v0.33.0: Microtonal systems, historical tuning, Bohlen-Pierce

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

CHANGELOG.md

@@ -2,6 +2,33 @@
 
 All notable changes to PyTheory are documented here.
 
+## 0.33.0
+
+- **Non-12-TET support** — `TET(n)` factory creates any equal temperament
+- **11 microtonal systems:**
+  - `"shruti"` (22-TET Indian, 10 thaats with proper shruti intervals)
+  - `"maqam"` (24-TET Arabic, quarter-tone Rast/Bayati/Hijaz + 7 more)
+  - `"slendro"` (5-TET gamelan), `"pelog"` (9-TET gamelan with 3 pathet)
+  - `"thai"` (7-TET, 171 cents/step)
+  - `"makam"` (53-TET Turkish Arel-Ezgi-Uzdilek, 9 makams)
+  - `"carnatic"` (72-TET, 10 melakartas)
+  - `"19-tet"`, `"31-tet"` (historical Western)
+  - `"bohlen-pierce"` (13 divisions of the tritave 3:1 — non-octave!)
+- **Just intonation** — `temperament="just"` for pure 5-limit ratios
+- **Historical pitch** — `Score(reference_pitch=415.0)` for Baroque A=415
+- **`Score(system=, temperament=, reference_pitch=)`** flows through to all playback
+- Per-system `c_index` and `period` replace hardcoded constants
+- Fixed all hardcoded `12`s in tone arithmetic
+- Song #22: Greensleeves (Renaissance lute, meantone, A=415)
+- 22 new microtonal tests (819 total)
+
+## 0.32.1
+
+- `Tone("X")` now raises `ValueError` immediately instead of silently accepting invalid names (#39)
+- Support enharmonic spellings: `Cb`, `Fb`, `E#`, `B#` resolve correctly (#40)
+- Support double sharps (`C##`, `Fx`) and double flats (`Dbb`) via semitone arithmetic (#41)
+- Accept unicode music symbols: `♯` `♭` `𝄪` `𝄫`
+
 ## 0.32.0
 
 - **8 new synth engine features:**

examples/songs.py

@@ -1204,6 +1204,37 @@ def cinematic_showcase():
     play_song(score, "Cinematic Showcase — A minor")
 
 
+def greensleeves():
+    """Greensleeves — Renaissance lute, meantone tuning, A=415 Hz."""
+    score = Score("3/4", bpm=120, temperament="meantone", reference_pitch=415.0)
+
+    lute = score.part("lute", instrument="acoustic_guitar",
+                      reverb=0.3, reverb_type="taj_mahal")
+
+    melody = [
+        ("A4", 1.0, 80),
+        ("C5", 2.0, 85),   ("D5", 1.0, 80),
+        ("E5", 3.0, 90),
+        ("F5", 1.0, 75),   ("E5", 2.0, 85),
+        ("D5", 1.0, 80),
+        ("B4", 3.0, 85),
+        ("G4", 1.0, 70),   ("B4", 2.0, 80),
+        ("C5", 1.0, 75),
+        ("A4", 3.0, 85),
+        ("A4", 1.0, 70),   ("A4", 2.0, 75),
+        ("G#4", 1.0, 70),
+        ("A4", 2.0, 80),   ("B4", 1.0, 75),
+        ("G4", 3.0, 85),
+        ("E4", 1.0, 70),
+        ("A4", 3.0, 90),
+    ]
+
+    for note, dur, vel in melody:
+        lute.add(note, dur, velocity=vel)
+
+    play_song(score, "Greensleeves — Renaissance Lute (Meantone, A=415)")
+
+
 SONGS = {
     "1": ("Bossa Nova in A minor", bossa_nova_girl),
     "2": ("Bebop in Bb major", bebop_in_bb),
@@ -1226,6 +1257,7 @@ SONGS = {
     "19": ("Dance Party at the Reitz House", dance_party),
     "20": ("Temple Bell (Japanese)", temple_bell),
     "21": ("Cinematic Showcase (Orchestral)", cinematic_showcase),
+    "22": ("Greensleeves (Renaissance Lute)", greensleeves),
 }
 
 if __name__ == "__main__":
@@ -1239,7 +1271,7 @@ if __name__ == "__main__":
             print(f"    {key:>2}. {name}")
 
         print()
-        choice = input("  Pick a song (1-21, or 'all'): ").strip()
+        choice = input("  Pick a song (1-22, or 'all'): ").strip()
         print()
 
         if choice == "all":

pyproject.toml

@@ -1,6 +1,6 @@
 [project]
 name = "pytheory"
-version = "0.32.0"
+version = "0.33.0"
 description = "Music Theory for Humans"
 readme = "README.md"
 license = "MIT"

pytheory/__init__.py

@@ -1,9 +1,9 @@
 """PyTheory: Music Theory for Humans."""
 
-__version__ = "0.32.0"
+__version__ = "0.33.0"
 
 from .tones import Tone, Interval
-from .systems import System, SYSTEMS
+from .systems import System, SYSTEMS, TET
 from .scales import TonedScale, Key, PROGRESSIONS
 from .chords import Chord, Fretboard, analyze_progression
 from .charts import CHARTS, Fingering, charts_for_fretboard
@@ -21,7 +21,7 @@ Scale = TonedScale
 __all__ = [
     "Tone", "Note", "Interval", "Scale", "TonedScale", "Key",
     "PROGRESSIONS", "Chord", "Fretboard", "Fingering", "analyze_progression",
-    "System", "SYSTEMS", "CHARTS", "charts_for_fretboard",
+    "System", "SYSTEMS", "TET", "CHARTS", "charts_for_fretboard",
     "play", "save", "save_midi", "play_progression", "play_pattern",
     "play_score", "Synth", "Envelope",
     "Duration", "TimeSignature", "RhythmNote", "Rest", "Score", "Part",

pytheory/_statics.py

@@ -6,10 +6,42 @@ REFERENCE_A = 440
 # Scientific pitch notation changes octave at C, not A, so this offset
 # is needed for all octave arithmetic.
 C_INDEX = 3
+def _create_just_intonation_scale(n):
+    """5-limit just intonation ratios for 12-tone systems.
+
+    These are the pure frequency ratios derived from the harmonic series —
+    the way intervals "want" to sound before equal temperament imposed
+    compromise. Each ratio is mathematically exact: a perfect fifth is
+    exactly 3/2, a major third is exactly 5/4.
+
+    For non-12 systems, falls back to equal temperament.
+    """
+    from fractions import Fraction
+    if n != 12:
+        return scales.create_edo_scale(n)
+    # Standard 5-limit JI ratios (A-based: A=1/1)
+    ratios = [
+        Fraction(1, 1),       # A  — unison
+        Fraction(16, 15),     # A# — minor second
+        Fraction(9, 8),       # B  — major second
+        Fraction(6, 5),       # C  — minor third
+        Fraction(5, 4),       # C# — major third
+        Fraction(4, 3),       # D  — perfect fourth
+        Fraction(45, 32),     # D# — augmented fourth
+        Fraction(3, 2),       # E  — perfect fifth
+        Fraction(8, 5),       # F  — minor sixth
+        Fraction(5, 3),       # F# — major sixth
+        Fraction(9, 5),       # G  — minor seventh
+        Fraction(15, 8),      # G# — major seventh
+        Fraction(2, 1),       # A  — octave
+    ]
+    return [float(r) for r in ratios]
+
 TEMPERAMENTS = {
     "equal": scales.create_edo_scale,
     "pythagorean": scales.create_pythagorean_scale,
     "meantone": scales.create_quarter_comma_meantone_scale,
+    "just": _create_just_intonation_scale,
 }
 
 TONES = {
@@ -220,6 +252,442 @@ INDIAN_SCALES = {
     }
 }
 
+# ── 22-shruti Indian system ──────────────────────────────────────────────────
+# The shruti system divides the octave into 22 microtonal steps, capturing
+# the melodic nuances that 12-TET cannot represent. Each of the 7 swaras
+# has multiple shruti positions (e.g. komal Re at shruti 2, shuddha Re at
+# shruti 4). 22-TET is the standard equal-tempered approximation.
+#
+# Ordered from Dha (=A) to match Western index positions (Sa at index 5 ≈ C).
+TONES_SHRUTI = [
+    ("Dha",),               #  0 — A  — shuddha dhaivat (reference = 440 Hz)
+    ("atikomal Ni",),       #  1 — shruti between Dha and komal Ni
+    ("komal Ni",),          #  2 — Bb — komal nishad
+    ("shuddha Ni",),        #  3 — between komal Ni and Ni
+    ("Ni",),                #  4 — B  — shuddha (kakali) nishad
+    ("Sa",),                #  5 — C  — shadja (tonic)
+    ("atikomal Re",),       #  6 — shruti between Sa and komal Re
+    ("komal Re",),          #  7 — Db — komal rishabh
+    ("shuddha Re",),        #  8 — between komal Re and Re
+    ("Re",),                #  9 — D  — chatushruti rishabh
+    ("atikomal Ga",),       # 10 — shruti between Re and komal Ga
+    ("komal Ga",),          # 11 — Eb — komal gandhar
+    ("Ga",),                # 12 — E  — antara gandhar
+    ("tivra Ga",),          # 13 — shruti between Ga and Ma
+    ("Ma",),                # 14 — F  — shuddha madhyam
+    ("ekashruti Ma",),      # 15 — shruti between Ma and tivra Ma
+    ("tivra Ma",),          # 16 — F# — tivra madhyam
+    ("atitivra Ma",),       # 17 — shruti between tivra Ma and Pa
+    ("Pa",),                # 18 — G  — pancham
+    ("atikomal Dha",),      # 19 — shruti between Pa and komal Dha
+    ("komal Dha",),         # 20 — Ab — komal dhaivat
+    ("shuddha Dha",),       # 21 — shruti between komal Dha and Dha
+]
+
+DEGREES_SHRUTI = [
+    ("shadja", ("bilawal",)),       # Sa — tonic
+    ("rishabh", ("marwa",)),        # Re
+    ("gandhar", ("bhairavi",)),     # Ga
+    ("madhyam", ("kalyan",)),       # Ma
+    ("pancham", ("kafi",)),         # Pa
+    ("dhaivat", ("asavari",)),      # Dha
+    ("nishad", ("khamaj",)),        # Ni
+    ("shadja", ()),                 # Sa (octave)
+]
+
+# 22-shruti thaat scales with proper microtonal intervals.
+# Each interval is counted in shrutis (22-TET steps).
+# Compare to the 12-TET approximations in INDIAN_SCALES which lose
+# the distinction between 2-shruti and 3-shruti steps.
+SHRUTI_SCALES = {
+    "chromatic": (22, {}),
+    "thaat": [
+        7,
+        {
+            # Bilawal (≈ Ionian) — Sa Re Ga Ma Pa Dha Ni
+            "bilawal": {"intervals": (4, 3, 2, 4, 4, 3, 2)},
+            # Khamaj (≈ Mixolydian) — Sa Re Ga Ma Pa Dha komal-Ni
+            "khamaj": {"intervals": (4, 3, 2, 4, 4, 1, 4)},
+            # Kafi (≈ Dorian) — Sa Re komal-Ga Ma Pa Dha komal-Ni
+            "kafi": {"intervals": (4, 2, 3, 4, 4, 1, 4)},
+            # Asavari (≈ Aeolian) — Sa Re komal-Ga Ma Pa komal-Dha komal-Ni
+            "asavari": {"intervals": (4, 2, 3, 4, 2, 3, 4)},
+            # Bhairavi (≈ Phrygian) — Sa komal-Re komal-Ga Ma Pa komal-Dha komal-Ni
+            "bhairavi": {"intervals": (2, 4, 3, 4, 2, 3, 4)},
+            # Bhairav — Sa komal-Re Ga Ma Pa komal-Dha Ni (unique to Indian music)
+            "bhairav": {"intervals": (2, 5, 2, 4, 2, 5, 2)},
+            # Kalyan (≈ Lydian) — Sa Re Ga tivra-Ma Pa Dha Ni
+            "kalyan": {"intervals": (4, 3, 4, 2, 4, 3, 2)},
+            # Marwa — Sa komal-Re Ga tivra-Ma Pa Dha Ni (unique)
+            "marwa": {"intervals": (2, 5, 4, 2, 4, 3, 2)},
+            # Poorvi — Sa komal-Re Ga tivra-Ma Pa komal-Dha Ni (unique)
+            "poorvi": {"intervals": (2, 5, 4, 2, 2, 5, 2)},
+            # Todi — Sa komal-Re komal-Ga tivra-Ma Pa komal-Dha Ni (unique)
+            "todi": {"intervals": (2, 4, 5, 2, 2, 5, 2)},
+        },
+    ],
+    "pentatonic": [
+        5,
+        {
+            # Bhupali (≈ major pentatonic) — Sa Re Ga Pa Dha
+            "bhupali": {"intervals": (4, 3, 6, 4, 5)},
+            # Malkauns — Sa komal-Ga Ma komal-Dha komal-Ni
+            "malkauns": {"intervals": (6, 3, 4, 5, 4)},
+            # Durga — Sa Re Ma Pa Dha
+            "durga": {"intervals": (4, 5, 4, 4, 5)},
+            # Bhairavi pentatonic — Sa komal-Re Ma Pa komal-Ni
+            "bhairavi pentatonic": {"intervals": (2, 7, 4, 2, 7)},
+        },
+    ],
+}
+
+# ── 24-TET Arabic maqam system ─────────────────────────────────────────────
+# Arabic maqam uses quarter-tones (half-flat, half-sharp). 24-TET captures
+# these intervals exactly. Each step = 50 cents (vs 100 in 12-TET).
+# The half-flat (♭½) is the defining sound of Arabic music — it's what
+# makes maqam Rast and Bayati sound distinctly Middle Eastern.
+#
+# Ordered from La (=A) to match Western index positions.
+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 = {

pytheory/play.py

@@ -1971,7 +1971,8 @@ def _render_notes_to_buf(notes, buf, samples_per_beat, total_samples,
                          filter_attack=0.01, filter_decay=0.3,
                          filter_sustain=0.0, filter_amount=0.0,
                          vel_to_filter=0.0, filter_q=0.707,
-                         synth_kwargs=None):
+                         synth_kwargs=None, temperament="equal",
+                         reference_pitch=440.0):
     """Render a list of Notes into an existing buffer at the correct positions."""
     import random as _rnd
 
@@ -2000,9 +2001,9 @@ def _render_notes_to_buf(notes, buf, samples_per_beat, total_samples,
             if n_samples > 0 and start >= 0:
                 # Get pitches
                 if hasattr(note.tone, 'tones'):
-                    pitches = [t.pitch() for t in note.tone.tones]
+                    pitches = [t.pitch(temperament=temperament, reference_pitch=reference_pitch) for t in note.tone.tones]
                 else:
-                    pitches = [note.tone.pitch()]
+                    pitches = [note.tone.pitch(temperament=temperament, reference_pitch=reference_pitch)]
                 # Render oscillators (pass synth_kwargs for FM etc.)
                 waves = [synth_fn(hz, n_samples=n_samples, **_skw)
                          for hz in pitches]
@@ -2087,7 +2088,8 @@ def _render_notes_to_buf(notes, buf, samples_per_beat, total_samples,
 
 def _render_legato_to_buf(notes, buf, samples_per_beat, total_samples,
                           synth_fn, envelope_tuple, volume, bpm,
-                          glide_time=0.0, swing=0.0, tempo_map=None):
+                          glide_time=0.0, swing=0.0, tempo_map=None,
+                          temperament="equal", reference_pitch=440.0):
     """Render notes as one continuous waveform with pitch glide.
 
     Instead of rendering each note separately with its own envelope,
@@ -2117,9 +2119,9 @@ def _render_legato_to_buf(notes, buf, samples_per_beat, total_samples,
         vel = getattr(note, 'velocity', 100)
         if note.tone is not None:
             if hasattr(note.tone, 'tones'):
-                hz = note.tone.tones[0].pitch()  # use root for chords
+                hz = note.tone.tones[0].pitch(temperament=temperament, reference_pitch=reference_pitch)
             else:
-                hz = note.tone.pitch()
+                hz = note.tone.pitch(temperament=temperament, reference_pitch=reference_pitch)
             events.append((start, end, hz, vel))
         else:
             events.append((start, end, 0, vel))  # rest
@@ -2237,12 +2239,15 @@ def render_score(score):
             if part.synth in ("fm",):
                 synth_kwargs["mod_ratio"] = part.fm_ratio
                 synth_kwargs["mod_index"] = part.fm_index
+            _temperament = getattr(score, 'temperament', 'equal')
+            _ref_pitch = getattr(score, 'reference_pitch', 440.0)
             if part.legato:
                 _render_legato_to_buf(
                     part.notes, part_buf, samples_per_beat, total_samples,
                     synth_fn, env_tuple, part.volume, score.bpm,
                     glide_time=part.glide, swing=effective_swing,
-                    tempo_map=tempo_map if has_tempo_changes else None)
+                    tempo_map=tempo_map if has_tempo_changes else None,
+                    temperament=_temperament, reference_pitch=_ref_pitch)
             else:
                 _render_notes_to_buf(
                     part.notes, part_buf, samples_per_beat, total_samples,
@@ -2261,7 +2266,9 @@ def render_score(score):
                     filter_amount=part.filter_amount,
                     vel_to_filter=part.vel_to_filter,
                     filter_q=part.lowpass_q,
-                    synth_kwargs=synth_kwargs)
+                    synth_kwargs=synth_kwargs,
+                    temperament=_temperament,
+                    reference_pitch=_ref_pitch)
 
             # Apply effects — segmented if automation exists
             auto_points = part._get_automation_points()

pytheory/rhythm.py

@@ -1677,6 +1677,7 @@ class Part:
         self.phaser_rate = phaser_rate
         self.fm_ratio = fm_ratio
         self.fm_index = fm_index
+        self._system = "western"  # default, overridden by Score.part()
         self.notes: list[Note] = []
         self._drum_hits: list[_Hit] = []
         self._drum_pattern_beats: float = 0.0
@@ -1692,7 +1693,7 @@ class Part:
         """
         if isinstance(tone_or_string, str):
             from .tones import Tone
-            tone_or_string = Tone.from_string(tone_or_string, system="western")
+            tone_or_string = Tone.from_string(tone_or_string, system=self._system)
         if isinstance(duration, (int, float)):
             duration = _RawDuration(duration)
         self.notes.append(Note(tone=tone_or_string, duration=duration, velocity=velocity))
@@ -2072,13 +2073,17 @@ class Score:
     """
 
     def __init__(self, time_signature="4/4", bpm=120, swing: float = 0.0,
-                 drum_humanize: float = 0.15):
+                 drum_humanize: float = 0.15, system: str = "western",
+                 temperament: str = "equal", reference_pitch: float = 440.0):
         if isinstance(time_signature, str):
             self.time_signature = TimeSignature.from_string(time_signature)
         else:
             self.time_signature = time_signature
         self.bpm = bpm
         self.swing = swing
+        self.system = system
+        self.temperament = temperament
+        self.reference_pitch = reference_pitch
         self._drum_humanize = drum_humanize
         self.notes: list[Note] = []
         self.parts: dict[str, Part] = {}
@@ -2294,6 +2299,7 @@ class Score:
         merged = {**_defaults, **explicit}
 
         p = Part(name, **merged)
+        p._system = self.system
         self.parts[name] = p
         return p
 

pytheory/systems.py

@@ -2,18 +2,53 @@ from ._statics import (
     TEMPERAMENTS, TONES, DEGREES, SCALES,
     INDIAN_SCALES, ARABIC_SCALES, JAPANESE_SCALES,
     BLUES_SCALES, GAMELAN_SCALES, SYSTEMS,
+    TONES_SHRUTI, DEGREES_SHRUTI, SHRUTI_SCALES,
+    TONES_ARABIC_24, DEGREES_ARABIC_24, ARABIC_24_SCALES,
+    TONES_SLENDRO, DEGREES_SLENDRO, SLENDRO_SCALES,
+    TONES_PELOG, DEGREES_PELOG, PELOG_SCALES,
+    TONES_THAI, DEGREES_THAI, THAI_SCALES,
+    TONES_TURKISH, DEGREES_TURKISH, TURKISH_SCALES,
+    TONES_CARNATIC, DEGREES_CARNATIC, CARNATIC_SCALES,
 )
 
 
 class System:
-    def __init__(self, *, tone_names, degrees, scales=None):
+    def __init__(self, *, tone_names, degrees, scales=None, c_index=None,
+                 period=2.0):
         self.tone_names = tone_names
 
         self.degrees = degrees
         self._scales = scales
 
+        # Period: the frequency ratio of one "octave" in this system.
+        # 2.0 for standard octave-based systems.
+        # 3.0 for Bohlen-Pierce (tritave).
+        self.period = period
+
+        # c_index: the index of the "reference C" in the tone list.
+        # For octave arithmetic — scientific pitch changes octave at C.
+        # Default 3 for 12-TET western (A=0, A#=1, B=2, C=3).
+        # For non-12-TET systems, this is the index of the tone nearest C,
+        # or 0 if no C equivalent exists.
+        if c_index is not None:
+            self.c_index = c_index
+        else:
+            # Try to find C in the tone names, fall back to 0
+            self.c_index = 0
+            for i, names in enumerate(tone_names):
+                if "C" in names:
+                    self.c_index = i
+                    break
+
         if scales is None:
-            self._scales = SCALES[self.semitones]
+            n = self.semitones
+            if n in SCALES:
+                self._scales = SCALES[n]
+            else:
+                # Generate chromatic scale for unknown sizes
+                self._scales = {
+                    "chromatic": (n, {}),
+                }
 
     @property
     def semitones(self):
@@ -25,13 +60,56 @@ class System:
         return tuple([Tone.from_tuple(tone) for tone in self.tone_names])
 
     def resolve_name(self, name: str) -> str | None:
-        """Resolve a note name (including flats) to the canonical name.
+        """Resolve a note name (including flats, double sharps/flats) to the canonical name.
+
+        Handles enharmonic equivalents:
+        - Standard names and their alternates (e.g. Bb, C#)
+        - Double sharps (C## = D, F## = G)
+        - Double flats (Dbb = C, Ebb = D)
 
         Returns the primary name if found, or None if not recognized.
         """
+        # Direct lookup first
         for names in self.tone_names:
             if name in names:
                 return names[0]
+
+        # Handle double sharps (e.g. C## → D, F## → G)
+        if name.endswith('##') and len(name) >= 3:
+            base = name[:-2]
+            base_idx = self._name_to_index(base)
+            if base_idx is not None:
+                resolved_idx = (base_idx + 2) % len(self.tone_names)
+                return self.tone_names[resolved_idx][0]
+
+        # Handle double flats (e.g. Dbb → C, Ebb → D)
+        if name.endswith('bb') and len(name) >= 3 and name[0] != 'b':
+            base = name[:-2]
+            base_idx = self._name_to_index(base)
+            if base_idx is not None:
+                resolved_idx = (base_idx - 2) % len(self.tone_names)
+                return self.tone_names[resolved_idx][0]
+
+        # Handle single sharps/flats on natural notes (e.g. Cb → B, E# → F)
+        if len(name) == 2:
+            base = name[0]
+            modifier = name[1]
+            base_idx = self._name_to_index(base)
+            if base_idx is not None:
+                if modifier == '#':
+                    resolved_idx = (base_idx + 1) % len(self.tone_names)
+                    return self.tone_names[resolved_idx][0]
+                elif modifier == 'b':
+                    resolved_idx = (base_idx - 1) % len(self.tone_names)
+                    return self.tone_names[resolved_idx][0]
+
+        return None
+
+    def _name_to_index(self, name: str) -> int | None:
+        """Return the index of a tone name, or None if not found."""
+        for i, names in enumerate(self.tone_names):
+            if name in names:
+                return i
         return None
 
 
@@ -139,11 +217,159 @@ class System:
     def __repr__(self):
         return f"<System semitones={self.semitones!r}>"
 
+
+def TET(n, *, names=None, reference_index=0, period=2.0):
+    """Create an N-tone equal temperament system.
+
+    Each step divides the period into *n* equal parts. The frequency
+    ratio between adjacent tones is ``period^(1/n)``.
+
+    For standard tunings the period is 2.0 (octave). For exotic systems
+    like Bohlen-Pierce, set ``period=3.0`` (tritave).
+
+    Args:
+        n: Number of equal divisions of the octave (e.g. 19, 24, 31, 53).
+        names: Optional list of *n* tone name strings. If omitted,
+            tones are numbered ``"0"`` through ``"n-1"``.
+        reference_index: Index of the tone that corresponds to A440
+            (default 0, meaning tone "0" = A4 = 440 Hz).
+
+    Returns:
+        A :class:`System` instance.
+
+    Example::
+
+        >>> edo19 = TET(19)
+        >>> from pytheory import Tone
+        >>> t = Tone("0", octave=4, system=edo19)
+        >>> t.frequency  # 440.0 Hz (tone 0 = A4)
+        440.0
+
+        >>> edo31 = TET(31)
+        >>> t = Tone("18", octave=4, system=edo31)
+        >>> t.frequency  # 18 steps above A in 31-TET
+    """
+    if names is not None:
+        if len(names) != n:
+            raise ValueError(f"Expected {n} names, got {len(names)}")
+        tone_names = [(name,) for name in names]
+    else:
+        tone_names = [(str(i),) for i in range(n)]
+
+    # Degrees: numbered, with no modal names
+    degrees = [(f"degree {i+1}", ()) for i in range(n)]
+
+    # Scales: chromatic (all steps = 1) plus MOS scales for common EDOs
+    scale_data = {
+        "chromatic": (n, {}),
+    }
+
+    # Add well-known scales for specific EDOs
+    if n == 19:
+        # 19-TET: major and minor have different step sizes
+        # Major: 3 3 2 3 3 3 2 (sums to 19)
+        # Minor: 3 2 3 3 2 3 3
+        scale_data["heptatonic"] = [7, {
+            "major": {"intervals": (3, 3, 2, 3, 3, 3, 2)},
+            "minor": {"intervals": (3, 2, 3, 3, 2, 3, 3)},
+            "harmonic minor": {"intervals": (3, 2, 3, 3, 2, 4, 2)},
+        }]
+        scale_data["pentatonic"] = [5, {
+            "major pentatonic": {"intervals": (3, 3, 5, 3, 5)},
+            "minor pentatonic": {"intervals": (5, 3, 3, 5, 3)},
+        }]
+    elif n == 24:
+        # 24-TET (quarter-tone): standard 12-TET scales with doubled steps
+        scale_data["heptatonic"] = [7, {
+            "major": {"intervals": (4, 4, 2, 4, 4, 4, 2)},
+            "minor": {"intervals": (4, 2, 4, 4, 2, 4, 4)},
+        }]
+    elif n == 31:
+        # 31-TET: excellent approximation of quarter-comma meantone
+        # Major: 5 5 3 5 5 5 3 (sums to 31)
+        # Minor: 5 3 5 5 3 5 5
+        scale_data["heptatonic"] = [7, {
+            "major": {"intervals": (5, 5, 3, 5, 5, 5, 3)},
+            "minor": {"intervals": (5, 3, 5, 5, 3, 5, 5)},
+            "harmonic minor": {"intervals": (5, 3, 5, 5, 3, 7, 3)},
+        }]
+        scale_data["pentatonic"] = [5, {
+            "major pentatonic": {"intervals": (5, 5, 8, 5, 8)},
+            "minor pentatonic": {"intervals": (8, 5, 5, 8, 5)},
+        }]
+    elif n == 53:
+        # 53-TET: nearly perfect fifths and thirds
+        # Major: 9 9 4 9 9 9 4 (sums to 53)
+        scale_data["heptatonic"] = [7, {
+            "major": {"intervals": (9, 9, 4, 9, 9, 9, 4)},
+            "minor": {"intervals": (9, 4, 9, 9, 4, 9, 9)},
+        }]
+
+    # Find C equivalent for c_index (reference_index is A, C is 3 steps in 12-TET)
+    # Proportionally: C is 3/12 of the way around from A
+    c_idx = round(n * 3 / 12) if n != 12 else 3
+
+    return System(
+        tone_names=tone_names,
+        degrees=degrees,
+        scales=scale_data,
+        c_index=c_idx,
+        period=period,
+    )
+
+
+# ── 19-TET named system ──
+# Traditional note names for 19-TET: all 12 western notes plus
+# 7 quarter-tone positions (enharmonic splits)
+_19TET_NAMES = [
+    "A", "A#", "Bb", "B", "B#",
+    "C", "C#", "Db", "D", "D#",
+    "Eb", "E", "E#", "F", "F#",
+    "Gb", "G", "G#", "Ab",
+]
+
+# ── 31-TET named system ──
+# Adriaan Fokker's naming: sharps and flats are distinct pitches
+_31TET_NAMES = [
+    "A", "A↑", "A#", "Bb", "B↓",
+    "B", "B↑", "C", "C↑", "C#",
+    "Db", "D↓", "D", "D↑", "D#",
+    "Eb", "E↓", "E", "E↑", "E#",
+    "F", "F↑", "F#", "Gb", "G↓",
+    "G", "G↑", "G#", "Ab", "A↓",
+    "A♮",  # enharmonic return (distinct from "A" by a diesis)
+]
+
+
 SYSTEMS = {
     "western": System(tone_names=TONES["western"], degrees=DEGREES["western"]),
-    "indian": System(tone_names=TONES["indian"], degrees=DEGREES["indian"], scales=INDIAN_SCALES[12]),
-    "arabic": System(tone_names=TONES["arabic"], degrees=DEGREES["arabic"], scales=ARABIC_SCALES[12]),
+    "indian": System(tone_names=TONES["indian"], degrees=DEGREES["indian"], scales=INDIAN_SCALES[12], c_index=3),
+    "arabic": System(tone_names=TONES["arabic"], degrees=DEGREES["arabic"], scales=ARABIC_SCALES[12], c_index=3),
     "japanese": System(tone_names=TONES["japanese"], degrees=DEGREES["japanese"], scales=JAPANESE_SCALES[12]),
     "blues": System(tone_names=TONES["blues"], degrees=DEGREES["blues"], scales=BLUES_SCALES[12]),
-    "gamelan": System(tone_names=TONES["gamelan"], degrees=DEGREES["gamelan"], scales=GAMELAN_SCALES[12]),
+    "gamelan": System(tone_names=TONES["gamelan"], degrees=DEGREES["gamelan"], scales=GAMELAN_SCALES[12], c_index=3),
+    "19-tet": TET(19, names=_19TET_NAMES),
+    "31-tet": TET(31, names=_31TET_NAMES),
+    # Microtonal systems with proper intervals (not 12-TET approximations)
+    "shruti": System(tone_names=TONES_SHRUTI, degrees=DEGREES_SHRUTI,
+                     scales=SHRUTI_SCALES, c_index=5),
+    "maqam": System(tone_names=TONES_ARABIC_24, degrees=DEGREES_ARABIC_24,
+                    scales=ARABIC_24_SCALES, c_index=5),
+    "slendro": System(tone_names=TONES_SLENDRO, degrees=DEGREES_SLENDRO,
+                      scales=SLENDRO_SCALES, c_index=1),
+    "pelog": System(tone_names=TONES_PELOG, degrees=DEGREES_PELOG,
+                    scales=PELOG_SCALES, c_index=2),
+    "thai": System(tone_names=TONES_THAI, degrees=DEGREES_THAI,
+                   scales=THAI_SCALES, c_index=0),
+    "makam": System(tone_names=TONES_TURKISH, degrees=DEGREES_TURKISH,
+                    scales=TURKISH_SCALES, c_index=13),
+    "carnatic": System(tone_names=TONES_CARNATIC, degrees=DEGREES_CARNATIC,
+                       scales=CARNATIC_SCALES, c_index=18),  # Sa ≈ C, 18 steps from A
+    # Bohlen-Pierce: 13 equal divisions of the tritave (3:1).
+    # Genuinely alien — no octaves, no fifths, built on 3:5:7 harmonics.
+    # Used by composers like Heinz Bohlen, Kees van Prooijen, Georg Hajdu.
+    "bohlen-pierce": TET(13, period=3.0, names=[
+        "A", "B", "C", "D", "E", "F", "G",
+        "H", "J", "K", "L", "M", "N",
+    ]),
 }

pytheory/tones.py

@@ -47,15 +47,28 @@ class Tone:
             alt_names = []
 
         if isinstance(name, str):
-            try:
-                parsed_octave = int("".join([c for c in filter(str.isdigit, name)]))
-            except ValueError:
-                parsed_octave = None
+            # Normalize unicode music symbols to ASCII equivalents
+            name = (name
+                    .replace('\u266f', '#')   # ♯ → #
+                    .replace('\u266d', 'b')   # ♭ → b
+                    .replace('\U0001d12a', '##')  # 𝄪 → ##
+                    .replace('\U0001d12b', 'bb')  # 𝄫 → bb
+                    )
+            # Normalize 'x' / 'X' as double sharp (only after letter name)
+            if len(name) >= 2 and name[1] in ('x', 'X') and name[0].isalpha():
+                name = name[0] + '##' + name[2:]
 
-            if parsed_octave is not None:
-                name = name.replace(str(parsed_octave), "")
-                if octave is None:
-                    octave = parsed_octave
+            # Only parse trailing digits as octave (e.g. "C4" → "C", octave=4).
+            # Digits embedded in the name (e.g. "Mib+1") are NOT octaves.
+            # Numeric pitch class names ("0", "11") are also left alone.
+            if name and name[0].isalpha():
+                import re as _re
+                m = _re.search(r'(\d+)$', name)
+                if m:
+                    parsed_octave = int(m.group(1))
+                    name = name[:m.start()]
+                    if octave is None:
+                        octave = parsed_octave
 
         self.name = name
         self.octave = octave
@@ -343,12 +356,15 @@ class Tone:
         Returns:
             A new ``Tone`` instance.
         """
-        try:
-            octave = int("".join([c for c in filter(str.isdigit, s)]))
-        except ValueError:
-            octave = None
-
-        tone = s.replace(str(octave), "") if octave else s
+        import re as _re
+        octave = None
+        tone = s
+        # Only parse trailing digits as octave
+        if s and s[0].isalpha():
+            m = _re.search(r'(\d+)$', s)
+            if m:
+                octave = int(m.group(1))
+                tone = s[:m.start()]
 
         if system:
             return klass(name=tone, octave=octave, system=system)
@@ -389,19 +405,20 @@ class Tone:
         import math
         if hz <= 0:
             raise ValueError("Frequency must be positive")
-        # Semitones from A4
-        semitones_from_a4 = 12 * math.log2(hz / REFERENCE_A)
-        semitones = round(semitones_from_a4)
-        # A4 is index 0 in the Western system, octave 4
-        # Convert to absolute position from C0
-        a4_from_c0 = ((0 - C_INDEX) % 12) + (4 * 12)  # = 57
-        abs_pos = a4_from_c0 + semitones
-        octave = abs_pos // 12
-        relative = abs_pos % 12
-        index = (relative + C_INDEX) % 12
         if isinstance(system, str):
             from .systems import SYSTEMS
             system = SYSTEMS[system]
+        n = len(system.tone_names)
+        c_idx = getattr(system, 'c_index', C_INDEX)
+        # Steps from A4 in this EDO
+        steps_from_a4 = n * math.log2(hz / REFERENCE_A)
+        steps = round(steps_from_a4)
+        # A4 is index 0, octave 4. Convert to absolute position from C0.
+        a4_from_c0 = ((0 - c_idx) % n) + (4 * n)
+        abs_pos = a4_from_c0 + steps
+        octave = abs_pos // n
+        relative = abs_pos % n
+        index = (relative + c_idx) % n
         return klass.from_index(index, octave=octave, system=system)
 
     @classmethod
@@ -417,13 +434,19 @@ class Tone:
             >>> Tone.from_midi(69)
             <Tone A4>
         """
+        if isinstance(system, str):
+            from .systems import SYSTEMS
+            system = SYSTEMS[system]
+        # MIDI is a 12-TET standard. Convert to Hz and use from_frequency
+        # for non-12 systems.
+        n = len(system.tone_names)
+        if n != 12:
+            hz = REFERENCE_A * (2 ** ((note_number - 69) / 12))
+            return klass.from_frequency(hz, system=system)
         adjusted = note_number - 12  # MIDI C0=12
         octave = adjusted // 12
         relative = adjusted % 12
         index = (relative + C_INDEX) % 12
-        if isinstance(system, str):
-            from .systems import SYSTEMS
-            system = SYSTEMS[system]
         return klass.from_index(index, octave=octave, system=system)
 
     @classmethod
@@ -442,10 +465,27 @@ class Tone:
         """
         tone_names = system.tone_names[i]
         if prefer_flats and len(tone_names) > 1:
-            tone = tone_names[1]  # flat spelling (e.g. "Bb")
+            # Find the first flat spelling (contains 'b' but isn't just 'B')
+            tone = tone_names[0]  # fallback to primary
+            for tn in tone_names[1:]:
+                if 'b' in tn and tn != 'B':
+                    tone = tn
+                    break
         else:
-            tone = tone_names[0]  # sharp spelling (e.g. "A#")
-        return klass(name=tone, octave=octave, system=system)
+            tone = tone_names[0]  # primary spelling
+        # Bypass parsing and validation — name comes from a known system index
+        obj = klass.__new__(klass)
+        obj.name = tone
+        obj.octave = octave
+        obj.alt_names = list(tone_names[1:]) if len(tone_names) > 1 else []
+        obj._frequency = None
+        if isinstance(system, str):
+            obj.system_name = system
+            obj._system = None
+        else:
+            obj.system_name = None
+            obj._system = system
+        return obj
 
     @property
     def _index(self) -> int:
@@ -461,7 +501,15 @@ class Tone:
             canonical = self.system.resolve_name(self.name)
             if canonical is None:
                 raise ValueError(f"Tone {self.name!r} not found in system")
-            return self.system.tones.index(canonical)
+            # Use _name_to_index for direct lookup (avoids creating Tone objects)
+            idx = self.system._name_to_index(canonical)
+            if idx is not None:
+                return idx
+            # Fallback: linear search through tone_names
+            for i, names in enumerate(self.system.tone_names):
+                if canonical in names:
+                    return i
+            raise ValueError(f"Tone {self.name!r} not found in system")
         except AttributeError:
             raise ValueError("Tone index cannot be referenced without a system!")
 
@@ -475,19 +523,21 @@ class Tone:
         octave = self.octave or 0
 
         try:
-            mod = len(self.system.tones)
+            mod = len(self.system.tone_names)
         except AttributeError:
             raise ValueError(
                 "Tone math can only be computed with an associated system!"
             )
 
-        # Convert to absolute semitones from C0
-        note_from_c0 = ((self._index - C_INDEX) % mod) + (octave * mod)
+        c_idx = getattr(self.system, 'c_index', C_INDEX)
+
+        # Convert to absolute steps from C0
+        note_from_c0 = ((self._index - c_idx) % mod) + (octave * mod)
         note_from_c0 += interval
 
         new_octave = note_from_c0 // mod
         relative = note_from_c0 % mod
-        new_index = (relative + C_INDEX) % mod
+        new_index = (relative + c_idx) % mod
 
         return (new_index, new_octave)
 
@@ -538,9 +588,10 @@ class Tone:
             'octave'
         """
         semitones = abs(self - other)
-        octaves = semitones // 12
-        remainder = semitones % 12
-        name = self._INTERVAL_NAMES.get(remainder, f"{remainder} semitones")
+        n = len(self.system.tones)
+        octaves = semitones // n
+        remainder = semitones % n
+        name = self._INTERVAL_NAMES.get(remainder, f"{remainder} steps")
         if octaves == 0:
             return name
         if remainder == 0:
@@ -563,6 +614,12 @@ class Tone:
         """
         if self.octave is None:
             return None
+        n = len(self.system.tones)
+        if n != 12:
+            # Non-12-TET: approximate MIDI via frequency
+            import math
+            hz = self.pitch()
+            return round(69 + 12 * math.log2(hz / REFERENCE_A))
         semitones_from_c0 = ((self._index - C_INDEX) % 12) + (self.octave * 12)
         return semitones_from_c0 + 12  # MIDI C0 = 12 (C-1 = 0)
 
@@ -604,42 +661,43 @@ class Tone:
         return 1200 * math.log2(f2 / f1)
 
     def circle_of_fifths(self) -> list[Tone]:
-        """The 12 tones of the circle of fifths starting from this tone.
+        """The circle of fifths starting from this tone.
 
-        Each step ascends by a perfect fifth (7 semitones). After 12
-        steps you return to the starting tone. The circle of fifths
-        is the backbone of Western harmony — it determines key
-        signatures, chord relationships, and modulation paths.
-
-        Clockwise = add sharps: C → G → D → A → E → B → F# → ...
-        Counter-clockwise = add flats (see ``circle_of_fourths``).
+        Each step ascends by a perfect fifth (7 semitones in 12-TET).
+        After N steps (where N = number of tones in the system) you
+        return to the starting tone. The circle of fifths is the
+        backbone of Western harmony — it determines key signatures,
+        chord relationships, and modulation paths.
 
         Returns:
-            A list of 12 Tones.
+            A list of Tones (12 for Western, N for other systems).
         """
+        n = len(self.system.tones)
+        # Perfect fifth: the closest approximation to 3:2 ratio
+        fifth = round(n * 7 / 12)  # 7 in 12-TET, 11 in 19-TET, 18 in 31-TET
         tones: list[Tone] = []
         t = self
-        for _ in range(12):
+        for _ in range(n):
             tones.append(t)
-            t = t.add(7)
+            t = t.add(fifth)
         return tones
 
     def circle_of_fourths(self) -> list[Tone]:
-        """The 12 tones of the circle of fourths starting from this tone.
+        """The circle of fourths starting from this tone.
 
-        Each step ascends by a perfect fourth (5 semitones) — the
-        reverse direction of the circle of fifths.
-
-        Clockwise = add flats: C → F → Bb → Eb → Ab → ...
+        Each step ascends by a perfect fourth — the reverse direction
+        of the circle of fifths.
 
         Returns:
-            A list of 12 Tones.
+            A list of Tones (12 for Western, N for other systems).
         """
+        n = len(self.system.tones)
+        fourth = round(n * 5 / 12)  # 5 in 12-TET, 8 in 19-TET, 13 in 31-TET
         tones: list[Tone] = []
         t = self
-        for _ in range(12):
+        for _ in range(n):
             tones.append(t)
-            t = t.add(5)
+            t = t.add(fourth)
         return tones
 
     @property
@@ -695,21 +753,32 @@ class Tone:
         precision: Optional[int] = None,
     ) -> float:
         try:
-            tones = len(self.system.tones)
+            tones = len(self.system.tone_names)
         except AttributeError:
             raise ValueError("Pitches can only be computed with an associated system!")
 
-        pitch_scale = TEMPERAMENTS[temperament](tones)
+        # Period ratio: 2.0 for standard octave-based systems,
+        # 3.0 for Bohlen-Pierce (tritave), configurable per system.
+        period = getattr(self.system, 'period', 2.0)
+        c_idx = getattr(self.system, 'c_index', C_INDEX)
+
+        if period != 2.0 and temperament == "equal":
+            # Non-octave period (e.g. Bohlen-Pierce tritave=3.0):
+            # generate ratios as period^(n/tones) instead of 2^(n/tones)
+            import sympy
+            pitch_scale = [period ** sympy.Rational(i, tones) for i in range(tones + 1)]
+        else:
+            pitch_scale = TEMPERAMENTS[temperament](tones)
         octave = self.octave if self.octave is not None else 4
 
-        note_from_c0 = ((self._index - C_INDEX) % tones) + (octave * tones)
-        a4_from_c0 = ((0 - C_INDEX) % tones) + (4 * tones)  # A4
+        note_from_c0 = ((self._index - c_idx) % tones) + (octave * tones)
+        a4_from_c0 = ((0 - c_idx) % tones) + (4 * tones)  # A4
 
         diff = note_from_c0 - a4_from_c0
         octave_shift = diff // tones
         within_octave = diff % tones
 
-        ratio = pitch_scale[within_octave] * (2 ** octave_shift)
+        ratio = pitch_scale[within_octave] * (period ** octave_shift)
 
         if symbolic:
             return reference_pitch * ratio

test_pytheory.py

@@ -6534,3 +6534,186 @@ def test_instrument_808_bass():
     assert p.lowpass_q == 1.5
     assert p.synth == "sine"
     assert p.envelope == "pluck"
+
+
+# ── Non-12-TET / Microtonal systems ─────────────────────────────────────────
+
+from pytheory import TET
+
+
+def test_tet_factory_creates_system():
+    edo17 = TET(17)
+    assert len(edo17.tone_names) == 17
+    assert edo17.semitones == 17
+
+
+def test_tet_factory_numbered_tones():
+    edo17 = TET(17)
+    t = Tone("0", octave=4, system=edo17)
+    assert t.frequency == pytest.approx(440.0, rel=1e-3)
+    # One octave up
+    t_up = t.add(17)
+    assert t_up.frequency == pytest.approx(880.0, rel=1e-3)
+
+
+def test_tet_factory_custom_names():
+    names = ["A", "B", "C", "D", "E"]
+    edo5 = TET(5, names=names)
+    assert len(edo5.tone_names) == 5
+    t = Tone("A", octave=4, system=edo5)
+    assert t.frequency == pytest.approx(440.0, rel=1e-3)
+
+
+def test_tet_factory_wrong_name_count():
+    with pytest.raises(ValueError):
+        TET(5, names=["A", "B", "C"])
+
+
+def test_19tet_system():
+    sys19 = SYSTEMS["19-tet"]
+    assert sys19.semitones == 19
+    a = Tone("A", octave=4, system=sys19)
+    assert a.frequency == pytest.approx(440.0, rel=1e-3)
+    # Octave should double
+    a5 = a.add(19)
+    assert a5.frequency == pytest.approx(880.0, rel=1e-3)
+
+
+def test_19tet_scale():
+    sys19 = SYSTEMS["19-tet"]
+    ts = TonedScale(system=sys19, tonic=Tone("C", octave=4, system=sys19))
+    major = ts["major"]
+    assert len(major.tones) == 8  # 7 + octave
+
+
+def test_31tet_system():
+    sys31 = SYSTEMS["31-tet"]
+    assert sys31.semitones == 31
+    a = Tone("A", octave=4, system=sys31)
+    assert a.frequency == pytest.approx(440.0, rel=1e-3)
+
+
+def test_shruti_system():
+    shruti = SYSTEMS["shruti"]
+    assert shruti.semitones == 22
+    sa = Tone("Sa", octave=4, system=shruti)
+    # Sa should be near C4 (261.63 Hz) — not exact due to 22-TET
+    assert 250 < sa.frequency < 270
+
+
+def test_shruti_octave():
+    shruti = SYSTEMS["shruti"]
+    sa4 = Tone("Sa", octave=4, system=shruti)
+    sa5 = sa4.add(22)
+    assert sa5.frequency == pytest.approx(sa4.frequency * 2, rel=1e-3)
+
+
+def test_shruti_bhairav_scale():
+    shruti = SYSTEMS["shruti"]
+    ts = TonedScale(system=shruti, tonic=Tone("Sa", octave=4, system=shruti))
+    bhairav = ts["bhairav"]
+    names = [t.name for t in bhairav.tones]
+    assert names[0] == "Sa"
+    assert "komal Re" in names  # the microtonal komal Re
+    assert len(bhairav.tones) == 8
+
+
+def test_maqam_system():
+    maqam = SYSTEMS["maqam"]
+    assert maqam.semitones == 24
+    do = Tone("Do", octave=4, system=maqam)
+    assert 250 < do.frequency < 270
+
+
+def test_maqam_rast_has_quarter_tones():
+    maqam = SYSTEMS["maqam"]
+    ts = TonedScale(system=maqam, tonic=Tone("Do", octave=4, system=maqam))
+    rast = ts["rast"]
+    names = [t.name for t in rast.tones]
+    # Rast should contain quarter-tone positions
+    assert any("↓" in n or "↑" in n for n in names)
+
+
+def test_slendro_system():
+    slendro = SYSTEMS["slendro"]
+    assert slendro.semitones == 5
+    ji = Tone("ji", octave=4, system=slendro)
+    # 5 steps = octave
+    ji_up = ji.add(5)
+    assert ji_up.frequency == pytest.approx(ji.frequency * 2, rel=1e-3)
+
+
+def test_pelog_system():
+    pelog = SYSTEMS["pelog"]
+    assert pelog.semitones == 9
+    ts = TonedScale(system=pelog, tonic=Tone("ji", octave=4, system=pelog))
+    full_pelog = ts["pelog"]
+    assert len(full_pelog.tones) == 8
+
+
+def test_thai_system():
+    thai = SYSTEMS["thai"]
+    assert thai.semitones == 7
+    do = Tone("do", octave=4, system=thai)
+    # 7 steps = octave
+    do_up = do.add(7)
+    assert do_up.frequency == pytest.approx(do.frequency * 2, rel=1e-3)
+
+
+def test_turkish_makam_system():
+    makam = SYSTEMS["makam"]
+    assert makam.semitones == 53
+    ts = TonedScale(system=makam, tonic=Tone("Do", octave=4, system=makam))
+    rast = ts["rast"]
+    assert len(rast.tones) == 8
+
+
+def test_carnatic_system():
+    carnatic = SYSTEMS["carnatic"]
+    assert carnatic.semitones == 72
+    ts = TonedScale(system=carnatic, tonic=Tone("Sa", octave=4, system=carnatic))
+    shankarabharanam = ts["shankarabharanam"]
+    assert len(shankarabharanam.tones) == 8
+
+
+def test_circle_of_fifths_19tet():
+    sys19 = SYSTEMS["19-tet"]
+    c = Tone("C", octave=4, system=sys19)
+    cof = c.circle_of_fifths()
+    assert len(cof) == 19  # should cycle through all 19 tones
+
+
+def test_circle_of_fifths_western_unchanged():
+    """Existing 12-TET circle of fifths should not be affected."""
+    c = Tone("C", octave=4, system="western")
+    cof = c.circle_of_fifths()
+    assert len(cof) == 12
+    assert cof[0].name == "C"
+    assert cof[1].name == "G"
+
+
+def test_from_frequency_non12():
+    sys19 = SYSTEMS["19-tet"]
+    t = Tone.from_frequency(440.0, system=sys19)
+    assert t.name == "A"
+    assert t.octave == 4
+
+
+def test_score_system_param():
+    """Score passes system to parts for string→Tone resolution."""
+    from pytheory import Score, Duration
+    shruti = SYSTEMS["shruti"]
+    score = Score("4/4", bpm=120, system=shruti)
+    p = score.part("test", synth="sine")
+    assert p._system is shruti
+    # String "Sa" should resolve via shruti system, not western
+    p.add(Tone("Sa", octave=4, system=shruti), Duration.QUARTER)
+    assert len(p.notes) == 1
+
+
+def test_interval_to_non12():
+    sys19 = SYSTEMS["19-tet"]
+    a = Tone("A", octave=4, system=sys19)
+    a5 = a.add(19)
+    result = a.interval_to(a5)
+    assert "octave" in result

uv.lock

@@ -707,7 +707,7 @@ wheels = [
 
 [[package]]
 name = "pytheory"
-version = "0.32.0"
+version = "0.33.0"
 source = { editable = "." }
 dependencies = [
     { name = "numeral" },