Carnatic 72-TET, Score system param, 22 microtonal tests

- Carnatic (72-TET): 10 melakartas including shankarabharanam,
  kalyani, mayamalavagowla, kharaharapriya, etc.
- Score(system=) param passes tuning system to all parts, so
  Part.add("Sa") resolves through the correct system
- 22 new tests covering all microtonal systems: TET factory,
  19/31-TET, shruti, maqam, slendro, pelog, thai, makam,
  carnatic, circle of fifths, from_frequency, Score integration

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

pytheory/_statics.py

@@ -579,6 +579,83 @@ TURKISH_SCALES = {
     ],
 }
 
+# ── 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/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 +2073,14 @@ 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"):
         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._drum_humanize = drum_humanize
         self.notes: list[Note] = []
         self.parts: dict[str, Part] = {}
@@ -2294,6 +2296,7 @@ class Score:
         merged = {**_defaults, **explicit}
 
         p = Part(name, **merged)
+        p._system = self.system
         self.parts[name] = p
         return p
 

pytheory/systems.py

@@ -8,6 +8,7 @@ from ._statics import (
     TONES_PELOG, DEGREES_PELOG, PELOG_SCALES,
     TONES_THAI, DEGREES_THAI, THAI_SCALES,
     TONES_TURKISH, DEGREES_TURKISH, TURKISH_SCALES,
+    TONES_CARNATIC, DEGREES_CARNATIC, CARNATIC_SCALES,
 )
 
 
@@ -352,4 +353,6 @@ SYSTEMS = {
                    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
 }

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