Musical Systems¶
PyTheory supports four musical systems, each with its own tone names and scale patterns.
Western¶
The standard 12-tone equal temperament system with major/minor scales and all seven modes.
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', 'D#', 'F', 'G', 'A', 'A#', 'C']
Scales: major, minor, harmonic minor, ionian, dorian, phrygian, lydian, mixolydian, aeolian, locrian, chromatic
Indian Classical (Hindustani)¶
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
komalprefix = flat: komal Re, komal Ga, komal Dha, komal Nitivraprefix = sharp: tivra Ma
Arabic Maqam¶
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¶
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', 'D#', 'G', 'G#', 'C']
c["in"].note_names # Miyako-bushi, used in koto music
# ['C', 'C#', 'F', 'G', 'G#', 'C']
c["yo"].note_names # folk music scale
# ['C', 'D', 'F', 'G', 'A#', 'C']
c["ritsu"].note_names # gagaku court music (= Dorian)
# ['C', 'D', 'D#', 'F', 'G', 'A', 'A#', 'C']
Pentatonic scales: hirajoshi, in, yo, iwato, kumoi, insen
Heptatonic scales: ritsu, ryo
Blues and Pentatonic¶
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', 'D#', 'F', 'F#', 'G', 'A#', 'C']
c["major blues"].note_names # major pentatonic + blue note
# ['C', 'D', 'D#', '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¶
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 # 261.63
sa4.frequency # 261.63
do4.frequency # 261.63
