scales-modes-and-tunings-with-pytheory

name	scales-modes-and-tunings-with-pytheory
description	Explore scales, modes, tones, and tuning systems with PyTheory. Use when the user asks about a scale or mode (notes of D dorian, harmonize a scale), which scale to solo with over some notes, intervals between notes, the overtone series, the circle of fifths, Hindustani ragas (aroha/avaroha, pakad, time of day, shruti just intonation), microtonal / non-Western systems (maqam, gamelan, 19-TET, just/meantone temperament), or note↔frequency↔MIDI conversions. For chords/keys use the chord-lab or keys-and-harmony skills.
license	MIT
allowed-tools	Write, Read, Bash(python3:*), Bash(uv run:*)

Scales, Modes & Tunings

Scales and modes, the notes/intervals beneath them, and PyTheory's 16 tuning systems.

Scales & modes

from pytheory import TonedScale

ts = TonedScale(tonic="C4", system="western")
ts.scales                       # ('chromatic','major','minor','dorian','lydian', …)

s = ts["dorian"]
s.note_names                    # ['C', 'D', 'Eb', 'F', 'G', 'A', 'Bb', 'C']
[str(t) for t in s.tones]       # ['C4', 'D4', 'Eb4', 'F4', …]
s.harmonize()                   # diatonic chords built on each degree

Pentatonic & blues scales live in the blues system, not western: TonedScale(tonic="E2", system="blues")["minor pentatonic"] (also "major pentatonic", "blues", "major blues").

Which scale fits these notes?

Scale.recommend ranks scales by how well they contain a set of notes — great for "what can I solo with here?". Note the import: pytheory.Scale is an alias for TonedScale, so import the real class from pytheory.scales:

from pytheory.scales import Scale
Scale.recommend("C", "Eb", "G", "Bb", "D", top=3)
# [('C', 'aeolian', 1.0), ('G', 'aeolian', 1.0), ('C', 'dorian', 1.0)]
# -> (tonic, scale_name, fitness 0..1)

Detect the scale of a note set:

TonedScale(tonic="C4", system="western")["major"].detect("C","D","E","F","G","A","B")
# ('C', 'major', 7)   -> (tonic, scale, matched-note count)

Tones, intervals, overtones

from pytheory import Tone

Tone.from_string("A4").frequency          # 440.0
Tone.from_midi(69)                        # <Tone A4>
Tone.from_frequency(440.0)                # <Tone A4>
Tone.from_string("C4").interval_to(Tone.from_string("G4"))   # 'perfect 5th'
Tone.from_string("A2").overtones(4)       # [110.0, 220.0, 330.0, 440.0]
[str(t) for t in Tone.from_string("C4").circle_of_fifths()]  # ['C4','G4','D5','A5', …]

Twelve-tone rows (serialism)

A ToneRow is an ordering of all 12 pitch classes, each once. From it come the 48 forms (P/R/I/RI × 12 transpositions) and the row matrix. The transposition number is the pitch class the form begins on.

from pytheory import ToneRow

row = ToneRow.from_names("C","C#","E","D","F","D#","F#","A","G#","G","B","A#")
row.P(0); row.I(0); row.R(0); row.RI(0)   # the four operations, starting on C
row.form("RI7")                            # any form by label
row.all_forms()                            # all 48, {label: [pitch classes]}
print(row.matrix_str())                    # the 12x12 matrix (P→ R← I↓ RI↑)
row.is_all_interval                        # uses each interval 1–11 once?

Every row/column of the matrix is a permutation of 0–11 and the diagonal is all zeros — handy invariants if you ever need to sanity-check output.

Tuning systems & temperaments

from pytheory import SYSTEMS
list(SYSTEMS)        # 16: 'western','indian','arabic','japanese','blues',
                     # 'gamelan','19-tet','31-tet','shruti', …

Build scales in any system, e.g. an Indian raga or Arabic maqam:

TonedScale(tonic="C4", system="indian").scales      # the 10 thaats (parent scales)
TonedScale(tonic="C4", system="arabic")["..."]      # maqamat

Ragas (Hindustani)

The indian system gives the ten thaats (parent scales). For the living ragas — ascending/descending lines, characteristic phrase, time of day, and rasa — use Raga, which intones them in the shruti (just) tuning, not 12-TET:

from pytheory import Raga

r = Raga.get("yaman")
r.aroha_swaras()        # ['N.', 'R', 'G', 'M', 'D', 'N', "S'"]
r.avaroha_swaras()
r.note_names("D")       # voice it in any key — Sa is movable
r.vadi, r.samvadi, r.time, r.rasa, r.jati

r.shruti_table("C")     # each swara's just ratio + cents off 12-TET
r.just_ratios()["G"]    # Fraction(5, 4) — the just major third

r.play("C4")            # sitar, just intonation, light reverb (just=False = 12-TET)

Raga.names()            # all 36
Raga.by_thaat("kafi")
Raga.by_time("night")

From the CLI: pytheory raga yaman --shruti --play (prints the shruti table, then plays it); pytheory raga --thaat bhairav lists ragas by thaat.

Temperament

Temperament affects the actual pitch (Hz) of a tone:

Tone.from_string("E4").pitch(temperament="just")    # 330.0 (vs ~329.6 equal)
# Whole-score tuning: Score("4/4", bpm=90, system="shruti", temperament="just")

Tips

• Scale.recommend and Scale.detect-style helpers take note name strings.
• pytheory.Scale is aliased to TonedScale; the static recommend lives on pytheory.scales.Scale.
• Temperaments include equal (default), just, meantone, pythagorean.
• To actually play in an alternate system, pass system=/temperament= to Score(...) (see the composing skill).