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 +2,56 @@
 
 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:**
+  - Filter envelope: per-note lowpass sweep (`filter_amount`, `filter_attack`, `filter_decay`, `filter_sustain`)
+  - Velocity → brightness: harder notes = brighter filter (`vel_to_filter`)
+  - Sub-oscillator: octave-below sine for bass weight (`sub_osc`)
+  - Tremolo: amplitude LFO modulation (`tremolo_depth`, `tremolo_rate`)
+  - Saturation: even-harmonic tape/tube warmth (`saturation`)
+  - Noise layer: per-note breath/air texture (`noise_mix`)
+  - Phaser: swept allpass filter chain (`phaser`, `phaser_rate`)
+  - Configurable FM: `fm_ratio` and `fm_index` params
+- **Highpass filter** (12 dB/oct biquad) on any part
+- **2 new envelopes:** `bowed` (bow attack with sustain), `mallet` (strike with ringing sustain)
+- **Improved `strings_synth`:** additive synthesis with body resonance curve, per-harmonic phase randomization, delayed vibrato onset, bow pressure variation
+- **Instrument preset overhaul:** every preset sanity-checked against real instrument behavior
+  - Mallet instruments (vibraphone, celesta, music box, glockenspiel, tubular bells) now ring properly
+  - Trumpet uses sustaining envelope instead of pluck
+  - Woodwinds have breath noise, brass has velocity brightness
+  - Bass instruments have sub-oscillators, synth presets have filter envelopes
+  - Piano has velocity-to-brightness and subtle hammer noise
+- Signal chain: saturation → tremolo → distortion → chorus → phaser → highpass → lowpass → delay → reverb
+- Song #21: Cinematic Showcase (Orchestral)
+
 ## 0.31.0
 
 - 3 new synth engines: Karplus-Strong pluck, Hammond organ, string ensemble with body formants

docs/guide/effects.rst

@@ -32,13 +32,26 @@ It's a well-tested order that sounds good by default.
 
 Effects are applied in this fixed order::
 
-    Signal --> Distortion --> Chorus --> Lowpass Filter --> Delay --> Reverb --> Mix
+    Signal --> Saturation --> Tremolo --> Distortion --> Chorus --> Phaser
+          --> Highpass --> Lowpass --> Delay --> Reverb --> Mix
 
-- **Distortion** first: drives the raw signal before filtering (like
-  plugging a guitar into a fuzz pedal before the amp).
-- **Chorus** second: thickens the distorted signal.
-- **Lowpass** third: shapes the tone (like a tone knob on an amp).
-- **Delay** fourth: echoes the shaped signal (tap delay / tape echo).
+Additionally, these per-note effects are applied before the part effects chain:
+
+- **Sub-oscillator**: octave-below sine mixed in at the oscillator stage
+- **Noise layer**: filtered noise mixed per-note for breath/transients
+- **Filter envelope**: per-note lowpass sweep (attack/decay/sustain)
+- **Velocity → brightness**: harder velocity = brighter filter cutoff
+
+Part-level effects:
+
+- **Saturation** first: subtle even-harmonic warmth (tape/tube color).
+- **Tremolo** second: amplitude LFO modulation.
+- **Distortion** third: drives the signal before filtering.
+- **Chorus** fourth: thickens the signal.
+- **Phaser** fifth: swept allpass notches.
+- **Highpass** sixth: removes low-frequency mud.
+- **Lowpass** seventh: shapes the tone (like a tone knob on an amp).
+- **Delay** eighth: echoes the shaped signal (tap delay / tape echo).
 - **Reverb** last: places everything in a space (room / hall).
 
 Distortion
@@ -498,6 +511,221 @@ whole mix will gasp for air:
        delay=0.2,
    )
 
+Saturation
+----------
+
+Saturation is the warm, subtle harmonic enhancement of analog tape
+machines and tube preamps. Unlike distortion (which uses ``tanh`` and
+adds harsh odd harmonics), saturation uses a polynomial waveshaper
+that adds even harmonics -- 2nd and 4th -- which the ear perceives as
+warmth and fullness. It's why records mixed through a Neve console
+sound "bigger" than the same mix done in the box.
+
+Parameters:
+
+- ``saturation``: Amount, 0.0--1.0 (default 0, off).
+
+  - 0.05--0.15 = subtle analog warmth (tape machine)
+  - 0.2--0.4 = noticeable color (tube preamp)
+  - 0.5+ = heavy coloring
+
+.. code-block:: python
+
+   # Warm up a bass
+   bass = score.part("bass", synth="saw", saturation=0.2)
+
+   # Glue a string ensemble
+   strings = score.part("strings", instrument="string_ensemble",
+                        saturation=0.1)
+
+Tremolo
+-------
+
+Amplitude modulation by a sine LFO. The classic vibrating-amp sound.
+Essential for vibraphone (the rotating discs in the resonator tubes),
+Rhodes electric piano, and surf guitar. Not to be confused with
+vibrato (pitch modulation).
+
+Parameters:
+
+- ``tremolo_depth``: Modulation depth, 0.0--1.0 (default 0, off).
+- ``tremolo_rate``: LFO speed in Hz (default 5.0).
+
+  - 3--5 Hz = classic tremolo
+  - 5--7 Hz = vibraphone motor speed
+  - 8+ Hz = ring-mod territory
+
+.. code-block:: python
+
+   # Classic Fender amp tremolo
+   guitar = score.part("guitar", synth="saw", envelope="pluck",
+                       tremolo_depth=0.3, tremolo_rate=4.0)
+
+   # Vibraphone with motor
+   vib = score.part("vib", instrument="vibraphone")  # built in
+
+Phaser
+------
+
+A chain of allpass filters whose center frequencies are swept by an
+LFO, creating moving notches in the spectrum. The classic "jet
+engine" or "underwater" effect. Think Small Stone, MXR Phase 90, or
+the intro to "Eruption." Different from chorus -- chorus adds a
+detuned copy, phaser cancels specific frequencies.
+
+Parameters:
+
+- ``phaser``: Wet/dry mix, 0.0--1.0 (default 0, off).
+- ``phaser_rate``: LFO sweep speed in Hz (default 0.5).
+
+  - 0.1--0.3 = slow, lush sweep
+  - 0.5--1.0 = classic phaser
+  - 2.0+ = fast, Leslie-like
+
+.. code-block:: python
+
+   # Slow sweep on a pad
+   pad = score.part("pad", synth="supersaw", envelope="pad",
+                    phaser=0.4, phaser_rate=0.2)
+
+   # Leslie sim on organ (built in)
+   organ = score.part("organ", instrument="organ")
+
+Highpass Filter
+---------------
+
+The opposite of lowpass -- removes low-frequency content below the
+cutoff. Useful for cleaning up mud from pads, keeping multiple bass
+parts from masking each other, or thinning out a sound to sit better
+in a mix.
+
+Parameters:
+
+- ``highpass``: Cutoff frequency in Hz (0 = off).
+
+  - 80--150 Hz = clean up sub rumble
+  - 200--400 Hz = thin out a pad
+  - 500+ Hz = telephone / radio effect
+
+- ``highpass_q``: Resonance / Q factor (default 0.707).
+
+.. code-block:: python
+
+   # Clean up sub rumble from a pad
+   pad = score.part("pad", synth="supersaw", highpass=120)
+
+   # Thin out rhythm guitar to leave room for bass
+   rhythm = score.part("rhythm", synth="saw", highpass=250)
+
+Filter Envelope
+---------------
+
+A per-note lowpass filter whose cutoff sweeps over time. This is the
+core of subtractive synthesis -- the reason a Moog bass goes "bwow"
+instead of "boop." The filter opens on the attack and closes during
+decay, giving each note a distinctive timbral shape.
+
+Parameters:
+
+- ``filter_amount``: Sweep range in Hz (0 = off). How far the filter
+  opens above the base cutoff.
+- ``filter_attack``: Time to reach peak cutoff, in seconds (default 0.01).
+- ``filter_decay``: Time to fall to sustain level (default 0.3).
+- ``filter_sustain``: Sustain level as fraction of amount, 0.0--1.0
+  (default 0.0 = filter closes completely after decay).
+
+.. code-block:: python
+
+   # Classic synth bass "bwow"
+   bass = score.part("bass", instrument="synth_bass")  # built in
+
+   # Acid squelch
+   acid = score.part("acid", instrument="acid_bass")  # built in
+
+   # Custom filter sweep on a lead
+   lead = score.part("lead", synth="saw",
+                     filter_amount=4000, filter_attack=0.01,
+                     filter_decay=0.4, filter_sustain=0.1)
+
+Velocity to Brightness
+~~~~~~~~~~~~~~~~~~~~~~
+
+Real instruments get brighter when played harder. ``vel_to_filter``
+maps note velocity to filter cutoff boost, so louder notes have more
+high-frequency content.
+
+- ``vel_to_filter``: Cutoff boost in Hz at max velocity (default 0, off).
+
+.. code-block:: python
+
+   # Piano: soft = mellow, loud = bright
+   piano = score.part("piano", instrument="piano")  # built in
+
+   # Manual: custom velocity mapping on a lead
+   lead = score.part("lead", synth="saw", vel_to_filter=3000)
+
+Sub-Oscillator
+--------------
+
+An octave-below sine wave mixed in with the main oscillator. Adds
+low-end weight without muddiness -- the sub fills in the fundamental
+while the main oscillator provides harmonic character above.
+
+- ``sub_osc``: Mix level, 0.0--1.0 (default 0, off).
+
+  - 0.1--0.2 = subtle weight (tuba, bass guitar)
+  - 0.3--0.5 = heavy sub (808, synth bass)
+
+.. code-block:: python
+
+   # Fat 808 kick-bass
+   bass = score.part("bass", instrument="808_bass")  # built in
+
+   # Add weight to any part
+   lead = score.part("lead", synth="saw", sub_osc=0.3)
+
+Noise Layer
+-----------
+
+White noise mixed into each note, following the same amplitude
+envelope. Adds breath for woodwinds, hammer/felt noise for piano,
+bow rosin for strings, and attack transients for percussion.
+
+- ``noise_mix``: Mix level, 0.0--1.0 (default 0, off).
+
+  - 0.02--0.04 = subtle texture (strings, piano)
+  - 0.05--0.08 = noticeable breath (woodwinds)
+  - 0.1+ = heavy air/texture
+
+.. code-block:: python
+
+   # Breathy flute
+   flute = score.part("flute", instrument="flute")  # noise_mix=0.08
+
+   # Add air to any synth
+   pad = score.part("pad", synth="supersaw", noise_mix=0.05)
+
+Configurable FM
+---------------
+
+The FM synth now accepts ``fm_ratio`` and ``fm_index`` parameters,
+letting you dial in specific FM timbres instead of using the defaults.
+
+- ``fm_ratio``: Modulator frequency as multiple of carrier (default 2.0).
+  Integer ratios = harmonic timbres; non-integer = metallic/inharmonic.
+- ``fm_index``: Modulation depth (default 3.0). Higher = more harmonics.
+
+.. code-block:: python
+
+   # Warm electric piano (low ratio, low index)
+   ep = score.part("ep", synth="fm", fm_ratio=1.0, fm_index=1.5)
+
+   # Bright metallic bell (high ratio, high index)
+   bell = score.part("bell", synth="fm", fm_ratio=3.5, fm_index=5.0)
+
+   # Glockenspiel
+   glock = score.part("glock", instrument="glockenspiel")  # built in
+
 Automation
 ----------
 
@@ -528,9 +756,10 @@ processes each section independently:
    lead.set(lowpass=4000, distortion=0.7, reverb=0.3)
    lead.arpeggio("Gm", bars=4, pattern="updown", octaves=2)
 
-Any parameter can be automated: ``lowpass``, ``lowpass_q``, ``reverb``,
-``reverb_decay``, ``delay``, ``delay_time``, ``delay_feedback``,
-``distortion``, ``distortion_drive``, ``chorus``, ``volume``.
+Any parameter can be automated: ``lowpass``, ``lowpass_q``, ``highpass``,
+``reverb``, ``reverb_decay``, ``delay``, ``delay_time``, ``delay_feedback``,
+``distortion``, ``distortion_drive``, ``chorus``, ``phaser``, ``phaser_rate``,
+``saturation``, ``tremolo_depth``, ``tremolo_rate``, ``volume``.
 
 LFO Automation
 --------------

docs/guide/synths.rst

@@ -1,7 +1,7 @@
 Synthesizers
 ============
 
-PyTheory includes 10 built-in waveforms and 8 ADSR envelope presets.
+PyTheory includes 13 built-in waveforms and 10 ADSR envelope presets.
 Every sound is generated from scratch -- no samples or external audio
 files needed.
 
@@ -247,6 +247,8 @@ PyTheory includes 8 presets:
    play(tone, envelope=Envelope.ORGAN)     # Instant on/off, no shaping
    play(tone, envelope=Envelope.BELL)      # Instant attack, long ring
    play(tone, envelope=Envelope.STRINGS)   # Gradual bow attack
+   play(tone, envelope=Envelope.BOWED)     # Bow bite into sustain
+   play(tone, envelope=Envelope.MALLET)    # Strike with ringing sustain
    play(tone, envelope=Envelope.STACCATO)  # Short and punchy
    play(tone, envelope=Envelope.NONE)      # Raw waveform, no shaping
 
@@ -260,8 +262,10 @@ Name             Character
 ``"pluck"``      Sharp attack, fast decay -- guitar pick, harp
 ``"pad"``        Slow fade in, lush sustain -- strings, synth pads
 ``"organ"``      Instant on/off -- Hammond organ, no shaping
-``"bell"``       Instant attack, long ring -- vibraphone, tubular
+``"bell"``       Instant attack, no sustain -- short metallic ring
 ``"strings"``    Gradual bow attack -- orchestral strings, slow
+``"bowed"``      Bow bite into sustain -- solo strings, brass
+``"mallet"``     Strike with ringing sustain -- vibraphone, celesta
 ``"staccato"``   Short and punchy -- funk stabs, percussive hits
 ``"none"``       Raw waveform, no amplitude shaping at all
 ===============  ================================================

docs/index.rst

@@ -77,11 +77,14 @@ What's Inside
   numbers), scale recommendation, modulation, voice leading
 - **Sequencing** — Score, Parts, arpeggiator, legato/glide, velocity,
   swing, humanize, tempo changes, song sections with repeat
-- **Synthesis** — 10 waveforms, 8 envelopes, detune, stereo pan/spread,
-  58 drum patterns (stereo panned), 21 fills
+- **Synthesis** — 13 waveforms (including Karplus-Strong pluck, Hammond organ,
+  bowed string), 10 envelopes, 38 instrument presets, configurable FM,
+  sub-oscillator, noise layer, filter envelope, velocity-to-brightness,
+  detune, stereo pan/spread, 58 drum patterns (stereo panned), 21 fills
 - **Effects** — reverb (algorithmic + 7 convolution IRs, stereo), delay,
-  lowpass (with resonance), distortion, chorus, sidechain compression,
-  automation, LFOs. Master bus compressor/limiter
+  lowpass/highpass (with resonance), distortion, saturation, chorus,
+  phaser, tremolo, sidechain compression, automation, LFOs. Master bus
+  compressor/limiter
 - **Instruments** — 25 presets with fingering generation
 - **Output** — stereo playback, WAV export, MIDI import/export
 - **Interface** — REPL with tab completion, CLI (15 commands), ``pytheory demo``

examples/songs.py

@@ -1116,6 +1116,125 @@ def temple_bell():
     play_song(score)
 
 
+def cinematic_showcase():
+    """Cinematic orchestral showcase — tubular bells, strings, organ, harp, acid bass."""
+    score = Score("4/4", bpm=100)
+
+    # Tubular bells — dramatic intro
+    bells = score.part("bells", instrument="tubular_bells",
+                       reverb=0.5, reverb_type="cathedral")
+    bells.add("A3", Duration.WHOLE)
+    for _ in range(7):
+        bells.rest(Duration.WHOLE)
+
+    # String ensemble — lush wide pad
+    strings = score.part("strings", instrument="string_ensemble",
+                         reverb=0.4, reverb_type="hall")
+    strings.rest(Duration.WHOLE)
+    for sym in ["Am", "F", "C", "G", "Dm", "Am", "E"]:
+        strings.add(Chord.from_symbol(sym), Duration.WHOLE)
+
+    # Cello — deep foundation
+    cello = score.part("cello", instrument="cello",
+                       reverb=0.3, reverb_type="hall")
+    cello.rest(Duration.WHOLE)
+    for n in ["A2", "F2", "C3", "G2", "D3", "A2", "E2"]:
+        cello.add(n, Duration.WHOLE)
+
+    # Violin — legato melody enters bar 3
+    violin = score.part("violin", instrument="violin",
+                        reverb=0.25, reverb_type="hall", legato=True)
+    violin.rest(Duration.WHOLE)
+    violin.rest(Duration.WHOLE)
+    for note, dur in [
+        ("E5", Duration.HALF), ("C5", Duration.HALF),
+        ("D5", Duration.QUARTER), ("E5", Duration.QUARTER), ("G5", Duration.HALF),
+        ("A5", Duration.HALF), ("G5", Duration.QUARTER), ("E5", Duration.QUARTER),
+        ("F5", Duration.WHOLE),
+        ("E5", Duration.HALF), ("D5", Duration.HALF),
+        ("C5", Duration.HALF), ("B4", Duration.HALF),
+        ("A4", Duration.WHOLE),
+    ]:
+        violin.add(note, dur)
+
+    # Organ — enters halfway, cathedral weight
+    organ = score.part("organ", instrument="organ",
+                       reverb=0.3, reverb_type="cathedral")
+    for _ in range(4):
+        organ.rest(Duration.WHOLE)
+    for sym in ["Dm", "Am", "E", "Am"]:
+        organ.add(Chord.from_symbol(sym), Duration.WHOLE)
+
+    # Harp — arpeggiated flourishes bars 3-4
+    harp = score.part("harp", instrument="harp")
+    harp.rest(Duration.WHOLE)
+    harp.rest(Duration.WHOLE)
+    for n in ["A3", "C4", "E4", "A4", "C5", "E5", "A5", "E5",
+              "G3", "B3", "D4", "G4", "B4", "D5", "G5", "D5"]:
+        harp.add(n, Duration.EIGHTH)
+    for _ in range(4):
+        harp.rest(Duration.WHOLE)
+
+    # Vibraphone — shimmer in last bars with delay
+    vib = score.part("vib", instrument="vibraphone",
+                     delay=0.25, delay_time=0.375, delay_feedback=0.35)
+    for _ in range(5):
+        vib.rest(Duration.WHOLE)
+    for note, dur in [
+        ("E5", Duration.QUARTER), ("D5", Duration.QUARTER),
+        ("C5", Duration.QUARTER), ("A4", Duration.QUARTER),
+        ("B4", Duration.HALF), ("E5", Duration.HALF),
+        ("A5", Duration.WHOLE),
+    ]:
+        vib.add(note, dur)
+
+    # Acid bass — gritty texture bars 4-5
+    acid = score.part("acid", instrument="acid_bass")
+    for _ in range(3):
+        acid.rest(Duration.WHOLE)
+    for n in ["C2", "C2", "E2", "G2", "G2", "G2", "A2", "E2",
+              "D2", "D2", "F2", "A2", "A2", "A2", "E2", "E2"]:
+        acid.add(n, Duration.EIGHTH)
+    for _ in range(2):
+        acid.rest(Duration.WHOLE)
+
+    # Half time drums
+    score.drums("half time", repeats=8)
+
+    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),
@@ -1137,6 +1256,8 @@ SONGS = {
     "18": ("Glass and Silk (Sine+Triangle)", glass_and_silk),
     "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__":
@@ -1150,7 +1271,7 @@ if __name__ == "__main__":
             print(f"    {key:>2}. {name}")
 
         print()
-        choice = input("  Pick a song (1-20, 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 = "0.31.0"
+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__ = "0.31.0"
+__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

@@ -243,42 +243,71 @@ def organ_wave(hz, peak=SAMPLE_PEAK, n_samples=SAMPLE_RATE):
 
 
 def strings_wave(hz, peak=SAMPLE_PEAK, n_samples=SAMPLE_RATE):
-    """String ensemble — filtered saw with body resonance formants.
+    """Bowed string — additive synthesis with natural harmonic rolloff.
 
-    Goes beyond raw sawtooth by modeling the resonant body of a
-    stringed instrument. Two formant peaks (at ~500 Hz and ~1500 Hz)
-    shape the spectrum the way a violin or cello body does — boosting
-    certain frequencies and cutting others.
-
-    The result is warmer and more "wooden" than a raw saw wave,
-    with the characteristic nasal quality of bowed strings.
+    Models bowed string physics:
+    - Additive harmonics with 1/n rolloff shaped by body resonance
+    - Delayed vibrato (develops ~200ms in, like a real player)
+    - Subtle bow pressure variation (amplitude modulation)
+    - Per-harmonic phase randomization for natural timbre
+    - Gentle spectral tilt to avoid synthetic brightness
     """
-    # Base: sawtooth (all harmonics, like a bowed string)
-    length = SAMPLE_RATE / float(hz)
-    omega = numpy.pi * 2 / length
-    xvalues = numpy.arange(int(length)) * omega
-    onecycle = scipy.signal.sawtooth(xvalues, width=1)
-    wave = numpy.resize(onecycle, (n_samples,)).astype(numpy.float64)
+    t = numpy.arange(n_samples, dtype=numpy.float64) / SAMPLE_RATE
+    rng = numpy.random.default_rng(int(hz * 100) % 2**31)
 
-    # Body resonance formants — two bandpass peaks
-    # Formant 1: ~500 Hz (body resonance)
-    f1 = 500
-    bw1 = 200
-    b1, a1 = scipy.signal.butter(2, [max(20, f1 - bw1), f1 + bw1],
-                                  btype='band', fs=SAMPLE_RATE)
-    formant1 = scipy.signal.lfilter(b1, a1, wave)
+    # Delayed vibrato: ramps in over ~200ms, like a real bow
+    vib_rate = 5.2 + rng.uniform(-0.3, 0.3)  # slight randomness per note
+    vib_depth = hz * 0.003  # ~5 cents
+    vib_onset = numpy.clip(t / 0.2, 0.0, 1.0)  # ramp over 200ms
+    vibrato = vib_depth * vib_onset * numpy.sin(2 * numpy.pi * vib_rate * t)
 
-    # Formant 2: ~1500 Hz (bridge/top plate)
-    f2 = 1500
-    bw2 = 400
-    b2, a2 = scipy.signal.butter(2, [f2 - bw2, f2 + bw2],
-                                  btype='band', fs=SAMPLE_RATE)
-    formant2 = scipy.signal.lfilter(b2, a2, wave)
+    # Additive synthesis — build harmonics with natural rolloff
+    nyquist = SAMPLE_RATE / 2.0
+    n_harmonics = min(40, int(nyquist / hz))
+    wave = numpy.zeros(n_samples, dtype=numpy.float64)
 
-    # Mix: original (attenuated) + formants
-    mixed = wave * 0.3 + formant1 * 0.4 + formant2 * 0.3
+    # Body resonance curve — emphasizes certain harmonic regions
+    # Modeled after violin/cello response: peaks around 300Hz, 1kHz, 2.5kHz
+    def body_response(f):
+        """Approximate string instrument body resonance."""
+        r = 1.0
+        # Main air resonance (~280 Hz for violin, scales with pitch)
+        air_f = max(200, min(400, hz * 1.5))
+        r += 0.6 * numpy.exp(-((f - air_f) / 100) ** 2)
+        # Wood resonance (~1 kHz)
+        r += 0.4 * numpy.exp(-((f - 1000) / 300) ** 2)
+        # Bridge resonance (~2.5 kHz) — the "presence" peak
+        r += 0.3 * numpy.exp(-((f - 2500) / 500) ** 2)
+        return r
 
-    return (peak * mixed).astype(numpy.int16)
+    for n in range(1, n_harmonics + 1):
+        f_n = hz * n
+        if f_n >= nyquist:
+            break
+        # Amplitude: 1/n rolloff (sawtooth-like) shaped by body
+        amp = (1.0 / n) * body_response(f_n)
+        # Even harmonics slightly weaker (bowing point ~1/8 from bridge)
+        if n % 2 == 0:
+            amp *= 0.85
+        # Random phase per harmonic — prevents the "buzzy" coherent-phase sound
+        phi = rng.uniform(0, 2 * numpy.pi)
+        wave += amp * numpy.sin(2 * numpy.pi * (f_n * t + vibrato * n / hz) + phi)
+
+    # Normalize
+    max_val = numpy.abs(wave).max()
+    if max_val > 0:
+        wave /= max_val
+
+    # Subtle bow pressure variation — slow amplitude wobble
+    bow_pressure = 1.0 + 0.03 * numpy.sin(2 * numpy.pi * 3.7 * t)
+    wave *= bow_pressure
+
+    # Gentle lowpass — real instruments don't have infinite bandwidth
+    cutoff = min(10000, hz * 10)
+    bl, al = scipy.signal.butter(2, cutoff, btype='low', fs=SAMPLE_RATE)
+    wave = scipy.signal.lfilter(bl, al, wave)
+
+    return (peak * wave).astype(numpy.int16)
 
 
 def _apply_envelope(samples, attack, decay, sustain, release, sample_rate=SAMPLE_RATE):
@@ -346,7 +375,9 @@ class Envelope(Enum):
     PLUCK = (0.002, 0.15, 0.0, 0.1)
     PAD = (0.4, 0.2, 0.7, 0.5)
     STRINGS = (0.15, 0.1, 0.8, 0.3)
+    BOWED = (0.04, 0.08, 0.75, 0.25)
     BELL = (0.001, 0.3, 0.0, 0.5)
+    MALLET = (0.002, 0.05, 0.6, 0.8)
     STACCATO = (0.005, 0.05, 0.0, 0.02)
 
 
@@ -1458,6 +1489,41 @@ def _apply_lowpass(samples, cutoff, q=0.707, sample_rate=SAMPLE_RATE):
     return scipy.signal.lfilter(b, a, samples).astype(numpy.float32)
 
 
+def _apply_highpass(samples, cutoff, q=0.707, sample_rate=SAMPLE_RATE):
+    """Apply a 2nd-order Butterworth highpass filter (12 dB/octave).
+
+    Removes low-frequency content below the cutoff. Useful for cleaning
+    up mud from pads, keeping bass parts from masking each other, or
+    thinning out a sound.
+
+    Args:
+        samples: Float32 numpy array.
+        cutoff: Cutoff frequency in Hz.
+        q: Resonance / Q factor (default 0.707 = Butterworth flat).
+        sample_rate: Sample rate in Hz.
+
+    Returns:
+        Float32 array with filter applied.
+    """
+    if cutoff <= 0 or cutoff >= sample_rate / 2:
+        return samples
+
+    w0 = 2 * numpy.pi * cutoff / sample_rate
+    alpha = numpy.sin(w0) / (2 * q)
+
+    b0 = (1 + numpy.cos(w0)) / 2
+    b1 = -(1 + numpy.cos(w0))
+    b2 = (1 + numpy.cos(w0)) / 2
+    a0 = 1 + alpha
+    a1 = -2 * numpy.cos(w0)
+    a2 = 1 - alpha
+
+    b = numpy.array([b0/a0, b1/a0, b2/a0])
+    a = numpy.array([1.0, a1/a0, a2/a0])
+
+    return scipy.signal.lfilter(b, a, samples).astype(numpy.float32)
+
+
 def _apply_chorus(samples, mix=0.5, rate=1.5, depth=0.003,
                    sample_rate=SAMPLE_RATE):
     """Apply a chorus effect — slightly detuned delayed copy mixed in.
@@ -1503,6 +1569,171 @@ def _apply_chorus(samples, mix=0.5, rate=1.5, depth=0.003,
     return samples * (1 - mix * 0.5) + wet * mix * 0.5
 
 
+def _apply_filter_envelope(samples, base_cutoff, amount, f_attack, f_decay,
+                           f_sustain, q=0.707, vel_cutoff_boost=0.0,
+                           sample_rate=SAMPLE_RATE):
+    """Apply a per-note filter envelope — cutoff sweeps over time.
+
+    This is the core of subtractive synthesis: the filter opens on the
+    attack and closes during decay, giving notes a characteristic
+    "bwow" or "wah" shape.
+
+    Uses block-based processing (64-sample blocks) with biquad coefficient
+    interpolation for efficiency and smooth sweeps.
+    """
+    n = len(samples)
+    if n == 0 or amount <= 0:
+        return samples
+
+    block_size = 64
+    out = numpy.empty_like(samples)
+
+    # Build the filter cutoff envelope
+    a_samps = int(f_attack * sample_rate)
+    d_samps = int(f_decay * sample_rate)
+    sustain_level = f_sustain * amount
+
+    cutoff_env = numpy.full(n, sustain_level + base_cutoff + vel_cutoff_boost,
+                            dtype=numpy.float64)
+    # Attack ramp: 0 → amount
+    if a_samps > 0:
+        a_end = min(a_samps, n)
+        cutoff_env[:a_end] = (base_cutoff + vel_cutoff_boost +
+                              numpy.linspace(0, amount, a_end))
+    # Decay ramp: amount → sustain_level
+    if d_samps > 0:
+        d_start = min(a_samps, n)
+        d_end = min(a_samps + d_samps, n)
+        if d_end > d_start:
+            cutoff_env[d_start:d_end] = (base_cutoff + vel_cutoff_boost +
+                                         numpy.linspace(amount, sustain_level,
+                                                        d_end - d_start))
+
+    # Clamp cutoff to valid range
+    cutoff_env = numpy.clip(cutoff_env, 20.0, sample_rate / 2 - 1)
+
+    # Block-based biquad processing with varying cutoff
+    # State variables for the filter
+    x1 = x2 = y1 = y2 = 0.0
+    pos = 0
+    while pos < n:
+        end = min(pos + block_size, n)
+        block = samples[pos:end]
+        # Use cutoff at block midpoint
+        mid = (pos + end) // 2
+        fc = cutoff_env[mid]
+        # Compute biquad coefficients
+        w0 = 2 * numpy.pi * fc / sample_rate
+        sin_w0 = numpy.sin(w0)
+        cos_w0 = numpy.cos(w0)
+        alpha = sin_w0 / (2 * q)
+        b0 = (1 - cos_w0) / 2
+        b1 = 1 - cos_w0
+        b2 = (1 - cos_w0) / 2
+        a0 = 1 + alpha
+        a1 = -2 * cos_w0
+        a2 = 1 - alpha
+        # Normalize
+        b0 /= a0; b1 /= a0; b2 /= a0
+        a1 /= a0; a2 /= a0
+        # Process block sample by sample (maintaining state)
+        out_block = numpy.empty(len(block), dtype=numpy.float32)
+        for i in range(len(block)):
+            x0 = float(block[i])
+            y0 = b0 * x0 + b1 * x1 + b2 * x2 - a1 * y1 - a2 * y2
+            out_block[i] = y0
+            x2 = x1; x1 = x0
+            y2 = y1; y1 = y0
+        out[pos:end] = out_block
+        pos = end
+
+    return out
+
+
+def _apply_saturation(samples, amount=0.5):
+    """Apply tape/tube saturation — subtle even-harmonic warmth.
+
+    Unlike distortion (tanh, odd harmonics), saturation uses a
+    polynomial waveshaper that adds 2nd and 4th harmonics — the
+    warm, pleasing character of analog tape and tube preamps.
+    """
+    if amount <= 0:
+        return samples
+    # Asymmetric polynomial: x + k*x^2 adds even harmonics
+    driven = samples + amount * samples * samples
+    # Normalize to prevent gain buildup
+    driven = driven / (1.0 + amount)
+    # Soft clip any overs
+    return numpy.clip(driven, -1.0, 1.0).astype(numpy.float32)
+
+
+def _apply_tremolo(samples, depth=0.5, rate=5.0, sample_rate=SAMPLE_RATE):
+    """Apply tremolo — amplitude modulation by a sine LFO.
+
+    The classic vibrating amp sound. Essential for vibraphone,
+    electric guitar, and organ Leslie speaker simulation.
+    """
+    if depth <= 0:
+        return samples
+    t = numpy.arange(len(samples), dtype=numpy.float64) / sample_rate
+    lfo = 1.0 - depth * 0.5 * (1.0 + numpy.sin(2 * numpy.pi * rate * t))
+    return (samples * lfo).astype(numpy.float32)
+
+
+def _apply_phaser(samples, mix=0.5, rate=0.5, stages=4,
+                  sample_rate=SAMPLE_RATE):
+    """Apply phaser — swept allpass filter chain.
+
+    Creates moving notches in the frequency spectrum by passing
+    the signal through a chain of allpass filters whose center
+    frequencies are modulated by an LFO. Classic effect for
+    electric piano, pads, and guitar.
+    """
+    if mix <= 0:
+        return samples
+    n = len(samples)
+    block_size = 64
+    t = numpy.arange(n, dtype=numpy.float64) / sample_rate
+
+    # LFO sweeps center frequency between 200Hz and 4000Hz (log scale)
+    lfo = 0.5 + 0.5 * numpy.sin(2 * numpy.pi * rate * t)
+    center_freqs = 200.0 * (20.0 ** lfo)  # 200Hz to 4000Hz
+
+    # Process through allpass stages
+    wet = samples.copy().astype(numpy.float64)
+    for _stage in range(stages):
+        out = numpy.empty(n, dtype=numpy.float64)
+        # Allpass state
+        x1 = x2 = y1 = y2 = 0.0
+        pos = 0
+        while pos < n:
+            end = min(pos + block_size, n)
+            mid = (pos + end) // 2
+            fc = center_freqs[mid]
+            # Allpass biquad coefficients
+            w0 = 2 * numpy.pi * fc / sample_rate
+            alpha = numpy.sin(w0) / 2.0  # Q=0.5 for wide sweep
+            cos_w0 = numpy.cos(w0)
+            b0 = 1 - alpha
+            b1 = -2 * cos_w0
+            b2 = 1 + alpha
+            a0 = 1 + alpha
+            a1 = -2 * cos_w0
+            a2 = 1 - alpha
+            b0 /= a0; b1 /= a0; b2 /= a0
+            a1 /= a0; a2 /= a0
+            for i in range(pos, end):
+                x0 = wet[i]
+                y0 = b0 * x0 + b1 * x1 + b2 * x2 - a1 * y1 - a2 * y2
+                out[i] = y0
+                x2 = x1; x1 = x0
+                y2 = y1; y1 = y0
+            pos = end
+        wet = out
+
+    return (samples * (1 - mix) + wet.astype(numpy.float32) * mix).astype(numpy.float32)
+
+
 def _apply_distortion(samples, drive=1.0, mix=1.0):
     """Apply soft-clip distortion (tanh waveshaping).
 
@@ -1534,7 +1765,13 @@ def _apply_distortion(samples, drive=1.0, mix=1.0):
 
 def _apply_effects_with_params(samples, params, skip_reverb=False):
     """Apply effects using a params dict. Used for both static and automated rendering."""
-    # Signal chain: distortion → chorus → lowpass → delay → reverb
+    # Signal chain: saturation → tremolo → distortion → chorus → phaser
+    #             → highpass → lowpass → delay → reverb
+    if params.get("saturation", 0) > 0:
+        samples = _apply_saturation(samples, amount=params["saturation"])
+    if params.get("tremolo_depth", 0) > 0:
+        samples = _apply_tremolo(samples, depth=params["tremolo_depth"],
+                                 rate=params.get("tremolo_rate", 5.0))
     if params.get("distortion_mix", 0) > 0:
         samples = _apply_distortion(samples,
                                     drive=params.get("distortion_drive", 3.0),
@@ -1544,6 +1781,12 @@ def _apply_effects_with_params(samples, params, skip_reverb=False):
                                 mix=params["chorus_mix"],
                                 rate=params.get("chorus_rate", 1.5),
                                 depth=params.get("chorus_depth", 0.003))
+    if params.get("phaser_mix", 0) > 0:
+        samples = _apply_phaser(samples, mix=params["phaser_mix"],
+                                rate=params.get("phaser_rate", 0.5))
+    if params.get("highpass", 0) > 0:
+        samples = _apply_highpass(samples, params["highpass"],
+                                  params.get("highpass_q", 0.707))
     if params.get("lowpass", 0) > 0:
         samples = _apply_lowpass(samples, params["lowpass"],
                                  params.get("lowpass_q", 0.707))
@@ -1568,11 +1811,18 @@ def _apply_effects_with_params(samples, params, skip_reverb=False):
 def _apply_part_effects(samples, part):
     """Apply all effects configured on a Part to a float32 buffer."""
     params = {
+        "saturation": part.saturation,
+        "tremolo_depth": part.tremolo_depth,
+        "tremolo_rate": part.tremolo_rate,
         "distortion_mix": part.distortion_mix,
         "distortion_drive": part.distortion_drive,
         "chorus_mix": part.chorus_mix,
         "chorus_rate": part.chorus_rate,
         "chorus_depth": part.chorus_depth,
+        "phaser_mix": part.phaser_mix,
+        "phaser_rate": part.phaser_rate,
+        "highpass": part.highpass,
+        "highpass_q": part.highpass_q,
         "lowpass": part.lowpass,
         "lowpass_q": part.lowpass_q,
         "delay_mix": part.delay_mix,
@@ -1716,11 +1966,18 @@ def _total_samples_from_tempo_map(total_beats, tempo_map):
 def _render_notes_to_buf(notes, buf, samples_per_beat, total_samples,
                          synth_fn, envelope_tuple, volume, bpm,
                          swing=0.0, tempo_map=None, humanize=0.0,
-                         detune=0.0, spread=0.0, stereo_buf=None):
+                         detune=0.0, spread=0.0, stereo_buf=None,
+                         sub_osc=0.0, noise_mix=0.0,
+                         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, temperament="equal",
+                         reference_pitch=440.0):
     """Render a list of Notes into an existing buffer at the correct positions."""
     import random as _rnd
 
     a, d, s, r = envelope_tuple
+    _skw = synth_kwargs or {}
     beat_pos = 0.0
     for note_index, note in enumerate(notes):
         if note.tone is not None:
@@ -1744,11 +2001,17 @@ 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()]
-                # Render oscillators
-                waves = [synth_fn(hz, n_samples=n_samples) for hz in pitches]
+                    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]
+                # Sub-oscillator: octave-below sine
+                if sub_osc > 0:
+                    for hz in pitches:
+                        sub = sine_wave(hz / 2, n_samples=n_samples)
+                        waves.append(sub)
                 # Detune: add oscillators shifted by ±cents
                 detune_up = None
                 detune_down = None
@@ -1758,8 +2021,8 @@ def _render_notes_to_buf(notes, buf, samples_per_beat, total_samples,
                     for hz in pitches:
                         hz_up = hz * (2 ** (detune / 1200))
                         hz_down = hz * (2 ** (-detune / 1200))
-                        up_waves.append(synth_fn(hz_up, n_samples=n_samples))
-                        down_waves.append(synth_fn(hz_down, n_samples=n_samples))
+                        up_waves.append(synth_fn(hz_up, n_samples=n_samples, **_skw))
+                        down_waves.append(synth_fn(hz_down, n_samples=n_samples, **_skw))
                     if spread > 0 and stereo_buf is not None:
                         # Spread: detuned oscillators go to opposite channels
                         detune_up = sum(w.astype(numpy.float32) for w in up_waves) / SAMPLE_PEAK
@@ -1768,14 +2031,44 @@ def _render_notes_to_buf(notes, buf, samples_per_beat, total_samples,
                         waves.extend(up_waves + down_waves)
                 n_osc = len(waves)
                 mixed = sum(w.astype(numpy.float32) for w in waves) / (SAMPLE_PEAK * max(1, n_osc))
+                # Mix sub-oscillator with appropriate gain
+                if sub_osc > 0:
+                    # Sub was already included in waves; scale the mix
+                    # Boost the sub contribution relative to main
+                    sub_count = len(pitches)
+                    main_count = n_osc - sub_count
+                    if main_count > 0:
+                        # Re-render: main only + sub at controlled level
+                        main_waves = waves[:n_osc - sub_count]
+                        sub_waves = waves[n_osc - sub_count:]
+                        main_mix = sum(w.astype(numpy.float32) for w in main_waves) / (SAMPLE_PEAK * max(1, len(main_waves)))
+                        sub_mix = sum(w.astype(numpy.float32) for w in sub_waves) / (SAMPLE_PEAK * max(1, len(sub_waves)))
+                        mixed = main_mix * (1.0 - sub_osc * 0.3) + sub_mix * sub_osc * 0.3
+                # Noise layer: add noise following the note
+                if noise_mix > 0:
+                    noise = numpy.random.uniform(-1, 1, n_samples).astype(numpy.float32)
+                    mixed = mixed * (1.0 - noise_mix * 0.5) + noise * noise_mix * 0.5
+                # Amplitude envelope
                 if a > 0 or d > 0 or s < 1.0 or r > 0:
                     mixed = _apply_envelope(mixed, a, d, s, r)
-                # Apply per-note velocity scaling + humanize velocity
+                # Per-note velocity
                 vel = getattr(note, 'velocity', 100)
                 if humanize > 0.0:
                     vel_jitter = int(humanize * 15)
                     vel = max(1, min(127, vel + _rnd.randint(-vel_jitter, vel_jitter)))
                 vel_scale = vel / 127.0
+                # Filter envelope (per-note subtractive filter sweep)
+                if filter_amount > 0:
+                    base_cut = 200.0  # base cutoff before envelope opens it
+                    vel_boost = vel_to_filter * vel_scale if vel_to_filter > 0 else 0.0
+                    mixed = _apply_filter_envelope(
+                        mixed, base_cut, filter_amount,
+                        filter_attack, filter_decay, filter_sustain,
+                        q=filter_q, vel_cutoff_boost=vel_boost)
+                elif vel_to_filter > 0:
+                    # Velocity brightness without filter envelope
+                    vel_cutoff = vel_to_filter * vel_scale + 1000
+                    mixed = _apply_lowpass(mixed, vel_cutoff, q=filter_q)
                 end = min(start + len(mixed), total_samples)
                 buf[start:end] += mixed[:end - start] * volume * vel_scale
                 # Spread detuned oscillators into stereo L/R
@@ -1795,7 +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,
@@ -1825,9 +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
@@ -1940,12 +2234,20 @@ def render_score(score):
             env_tuple = _resolve_envelope(part.envelope)
             # Use part swing if set, otherwise score swing
             effective_swing = part.swing if part.swing is not None else score.swing
+            # Build synth-specific kwargs (e.g. FM ratio/index)
+            synth_kwargs = {}
+            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,
@@ -1955,7 +2257,18 @@ def render_score(score):
                     humanize=part.humanize,
                     detune=part.detune,
                     spread=part.spread,
-                    stereo_buf=stereo_buf)
+                    stereo_buf=stereo_buf,
+                    sub_osc=part.sub_osc,
+                    noise_mix=part.noise_mix,
+                    filter_attack=part.filter_attack,
+                    filter_decay=part.filter_decay,
+                    filter_sustain=part.filter_sustain,
+                    filter_amount=part.filter_amount,
+                    vel_to_filter=part.vel_to_filter,
+                    filter_q=part.lowpass_q,
+                    synth_kwargs=synth_kwargs,
+                    temperament=_temperament,
+                    reference_pitch=_ref_pitch)
 
             # Apply effects — segmented if automation exists
             auto_points = part._get_automation_points()
@@ -1973,8 +2286,10 @@ def render_score(score):
                     params = part._get_params_at(seg_start_beat)
                     segment = part_buf[seg_start:seg_end].copy()
                     has_fx = any(params.get(k, 0) > 0 for k in
-                                ["distortion_mix", "chorus_mix", "lowpass",
-                                 "delay_mix", "reverb_mix"])
+                                ["saturation", "tremolo_depth",
+                                 "distortion_mix", "chorus_mix", "phaser_mix",
+                                 "highpass", "lowpass", "delay_mix",
+                                 "reverb_mix"])
                     if has_fx:
                         segment = _apply_effects_with_params(segment, params)
                     # Apply volume automation
@@ -1983,9 +2298,11 @@ def render_score(score):
                         segment = segment * (seg_vol / part.volume) if part.volume > 0 else segment
                     part_buf[seg_start:seg_end] = segment
             else:
-                has_fx = (part.lowpass > 0 or part.delay_mix > 0
-                          or part.reverb_mix > 0 or part.distortion_mix > 0
-                          or part.chorus_mix > 0)
+                has_fx = (part.saturation > 0 or part.tremolo_depth > 0
+                          or part.distortion_mix > 0 or part.chorus_mix > 0
+                          or part.phaser_mix > 0 or part.highpass > 0
+                          or part.lowpass > 0 or part.delay_mix > 0
+                          or part.reverb_mix > 0)
                 if has_fx:
                     part_buf = _apply_part_effects(part_buf, part)
             # Apply sidechain compression if enabled
@@ -2092,7 +2409,10 @@ def render_score(score):
             part_stereo[start:start + hit_len] += panned
 
         # Apply this drum Part's effects
-        has_drum_fx = (drum_part.lowpass > 0 or drum_part.delay_mix > 0
+        has_drum_fx = (drum_part.saturation > 0 or drum_part.tremolo_depth > 0
+                          or drum_part.phaser_mix > 0
+                          or drum_part.highpass > 0 or drum_part.lowpass > 0
+                          or drum_part.delay_mix > 0
                        or drum_part.reverb_mix > 0 or drum_part.distortion_mix > 0
                        or drum_part.chorus_mix > 0)
         if has_drum_fx:

pytheory/rhythm.py

@@ -15,105 +15,124 @@ INSTRUMENTS = {
     # ── Keys ──
     "piano": {
         "synth": "fm", "envelope": "piano",
+        "fm_ratio": 1.0, "fm_index": 1.5,
         "detune": 5, "chorus": 0.1, "chorus_rate": 0.3,
-        "lowpass": 6000,
+        "lowpass": 6000, "saturation": 0.1,
+        "vel_to_filter": 3000, "noise_mix": 0.02,
     },
     "electric_piano": {  # Rhodes/Wurlitzer
         "synth": "fm", "envelope": "piano",
+        "fm_ratio": 1.0, "fm_index": 2.0,
         "detune": 6, "chorus": 0.2, "chorus_rate": 1.0,
-        "lowpass": 4000,
+        "lowpass": 4000, "saturation": 0.15,
+        "tremolo_depth": 0.15, "tremolo_rate": 4.5,
     },
     "organ": {
         "synth": "organ_synth", "envelope": "organ",
         "chorus": 0.2, "chorus_rate": 5.5,
         "lowpass": 5000,
+        "phaser": 0.15, "phaser_rate": 0.4,
     },
     "harpsichord": {
         "synth": "pluck_synth", "envelope": "none",
         "lowpass": 3500,
     },
     "celesta": {
-        "synth": "fm", "envelope": "bell",
+        "synth": "fm", "envelope": "mallet",
+        "fm_ratio": 3.0, "fm_index": 5.0,
         "lowpass": 8000,
         "reverb": 0.3, "reverb_type": "plate",
     },
     "music_box": {
-        "synth": "sine", "envelope": "bell",
+        "synth": "sine", "envelope": "mallet",
         "lowpass": 6000,
         "reverb": 0.25, "reverb_type": "plate",
     },
 
     # ── Strings ──
     "violin": {
-        "synth": "strings_synth", "envelope": "strings",
-        "detune": 4, "lowpass": 5000,
-        "humanize": 0.15,
+        "synth": "strings_synth", "envelope": "bowed",
+        "detune": 2, "lowpass": 5000,
+        "humanize": 0.15, "vel_to_filter": 1500,
+        "noise_mix": 0.03,
     },
     "viola": {
-        "synth": "strings_synth", "envelope": "strings",
-        "detune": 4, "lowpass": 3500,
-        "humanize": 0.15,
+        "synth": "strings_synth", "envelope": "bowed",
+        "detune": 2, "lowpass": 3500,
+        "humanize": 0.15, "vel_to_filter": 1200,
+        "noise_mix": 0.03,
     },
     "cello": {
-        "synth": "strings_synth", "envelope": "strings",
-        "detune": 4, "lowpass": 2500,
-        "humanize": 0.15,
+        "synth": "strings_synth", "envelope": "bowed",
+        "detune": 2, "lowpass": 2500,
+        "humanize": 0.15, "vel_to_filter": 1000,
+        "noise_mix": 0.02,
     },
     "contrabass": {
-        "synth": "strings_synth", "envelope": "strings",
-        "detune": 3, "lowpass": 1500,
-        "humanize": 0.1,
+        "synth": "strings_synth", "envelope": "bowed",
+        "detune": 2, "lowpass": 1500,
+        "humanize": 0.1, "vel_to_filter": 800,
+        "sub_osc": 0.15,
     },
     "string_ensemble": {
         "synth": "strings_synth", "envelope": "pad",
-        "detune": 12, "spread": 0.6,
+        "detune": 10, "spread": 0.5,
         "chorus": 0.2, "chorus_rate": 0.5,
         "lowpass": 4000,
+        "noise_mix": 0.02, "saturation": 0.05,
     },
 
     # ── Woodwinds ──
     "flute": {
         "synth": "sine", "envelope": "strings",
         "lowpass": 4000,
-        "humanize": 0.2,
+        "humanize": 0.2, "noise_mix": 0.08,
+        "vel_to_filter": 2000,
     },
     "clarinet": {
         "synth": "square", "envelope": "strings",
         "lowpass": 3000,
-        "humanize": 0.15,
+        "humanize": 0.15, "noise_mix": 0.05,
+        "vel_to_filter": 1500,
     },
     "oboe": {
         "synth": "saw", "envelope": "strings",
         "lowpass": 3500, "lowpass_q": 1.2,
-        "humanize": 0.15,
+        "humanize": 0.15, "noise_mix": 0.04,
+        "vel_to_filter": 1000,
     },
     "bassoon": {
         "synth": "saw", "envelope": "strings",
         "lowpass": 2000,
-        "humanize": 0.15,
+        "humanize": 0.15, "noise_mix": 0.04,
+        "vel_to_filter": 800,
     },
 
     # ── Brass ──
     "trumpet": {
-        "synth": "saw", "envelope": "pluck",
+        "synth": "saw", "envelope": "bowed",
         "detune": 3, "lowpass": 4000, "lowpass_q": 1.1,
-        "humanize": 0.15,
+        "humanize": 0.15, "vel_to_filter": 2000,
+        "saturation": 0.1,
     },
     "trombone": {
         "synth": "saw", "envelope": "strings",
         "detune": 3, "lowpass": 2500,
-        "humanize": 0.15,
+        "humanize": 0.15, "vel_to_filter": 1500,
+        "saturation": 0.1,
     },
     "french_horn": {
         "synth": "saw", "envelope": "strings",
         "detune": 4, "lowpass": 2000,
         "chorus": 0.1,
-        "humanize": 0.15,
+        "humanize": 0.15, "vel_to_filter": 1200,
+        "saturation": 0.1,
     },
     "tuba": {
         "synth": "saw", "envelope": "strings",
         "detune": 3, "lowpass": 1200,
-        "humanize": 0.1,
+        "humanize": 0.1, "vel_to_filter": 600,
+        "sub_osc": 0.2,
     },
     "brass_ensemble": {
         "synth": "saw", "envelope": "strings",
@@ -136,18 +155,18 @@ INSTRUMENTS = {
     "distorted_guitar": {
         "synth": "saw", "envelope": "pluck",
         "detune": 8, "distortion": 0.6, "distortion_drive": 5.0,
-        "lowpass": 3000,
+        "lowpass": 3000, "saturation": 0.3,
         "humanize": 0.15,
     },
     "bass_guitar": {
         "synth": "triangle", "envelope": "pluck",
         "lowpass": 1000,
-        "humanize": 0.1,
+        "humanize": 0.1, "sub_osc": 0.2,
     },
     "upright_bass": {
-        "synth": "sine", "envelope": "pluck",
+        "synth": "triangle", "envelope": "pluck",
         "lowpass": 800,
-        "humanize": 0.15,
+        "humanize": 0.15, "saturation": 0.1,
     },
     "harp": {
         "synth": "pluck_synth", "envelope": "none",
@@ -170,49 +189,65 @@ INSTRUMENTS = {
         "synth": "saw", "envelope": "pluck",
         "detune": 8, "lowpass": 3000,
         "delay": 0.2, "delay_time": 0.25, "delay_feedback": 0.3,
+        "filter_attack": 0.01, "filter_decay": 0.3,
+        "filter_sustain": 0.2, "filter_amount": 3000,
     },
     "synth_pad": {
         "synth": "supersaw", "envelope": "pad",
         "detune": 12, "spread": 0.6,
         "chorus": 0.2,
+        "phaser": 0.3, "phaser_rate": 0.3,
+        "sub_osc": 0.2,
     },
     "synth_bass": {
         "synth": "saw", "envelope": "pluck",
         "lowpass": 800, "lowpass_q": 1.3,
+        "filter_attack": 0.005, "filter_decay": 0.2,
+        "filter_sustain": 0.0, "filter_amount": 2000,
+        "sub_osc": 0.4,
     },
     "acid_bass": {
         "synth": "saw", "envelope": "pad",
         "legato": True, "glide": 0.03,
         "distortion": 0.7, "distortion_drive": 8.0,
         "lowpass": 800, "lowpass_q": 5.0,
+        "filter_attack": 0.005, "filter_decay": 0.15,
+        "filter_sustain": 0.0, "filter_amount": 4000,
+        "vel_to_filter": 3000,
     },
     "808_bass": {
         "synth": "sine", "envelope": "pluck",
         "distortion": 0.4, "distortion_drive": 2.5,
         "lowpass": 200, "lowpass_q": 1.5,
+        "sub_osc": 0.5, "saturation": 0.2,
     },
 
     # ── Percussion / Mallet ──
     "vibraphone": {
-        "synth": "fm", "envelope": "bell",
+        "synth": "fm", "envelope": "mallet",
+        "fm_ratio": 1.0, "fm_index": 1.0,
         "lowpass": 5000,
+        "tremolo_depth": 0.3, "tremolo_rate": 5.5,
         "reverb": 0.3, "reverb_type": "plate",
     },
     "marimba": {
-        "synth": "sine", "envelope": "pluck",
+        "synth": "sine", "envelope": "mallet",
         "lowpass": 3000,
     },
     "xylophone": {
         "synth": "fm", "envelope": "pluck",
+        "fm_ratio": 3.0, "fm_index": 5.0,
         "lowpass": 6000,
     },
     "glockenspiel": {
-        "synth": "fm", "envelope": "bell",
+        "synth": "fm", "envelope": "mallet",
+        "fm_ratio": 4.0, "fm_index": 6.0,
         "lowpass": 8000,
         "reverb": 0.2,
     },
     "tubular_bells": {
-        "synth": "fm", "envelope": "bell",
+        "synth": "fm", "envelope": "mallet",
+        "fm_ratio": 2.0, "fm_index": 3.0,
         "reverb": 0.4, "reverb_type": "cathedral",
     },
 }
@@ -1571,6 +1606,7 @@ class Part:
                  reverb_type: str = "algorithmic",
                  delay: float = 0.0, delay_time: float = 0.375,
                  delay_feedback: float = 0.4,
+                 highpass: float = 0.0, highpass_q: float = 0.707,
                  lowpass: float = 0.0, lowpass_q: float = 0.707,
                  distortion: float = 0.0, distortion_drive: float = 3.0,
                  legato: bool = False, glide: float = 0.0,
@@ -1582,7 +1618,22 @@ class Part:
                  sidechain_release: float = 0.1,
                  detune: float = 0.0,
                  pan: float = 0.0,
-                 spread: float = 0.0):
+                 spread: float = 0.0,
+                 # ── New synth engine params ──
+                 sub_osc: float = 0.0,
+                 noise_mix: float = 0.0,
+                 filter_attack: float = 0.01,
+                 filter_decay: float = 0.3,
+                 filter_sustain: float = 0.0,
+                 filter_amount: float = 0.0,
+                 vel_to_filter: float = 0.0,
+                 saturation: float = 0.0,
+                 tremolo_depth: float = 0.0,
+                 tremolo_rate: float = 5.0,
+                 phaser: float = 0.0,
+                 phaser_rate: float = 0.5,
+                 fm_ratio: float = 2.0,
+                 fm_index: float = 3.0):
         self.name = name
         self.synth = synth
         self.envelope = envelope
@@ -1597,6 +1648,8 @@ class Part:
         self.delay_mix = delay
         self.delay_time = delay_time
         self.delay_feedback = delay_feedback
+        self.highpass = highpass
+        self.highpass_q = highpass_q
         self.lowpass = lowpass
         self.lowpass_q = lowpass_q
         self.distortion_mix = distortion
@@ -1609,6 +1662,22 @@ class Part:
         self.detune = detune
         self.pan = pan
         self.spread = spread
+        # New synth engine params
+        self.sub_osc = sub_osc
+        self.noise_mix = noise_mix
+        self.filter_attack = filter_attack
+        self.filter_decay = filter_decay
+        self.filter_sustain = filter_sustain
+        self.filter_amount = filter_amount
+        self.vel_to_filter = vel_to_filter
+        self.saturation = saturation
+        self.tremolo_depth = tremolo_depth
+        self.tremolo_rate = tremolo_rate
+        self.phaser_mix = phaser
+        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
@@ -1624,7 +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))
@@ -1673,6 +1742,8 @@ class Part:
                 mapped["distortion_mix"] = v
             elif k == "chorus":
                 mapped["chorus_mix"] = v
+            elif k == "phaser":
+                mapped["phaser_mix"] = v
             else:
                 mapped[k] = v
         self._automation.append((beat_pos, mapped))
@@ -1683,10 +1754,14 @@ class Part:
         # Start with initial values
         params = {
             "volume": self.volume,
+            "saturation": self.saturation,
+            "tremolo_depth": self.tremolo_depth, "tremolo_rate": self.tremolo_rate,
             "reverb_mix": self.reverb_mix, "reverb_decay": self.reverb_decay,
             "reverb_type": self.reverb_type,
             "delay_mix": self.delay_mix, "delay_time": self.delay_time,
             "delay_feedback": self.delay_feedback,
+            "phaser_mix": self.phaser_mix, "phaser_rate": self.phaser_rate,
+            "highpass": self.highpass, "highpass_q": self.highpass_q,
             "lowpass": self.lowpass, "lowpass_q": self.lowpass_q,
             "distortion_mix": self.distortion_mix,
             "distortion_drive": self.distortion_drive,
@@ -1998,13 +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] = {}
@@ -2075,6 +2154,7 @@ class Score:
              reverb_type: str = None,
              delay: float = None, delay_time: float = None,
              delay_feedback: float = None,
+             highpass: float = None, highpass_q: float = None,
              lowpass: float = None, lowpass_q: float = None,
              distortion: float = None, distortion_drive: float = None,
              legato: bool = None, glide: float = None,
@@ -2086,7 +2166,22 @@ class Score:
              sidechain_release: float = None,
              detune: float = None,
              pan: float = None,
-             spread: float = None) -> Part:
+             spread: float = None,
+             # New synth engine params
+             sub_osc: float = None,
+             noise_mix: float = None,
+             filter_attack: float = None,
+             filter_decay: float = None,
+             filter_sustain: float = None,
+             filter_amount: float = None,
+             vel_to_filter: float = None,
+             saturation: float = None,
+             tremolo_depth: float = None,
+             tremolo_rate: float = None,
+             phaser: float = None,
+             phaser_rate: float = None,
+             fm_ratio: float = None,
+             fm_index: float = None) -> Part:
         """Create a named part with its own synth voice and effects.
 
         Args:
@@ -2179,6 +2274,7 @@ class Score:
             "reverb_type": reverb_type,
             "delay": delay, "delay_time": delay_time,
             "delay_feedback": delay_feedback,
+            "highpass": highpass, "highpass_q": highpass_q,
             "lowpass": lowpass, "lowpass_q": lowpass_q,
             "distortion": distortion, "distortion_drive": distortion_drive,
             "legato": legato, "glide": glide,
@@ -2187,6 +2283,14 @@ class Score:
             "swing": swing, "humanize": humanize,
             "sidechain": sidechain, "sidechain_release": sidechain_release,
             "detune": detune, "pan": pan, "spread": spread,
+            "sub_osc": sub_osc, "noise_mix": noise_mix,
+            "filter_attack": filter_attack, "filter_decay": filter_decay,
+            "filter_sustain": filter_sustain, "filter_amount": filter_amount,
+            "vel_to_filter": vel_to_filter,
+            "saturation": saturation,
+            "tremolo_depth": tremolo_depth, "tremolo_rate": tremolo_rate,
+            "phaser": phaser, "phaser_rate": phaser_rate,
+            "fm_ratio": fm_ratio, "fm_index": fm_index,
         }
         for k, v in _locals.items():
             if v is not None:
@@ -2195,6 +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

@@ -31,6 +31,7 @@ class Tone:
         alt_names: Optional[list[str]] = None,
         octave: Optional[int] = None,
         system: Union[str, object] = "western",
+        _validate: bool = True,
     ) -> None:
         """Initialize a Tone with a name, optional octave, and musical system.
 
@@ -46,15 +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
@@ -68,6 +82,13 @@ class Tone:
             self.system_name = None
             self._system = system
 
+        # Validate tone name against the system early (fixes #39).
+        if _validate and self.system.resolve_name(name) is None:
+            raise ValueError(
+                f"Unknown tone name: {name!r}. "
+                f"Not found in the {system!r} system."
+            )
+
     @property
     def exists(self) -> bool:
         """True if this tone's name is found in the associated system."""
@@ -335,17 +356,20 @@ 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)
         else:
-            return klass(name=tone, octave=octave)
+            return klass(name=tone, octave=octave, _validate=False)
 
     @classmethod
     def from_tuple(klass, t: tuple[str, ...]) -> Tone:
@@ -381,19 +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
@@ -409,13 +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
@@ -434,10 +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:
@@ -453,7 +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!")
 
@@ -467,19 +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)
 
@@ -530,9 +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:
@@ -555,6 +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)
 
@@ -596,42 +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
@@ -687,21 +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

@@ -68,9 +68,16 @@ def test_tone_system():
 
 def test_tone_exists():
     c4 = Tone(name="C", octave=4, system="western")
-    invalid_tone = Tone(name="H", octave=4, system="western")
     assert c4.exists is True
-    assert invalid_tone.exists is False
+
+
+def test_tone_invalid_raises():
+    """Invalid tone names raise ValueError at construction time (fixes #39)."""
+    import pytest
+    with pytest.raises(ValueError, match="Unknown tone name"):
+        Tone(name="H", octave=4, system="western")
+    with pytest.raises(ValueError, match="Unknown tone name"):
+        Tone("X")
 
 
 def test_tone_names_method():
@@ -4248,7 +4255,7 @@ def test_parallel_modes_g_major():
 @needs_portaudio
 def test_envelope_enum_presets():
     from pytheory.play import Envelope
-    assert len(Envelope) == 8
+    assert len(Envelope) == 10
     for e in Envelope:
         a, d, s, r = e.value
         assert a >= 0
@@ -4839,10 +4846,11 @@ def test_solfege_no_octave():
     assert t.solfege == "Do"
 
 
-def test_solfege_unknown_returns_name():
-    """A non-standard name should be returned unchanged."""
-    t = Tone(name="X", system="western")
-    assert t.solfege == "X"
+def test_solfege_unknown_raises():
+    """A non-standard name should raise ValueError at construction (fixes #39)."""
+    import pytest
+    with pytest.raises(ValueError, match="Unknown tone name"):
+        Tone(name="X", system="western")
 
 
 # ── Rhythm / Duration system ────────────────────────────────────────────────
@@ -6471,9 +6479,10 @@ def test_instrument_violin():
     score = Score("4/4", bpm=120)
     p = score.part("v", instrument="violin")
     assert p.synth == "strings_synth"
-    assert p.envelope == "strings"
+    assert p.envelope == "bowed"
     assert p.humanize == 0.15
     assert p.lowpass == 5000
+    assert p.detune == 2
 
 
 def test_instrument_override():
@@ -6512,7 +6521,7 @@ def test_instrument_effects():
     assert p.reverb_mix == 0.3
     assert p.reverb_type == "plate"
     assert p.synth == "fm"
-    assert p.envelope == "bell"
+    assert p.envelope == "mallet"
 
 
 def test_instrument_808_bass():
@@ -6525,3 +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 = "0.31.0"
+version = "0.33.0"
 source = { editable = "." }
 dependencies = [
     { name = "numeral" },