng)
phrase = [Analysis.parse(s) for s in specs]
key_ = tuple(a.dcml_label() for a in phrase)
if key_ in seen:
continue
seen.add(key_)
out.append(phrase)
return out
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