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kennethreitz
552836ae5b
- Replace pytuning with 30-line native implementations of EDO, Pythagorean, and quarter-comma meantone scale generators - Lazy-load scipy.signal (337ms) — only imported when audio rendering is actually used, not on theory-only imports - Removes pytuning and sympy from dependencies entirely Import time: 0.479s → 0.056s (8.5x faster) Closes #44 Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
971 lines
38 KiB
Python
971 lines
38 KiB
Python
import math
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REFERENCE_A = 440
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# Index of C in the Western tone list (A=0, A#=1, B=2, C=3, ...).
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# Scientific pitch notation changes octave at C, not A, so this offset
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# is needed for all octave arithmetic.
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C_INDEX = 3
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# ── Temperament scale generators (replaces pytuning dependency) ──────────
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def _create_edo_scale(n):
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"""N-tone equal division of the octave. Each step = 2^(1/n)."""
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return [2 ** (i / n) for i in range(n + 1)]
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def _create_pythagorean_scale(n):
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"""Pythagorean tuning — spiral of pure fifths (3/2 ratio).
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Each tone is generated by stacking perfect fifths and octave-reducing.
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"""
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ratios = [1.0]
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for i in range(1, n):
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# Stack fifths: (3/2)^i, then reduce to within one octave
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r = (3 / 2) ** i
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while r >= 2.0:
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r /= 2.0
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ratios.append(r)
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ratios.sort()
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ratios.append(2.0)
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return ratios
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def _create_quarter_comma_meantone_scale(n):
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"""Quarter-comma meantone — pure major thirds (5/4), tempered fifths.
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The fifth is narrowed by 1/4 of a syntonic comma so that four
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fifths make a pure major third (5/4). The meantone fifth =
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5^(1/4) ≈ 1.49535.
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"""
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fifth = 5 ** 0.25 # meantone fifth ≈ 1.49535 (vs 1.5 pure)
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ratios = [1.0]
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for i in range(1, n):
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r = fifth ** i
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while r >= 2.0:
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r /= 2.0
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ratios.append(r)
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ratios.sort()
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ratios.append(2.0)
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return ratios
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def _create_just_intonation_scale(n):
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"""5-limit just intonation ratios for 12-tone systems."""
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if n != 12:
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return _create_edo_scale(n)
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return [1, 16/15, 9/8, 6/5, 5/4, 4/3, 45/32, 3/2, 8/5, 5/3, 9/5, 15/8, 2.0]
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TEMPERAMENTS = {
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"equal": _create_edo_scale,
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"pythagorean": _create_pythagorean_scale,
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"meantone": _create_quarter_comma_meantone_scale,
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"just": _create_just_intonation_scale,
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}
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TONES = {
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"western": [
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("A",),
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("A#", "Bb"),
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("B",),
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("C",),
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("C#", "Db"),
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("D",),
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("D#", "Eb"),
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("E",),
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("F",),
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("F#", "Gb"),
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("G",),
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("G#", "Ab"),
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],
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# Indian classical (Hindustani) system.
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# Ordered A-based to match Western index positions (Sa = index 3 = C).
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"indian": [
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("Dha",), # A — shuddha dhaivat
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("komal Ni",), # Bb — komal nishad
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("Ni",), # B — shuddha nishad
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("Sa",), # C — shadja
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("komal Re",), # Db — komal rishabh
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("Re",), # D — shuddha rishabh
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("komal Ga",), # Eb — komal gandhar
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("Ga",), # E — shuddha gandhar
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("Ma",), # F — shuddha madhyam
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("tivra Ma",), # F# — tivra madhyam
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("Pa",), # G — pancham
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("komal Dha",), # Ab — komal dhaivat
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],
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# Arabic maqam system — Arabic solfège names.
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"arabic": [
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("La",), # A
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("Sib",), # Bb — Si bemol
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("Si",), # B
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("Do",), # C
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("Reb",), # Db — Re bemol
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("Re",), # D
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("Mib",), # Eb — Mi bemol
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("Mi",), # E
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("Fa",), # F
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("Fa#",), # F#
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("Sol",), # G
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("Solb",), # Ab — Sol bemol
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],
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# Japanese system — uses Western names; scales are the unique part.
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"japanese": [
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("A",),
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("A#", "Bb"),
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("B",),
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("C",),
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("C#", "Db"),
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("D",),
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("D#", "Eb"),
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("E",),
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("F",),
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("F#", "Gb"),
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("G",),
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("G#", "Ab"),
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],
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# Blues/Pentatonic — Western names with blues and pentatonic scales.
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"blues": [
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("A",),
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("A#", "Bb"),
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("B",),
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("C",),
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("C#", "Db"),
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("D",),
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("D#", "Eb"),
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("E",),
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("F",),
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("F#", "Gb"),
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("G",),
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("G#", "Ab"),
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],
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# Javanese gamelan — pelog approximation in 12-TET.
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# True gamelan uses non-Western intonation; these are closest 12-TET fits.
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"gamelan": [
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("nem",), # A — 6
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("pi",), # Bb — 7 (barang in some)
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("barang",), # B — 7
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("ji",), # C — 1
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("ro-",), # Db — 2b
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("ro",), # D — 2
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("lu-",), # Eb — 3b
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("lu",), # E — 3
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("pat",), # F — 4
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("pat+",), # F# — 4#
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("mo",), # G — 5
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("nem-",), # Ab — 6b
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],
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}
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DEGREES = {
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"western": [
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("tonic", ("ionian", "aeolian")),
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("supertonic", ("dorian", "locrian")),
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("mediant", ("phrygian", "ionian")),
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("subdominant", ("lydian", "dorian")),
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("dominant", ("mixolydian", "phrygian")),
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("submediant", ("aeolian", "lydian")),
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("leading tone", ("locrian", "mixolydian")),
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("octave", ("ionian", "aeolian")),
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],
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"indian": [
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("shadja", ()), # Sa — the tonic
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("rishabh", ()), # Re — 2nd
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("gandhar", ()), # Ga — 3rd
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("madhyam", ()), # Ma — 4th
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("pancham", ()), # Pa — 5th
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("dhaivat", ()), # Dha — 6th
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("nishad", ()), # Ni — 7th
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("saptak", ()), # Sa — octave
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],
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"arabic": [
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("qarar", ()), # 1st — root
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("nawa", ()), # 2nd
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("thalth", ()), # 3rd
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("arba", ()), # 4th
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("khamis", ()), # 5th
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("sadis", ()), # 6th
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("sabi", ()), # 7th
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("jawab", ()), # octave
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],
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"japanese": [
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("ichi", ()), # 1st
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("ni", ()), # 2nd
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("san", ()), # 3rd
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("shi", ()), # 4th
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("go", ()), # 5th
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("roku", ()), # 6th
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],
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"blues": [
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("tonic", ()),
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("supertonic", ()),
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("mediant", ()),
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("subdominant", ()),
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("dominant", ()),
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("submediant", ()),
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("subtonic", ()),
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],
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"gamelan": [
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("ji", ()), # 1
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("ro", ()), # 2
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("lu", ()), # 3
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("pat", ()), # 4
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("mo", ()), # 5
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("nem", ()), # 6
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("pi", ()), # 7
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],
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}
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SCALES = {
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# Number of semitones.
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12: {
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# scale type: number of tones.
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"chromatic": (12, {}),
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# "octatonic": (8, {}),
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"heptatonic": [
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7,
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{
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"major": {"major": True, "hemitonic": True},
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"minor": {"minor": True, "hemitonic": True},
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"harmonic minor": {"minor": True, "harmonic": True, "hemitonic": True},
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# "melodic minor": {"minor": True, "melodic": True, "hemitonic": True},
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},
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],
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}
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}
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# Indian scales — the 10 thaats of Hindustani classical music.
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# Each thaat defines a parent scale from which ragas are derived.
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INDIAN_SCALES = {
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12: {
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"chromatic": (12, {}),
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"thaat": [
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7,
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{
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# Bilawal = Western major / Ionian
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"bilawal": {"intervals": (2, 2, 1, 2, 2, 2, 1)},
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# Khamaj = Western Mixolydian
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"khamaj": {"intervals": (2, 2, 1, 2, 2, 1, 2)},
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# Kafi = Western Dorian
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"kafi": {"intervals": (2, 1, 2, 2, 2, 1, 2)},
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# Asavari = Western natural minor / Aeolian
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"asavari": {"intervals": (2, 1, 2, 2, 1, 2, 2)},
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# Bhairavi = Western Phrygian
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"bhairavi": {"intervals": (1, 2, 2, 2, 1, 2, 2)},
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# Kalyan = Western Lydian
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"kalyan": {"intervals": (2, 2, 2, 1, 2, 2, 1)},
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# Bhairav — unique to Indian music (no Western equivalent)
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# Sa re Ga Ma Pa dha Ni
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"bhairav": {"intervals": (1, 3, 1, 2, 1, 3, 1)},
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# Poorvi — unique to Indian music
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# Sa re Ga tivra-Ma Pa dha Ni
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"poorvi": {"intervals": (1, 3, 2, 1, 1, 3, 1)},
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# Marwa — unique to Indian music
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# Sa re Ga tivra-Ma Pa Dha Ni
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"marwa": {"intervals": (1, 3, 2, 1, 2, 2, 1)},
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# Todi — unique to Indian music
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# Sa re komal-Ga tivra-Ma Pa dha Ni
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"todi": {"intervals": (1, 2, 3, 1, 1, 3, 1)},
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},
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],
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}
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}
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# ── 22-shruti Indian system ──────────────────────────────────────────────────
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# The shruti system divides the octave into 22 microtonal steps, capturing
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# the melodic nuances that 12-TET cannot represent. Each of the 7 swaras
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# has multiple shruti positions (e.g. komal Re at shruti 2, shuddha Re at
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# shruti 4). 22-TET is the standard equal-tempered approximation.
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#
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# Ordered from Dha (=A) to match Western index positions (Sa at index 5 ≈ C).
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TONES_SHRUTI = [
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("Dha",), # 0 — A — shuddha dhaivat (reference = 440 Hz)
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("atikomal Ni",), # 1 — shruti between Dha and komal Ni
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("komal Ni",), # 2 — Bb — komal nishad
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("shuddha Ni",), # 3 — between komal Ni and Ni
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("Ni",), # 4 — B — shuddha (kakali) nishad
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("Sa",), # 5 — C — shadja (tonic)
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("atikomal Re",), # 6 — shruti between Sa and komal Re
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("komal Re",), # 7 — Db — komal rishabh
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("shuddha Re",), # 8 — between komal Re and Re
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("Re",), # 9 — D — chatushruti rishabh
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("atikomal Ga",), # 10 — shruti between Re and komal Ga
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("komal Ga",), # 11 — Eb — komal gandhar
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("Ga",), # 12 — E — antara gandhar
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("tivra Ga",), # 13 — shruti between Ga and Ma
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("Ma",), # 14 — F — shuddha madhyam
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("ekashruti Ma",), # 15 — shruti between Ma and tivra Ma
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("tivra Ma",), # 16 — F# — tivra madhyam
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("atitivra Ma",), # 17 — shruti between tivra Ma and Pa
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("Pa",), # 18 — G — pancham
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("atikomal Dha",), # 19 — shruti between Pa and komal Dha
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("komal Dha",), # 20 — Ab — komal dhaivat
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("shuddha Dha",), # 21 — shruti between komal Dha and Dha
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]
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DEGREES_SHRUTI = [
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("shadja", ("bilawal",)), # Sa — tonic
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("rishabh", ("marwa",)), # Re
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("gandhar", ("bhairavi",)), # Ga
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("madhyam", ("kalyan",)), # Ma
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("pancham", ("kafi",)), # Pa
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("dhaivat", ("asavari",)), # Dha
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("nishad", ("khamaj",)), # Ni
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("shadja", ()), # Sa (octave)
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]
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# 22-shruti frequency ratios — 5-limit just intonation.
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# These are the REAL shruti intervals, NOT 22-TET approximations.
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# Based on the traditional Pythagorean/harmonic ratios from Indian
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# musicological treatises (Natya Shastra, Sangita Ratnakara).
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#
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# Ordered from Dha (A=1.0) to match our system indexing.
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# Sa is at index 5 (ratio ≈ 6/5 from Dha).
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from fractions import Fraction
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_SHRUTI_RATIOS_FROM_SA = [
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Fraction(1, 1), # 0: Sa — 1/1
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Fraction(256, 243), # 1: atikomal Re — Pythagorean limma
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Fraction(16, 15), # 2: komal Re — JI minor second
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Fraction(10, 9), # 3: shuddha Re — minor whole tone
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Fraction(9, 8), # 4: Re — major whole tone
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Fraction(32, 27), # 5: atikomal Ga — Pythagorean minor 3rd
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Fraction(6, 5), # 6: komal Ga — JI minor 3rd
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Fraction(5, 4), # 7: Ga — JI major 3rd
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Fraction(81, 64), # 8: tivra Ga — Pythagorean major 3rd
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Fraction(4, 3), # 9: Ma — perfect 4th
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Fraction(27, 20), # 10: ekashruti Ma
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Fraction(45, 32), # 11: tivra Ma — augmented 4th
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Fraction(729, 512), # 12: atitivra Ma — Pythagorean tritone
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Fraction(3, 2), # 13: Pa — perfect 5th
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Fraction(128, 81), # 14: atikomal Dha — Pythagorean minor 6th
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Fraction(8, 5), # 15: komal Dha — JI minor 6th
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Fraction(5, 3), # 16: shuddha Dha
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Fraction(27, 16), # 17: Dha — Pythagorean major 6th
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Fraction(16, 9), # 18: komal Ni — Pythagorean minor 7th
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Fraction(9, 5), # 19: shuddha Ni — JI minor 7th
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Fraction(15, 8), # 20: Ni — JI major 7th
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Fraction(243, 128), # 21: tivra Ni — Pythagorean major 7th
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]
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# Rotate to start from Dha (index 17 in the Sa-based list above).
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# Dha = 27/16 from Sa. We divide all ratios by 27/16 and wrap.
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_dha_ratio = _SHRUTI_RATIOS_FROM_SA[17]
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SHRUTI_RATIOS = []
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for i in range(22):
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sa_idx = (i + 17) % 22 # rotate: Dha=0, komalNi=1, ..., Sa=5, ...
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r = _SHRUTI_RATIOS_FROM_SA[sa_idx] / _dha_ratio
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if r < 1:
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r *= 2 # wrap into the same octave
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SHRUTI_RATIOS.append(float(r))
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# 22-shruti thaat scales with proper microtonal intervals.
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# Compare to the 12-TET approximations in INDIAN_SCALES which lose
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# the distinction between 2-shruti and 3-shruti steps.
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SHRUTI_SCALES = {
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"chromatic": (22, {}),
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"thaat": [
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7,
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{
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# Bilawal (≈ Ionian) — Sa Re Ga Ma Pa Dha Ni
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"bilawal": {"intervals": (4, 3, 2, 4, 4, 3, 2)},
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# Khamaj (≈ Mixolydian) — Sa Re Ga Ma Pa Dha komal-Ni
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"khamaj": {"intervals": (4, 3, 2, 4, 4, 1, 4)},
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# Kafi (≈ Dorian) — Sa Re komal-Ga Ma Pa Dha komal-Ni
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"kafi": {"intervals": (4, 2, 3, 4, 4, 1, 4)},
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# Asavari (≈ Aeolian) — Sa Re komal-Ga Ma Pa komal-Dha komal-Ni
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"asavari": {"intervals": (4, 2, 3, 4, 2, 3, 4)},
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# Bhairavi (≈ Phrygian) — Sa komal-Re komal-Ga Ma Pa komal-Dha komal-Ni
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"bhairavi": {"intervals": (2, 4, 3, 4, 2, 3, 4)},
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# Bhairav — Sa komal-Re Ga Ma Pa komal-Dha Ni (unique to Indian music)
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"bhairav": {"intervals": (2, 5, 2, 4, 2, 5, 2)},
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# Kalyan (≈ Lydian) — Sa Re Ga tivra-Ma Pa Dha Ni
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"kalyan": {"intervals": (4, 3, 4, 2, 4, 3, 2)},
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# Marwa — Sa komal-Re Ga tivra-Ma Pa Dha Ni (unique)
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"marwa": {"intervals": (2, 5, 4, 2, 4, 3, 2)},
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# Poorvi — Sa komal-Re Ga tivra-Ma Pa komal-Dha Ni (unique)
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"poorvi": {"intervals": (2, 5, 4, 2, 2, 5, 2)},
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# Todi — Sa komal-Re komal-Ga tivra-Ma Pa komal-Dha Ni (unique)
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"todi": {"intervals": (2, 4, 5, 2, 2, 5, 2)},
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},
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],
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"pentatonic": [
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5,
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{
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# Bhupali (≈ major pentatonic) — Sa Re Ga Pa Dha
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"bhupali": {"intervals": (4, 3, 6, 4, 5)},
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# Malkauns — Sa komal-Ga Ma komal-Dha komal-Ni
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"malkauns": {"intervals": (6, 3, 4, 5, 4)},
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# Durga — Sa Re Ma Pa Dha
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"durga": {"intervals": (4, 5, 4, 4, 5)},
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# Bhairavi pentatonic — Sa komal-Re Ma Pa komal-Ni
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"bhairavi pentatonic": {"intervals": (2, 7, 4, 2, 7)},
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},
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],
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}
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# ── Arabic maqam system ───────────────────────────────────────────────────
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# Arabic maqam uses quarter-tones with specific JI ratios, NOT equal
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# 24-TET divisions. The neutral intervals (quarter-flat, quarter-sharp)
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# are based on ratios involving the 11th partial, as theorized by
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# Zalzal (8th century Baghdad). The quarter-flat E in Rast is 27/22,
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# not simply halfway between Eb and E.
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#
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# 24 positions per octave, but with unequal JI spacing.
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# Ordered from La (=A) to match Western index positions.
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# Maqam JI ratios from Do (C). Based on traditional practice:
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# - Standard JI intervals for the 12 chromatic positions
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# - Zalzalian ratios (11-limit) for the quarter-tone positions
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_MAQAM_RATIOS_FROM_DO = [
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Fraction(1, 1), # 0: Do — unison
|
||
Fraction(33, 32), # 1: Do↑ — quarter-sharp (~53¢, 33rd harmonic)
|
||
Fraction(16, 15), # 2: Reb — JI minor 2nd
|
||
Fraction(12, 11), # 3: Re↓ — Zalzalian neutral 2nd (~151¢)
|
||
Fraction(9, 8), # 4: Re — major whole tone
|
||
Fraction(11, 9) * Fraction(1, 1), # 5: Re↑ — undecimal (~347¢... too high)
|
||
Fraction(6, 5), # 6: Mib — JI minor 3rd
|
||
Fraction(27, 22), # 7: Mi↓ — Zalzalian neutral 3rd (~355¢) THE Rast note
|
||
Fraction(5, 4), # 8: Mi — JI major 3rd
|
||
Fraction(4, 3), # 9: Fa — perfect 4th
|
||
Fraction(11, 8), # 10: Fa↑ — undecimal tritone (~551¢)
|
||
Fraction(45, 32), # 11: Fa# — augmented 4th
|
||
Fraction(22, 15), # 12: Sol↓ — neutral (~663¢... adjusted)
|
||
Fraction(3, 2), # 13: Sol — perfect 5th
|
||
Fraction(99, 64), # 14: Sol↑ — quarter-sharp 5th
|
||
Fraction(8, 5), # 15: Lab — JI minor 6th
|
||
Fraction(18, 11), # 16: La↓ — Zalzalian neutral 6th
|
||
Fraction(5, 3), # 17: La — JI major 6th
|
||
Fraction(27, 16), # 18: La↑/Sib↓ — Pythagorean major 6th
|
||
Fraction(16, 9), # 19: Sib — Pythagorean minor 7th
|
||
Fraction(11, 6), # 20: Si↓ — undecimal neutral 7th
|
||
Fraction(15, 8), # 21: Si — JI major 7th
|
||
Fraction(243, 128), # 22: Si↑ — Pythagorean major 7th
|
||
Fraction(2, 1) * Fraction(33, 64), # 23: near-octave (~1049¢)
|
||
]
|
||
|
||
# Ratios directly from La (A=1/1), each position defined explicitly.
|
||
# Standard JI intervals for chromatic positions, Zalzalian (11-limit)
|
||
# ratios for the quarter-tone positions.
|
||
MAQAM_RATIOS = [
|
||
1.0, # 0: La — A (unison)
|
||
float(Fraction(256, 243)), # 1: La↑ — Pythagorean comma up
|
||
float(Fraction(16, 15)), # 2: Sib — Bb (JI minor 2nd)
|
||
float(Fraction(12, 11)), # 3: Si↓ — B quarter-flat (Zalzalian)
|
||
float(Fraction(9, 8)), # 4: Si — B (major 2nd)
|
||
float(Fraction(6, 5)), # 5: Do — C (minor 3rd from A)
|
||
float(Fraction(11, 9)), # 6: Do↑ — C quarter-sharp (undecimal)
|
||
float(Fraction(5, 4)), # 7: Reb — Db (major 3rd from A...= JI Db)
|
||
float(Fraction(9, 7)), # 8: Re↓ — D quarter-flat (septimal)
|
||
float(Fraction(4, 3)), # 9: Re — D (perfect 4th from A)
|
||
float(Fraction(11, 8)), # 10: Re↑ — D quarter-sharp (undecimal)
|
||
float(Fraction(45, 32)), # 11: Mib — Eb (augmented 4th from A)
|
||
float(Fraction(6, 5) * Fraction(27, 22)), # 12: Mi↓ — E quarter-flat (Do × 27/22)
|
||
float(Fraction(3, 2)), # 13: Mi — E (perfect 5th from A)
|
||
float(Fraction(8, 5)), # 14: Fa — F (minor 6th from A)
|
||
float(Fraction(18, 11)), # 15: Fa↑ — F quarter-sharp (Zalzalian)
|
||
float(Fraction(5, 3)), # 16: Fa# — F# (major 6th from A)
|
||
float(Fraction(27, 16)), # 17: Sol↓ — G quarter-flat
|
||
float(Fraction(16, 9)), # 18: Sol — G (minor 7th from A)
|
||
float(Fraction(11, 6)), # 19: Sol↑ — G quarter-sharp (undecimal)
|
||
float(Fraction(15, 8)), # 20: Lab — Ab (major 7th from A)
|
||
float(Fraction(27, 14)), # 21: La↓ — A quarter-flat (septimal)
|
||
float(Fraction(243, 128)), # 22: La½b — near-octave
|
||
float(Fraction(2, 1) * Fraction(256, 257)), # 23: La♮ — near-octave
|
||
]
|
||
TONES_ARABIC_24 = [
|
||
("La",), # 0 — A
|
||
("La↑",), # 1 — A quarter-sharp
|
||
("Sib",), # 2 — Bb
|
||
("Si↓",), # 3 — B quarter-flat
|
||
("Si",), # 4 — B
|
||
("Do",), # 5 — C
|
||
("Do↑",), # 6 — C quarter-sharp
|
||
("Reb",), # 7 — Db
|
||
("Re↓",), # 8 — D quarter-flat
|
||
("Re",), # 9 — D
|
||
("Re↑",), # 10 — D quarter-sharp
|
||
("Mib",), # 11 — Eb
|
||
("Mi↓",), # 12 — E quarter-flat
|
||
("Mi",), # 13 — E
|
||
("Fa",), # 14 — F
|
||
("Fa↑",), # 15 — F quarter-sharp
|
||
("Fa#",), # 16 — F#
|
||
("Sol↓",), # 17 — G quarter-flat
|
||
("Sol",), # 18 — G
|
||
("Sol↑",), # 19 — G quarter-sharp
|
||
("Lab",), # 20 — Ab
|
||
("La↓",), # 21 — A quarter-flat
|
||
("La½b",), # 22 — between Ab and A (rarely used)
|
||
("La♮",), # 23 — enharmonic A (rarely used)
|
||
]
|
||
|
||
DEGREES_ARABIC_24 = [
|
||
("tonic", ()),
|
||
("second", ()),
|
||
("third", ()),
|
||
("fourth", ()),
|
||
("fifth", ()),
|
||
("sixth", ()),
|
||
("seventh", ()),
|
||
("octave", ()),
|
||
]
|
||
|
||
# 24-TET maqam scales with true quarter-tone intervals.
|
||
# Each step = 1 quarter-tone (50 cents). A 12-TET semitone = 2 steps.
|
||
ARABIC_24_SCALES = {
|
||
"chromatic": (24, {}),
|
||
"maqam": [
|
||
7,
|
||
{
|
||
# Rast — the foundational maqam. E and B are quarter-flat.
|
||
# Do Re Mi↓ Fa Sol La Si↓ Do
|
||
"rast": {"intervals": (4, 3, 3, 4, 4, 3, 3)},
|
||
# Bayati — starts on D with quarter-flat 2nd.
|
||
# Re Mi↓ Fa Sol La Sib Do Re
|
||
"bayati": {"intervals": (3, 3, 4, 4, 2, 4, 4)},
|
||
# Saba — similar to Bayati with flattened 4th
|
||
"saba": {"intervals": (3, 3, 2, 6, 2, 4, 4)},
|
||
# Sikah — starts on E quarter-flat
|
||
"sikah": {"intervals": (3, 4, 3, 4, 3, 4, 3)},
|
||
# Hijaz — augmented 2nd (6 quarter-tones) between 2nd and 3rd
|
||
"hijaz": {"intervals": (2, 6, 2, 4, 2, 4, 4)},
|
||
# Nahawand (≈ harmonic minor)
|
||
"nahawand": {"intervals": (4, 2, 4, 4, 2, 6, 2)},
|
||
# Ajam (≈ major)
|
||
"ajam": {"intervals": (4, 4, 2, 4, 4, 4, 2)},
|
||
# Kurd (≈ Phrygian)
|
||
"kurd": {"intervals": (2, 4, 4, 4, 2, 4, 4)},
|
||
# Nikriz — augmented 2nd between 3rd and 4th
|
||
"nikriz": {"intervals": (4, 2, 6, 2, 4, 2, 4)},
|
||
# Jiharkah — like Rast but with natural B
|
||
"jiharkah": {"intervals": (4, 4, 2, 4, 4, 3, 3)},
|
||
},
|
||
],
|
||
}
|
||
|
||
# ── 5-TET Gamelan Slendro ────────────────────────────────────────────────────
|
||
# Slendro is a 5-tone equal temperament — each step is 240 cents.
|
||
# The actual tuning varies between gamelans (each set is unique), but
|
||
# 5-TET is the theoretical ideal that all slendro tunings approximate.
|
||
# Ordered from nem (≈A) to loosely match Western indexing.
|
||
TONES_SLENDRO = [
|
||
("nem",), # 0 — 6 (≈A)
|
||
("ji",), # 1 — 1 (≈C)
|
||
("ro",), # 2 — 2 (≈D)
|
||
("lu",), # 3 — 3 (≈F)
|
||
("mo",), # 4 — 5 (≈G)
|
||
]
|
||
|
||
DEGREES_SLENDRO = [
|
||
("nem", ()), ("ji", ()), ("ro", ()), ("lu", ()), ("mo", ()),
|
||
]
|
||
|
||
SLENDRO_SCALES = {
|
||
"chromatic": (5, {}),
|
||
"pentatonic": [5, {
|
||
# The full slendro IS the pentatonic — all 5 tones
|
||
"slendro": {"intervals": (1, 1, 1, 1, 1)},
|
||
}],
|
||
}
|
||
|
||
# ── 9-TET Gamelan Pelog ─────────────────────────────────────────────────────
|
||
# Pelog uses 7 tones from a roughly 9-step division of the octave.
|
||
# 9-TET (133 cents/step) approximates the unequal pelog intervals.
|
||
# The 3 pathet (modes) select 5 tones from the 7.
|
||
TONES_PELOG = [
|
||
("nem",), # 0 — 6
|
||
("pi",), # 1 — 7
|
||
("ji",), # 2 — 1
|
||
("ro",), # 3 — 2
|
||
("lu",), # 4 — 3
|
||
("pat",), # 5 — 4
|
||
("barang",), # 6 — complementary
|
||
("mo",), # 7 — 5
|
||
("nem+",), # 8 — auxiliary
|
||
]
|
||
|
||
DEGREES_PELOG = [
|
||
("nem", ()), ("pi", ()), ("ji", ()), ("ro", ()),
|
||
("lu", ()), ("pat", ()), ("barang", ()), ("mo", ()), ("nem+", ()),
|
||
]
|
||
|
||
PELOG_SCALES = {
|
||
"chromatic": (9, {}),
|
||
"heptatonic": [7, {
|
||
# Full pelog — 7 tones from 9 steps
|
||
"pelog": {"intervals": (1, 2, 1, 1, 2, 1, 1)},
|
||
}],
|
||
"pentatonic": [5, {
|
||
# Pathet nem — the most common mode
|
||
"pelog nem": {"intervals": (1, 2, 2, 2, 2)},
|
||
# Pathet lima
|
||
"pelog lima": {"intervals": (1, 2, 2, 1, 3)},
|
||
# Pathet barang
|
||
"pelog barang": {"intervals": (2, 1, 2, 2, 2)},
|
||
}],
|
||
}
|
||
|
||
# ── 7-TET Thai classical ────────────────────────────────────────────────────
|
||
# Thai classical music divides the octave into 7 exactly equal steps
|
||
# (~171 cents each). This is unique — no Western equivalent exists.
|
||
# The 7 tones are numbered 1-7 in Thai theory.
|
||
TONES_THAI = [
|
||
("do",), # 0 — 1st degree
|
||
("re",), # 1 — 2nd
|
||
("mi",), # 2 — 3rd
|
||
("fa",), # 3 — 4th
|
||
("sol",), # 4 — 5th
|
||
("la",), # 5 — 6th
|
||
("si",), # 6 — 7th
|
||
]
|
||
|
||
DEGREES_THAI = [
|
||
("thang 1", ()), ("thang 2", ()), ("thang 3", ()),
|
||
("thang 4", ()), ("thang 5", ()), ("thang 6", ()), ("thang 7", ()),
|
||
]
|
||
|
||
THAI_SCALES = {
|
||
"chromatic": (7, {}),
|
||
"pentatonic": [5, {
|
||
# The standard Thai pentatonic — 5 of 7 equal steps
|
||
"thai pentatonic": {"intervals": (1, 1, 2, 1, 2)},
|
||
# Alternate selection
|
||
"thai pentatonic 2": {"intervals": (2, 1, 1, 2, 1)},
|
||
}],
|
||
"heptatonic": [7, {
|
||
# The full 7-TET scale
|
||
"thai": {"intervals": (1, 1, 1, 1, 1, 1, 1)},
|
||
}],
|
||
}
|
||
|
||
# ── 53-TET Turkish makam (Arel-Ezgi-Uzdilek) ───────────────────────────────
|
||
# The gold standard for Turkish music theory. 53-TET has nearly perfect
|
||
# fifths (31 steps = 701.89 cents vs 701.96 just) and excellent thirds.
|
||
# A comma (1 step) = 22.6 cents. The basic intervals:
|
||
# Bakiye (B) = 4 commas ≈ 90 cents (like a limma)
|
||
# Küçük mücenneb (S) = 5 commas ≈ 113 cents
|
||
# Büyük mücenneb (K) = 8 commas ≈ 181 cents
|
||
# Tanini (T) = 9 commas ≈ 204 cents (like a whole tone)
|
||
TONES_TURKISH = [
|
||
("La",), # 0 — A (Dügah reference)
|
||
("La+1",), # 1
|
||
("La+2",), # 2
|
||
("La+3",), # 3
|
||
("Sib",), # 4 — Bb (4 commas from A)
|
||
("Sib+1",), # 5
|
||
("Sib+2",), # 6
|
||
("Sib+3",), # 7
|
||
("Sib+4",), # 8
|
||
("Si",), # 9 — B
|
||
("Si+1",), # 10
|
||
("Si+2",), # 11
|
||
("Si+3",), # 12
|
||
("Do",), # 13 — C (Rast)
|
||
("Do+1",), # 14
|
||
("Do+2",), # 15
|
||
("Do+3",), # 16
|
||
("Do+4",), # 17
|
||
("Reb",), # 18 — Db
|
||
("Reb+1",), # 19
|
||
("Reb+2",), # 20
|
||
("Reb+3",), # 21
|
||
("Re",), # 22 — D (Dügah)
|
||
("Re+1",), # 23
|
||
("Re+2",), # 24
|
||
("Re+3",), # 25
|
||
("Re+4",), # 26
|
||
("Mib",), # 27 — Eb
|
||
("Mib+1",), # 28
|
||
("Mib+2",), # 29
|
||
("Mib+3",), # 30
|
||
("Mi",), # 31 — E (Segah)
|
||
("Mi+1",), # 32
|
||
("Mi+2",), # 33
|
||
("Mi+3",), # 34
|
||
("Mi+4",), # 35
|
||
("Fa",), # 36 — F
|
||
("Fa+1",), # 37
|
||
("Fa+2",), # 38
|
||
("Fa+3",), # 39
|
||
("Fa#",), # 40 — F#
|
||
("Fa#+1",), # 41
|
||
("Fa#+2",), # 42
|
||
("Fa#+3",), # 43
|
||
("Sol",), # 44 — G (Neva)
|
||
("Sol+1",), # 45
|
||
("Sol+2",), # 46
|
||
("Sol+3",), # 47
|
||
("Lab",), # 48 — Ab
|
||
("Lab+1",), # 49
|
||
("Lab+2",), # 50
|
||
("Lab+3",), # 51
|
||
("Lab+4",), # 52
|
||
]
|
||
|
||
DEGREES_TURKISH = [(f"perde {i+1}", ()) for i in range(53)]
|
||
|
||
# Turkish makam scales in 53-TET commas.
|
||
# T=9 commas (whole tone), S=5 (small), K=8 (large), B=4 (limma)
|
||
TURKISH_SCALES = {
|
||
"chromatic": (53, {}),
|
||
"makam": [
|
||
7,
|
||
{
|
||
# Rast — the foundational makam. Uses segah (≈ neutral 3rd)
|
||
# T + T + S + T + T + T + S = 9+9+5+9+9+9+4 = 53...
|
||
# Actually: 9+8+5+9+9+8+5 = 53
|
||
"rast": {"intervals": (9, 8, 5, 9, 9, 8, 5)},
|
||
# Nihavend (≈ harmonic minor)
|
||
"nihavend": {"intervals": (9, 4, 9, 9, 4, 13, 5)},
|
||
# Hicaz — the augmented 2nd makam
|
||
"hicaz": {"intervals": (5, 12, 5, 9, 4, 9, 9)},
|
||
# Ussak — one of the most common makams
|
||
"ussak": {"intervals": (8, 5, 9, 9, 8, 5, 9)},
|
||
# Huseyni
|
||
"huseyni": {"intervals": (8, 5, 9, 9, 5, 8, 9)},
|
||
# Kurdi (≈ Phrygian)
|
||
"kurdi": {"intervals": (4, 9, 9, 9, 4, 9, 9)},
|
||
# Segah — starts on the neutral 3rd
|
||
"segah": {"intervals": (5, 9, 9, 8, 5, 9, 8)},
|
||
# Saba — descending differs from ascending
|
||
"saba": {"intervals": (8, 5, 4, 14, 4, 9, 9)},
|
||
# Hüzzam
|
||
"huzzam": {"intervals": (5, 9, 8, 5, 9, 8, 9)},
|
||
},
|
||
],
|
||
}
|
||
|
||
# ── 72-TET Carnatic (South Indian) ───────────────────────────────────────────
|
||
# The 72 melakarta system classifies all possible 7-note scales with
|
||
# fixed Sa and Pa. 72-TET (16.67 cents/step) captures the srutis used
|
||
# in Carnatic music with high precision. Each 12-TET semitone = 6 steps.
|
||
#
|
||
# Tone names: 12 swaras × 6 microtonal variants each.
|
||
# Main swaras at positions: Sa=0, Ri1=6, Ri2=12, Ga1=12, Ga2=18,
|
||
# Ma1=30, Ma2=36, Pa=42, Da1=48, Da2=54, Ni1=60, Ni2=66
|
||
TONES_CARNATIC = []
|
||
_SWARA_NAMES = [
|
||
"Sa", "atikomal Ri", "komal Ri", "shuddha Ri",
|
||
"Ri", "tivra Ri", "komal Ga", "atikomal Ga",
|
||
"Ga", "shuddha Ga", "tivra Ga", "antara Ga",
|
||
"komal Ma", "shuddha Ma", "Ma", "tivra shuddha Ma",
|
||
"ekashruti Ma", "chatushruti Ma", "tivra Ma", "atitivra Ma",
|
||
"prati Ma", "tivratara Ma", "atikomal Pa-", "komal Pa-",
|
||
"shuddha Pa-", "Pa-", "Pa-+1", "Pa-+2",
|
||
"Pa-+3", "Pa-+4", "Pa", "Pa+1",
|
||
"Pa+2", "Pa+3", "Pa+4", "Pa+5",
|
||
"komal Da", "atikomal Da", "Da-", "shuddha Da-",
|
||
"Da", "shuddha Da", "tivra Da", "atitivra Da",
|
||
"komal Ni", "atikomal Ni", "Ni-", "shuddha Ni-",
|
||
"Ni", "shuddha Ni", "tivra Ni", "chatushruti Ni",
|
||
"kakali Ni", "atikakali Ni",
|
||
]
|
||
# Generate 72 tone names: use standard names for the 12 main positions,
|
||
# numbered variants for the intermediates
|
||
for i in range(72):
|
||
main_pos = i // 6 # which semitone group (0-11)
|
||
micro = i % 6 # microtonal position within group
|
||
_base_names = ["Sa", "komal Ri", "Ri", "komal Ga", "Ga", "Ma",
|
||
"tivra Ma", "Pa", "komal Da", "Da", "komal Ni", "Ni"]
|
||
if micro == 0:
|
||
TONES_CARNATIC.append((_base_names[main_pos],))
|
||
else:
|
||
TONES_CARNATIC.append((f"{_base_names[main_pos]}+{micro}",))
|
||
|
||
DEGREES_CARNATIC = [(f"swara {i+1}", ()) for i in range(72)]
|
||
|
||
# A selection of important melakartas in 72-TET intervals.
|
||
# Each step = 1/72 of an octave ≈ 16.67 cents.
|
||
CARNATIC_SCALES = {
|
||
"chromatic": (72, {}),
|
||
"melakarta": [
|
||
7,
|
||
{
|
||
# Kanakangi (melakarta 1) — Sa Ri1 Ga1 Ma1 Pa Da1 Ni1
|
||
"kanakangi": {"intervals": (6, 6, 18, 12, 6, 6, 18)},
|
||
# Shankarabharanam (melakarta 29) — Sa Ri2 Ga3 Ma1 Pa Da2 Ni3
|
||
# The Carnatic equivalent of the major scale
|
||
"shankarabharanam": {"intervals": (12, 12, 6, 12, 12, 12, 6)},
|
||
# Kalyani (melakarta 65) — Sa Ri2 Ga3 Ma2 Pa Da2 Ni3
|
||
# Carnatic Lydian equivalent
|
||
"kalyani": {"intervals": (12, 12, 12, 6, 12, 12, 6)},
|
||
# Kharaharapriya (melakarta 22) — Sa Ri2 Ga2 Ma1 Pa Da2 Ni2
|
||
# Carnatic Dorian equivalent
|
||
"kharaharapriya": {"intervals": (12, 6, 12, 12, 12, 6, 12)},
|
||
# Hanumathodi (melakarta 8) — Sa Ri1 Ga2 Ma1 Pa Da1 Ni2
|
||
# Carnatic Phrygian equivalent
|
||
"hanumathodi": {"intervals": (6, 12, 12, 12, 6, 12, 12)},
|
||
# Natabhairavi (melakarta 20) — Sa Ri2 Ga2 Ma1 Pa Da1 Ni2
|
||
# Natural minor equivalent
|
||
"natabhairavi": {"intervals": (12, 6, 12, 12, 6, 12, 12)},
|
||
# Mayamalavagowla (melakarta 15) — Sa Ri1 Ga3 Ma1 Pa Da1 Ni3
|
||
# The "lesson scale" — first raga taught to students
|
||
"mayamalavagowla": {"intervals": (6, 18, 6, 12, 6, 18, 6)},
|
||
# Simhendramadhyamam (melakarta 57) — Sa Ri2 Ga3 Ma2 Pa Da1 Ni3
|
||
"simhendramadhyamam": {"intervals": (12, 12, 12, 6, 6, 18, 6)},
|
||
# Charukesi (melakarta 26) — Sa Ri2 Ga3 Ma1 Pa Da1 Ni2
|
||
"charukesi": {"intervals": (12, 12, 6, 12, 6, 12, 12)},
|
||
# Harikambhoji (melakarta 28) — Sa Ri2 Ga3 Ma1 Pa Da2 Ni2
|
||
# Mixolydian equivalent
|
||
"harikambhoji": {"intervals": (12, 12, 6, 12, 12, 6, 12)},
|
||
},
|
||
],
|
||
}
|
||
|
||
# Arabic maqam scales (12-TET approximations).
|
||
# True maqam uses quarter-tones; these are the closest 12-tone equivalents.
|
||
ARABIC_SCALES = {
|
||
12: {
|
||
"chromatic": (12, {}),
|
||
"maqam": [
|
||
7,
|
||
{
|
||
# Ajam = Western major
|
||
"ajam": {"intervals": (2, 2, 1, 2, 2, 2, 1)},
|
||
# Nahawand = Western harmonic minor
|
||
"nahawand": {"intervals": (2, 1, 2, 2, 1, 3, 1)},
|
||
# Kurd = Western Phrygian
|
||
"kurd": {"intervals": (1, 2, 2, 2, 1, 2, 2)},
|
||
# Hijaz — augmented 2nd between 2nd and 3rd degrees
|
||
"hijaz": {"intervals": (1, 3, 1, 2, 1, 2, 2)},
|
||
# Nikriz — augmented 2nd between 3rd and 4th
|
||
"nikriz": {"intervals": (2, 1, 3, 1, 2, 1, 2)},
|
||
# Bayati (12-TET approx) — true bayati has quarter-flat 2nd
|
||
"bayati": {"intervals": (1, 2, 2, 2, 1, 2, 2)},
|
||
# Rast (12-TET approx) — true rast has quarter-flat 3rd and 7th
|
||
"rast": {"intervals": (2, 1, 2, 2, 2, 1, 2)},
|
||
# Saba (12-TET approx) — true saba has quarter-flat 2nd
|
||
"saba": {"intervals": (1, 2, 1, 3, 1, 2, 2)},
|
||
# Sikah (12-TET approx) — true sikah starts on quarter-flat
|
||
"sikah": {"intervals": (1, 2, 2, 2, 1, 2, 2)},
|
||
# Jiharkah
|
||
"jiharkah": {"intervals": (2, 2, 1, 2, 2, 1, 2)},
|
||
},
|
||
],
|
||
}
|
||
}
|
||
|
||
# Japanese pentatonic scales.
|
||
JAPANESE_SCALES = {
|
||
12: {
|
||
"chromatic": (12, {}),
|
||
"pentatonic": [
|
||
5,
|
||
{
|
||
# Hirajoshi — the most well-known Japanese scale
|
||
# C D Eb G Ab
|
||
"hirajoshi": {"intervals": (2, 1, 4, 1, 4)},
|
||
# In (Miyako-bushi) — used in koto music
|
||
# C Db F G Ab
|
||
"in": {"intervals": (1, 4, 2, 1, 4)},
|
||
# Yo — folk music scale
|
||
# C D F G Bb
|
||
"yo": {"intervals": (2, 3, 2, 3, 2)},
|
||
# Iwato — dark, dissonant pentatonic
|
||
# C Db F Gb Bb
|
||
"iwato": {"intervals": (1, 4, 1, 4, 2)},
|
||
# Kumoi — similar to minor pentatonic
|
||
# C D Eb G A
|
||
"kumoi": {"intervals": (2, 1, 4, 2, 3)},
|
||
# Insen — modern Japanese scale
|
||
# C Db F G Bb
|
||
"insen": {"intervals": (1, 4, 2, 3, 2)},
|
||
},
|
||
],
|
||
"heptatonic": [
|
||
7,
|
||
{
|
||
# Ritsu — gagaku court music scale
|
||
# C D Eb F G A Bb (= Dorian)
|
||
"ritsu": {"intervals": (2, 1, 2, 2, 2, 1, 2)},
|
||
# Ryo — gagaku court music scale
|
||
# C D E F# G A B (= Lydian)
|
||
"ryo": {"intervals": (2, 2, 2, 1, 2, 2, 1)},
|
||
},
|
||
],
|
||
}
|
||
}
|
||
|
||
# Blues and pentatonic scales — foundational to American music.
|
||
BLUES_SCALES = {
|
||
12: {
|
||
"chromatic": (12, {}),
|
||
"pentatonic": [
|
||
5,
|
||
{
|
||
# Major pentatonic — C D E G A
|
||
"major pentatonic": {"intervals": (2, 2, 3, 2, 3)},
|
||
# Minor pentatonic — C Eb F G Bb
|
||
"minor pentatonic": {"intervals": (3, 2, 2, 3, 2)},
|
||
},
|
||
],
|
||
"hexatonic": [
|
||
6,
|
||
{
|
||
# Blues scale — C Eb F F# G Bb
|
||
"blues": {"intervals": (3, 2, 1, 1, 3, 2)},
|
||
# Major blues — C D D# E G A
|
||
"major blues": {"intervals": (2, 1, 1, 3, 2, 3)},
|
||
},
|
||
],
|
||
"heptatonic": [
|
||
7,
|
||
{
|
||
# Mixolydian (dominant blues sound) — C D E F G A Bb
|
||
"dominant": {"intervals": (2, 2, 1, 2, 2, 1, 2)},
|
||
# Dorian (minor blues/jazz) — C D Eb F G A Bb
|
||
"minor": {"intervals": (2, 1, 2, 2, 2, 1, 2)},
|
||
},
|
||
],
|
||
}
|
||
}
|
||
|
||
# Javanese gamelan scales — 12-TET approximations.
|
||
# True gamelan tuning varies between ensembles and does not conform
|
||
# to equal temperament. These approximations capture the melodic
|
||
# character of the scales.
|
||
GAMELAN_SCALES = {
|
||
12: {
|
||
"chromatic": (12, {}),
|
||
"pentatonic": [
|
||
5,
|
||
{
|
||
# Slendro — roughly equal 5-tone division of the octave
|
||
# Approximated as: C D F G Bb
|
||
"slendro": {"intervals": (2, 3, 2, 3, 2)},
|
||
# Pelog pathet nem — C Db E F G (approx)
|
||
"pelog nem": {"intervals": (1, 3, 1, 2, 5)},
|
||
# Pelog pathet barang — C Db E F# B (approx)
|
||
"pelog barang": {"intervals": (1, 3, 3, 4, 1)},
|
||
# Pelog pathet lima — C Db E F Ab (approx)
|
||
"pelog lima": {"intervals": (1, 3, 1, 3, 4)},
|
||
},
|
||
],
|
||
"heptatonic": [
|
||
7,
|
||
{
|
||
# Full pelog — all 7 tones: C Db E F G Ab B (approx)
|
||
"pelog": {"intervals": (1, 3, 1, 2, 1, 3, 1)},
|
||
},
|
||
],
|
||
}
|
||
}
|
||
|
||
SYSTEMS = NotImplemented
|
||
|
||
# Modes are rotations of the major scale pattern.
|
||
# Each mode's offset is its position in the major scale.
|
||
_MODES = {
|
||
"ionian": 0,
|
||
"dorian": 1,
|
||
"phrygian": 2,
|
||
"lydian": 3,
|
||
"mixolydian": 4,
|
||
"aeolian": 5,
|
||
"locrian": 6,
|
||
}
|
||
|
||
for mode_name, offset in _MODES.items():
|
||
SCALES[12]["heptatonic"][1][mode_name] = {
|
||
"major": True, "hemitonic": True, "offset": offset
|
||
}
|