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kennethreitz
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Blues: major/minor pentatonic, blues scale, major blues, dominant, minor (Dorian). The foundational scales of blues, rock, and jazz. Gamelan: slendro (5-tone equidistant), pelog (7-tone with 3 pathet subsets: nem, barang, lima). 12-TET approximations of Javanese gamelan tuning with traditional tone names (ji, ro, lu, pat, mo, nem, pi/barang). Total systems: 6 (western, indian, arabic, japanese, blues, gamelan) 277 tests passing. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
221 lines
6.3 KiB
ReStructuredText
221 lines
6.3 KiB
ReStructuredText
Musical Systems
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===============
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PyTheory supports four musical systems, each with its own tone names
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and scale patterns.
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Western
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-------
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The standard 12-tone equal temperament system with major/minor scales
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and all seven modes.
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.. code-block:: python
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from pytheory import TonedScale
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c = TonedScale(tonic="C4")
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c["major"].note_names
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# ['C', 'D', 'E', 'F', 'G', 'A', 'B', 'C']
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c["dorian"].note_names
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# ['C', 'D', 'D#', 'F', 'G', 'A', 'A#', 'C']
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**Scales:** major, minor, harmonic minor, ionian, dorian, phrygian,
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lydian, mixolydian, aeolian, locrian, chromatic
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Indian Classical (Hindustani)
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-----------------------------
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The Hindustani system uses **swaras** (Sa, Re, Ga, Ma, Pa, Dha, Ni) and
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organizes scales into **thaats** — the 10 parent scales from which ragas
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are derived.
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.. code-block:: python
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from pytheory import TonedScale
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from pytheory.systems import SYSTEMS
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sa = TonedScale(tonic="Sa4", system=SYSTEMS["indian"])
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sa["bilawal"].note_names # = major scale
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# ['Sa', 'Re', 'Ga', 'Ma', 'Pa', 'Dha', 'Ni', 'Sa']
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sa["bhairav"].note_names # unique to Indian music
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# ['Sa', 'komal Re', 'Ga', 'Ma', 'Pa', 'komal Dha', 'Ni', 'Sa']
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sa["todi"].note_names
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# ['Sa', 'komal Re', 'komal Ga', 'tivra Ma', 'Pa', 'komal Dha', 'Ni', 'Sa']
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**Thaats:** bilawal, khamaj, kafi, asavari, bhairavi, kalyan, bhairav,
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poorvi, marwa, todi
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**Swara notation:**
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- Uppercase = shuddha (natural): Sa, Re, Ga, Ma, Pa, Dha, Ni
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- ``komal`` prefix = flat: komal Re, komal Ga, komal Dha, komal Ni
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- ``tivra`` prefix = sharp: tivra Ma
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Arabic Maqam
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------------
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The Arabic system uses **solfège-based names** (Do, Re, Mi, Fa, Sol, La, Si)
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and organizes scales into **maqamat** (plural of maqam).
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.. note::
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True maqam music uses quarter-tones that cannot be represented in
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12-tone equal temperament. These scales are the closest 12-TET
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approximations.
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.. code-block:: python
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from pytheory import TonedScale
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from pytheory.systems import SYSTEMS
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do = TonedScale(tonic="Do4", system=SYSTEMS["arabic"])
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do["ajam"].note_names # = major scale
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# ['Do', 'Re', 'Mi', 'Fa', 'Sol', 'La', 'Si', 'Do']
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do["hijaz"].note_names # characteristic augmented 2nd
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# ['Do', 'Reb', 'Mi', 'Fa', 'Sol', 'Solb', 'Sib', 'Do']
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do["nikriz"].note_names
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# ['Do', 'Re', 'Mib', 'Fa#', 'Sol', 'La', 'Sib', 'Do']
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**Maqamat:** ajam, nahawand, kurd, hijaz, nikriz, bayati, rast, saba,
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sikah, jiharkah
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Japanese
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--------
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The Japanese system uses Western note names with traditional pentatonic
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and heptatonic scales from Japanese music.
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.. code-block:: python
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from pytheory import TonedScale
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from pytheory.systems import SYSTEMS
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c = TonedScale(tonic="C4", system=SYSTEMS["japanese"])
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c["hirajoshi"].note_names # most iconic Japanese scale
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# ['C', 'D', 'D#', 'G', 'G#', 'C']
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c["in"].note_names # Miyako-bushi, used in koto music
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# ['C', 'C#', 'F', 'G', 'G#', 'C']
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c["yo"].note_names # folk music scale
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# ['C', 'D', 'F', 'G', 'A#', 'C']
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c["ritsu"].note_names # gagaku court music (= Dorian)
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# ['C', 'D', 'D#', 'F', 'G', 'A', 'A#', 'C']
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**Pentatonic scales:** hirajoshi, in, yo, iwato, kumoi, insen
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**Heptatonic scales:** ritsu, ryo
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Blues and Pentatonic
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-------------------
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The blues system provides the scales foundational to blues, rock, jazz,
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and folk music worldwide. Pentatonic scales (5 notes) are the oldest
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known musical scales, found independently in cultures across every
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continent.
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The **blues scale** adds the "blue note" (flat 5th / sharp 4th) to the
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minor pentatonic — this chromatic passing tone is the defining sound
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of the blues.
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.. code-block:: python
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from pytheory import TonedScale
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from pytheory.systems import SYSTEMS
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c = TonedScale(tonic="C4", system=SYSTEMS["blues"])
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c["major pentatonic"].note_names # the "happy" pentatonic
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# ['C', 'D', 'E', 'G', 'A', 'C']
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c["minor pentatonic"].note_names # the "sad" pentatonic
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# ['C', 'D#', 'F', 'G', 'A#', 'C']
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c["blues"].note_names # minor pentatonic + blue note
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# ['C', 'D#', 'F', 'F#', 'G', 'A#', 'C']
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c["major blues"].note_names # major pentatonic + blue note
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# ['C', 'D', 'D#', 'E', 'G', 'A', 'C']
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**Pentatonic:** major pentatonic, minor pentatonic
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**Hexatonic:** blues, major blues
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**Heptatonic:** dominant (Mixolydian — the dominant 7th sound),
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minor (Dorian — the jazz minor sound)
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Javanese Gamelan
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----------------
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The gamelan system approximates the scales of the Javanese and Balinese
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gamelan orchestra in 12-tone equal temperament. True gamelan tuning is
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unique to each ensemble and does not conform to Western intonation —
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these are the closest 12-TET approximations.
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**Slendro** is a roughly equal 5-tone division of the octave, producing
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an ethereal, floating quality. **Pelog** is a 7-tone scale with unequal
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intervals, typically performed using 5-note subsets called *pathet*.
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.. code-block:: python
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from pytheory import TonedScale
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from pytheory.systems import SYSTEMS
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ji = TonedScale(tonic="ji4", system=SYSTEMS["gamelan"])
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ji["slendro"].note_names # the 5-tone equidistant scale
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# ['ji', 'ro', 'pat', 'mo', 'pi', 'ji']
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ji["pelog"].note_names # full 7-tone pelog
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# ['ji', 'ro-', 'lu', 'pat', 'mo', 'nem-', 'barang', 'ji']
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ji["pelog nem"].note_names # pathet nem subset
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# ['ji', 'ro-', 'lu', 'pat', 'mo', 'ji']
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**Pentatonic:** slendro, pelog nem, pelog barang, pelog lima
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**Heptatonic:** pelog (full 7-tone)
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.. note::
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Gamelan tone names follow Javanese numbering: ji (1), ro (2),
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lu (3), pat (4), mo (5), nem (6), pi/barang (7). Suffixes
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indicate microtonal variants approximated to the nearest semitone.
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Cross-System Comparison
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-----------------------
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Since all systems use 12-tone equal temperament, equivalent scales
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produce the same pitches:
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.. code-block:: python
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from pytheory import TonedScale, Tone
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from pytheory.systems import SYSTEMS
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# These are all the same scale with different names
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western = TonedScale(tonic="C4")["major"]
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indian = TonedScale(tonic="Sa4", system=SYSTEMS["indian"])["bilawal"]
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arabic = TonedScale(tonic="Do4", system=SYSTEMS["arabic"])["ajam"]
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# Same pitches
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c4 = Tone.from_string("C4", system="western")
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sa4 = Tone.from_string("Sa4", system="indian")
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do4 = Tone.from_string("Do4", system="arabic")
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c4.frequency # 261.63
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sa4.frequency # 261.63
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do4.frequency # 261.63
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