Musical Systems¶

PyTheory supports 16 musical systems — 6 core systems mapped onto 12-tone equal temperament, plus 10 microtonal systems with their own native tunings. The core systems let you compare scales across cultures; the microtonal systems go beyond 12-TET into genuinely different pitch universes.

Western¶

The standard 12-tone equal temperament system — the common language of European classical music, American popular music, and virtually all commercially recorded music since the early 20th century. Its major/minor tonality system, seven diatonic modes, and rich harmonic vocabulary form the foundation that most listeners around the world grew up hearing. If you’ve ever hummed along to a pop song, played piano, or picked up a guitar, you’ve been working within this system.

>>> from pytheory import TonedScale

>>> c = TonedScale(tonic="C4")
>>> c["major"].note_names
['C', 'D', 'E', 'F', 'G', 'A', 'B', 'C']

>>> c["dorian"].note_names
['C', 'D', 'Eb', 'F', 'G', 'A', 'Bb', 'C']

Scales: major, minor, harmonic minor, ionian, dorian, phrygian, lydian, mixolydian, aeolian, locrian, chromatic

Indian Classical (Hindustani)¶

One of the oldest and most sophisticated musical traditions on earth, Hindustani classical music dates back over two thousand years to the Natya Shastra. Where Western music emphasizes harmony (chords), Indian music emphasizes raga — melodic frameworks that evoke specific moods, times of day, and seasons. The sound is meditative, ornamental, and deeply expressive. You’ll hear it in classical sitar and tabla performances, Bollywood film scores, and the improvisatory traditions that influenced musicians from George Harrison to John Coltrane.

The Hindustani system uses swaras (Sa, Re, Ga, Ma, Pa, Dha, Ni) and organizes scales into thaats — the 10 parent scales from which ragas are derived.

>>> from pytheory import TonedScale

>>> sa = TonedScale(tonic="Sa4", system="indian")

>>> sa["bilawal"].note_names   # = major scale
['Sa', 'Re', 'Ga', 'Ma', 'Pa', 'Dha', 'Ni', 'Sa']

>>> sa["bhairav"].note_names   # unique to Indian music
['Sa', 'komal Re', 'Ga', 'Ma', 'Pa', 'komal Dha', 'Ni', 'Sa']

>>> sa["todi"].note_names
['Sa', 'komal Re', 'komal Ga', 'tivra Ma', 'Pa', 'komal Dha', 'Ni', 'Sa']

Thaats: bilawal, khamaj, kafi, asavari, bhairavi, kalyan, bhairav, poorvi, marwa, todi

Swara notation:

Uppercase = shuddha (natural): Sa, Re, Ga, Ma, Pa, Dha, Ni
komal prefix = flat: komal Re, komal Ga, komal Dha, komal Ni
tivra prefix = sharp: tivra Ma

Arabic Maqam¶

The maqam tradition spans the entire Arab world, Turkey, Iran, and Central Asia — a vast musical heritage stretching from medieval Andalusia to modern Cairo. Maqam music is melodically rich, often featuring microtonal inflections, elaborate ornamentation, and a sense of yearning that’s unmistakable once you’ve heard it. Think of the oud-driven classical traditions of Umm Kulthum and Fairuz, the call to prayer, Sufi devotional music, and the underpinning of much Middle Eastern and North African popular music today.

The Arabic system uses solfège-based names (Do, Re, Mi, Fa, Sol, La, Si) and organizes scales into maqamat (plural of maqam).

Note

True maqam music uses quarter-tones that cannot be represented in 12-tone equal temperament. These scales are the closest 12-TET approximations.

>>> from pytheory import TonedScale

>>> do = TonedScale(tonic="Do4", system="arabic")

>>> do["ajam"].note_names     # = major scale
['Do', 'Re', 'Mi', 'Fa', 'Sol', 'La', 'Si', 'Do']

>>> do["hijaz"].note_names    # characteristic augmented 2nd
['Do', 'Reb', 'Mi', 'Fa', 'Sol', 'Solb', 'Sib', 'Do']

>>> do["nikriz"].note_names
['Do', 'Re', 'Mib', 'Fa#', 'Sol', 'La', 'Sib', 'Do']

Maqamat: ajam, nahawand, kurd, hijaz, nikriz, bayati, rast, saba, sikah, jiharkah

Japanese¶

Japan’s traditional scales have a hauntingly beautiful quality that is immediately recognizable — dark, sparse, and full of tension. The pentatonic scales (especially hirajoshi and in) use semitone steps that give them an unmistakably Japanese character, distinct from the wider-spaced pentatonics found in Chinese and Western folk music. You’ll hear these scales in koto and shamisen music, the gagaku court orchestra, Kabuki and Noh theater, taiko drumming, anime and video game soundtracks, and the compositions of Toru Takemitsu.

The Japanese system uses Western note names with traditional pentatonic and heptatonic scales from Japanese music.

>>> from pytheory import TonedScale

>>> c = TonedScale(tonic="C4", system="japanese")

>>> c["hirajoshi"].note_names  # most iconic Japanese scale
['C', 'D', 'Eb', 'G', 'Ab', 'C']

>>> c["in"].note_names         # Miyako-bushi, used in koto music
['C', 'Db', 'F', 'G', 'Ab', 'C']

>>> c["yo"].note_names         # folk music scale
['C', 'D', 'F', 'G', 'A#', 'C']

>>> c["ritsu"].note_names      # gagaku court music (= Dorian)
['C', 'D', 'Eb', 'F', 'G', 'A', 'Bb', 'C']

Pentatonic scales: hirajoshi, in, yo, iwato, kumoi, insen

Heptatonic scales: ritsu, ryo

Blues and Pentatonic¶

The blues is America’s deepest musical root — born from the African American experience in the Mississippi Delta, it gave rise to jazz, rock and roll, R&B, soul, funk, and hip-hop. The blue note (a flattened 5th that bends between major and minor) is the sound of emotional truth in music, from Robert Johnson to B.B. King to Jimi Hendrix.

The blues system provides the scales foundational to blues, rock, jazz, and folk music worldwide. Pentatonic scales (5 notes) are the oldest known musical scales, found independently in cultures across every continent.

The blues scale adds the “blue note” (flat 5th / sharp 4th) to the minor pentatonic — this chromatic passing tone is the defining sound of the blues.

>>> from pytheory import TonedScale

>>> c = TonedScale(tonic="C4", system="blues")

>>> c["major pentatonic"].note_names  # the "happy" pentatonic
['C', 'D', 'E', 'G', 'A', 'C']

>>> c["minor pentatonic"].note_names  # the "sad" pentatonic
['C', 'D#', 'F', 'G', 'A#', 'C']

>>> c["blues"].note_names             # minor pentatonic + blue note
['C', 'Eb', 'F', 'Gb', 'G', 'Bb', 'C']

>>> c["major blues"].note_names       # major pentatonic + blue note
['C', 'D', 'Eb', 'E', 'G', 'A', 'C']

Pentatonic: major pentatonic, minor pentatonic

Hexatonic: blues, major blues

Heptatonic: dominant (Mixolydian — the dominant 7th sound), minor (Dorian — the jazz minor sound)

Javanese Gamelan¶

Gamelan is the shimmering, interlocking percussion orchestra of Java and Bali — one of the most otherworldly sounds in all of music. Ensembles of bronze metallophones, gongs, drums, and bamboo flutes create waves of resonance that influenced Claude Debussy, Steve Reich, and countless ambient and electronic artists. Each gamelan is tuned uniquely, so no two ensembles sound exactly alike. The music is communal, ceremonial, and deeply tied to Javanese and Balinese culture — it accompanies shadow puppet theater (wayang), dance, and religious ritual.

The gamelan system approximates the scales of the Javanese and Balinese gamelan orchestra in 12-tone equal temperament. True gamelan tuning is unique to each ensemble and does not conform to Western intonation — these are the closest 12-TET approximations.

Slendro is a roughly equal 5-tone division of the octave, producing an ethereal, floating quality. Pelog is a 7-tone scale with unequal intervals, typically performed using 5-note subsets called pathet.

>>> from pytheory import TonedScale

>>> ji = TonedScale(tonic="ji4", system="gamelan")

>>> ji["slendro"].note_names      # the 5-tone equidistant scale
['ji', 'ro', 'pat', 'mo', 'pi', 'ji']

>>> ji["pelog"].note_names         # full 7-tone pelog
['ji', 'ro-', 'lu', 'pat', 'mo', 'nem-', 'barang', 'ji']

>>> ji["pelog nem"].note_names     # pathet nem subset
['ji', 'ro-', 'lu', 'pat', 'mo', 'ji']

Pentatonic: slendro, pelog nem, pelog barang, pelog lima

Heptatonic: pelog (full 7-tone)

Note

Gamelan tone names follow Javanese numbering: ji (1), ro (2), lu (3), pat (4), mo (5), nem (6), pi/barang (7). Suffixes indicate microtonal variants approximated to the nearest semitone.

Cross-System Comparison¶

Since all systems use 12-tone equal temperament, equivalent scales produce the same pitches:

>>> from pytheory import TonedScale, Tone

>>> # These are all the same scale with different names
>>> western = TonedScale(tonic="C4")["major"]
>>> indian  = TonedScale(tonic="Sa4", system="indian")["bilawal"]
>>> arabic  = TonedScale(tonic="Do4", system="arabic")["ajam"]

>>> # Same pitches
>>> c4 = Tone.from_string("C4", system="western")
>>> sa4 = Tone.from_string("Sa4", system="indian")
>>> do4 = Tone.from_string("Do4", system="arabic")

>>> c4.frequency
261.6255653005986
>>> sa4.frequency
261.6255653005986
>>> do4.frequency
261.6255653005986

Microtonal Systems¶

Beyond the six 12-TET core systems, PyTheory includes 10 microtonal systems that use their own native tunings — more notes per octave, just intonation ratios, or entirely alien pitch structures.

Shruti (22 tones per octave)¶

The Indian 22-shruti system divides the octave into 22 unequal steps using just intonation ratios. These microtonal inflections are what give classical Indian music its characteristic expressiveness — pitches that fall “between the cracks” of the piano.

score = Score("4/4", bpm=75, system="shruti")

Maqam (24 tones per octave)¶

The Arabic 24-tone system adds Zalzalian quarter-tone intervals (derived from just intonation ratios of 11 and 13) to the standard 12 tones. These “neutral” intervals — halfway between major and minor — are the soul of maqam music.

score = Score("4/4", bpm=90, system="maqam")

Slendro (5-TET)¶

The Javanese slendro scale — 5 equal divisions of the octave. Each step is 240 cents, wider than any Western interval. Ethereal and floating.

Pelog (9-TET)¶

Approximation of the Javanese pelog tuning as 9 equal divisions of the octave.

Thai (7-TET)¶

Thai classical music divides the octave into 7 equal steps of ~171 cents each — every interval is the same size.

Makam (53-TET)¶

Turkish makam music uses 53 equal divisions of the octave — fine enough to approximate virtually any just interval. The system that underlies Ottoman classical music.

Carnatic (72-TET)¶

South Indian Carnatic music theory describes 72 melakarta ragas. The 72-TET system provides enough resolution to represent all the microtonal inflections of Carnatic practice.

19-TET and 31-TET¶

Extended equal temperaments that offer better approximations of just intonation intervals than 12-TET. 19-TET has excellent major thirds; 31-TET closely matches quarter-comma meantone.

score = Score("4/4", bpm=100, system="19-tet")

Bohlen-Pierce (13 equal divisions of the tritave)¶

A genuinely alien tuning system — 13 equal divisions of the tritave (3:1 ratio) instead of the octave (2:1). No octaves, no fifths, built on 3:5:7 harmonics. Used by experimental composers.

score = Score("4/4", bpm=100, system="bohlen-pierce")

The TET() Factory¶

Create any equal temperament on the fly with the TET() factory:

from pytheory import TET

edo19 = TET(19)   # 19-tone equal temperament
edo31 = TET(31)   # 31-tone equal temperament
score = Score("4/4", bpm=100, system=edo19)

Tone names in custom TET systems are integers (0, 1, 2, …, n-1).

System.tone() Method¶

Any system can create a Tone directly:

from pytheory import SYSTEMS

western = SYSTEMS["western"]
c4 = western.tone("C", octave=4)

Music is universal, but every culture hears it differently. These systems are different maps of the same territory – explore one you’ve never played in before and see what you find.