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kennethreitz
d2058668a6
Flat keys now display flats (Bb, Eb, Ab) instead of sharps (A#, D#, G#). Uses the "no duplicate letter names" rule: if building a scale with sharps produces two notes with the same letter (e.g. C and C# in C minor), the scale is rebuilt with flat spellings instead. - Tone.add() and Tone.from_index() accept prefer_flats parameter - TonedScale detects flat vs sharp per-scale automatically - F major: Bb (not A#), Eb major: Ab Bb (not G# A#), etc. - All tests and docs updated to match Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
218 lines
6.6 KiB
ReStructuredText
218 lines
6.6 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:: pycon
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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', 'Eb', 'F', 'G', 'A', 'Bb', '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 <https://en.wikipedia.org/wiki/Thaat>`_ — the 10 parent scales from which `ragas <https://en.wikipedia.org/wiki/Raga>`_
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are derived.
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.. code-block:: pycon
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>>> from pytheory import TonedScale
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>>> sa = TonedScale(tonic="Sa4", system="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 <https://en.wikipedia.org/wiki/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:: pycon
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>>> from pytheory import TonedScale
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>>> do = TonedScale(tonic="Do4", system="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:: pycon
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>>> from pytheory import TonedScale
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>>> c = TonedScale(tonic="C4", system="japanese")
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>>> c["hirajoshi"].note_names # most iconic Japanese scale
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['C', 'D', 'Eb', 'G', 'Ab', 'C']
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>>> c["in"].note_names # Miyako-bushi, used in koto music
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['C', 'Db', 'F', 'G', 'Ab', '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', 'Eb', 'F', 'G', 'A', 'Bb', '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 <https://en.wikipedia.org/wiki/Pentatonic_scale>`_ (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 <https://en.wikipedia.org/wiki/Blues_scale>`_ adds the "`blue note <https://en.wikipedia.org/wiki/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:: pycon
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>>> from pytheory import TonedScale
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>>> c = TonedScale(tonic="C4", system="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', 'Eb', 'F', 'Gb', 'G', 'Bb', 'C']
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>>> c["major blues"].note_names # major pentatonic + blue note
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['C', 'D', 'Eb', '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 <https://en.wikipedia.org/wiki/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 <https://en.wikipedia.org/wiki/Slendro>`_ is a roughly equal 5-tone division of the octave, producing
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an ethereal, floating quality. `Pelog <https://en.wikipedia.org/wiki/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:: pycon
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>>> from pytheory import TonedScale
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>>> ji = TonedScale(tonic="ji4", system="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:: pycon
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>>> from pytheory import TonedScale, Tone
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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="indian")["bilawal"]
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>>> arabic = TonedScale(tonic="Do4", system="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
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261.6255653005986
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>>> sa4.frequency
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261.6255653005986
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>>> do4.frequency
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261.6255653005986
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