# -*- coding: utf-8 -*- # ------------------------------------------------------------------------------ # Name: scale.py # Purpose: music21 classes for representing scales # # Authors: Christopher Ariza # Michael Scott Asato Cuthbert # Jose Cabal-Ugaz # # Copyright: Copyright © 2009-2011 Michael Scott Asato Cuthbert # License: BSD, see license.txt # ------------------------------------------------------------------------------ ''' The various Scale objects provide a bidirectional object representation of octave repeating and non-octave repeating scales built by network of :class:`~music21.interval.Interval` objects as modeled in :class:`~music21.intervalNetwork.IntervalNetwork`. The main public interface to these resources are subclasses of :class:`~music21.scale.ConcreteScale`, such as :class:`~music21.scale.MajorScale`, :class:`~music21.scale.MinorScale`, and :class:`~music21.scale.MelodicMinorScale`. More unusual scales are also available, such as :class:`~music21.scale.OctatonicScale`, :class:`~music21.scale.SieveScale`, and :class:`~music21.scale.RagMarwa`. All :class:`~music21.scale.ConcreteScale` subclasses provide the ability to get a pitches across any range, get a pitch for scale step, get a scale step for pitch, and, for any given pitch ascend or descend to the next pitch. In all cases :class:`~music21.pitch.Pitch` objects are returned. >>> sc1 = scale.MajorScale('a') >>> [str(p) for p in sc1.getPitches('g2', 'g4')] ['G#2', 'A2', 'B2', 'C#3', 'D3', 'E3', 'F#3', 'G#3', 'A3', 'B3', 'C#4', 'D4', 'E4', 'F#4'] >>> sc2 = scale.MelodicMinorScale('a') >>> [str(p) for p in sc2.getPitches('g2', 'g4', direction=scale.Direction.DESCENDING)] ['G4', 'F4', 'E4', 'D4', 'C4', 'B3', 'A3', 'G3', 'F3', 'E3', 'D3', 'C3', 'B2', 'A2', 'G2'] >>> [str(p) for p in sc2.getPitches('g2', 'g4', direction=scale.Direction.ASCENDING)] ['G#2', 'A2', 'B2', 'C3', 'D3', 'E3', 'F#3', 'G#3', 'A3', 'B3', 'C4', 'D4', 'E4', 'F#4'] ''' from __future__ import annotations __all__ = [ 'intervalNetwork', 'scala', 'Direction', 'Terminus', 'ScaleException', 'Scale', 'AbstractScale', 'AbstractDiatonicScale', 'AbstractOctatonicScale', 'AbstractHarmonicMinorScale', 'AbstractMelodicMinorScale', 'AbstractCyclicalScale', 'AbstractOctaveRepeatingScale', 'AbstractRagAsawari', 'AbstractRagMarwa', 'AbstractWeightedHexatonicBlues', 'ConcreteScale', 'DiatonicScale', 'MajorScale', 'MinorScale', 'DorianScale', 'PhrygianScale', 'LydianScale', 'MixolydianScale', 'HypodorianScale', 'HypophrygianScale', 'HypolydianScale', 'HypomixolydianScale', 'LocrianScale', 'HypolocrianScale', 'HypoaeolianScale', 'HarmonicMinorScale', 'MelodicMinorScale', 'OctatonicScale', 'OctaveRepeatingScale', 'CyclicalScale', 'ChromaticScale', 'WholeToneScale', 'SieveScale', 'ScalaScale', 'RagAsawari', 'RagMarwa', 'WeightedHexatonicBlues', ] import copy import typing as t from music21.scale import intervalNetwork from music21.scale.intervalNetwork import Direction, Terminus from music21.scale import scala # ------------------------- from music21 import base from music21 import common from music21.common.decorators import deprecated from music21 import defaults from music21 import environment from music21 import exceptions21 from music21 import note from music21 import pitch from music21 import interval from music21 import sieve environLocal = environment.Environment('scale') _PitchDegreeCacheKey = tuple[ type, # scale class str, # scale type str, # tonic name with octave int, # degree Direction, # direction bool # equating termini ] # a dictionary mapping an abstract scale class, tonic.nameWithOctave, # and degree to a pitchNameWithOctave. _pitchDegreeCache: dict[_PitchDegreeCacheKey, str] = {} # ------------------------------------------------------------------------------ class ScaleException(exceptions21.Music21Exception): pass class Scale(base.Music21Object): ''' Generic base class for all scales, both abstract and concrete. >>> s = scale.Scale() >>> s.type 'Scale' >>> s.name # default same as type. 'Scale' >>> s.isConcrete False Not a useful class on its own. See its subclasses. ''' def __init__(self, **keywords): super().__init__(**keywords) self.type = 'Scale' # could be mode, could be other indicator @property def name(self): ''' Return or construct the name of this scale ''' return self.type @property def isConcrete(self): ''' To be concrete, a Scale must have a defined tonic. An abstract Scale is not Concrete, nor is a Concrete scale without a defined tonic. Thus, is always false. ''' return False @staticmethod def extractPitchList(other, comparisonAttribute='nameWithOctave', removeDuplicates=True): # noinspection PyShadowingNames ''' Utility function and staticmethod Given a data format as "other" (a ConcreteScale, Chord, Stream, List of Pitches, or single Pitch), extract all unique Pitches using comparisonAttribute to test for them. >>> pStrList = ['A4', 'D4', 'E4', 'F-4', 'D4', 'D5', 'A', 'D#4'] >>> pList = [pitch.Pitch(p) for p in pStrList] >>> nList = [note.Note(p) for p in pStrList] >>> s = stream.Stream() >>> for n in nList: ... s.append(n) Here we only remove the second 'D4' because the default comparison is `nameWithOctave` >>> [str(p) for p in scale.Scale.extractPitchList(pList)] ['A4', 'D4', 'E4', 'F-4', 'D5', 'A4', 'D#4'] Note that octaveless notes like the 'A' get a default octave. In general, it is better to work with octave-possessing pitches. Now we remove the F-4, D5, and A also because we are working with `comparisonAttribute=pitchClass`. Note that we're using a Stream as `other` now: >>> [str(p) for p in scale.Scale.extractPitchList(s, comparisonAttribute='pitchClass')] ['A4', 'D4', 'E4', 'D#4'] Now let's get rid of all but one diatonic `D` by using :meth:`~music21.pitch.Pitch.step` as our `comparisonAttribute`. Note that we can just give a list of strings as well, and they become :class:`~music21.pitch.Pitch` objects. Oh, we will also show that `extractPitchList` works on any scale: >>> sc = scale.Scale() >>> [str(p) for p in sc.extractPitchList(pStrList, comparisonAttribute='step')] ['A4', 'D4', 'E4', 'F-4'] ''' pre = [] # if a ConcreteScale, Chord or Stream if hasattr(other, 'pitches'): pre = list(other.pitches) # if a list elif common.isIterable(other): # assume a list of pitches; possible permit conversions? pre = [] for p in other: if hasattr(p, 'pitch'): pre.append(p.pitch) elif isinstance(p, pitch.Pitch): pre.append(p) else: pre.append(pitch.Pitch(p)) elif hasattr(other, 'pitch'): pre = [other.pitch] # get pitch attribute if removeDuplicates is False: return pre uniquePitches = {} post = [] for p in pre: hashValue = getattr(p, comparisonAttribute) if hashValue not in uniquePitches: uniquePitches[hashValue] = True post.append(p) for p in post: if p.octave is None: p.octave = defaults.pitchOctave return post # ------------------------------------------------------------------------------ class AbstractScale(Scale): ''' An abstract scale is specific scale formation, but does not have a defined pitch collection or pitch reference. For example, all Major scales can be represented by an AbstractScale; a ConcreteScale, however, is a specific Major Scale, such as G Major. These classes provide an interface to, and create and manipulate, the stored :class:`~music21.intervalNetwork.IntervalNetwork` object. Thus, they are rarely created or manipulated directly by most users. The AbstractScale additionally stores an `_alteredDegrees` dictionary. Subclasses can define altered nodes in AbstractScale that are passed to the :class:`~music21.intervalNetwork.IntervalNetwork`. Equality -------- Two abstract scales are the same if they have the same class and the same tonicDegree and octaveDuplicating attributes and the same intervalNetwork, and it satisfies all other music21 superclass attributes. >>> as1 = scale.AbstractOctatonicScale() >>> as2 = scale.AbstractOctatonicScale() >>> as1 == as2 True >>> as2.tonicDegree = 5 >>> as1 == as2 False >>> as1 == scale.AbstractDiatonicScale() False ''' # TODO: make a subclass of IntervalNetwork and remove the ._net aspect. equalityAttributes = ('tonicDegree', '_net', 'octaveDuplicating') def __init__(self, **keywords): super().__init__(**keywords) # store interval network within abstract scale self._net = None # in most cases tonic/final of scale is step one, but not always self.tonicDegree = 1 # step of tonic # declare if this scale is octave duplicating # can be used as to optimize pitch gathering self.octaveDuplicating = True # passed to interval network self.deterministic = True # store parameter for interval network-based node modifications # entries are in the form: # step: {'direction':Direction.BI, 'interval':Interval} self._alteredDegrees = {} def buildNetwork(self): ''' Calling the buildNetwork, with or without parameters, is main job of the AbstractScale class. This needs to be subclassed by a derived class ''' raise NotImplementedError def buildNetworkFromPitches(self, pitchList): ''' Builds the network (list of motions) for an abstract scale from a list of pitch.Pitch objects. If the concluding note (usually the "octave") is not given, then it'll be created automatically. Here we treat the augmented triad as a scale: >>> p1 = pitch.Pitch('C4') >>> p2 = pitch.Pitch('E4') >>> p3 = pitch.Pitch('G#4') >>> abstractScale = scale.AbstractScale() >>> abstractScale.buildNetworkFromPitches([p1, p2, p3]) >>> abstractScale.octaveDuplicating True >>> abstractScale._net Now see it return a new "scale" of the augmentedTriad on D5 >>> abstractScale._net.realizePitch('D5') [, , , ] It is also possible to use implicit octaves: >>> abstract_scale = scale.AbstractScale() >>> abstract_scale.buildNetworkFromPitches(['C', 'F']) >>> abstract_scale.octaveDuplicating True >>> abstract_scale._net.realizePitch('G') [, , ] ''' pitchListReal = [] for p in pitchList: if isinstance(p, str): pitchListReal.append(pitch.Pitch(p)) elif isinstance(p, note.Note): pitchListReal.append(p.pitch) else: # assume this is a pitch object pitchListReal.append(p) pitchList = pitchListReal self.fixDefaultOctaveForPitchList(pitchList) if not common.isListLike(pitchList) or not pitchList: raise ScaleException(f'Cannot build a network from this pitch list: {pitchList}') intervalList = [] for currentPitch, nextPitch in zip(pitchList, pitchList[1:]): intervalList.append(interval.Interval(currentPitch, nextPitch)) if pitchList[-1].name == pitchList[0].name: # the completion of the scale has been given. # print('hi %s ' % pitchList) # this scale is only octave duplicating if the top note is exactly # 1 octave above the bottom; if it spans more than one octave, # all notes must be identical in each octave # if abs(pitchList[-1].ps - pitchList[0].ps) == 12: span = interval.Interval(pitchList[0], pitchList[-1]) # environLocal.printDebug(['got span', span, span.name]) if span.name == 'P8': self.octaveDuplicating = True else: self.octaveDuplicating = False else: p = copy.deepcopy(pitchList[0]) if p.octave is None: p.octave = p.implicitOctave if pitchList[-1] > pitchList[0]: # ascending while p.ps < pitchList[-1].ps: p.octave += 1 else: while p.ps > pitchList[-1].ps: p.octave += -1 intervalList.append(interval.Interval(pitchList[-1], p)) span = interval.Interval(pitchList[0], p) # environLocal.printDebug(['got span', span, span.name]) if span.name == 'P8': self.octaveDuplicating = True else: self.octaveDuplicating = False # if abs(p.ps - pitchList[0].ps) == 12: # self.octaveDuplicating == True # else: # self.octaveDuplicating == False # environLocal.printDebug(['intervalList', intervalList, # 'self.octaveDuplicating', self.octaveDuplicating]) self._net = intervalNetwork.IntervalNetwork(intervalList, octaveDuplicating=self.octaveDuplicating) @staticmethod def fixDefaultOctaveForPitchList(pitchList): # noinspection PyShadowingNames ''' Suppose you have a set of octaveless Pitches that you use to make a scale. Something like: >>> pitchListStrs = 'a b c d e f g a'.split() >>> pitchList = [pitch.Pitch(p) for p in pitchListStrs] Here's the problem, between `pitchList[1]` and `pitchList[2]` the `.implicitOctave` stays the same, so the `.ps` drops: >>> (pitchList[1].implicitOctave, pitchList[2].implicitOctave) (4, 4) >>> (pitchList[1].ps, pitchList[2].ps) (71.0, 60.0) Hence this helper staticmethod that makes it so that for octaveless pitches ONLY, each one has a .ps above the previous: >>> pl2 = scale.AbstractScale.fixDefaultOctaveForPitchList(pitchList) >>> (pl2[1].implicitOctave, pl2[2].implicitOctave, pl2[3].implicitOctave) (4, 5, 5) >>> (pl2[1].ps, pl2[2].ps) (71.0, 72.0) Note that the list is modified inPlace: >>> pitchList is pl2 True >>> pitchList[2] is pl2[2] True ''' # fix defaultOctave for pitchList lastPs = 0 lastOctave = pitchList[0].implicitOctave for p in pitchList: if p.octave is None: if lastPs > p.ps: p.octave = lastOctave while lastPs > p.ps: lastOctave += 1 p.octave = lastOctave lastPs = p.ps lastOctave = p.implicitOctave return pitchList def getDegreeMaxUnique(self): ''' Return the maximum number of scale steps, or the number to use as a modulus. ''' # access from property return self._net.degreeMaxUnique # def reverse(self): # ''' # Reverse all intervals in this scale. # ''' # pass # expose interface from network. these methods must be called (and not # ._net directly because they can pass the alteredDegrees dictionary def getRealization(self, pitchObj, stepOfPitch, minPitch=None, maxPitch=None, direction=Direction.ASCENDING, reverse=False): ''' Realize the abstract scale as a list of pitch objects, given a pitch object, the step of that pitch object, and a min and max pitch. ''' if self._net is None: raise ScaleException('no IntervalNetwork is defined by this "scale".') post = self._net.realizePitch(pitchObj, stepOfPitch, minPitch=minPitch, maxPitch=maxPitch, alteredDegrees=self._alteredDegrees, direction=direction, reverse=reverse) # here, we copy the list of pitches so as not to allow editing of # cached pitch values later return copy.deepcopy(post) def getIntervals(self, stepOfPitch=None, minPitch=None, maxPitch=None, direction=Direction.ASCENDING, reverse=False): ''' Realize the abstract scale as a list of pitch objects, given a pitch object, the step of that pitch object, and a min and max pitch. ''' if self._net is None: raise ScaleException('no network is defined.') post = self._net.realizeIntervals(stepOfPitch, minPitch=minPitch, maxPitch=maxPitch, alteredDegrees=self._alteredDegrees, direction=direction, reverse=reverse) # here, we copy the list of pitches so as not to allow editing of # cached pitch values later return post def getPitchFromNodeDegree(self, pitchReference, nodeName, nodeDegreeTarget, direction=Direction.ASCENDING, minPitch=None, maxPitch=None, equateTermini=True): ''' Get a pitch for desired scale degree. ''' post = self._net.getPitchFromNodeDegree( pitchReference=pitchReference, # pitch defined here nodeName=nodeName, # defined in abstract class nodeDegreeTarget=nodeDegreeTarget, # target looking for direction=direction, minPitch=minPitch, maxPitch=maxPitch, alteredDegrees=self._alteredDegrees, equateTermini=equateTermini ) return copy.deepcopy(post) def realizePitchByDegree(self, pitchReference, nodeId, nodeDegreeTargets, direction=Direction.ASCENDING, minPitch=None, maxPitch=None): ''' Given one or more scale degrees, return a list of all matches over the entire range. See :meth:`~music21.intervalNetwork.IntervalNetwork.realizePitchByDegree`. in `intervalNetwork.IntervalNetwork`. Create an abstract pentatonic scale: >>> pitchList = ['C#4', 'D#4', 'F#4', 'G#4', 'A#4'] >>> abstractScale = scale.AbstractScale() >>> abstractScale.buildNetworkFromPitches([pitch.Pitch(p) for p in pitchList]) ''' # TODO: rely here on intervalNetwork for caching post = self._net.realizePitchByDegree( pitchReference=pitchReference, # pitch defined here nodeId=nodeId, # defined in abstract class nodeDegreeTargets=nodeDegreeTargets, # target looking for direction=direction, minPitch=minPitch, maxPitch=maxPitch, alteredDegrees=self._alteredDegrees) return copy.deepcopy(post) def getRelativeNodeDegree(self, pitchReference, nodeName, pitchTarget, comparisonAttribute='pitchClass', direction=Direction.ASCENDING): ''' Expose functionality from :class:`~music21.intervalNetwork.IntervalNetwork`, passing on the stored alteredDegrees dictionary. ''' post = self._net.getRelativeNodeDegree( pitchReference=pitchReference, nodeId=nodeName, pitchTarget=pitchTarget, comparisonAttribute=comparisonAttribute, direction=direction, alteredDegrees=self._alteredDegrees ) return copy.deepcopy(post) def nextPitch(self, pitchReference, nodeName, pitchOrigin, direction: Direction = Direction.ASCENDING, stepSize=1, getNeighbor: Direction|bool = True): ''' Expose functionality from :class:`~music21.intervalNetwork.IntervalNetwork`, passing on the stored alteredDegrees dictionary. ''' post = self._net.nextPitch(pitchReference=pitchReference, nodeName=nodeName, pitchOrigin=pitchOrigin, direction=direction, stepSize=stepSize, alteredDegrees=self._alteredDegrees, getNeighbor=getNeighbor ) return copy.deepcopy(post) def getNewTonicPitch(self, pitchReference, nodeName, direction=Direction.ASCENDING, minPitch=None, maxPitch=None): ''' Define a pitch target and a node. ''' post = self._net.getPitchFromNodeDegree( pitchReference=pitchReference, nodeName=nodeName, nodeDegreeTarget=1, # get the pitch of the tonic direction=direction, minPitch=minPitch, maxPitch=maxPitch, alteredDegrees=self._alteredDegrees ) return copy.deepcopy(post) # -------------------------------------------------------------------------- def getScalaData(self, direction=Direction.ASCENDING): ''' Get the interval sequence as a :class:~music21.scala.ScalaData object for a particular scale: ''' # get one octave of intervals intervals = self.getIntervals(direction=direction) ss = scala.ScalaData() ss.setIntervalSequence(intervals) ss.description = repr(self) return ss def write(self, fmt=None, fp=None, direction=Direction.ASCENDING, **keywords): ''' Write the scale in a format. Here, prepare scala format if requested. ''' if fmt is not None: fileFormat, ext = common.findFormat(fmt) if fp is None: fpLocal = environLocal.getTempFile(ext) else: fpLocal = fp if fileFormat == 'scala': ss = self.getScalaData(direction=direction) sf = scala.ScalaFile(ss) # pass storage to the file sf.open(fpLocal, 'w') sf.write() sf.close() return fpLocal return Scale.write(self, fmt=fmt, fp=fp, **keywords) def show(self, fmt=None, app=None, direction=Direction.ASCENDING, **keywords): ''' Show the scale in a format. Here, prepare scala format if requested. ''' from music21.converter.subConverters import SubConverter if fmt is not None: fileFormat, unused_ext = common.findFormat(fmt) if fileFormat == 'scala': returnedFilePath = self.write(fileFormat, direction=direction) SubConverter().launch(returnedFilePath, fmt=fileFormat, app=app) return Scale.show(self, fmt=fmt, app=app, **keywords) # ------------------------------------------------------------------------------ # abstract subclasses class AbstractDiatonicScale(AbstractScale): ''' An abstract representation of a Diatonic scale w/ or without mode. >>> as1 = scale.AbstractDiatonicScale('major') >>> as1.type 'Abstract diatonic' >>> as1.mode 'major' >>> as1.octaveDuplicating True Equality -------- AbstractDiatonicScales must satisfy all the characteristics of a general AbstractScale but also need to have equal dominantDegrees. >>> as1 = scale.AbstractDiatonicScale('major') >>> as2 = scale.AbstractDiatonicScale('lydian') >>> as1 == as2 False Note that their modes do not need to be the same. For instance for the case of major and Ionian which have the same networks: >>> as3 = scale.AbstractDiatonicScale('ionian') >>> (as1.mode, as3.mode) ('major', 'ionian') >>> as1 == as3 True ''' def __init__(self, mode: str|None = None, **keywords): super().__init__(**keywords) self.mode = mode self.type = 'Abstract diatonic' self.tonicDegree = None # step of tonic self.dominantDegree = None # step of dominant # all diatonic scales are octave duplicating self.octaveDuplicating = True self.relativeMinorDegree: int = -1 self.relativeMajorDegree: int = -1 self.buildNetwork(mode=mode) def buildNetwork(self, mode=None): ''' Given subclass dependent parameters, build and assign the IntervalNetwork. >>> sc = scale.AbstractDiatonicScale() >>> sc.buildNetwork('Lydian') # N.B. case-insensitive name >>> [str(p) for p in sc.getRealization('f4', 1, 'f2', 'f6')] ['F2', 'G2', 'A2', 'B2', 'C3', 'D3', 'E3', 'F3', 'G3', 'A3', 'B3', 'C4', 'D4', 'E4', 'F4', 'G4', 'A4', 'B4', 'C5', 'D5', 'E5', 'F5', 'G5', 'A5', 'B5', 'C6', 'D6', 'E6', 'F6'] Unknown modes raise an exception: >>> sc.buildNetwork('blues-like') Traceback (most recent call last): music21.scale.ScaleException: Cannot create a scale of the following mode: 'blues-like' * Changed in v6: case-insensitive modes ''' # reference: http://cnx.org/content/m11633/latest/ # most diatonic scales will start with this collection srcList = ('M2', 'M2', 'm2', 'M2', 'M2', 'M2', 'm2') self.tonicDegree = 1 self.dominantDegree = 5 if isinstance(mode, str): mode = mode.lower() if mode in (None, 'major', 'ionian'): # c to C intervalList = srcList self.relativeMajorDegree = 1 self.relativeMinorDegree = 6 elif mode == 'dorian': intervalList = srcList[1:] + srcList[:1] # d to d self.relativeMajorDegree = 7 self.relativeMinorDegree = 5 elif mode == 'phrygian': intervalList = srcList[2:] + srcList[:2] # e to e self.relativeMajorDegree = 6 self.relativeMinorDegree = 4 elif mode == 'lydian': intervalList = srcList[3:] + srcList[:3] # f to f self.relativeMajorDegree = 5 self.relativeMinorDegree = 3 elif mode == 'mixolydian': intervalList = srcList[4:] + srcList[:4] # g to g self.relativeMajorDegree = 4 self.relativeMinorDegree = 2 elif mode in ('aeolian', 'minor'): intervalList = srcList[5:] + srcList[:5] # a to A self.relativeMajorDegree = 3 self.relativeMinorDegree = 1 elif mode == 'locrian': intervalList = srcList[6:] + srcList[:6] # b to B self.relativeMajorDegree = 2 self.relativeMinorDegree = 7 elif mode == 'hypodorian': intervalList = srcList[5:] + srcList[:5] # a to a self.tonicDegree = 4 self.dominantDegree = 6 self.relativeMajorDegree = 3 self.relativeMinorDegree = 1 elif mode == 'hypophrygian': intervalList = srcList[6:] + srcList[:6] # b to b self.tonicDegree = 4 self.dominantDegree = 7 self.relativeMajorDegree = 2 self.relativeMinorDegree = 7 elif mode == 'hypolydian': # c to c intervalList = srcList self.tonicDegree = 4 self.dominantDegree = 6 self.relativeMajorDegree = 1 self.relativeMinorDegree = 6 elif mode == 'hypomixolydian': intervalList = srcList[1:] + srcList[:1] # d to d self.tonicDegree = 4 self.dominantDegree = 7 self.relativeMajorDegree = 7 self.relativeMinorDegree = 5 elif mode == 'hypoaeolian': intervalList = srcList[2:] + srcList[:2] # e to e self.tonicDegree = 4 self.dominantDegree = 6 self.relativeMajorDegree = 6 self.relativeMinorDegree = 4 elif mode == 'hypolocrian': intervalList = srcList[3:] + srcList[:3] # f to f self.tonicDegree = 4 self.dominantDegree = 6 self.relativeMajorDegree = 5 self.relativeMinorDegree = 3 else: raise ScaleException(f'Cannot create a scale of the following mode: {mode!r}') self._net = intervalNetwork.IntervalNetwork( intervalList, octaveDuplicating=self.octaveDuplicating, pitchSimplification=None) class AbstractOctatonicScale(AbstractScale): ''' Abstract scale representing the two octatonic scales. ''' def __init__(self, mode=None, **keywords): super().__init__(**keywords) self.type = 'Abstract Octatonic' # all octatonic scales are octave duplicating self.octaveDuplicating = True # here, accept None self.buildNetwork(mode=mode) def buildNetwork(self, mode=None): ''' Given subclass dependent parameters, build and assign the IntervalNetwork. >>> sc = scale.AbstractDiatonicScale() >>> sc.buildNetwork('lydian') >>> [str(p) for p in sc.getRealization('f4', 1, 'f2', 'f6')] ['F2', 'G2', 'A2', 'B2', 'C3', 'D3', 'E3', 'F3', 'G3', 'A3', 'B3', 'C4', 'D4', 'E4', 'F4', 'G4', 'A4', 'B4', 'C5', 'D5', 'E5', 'F5', 'G5', 'A5', 'B5', 'C6', 'D6', 'E6', 'F6'] ''' srcList = ('M2', 'm2', 'M2', 'm2', 'M2', 'm2', 'M2', 'm2') if mode in (None, 2, 'M2'): intervalList = srcList # start with M2 self.tonicDegree = 1 elif mode in (1, 'm2'): intervalList = srcList[1:] + srcList[:1] # start with m2 self.tonicDegree = 1 else: raise ScaleException(f'cannot create a scale of the following mode: {mode}') self._net = intervalNetwork.IntervalNetwork(intervalList, octaveDuplicating=self.octaveDuplicating, pitchSimplification='maxAccidental') # might also set weights for tonic and dominant here class AbstractHarmonicMinorScale(AbstractScale): ''' A true bidirectional scale that with the augmented second to a leading tone. This is the only scale to use the "_alteredDegrees" property. mode is not used ''' def __init__(self, mode: str|None = None, **keywords) -> None: super().__init__(**keywords) self.type = 'Abstract Harmonic Minor' self.octaveDuplicating = True self.dominantDegree: int = -1 self.buildNetwork() def buildNetwork(self): intervalList = ['M2', 'm2', 'M2', 'M2', 'm2', 'M2', 'M2'] # a to A self.tonicDegree = 1 self.dominantDegree = 5 self._net = intervalNetwork.IntervalNetwork(intervalList, octaveDuplicating=self.octaveDuplicating, pitchSimplification=None) # raise the seventh in all directions # 7 here is scale step/degree, not node id self._alteredDegrees[7] = { 'direction': intervalNetwork.Direction.BI, 'interval': interval.Interval('a1') } class AbstractMelodicMinorScale(AbstractScale): ''' A directional scale. mode is not used. ''' def __init__(self, mode: str|None = None, **keywords) -> None: super().__init__(**keywords) self.type = 'Abstract Melodic Minor' self.octaveDuplicating = True self.dominantDegree: int = -1 self.buildNetwork() def buildNetwork(self): self.tonicDegree = 1 self.dominantDegree = 5 self._net = intervalNetwork.IntervalNetwork( octaveDuplicating=self.octaveDuplicating, pitchSimplification=None) self._net.fillMelodicMinor() class AbstractCyclicalScale(AbstractScale): ''' A scale of any size built with an interval list of any form. The resulting scale may be non octave repeating. ''' def __init__(self, mode=None, **keywords): super().__init__(**keywords) self.type = 'Abstract Cyclical' self.octaveDuplicating = False self.buildNetwork(mode=mode) # cannot assume that abstract cyclical scales are octave duplicating # until we have the intervals in use def buildNetwork(self, mode): ''' Here, mode is the list of intervals. ''' if not isinstance(mode, (list, tuple)): modeList = [mode] # place in list else: modeList = mode self.tonicDegree = 1 self._net = intervalNetwork.IntervalNetwork(modeList, octaveDuplicating=self.octaveDuplicating) class AbstractOctaveRepeatingScale(AbstractScale): ''' A scale of any size built with an interval list that assumes octave completion. An additional interval to complete the octave will be added to the provided intervals. This does not guarantee that the octave will be repeated in one octave, only the next octave above the last interval will be provided. ''' def __init__(self, mode=None, **keywords): super().__init__(**keywords) self.type = 'Abstract Octave Repeating' if mode is None: # supply a default mode = ['P8'] self.buildNetwork(mode=mode) # by definition, these are forced to be octave duplicating # though, do to some intervals, duplication may not happen every oct self.octaveDuplicating = True def buildNetwork(self, mode): ''' Here, mode is the list of intervals. ''' if not common.isListLike(mode): mode = [mode] # place in list # get the interval to complete the octave intervalSum = interval.add(mode) iComplement = intervalSum.complement if iComplement is not None: mode.append(iComplement) self.tonicDegree = 1 self._net = intervalNetwork.IntervalNetwork(mode, octaveDuplicating=self.octaveDuplicating) class AbstractRagAsawari(AbstractScale): ''' A pseudo raga-scale. ''' def __init__(self, **keywords) -> None: super().__init__(**keywords) self.type = 'Abstract Rag Asawari' self.octaveDuplicating = True self.dominantDegree: int = -1 self.buildNetwork() def buildNetwork(self): self.tonicDegree = 1 self.dominantDegree = 5 nodes = ({'id': Terminus.LOW, 'degree': 1}, # c {'id': 0, 'degree': 2}, # d {'id': 1, 'degree': 4}, # f {'id': 2, 'degree': 5}, # g {'id': 3, 'degree': 6}, # a- {'id': Terminus.HIGH, 'degree': 8}, # c {'id': 4, 'degree': 7}, # b- {'id': 5, 'degree': 6}, # a- {'id': 6, 'degree': 5}, # g {'id': 7, 'degree': 4}, # f {'id': 8, 'degree': 3}, # e- {'id': 9, 'degree': 2}, # d ) edges = ( # ascending {'interval': 'M2', 'connections': ( [Terminus.LOW, 0, Direction.ASCENDING], # c to d )}, {'interval': 'm3', 'connections': ( [0, 1, Direction.ASCENDING], # d to f )}, {'interval': 'M2', 'connections': ( [1, 2, Direction.ASCENDING], # f to g )}, {'interval': 'm2', 'connections': ( [2, 3, Direction.ASCENDING], # g to a- )}, {'interval': 'M3', 'connections': ( [3, Terminus.HIGH, Direction.ASCENDING], # a- to c )}, # descending {'interval': 'M2', 'connections': ( [Terminus.HIGH, 4, Direction.DESCENDING], # c to b- )}, {'interval': 'M2', 'connections': ( [4, 5, Direction.DESCENDING], # b- to a- )}, {'interval': 'm2', 'connections': ( [5, 6, Direction.DESCENDING], # a- to g )}, {'interval': 'M2', 'connections': ( [6, 7, Direction.DESCENDING], # g to f )}, {'interval': 'M2', 'connections': ( [7, 8, Direction.DESCENDING], # f to e- )}, {'interval': 'm2', 'connections': ( [8, 9, Direction.DESCENDING], # e- to d )}, {'interval': 'M2', 'connections': ( [9, Terminus.LOW, Direction.DESCENDING], # d to c )}, ) self._net = intervalNetwork.IntervalNetwork( octaveDuplicating=self.octaveDuplicating, pitchSimplification='mostCommon') # using representation stored in interval network self._net.fillArbitrary(nodes, edges) class AbstractRagMarwa(AbstractScale): ''' A pseudo raga-scale. ''' def __init__(self, **keywords) -> None: super().__init__(**keywords) self.type = 'Abstract Rag Marwa' self.octaveDuplicating = True self.dominantDegree: int = -1 self.buildNetwork() def buildNetwork(self): self.tonicDegree = 1 self.dominantDegree = 5 nodes = ({'id': Terminus.LOW, 'degree': 1}, # c {'id': 0, 'degree': 2}, # d- {'id': 1, 'degree': 3}, # e {'id': 2, 'degree': 4}, # f# {'id': 3, 'degree': 5}, # a {'id': 4, 'degree': 6}, # b {'id': 5, 'degree': 7}, # a (could use id 3 again?) {'id': Terminus.HIGH, 'degree': 8}, # c {'id': 6, 'degree': 7}, # d- (above terminus) {'id': 7, 'degree': 6}, # b {'id': 8, 'degree': 5}, # a {'id': 9, 'degree': 4}, # f# {'id': 10, 'degree': 3}, # e {'id': 11, 'degree': 2}, # d- ) edges = ( # ascending {'interval': 'm2', 'connections': ([Terminus.LOW, 0, Direction.ASCENDING],) # c to d- }, {'interval': 'A2', 'connections': ([0, 1, Direction.ASCENDING],) # d- to e }, {'interval': 'M2', 'connections': ([1, 2, Direction.ASCENDING],) # e to f# }, {'interval': 'm3', 'connections': ([2, 3, Direction.ASCENDING],) # f# to a }, {'interval': 'M2', 'connections': ([3, 4, Direction.ASCENDING],) # a to b }, {'interval': '-M2', 'connections': ([4, 5, Direction.ASCENDING],) # b to a (downward) }, {'interval': 'm3', 'connections': ([5, Terminus.HIGH, Direction.ASCENDING],) # a to c }, # descending {'interval': '-m2', 'connections': ([Terminus.HIGH, 6, Direction.DESCENDING],) # c to d- (up) }, {'interval': 'd3', 'connections': ([6, 7, Direction.DESCENDING],) # d- to b }, {'interval': 'M2', 'connections': ([7, 8, Direction.DESCENDING],) # b to a }, {'interval': 'm3', 'connections': ([8, 9, Direction.DESCENDING],) # a to f# }, {'interval': 'M2', 'connections': ([9, 10, Direction.DESCENDING],) # f# to e }, {'interval': 'A2', 'connections': ([10, 11, Direction.DESCENDING],) # e to d- }, {'interval': 'm2', 'connections': ([11, Terminus.LOW, Direction.DESCENDING],) # d- to c }, ) self._net = intervalNetwork.IntervalNetwork( octaveDuplicating=self.octaveDuplicating, ) # using representation stored in interval network self._net.fillArbitrary(nodes, edges) class AbstractWeightedHexatonicBlues(AbstractScale): ''' A dynamic, probabilistic mixture of minor pentatonic and a hexatonic blues scale ''' def __init__(self, **keywords): super().__init__(**keywords) self.type = 'Abstract Weighted Hexatonic Blues' # probably not, as all may not have some pitches in each octave self.octaveDuplicating = True self.deterministic = False self.dominantDegree = 5 self.buildNetwork() def buildNetwork(self): self.tonicDegree = 1 self.dominantDegree = 5 nodes = ({'id': Terminus.LOW, 'degree': 1}, # c {'id': 0, 'degree': 2}, # e- {'id': 1, 'degree': 3}, # f {'id': 2, 'degree': 4}, # f# {'id': 3, 'degree': 5}, # g {'id': 4, 'degree': 6}, # b- {'id': Terminus.HIGH, 'degree': 7}, # c ) edges = ( # all bidirectional {'interval': 'm3', 'connections': ( [Terminus.LOW, 0, Direction.BI], # c to e- )}, {'interval': 'M2', 'connections': ( [0, 1, Direction.BI], # e- to f )}, {'interval': 'M2', 'connections': ( [1, 3, Direction.BI], # f to g )}, {'interval': 'a1', 'connections': ( [1, 2, Direction.BI], # f to f# )}, {'interval': 'm2', 'connections': ( [2, 3, Direction.BI], # f# to g )}, {'interval': 'm3', 'connections': ( [3, 4, Direction.BI], # g to b- )}, {'interval': 'M2', 'connections': ( [4, Terminus.HIGH, Direction.BI], # b- to c )}, ) self._net = intervalNetwork.IntervalNetwork( octaveDuplicating=self.octaveDuplicating, deterministic=self.deterministic,) # using representation stored in interval network self._net.fillArbitrary(nodes, edges) # ------------------------------------------------------------------------------ class ConcreteScale(Scale): ''' A concrete scale is specific scale formation with a defined pitch collection (a `tonic` Pitch) that may or may not be bound by specific range. For example, a specific Major Scale, such as G Major, from G2 to G4. This class is can either be used directly or more commonly as a base class for all concrete scales. Here we treat a diminished triad as a scale: >>> myScale = scale.ConcreteScale(pitches=['C4', 'E-4', 'G-4', 'A4']) >>> myScale.getTonic() >>> myScale.nextPitch('G-2') >>> [str(p) for p in myScale.getPitches('E-5', 'G-7')] ['E-5', 'G-5', 'A5', 'C6', 'E-6', 'G-6', 'A6', 'C7', 'E-7', 'G-7'] A scale that lasts two octaves and uses quarter tones (D~) >>> complexScale = scale.ConcreteScale( ... pitches=['C#3', 'E-3', 'F3', 'G3', 'B3', 'D~4', 'F#4', 'A4', 'C#5'] ... ) >>> complexScale.getTonic() >>> complexScale.nextPitch('G3', direction=scale.Direction.DESCENDING) >>> [str(p) for p in complexScale.getPitches('C3', 'C7')] ['C#3', 'E-3', 'F3', 'G3', 'B3', 'D~4', 'F#4', 'A4', 'C#5', 'E-5', 'F5', 'G5', 'B5', 'D~6', 'F#6', 'A6'] Descending form: >>> [str(p) for p in complexScale.getPitches('C7', 'C5')] ['A6', 'F#6', 'D~6', 'B5', 'G5', 'F5', 'E-5', 'C#5'] Equality -------- Two ConcreteScales are the same if they satisfy all general Music21Object equality methods and their Abstract scales, their tonics, and their boundRanges are the same: OMIT_FROM_DOCS >>> scale.ConcreteScale(tonic=4) Traceback (most recent call last): ValueError: Tonic must be a Pitch, Note, or str, not This is in OMIT ''' usePitchDegreeCache = False def __init__(self, tonic: str|pitch.Pitch|note.Note|None = None, pitches: list[pitch.Pitch|str]|None = None, **keywords): super().__init__(**keywords) self.type = 'Concrete' # store an instance of an abstract scale # subclasses might use multiple abstract scales? self._abstract: AbstractScale|None = None # determine whether this is a limited range self.boundRange = False if (tonic is None and pitches is not None and common.isListLike(pitches) and pitches): tonic = pitches[0] # here, tonic is a pitch # the abstract scale defines what step the tonic is expected to be # found on # no default tonic is defined; as such, it is mostly an abstract scale, and # can't be used concretely until it is created. self.tonic: pitch.Pitch|None if tonic is None: self.tonic = None # pitch.Pitch() elif isinstance(tonic, str): self.tonic = pitch.Pitch(tonic) elif isinstance(tonic, note.Note): self.tonic = tonic.pitch elif isinstance(tonic, pitch.Pitch): # assume this is a pitch object self.tonic = tonic else: raise ValueError(f'Tonic must be a Pitch, Note, or str, not {type(tonic)}') if (pitches is not None and common.isListLike(pitches) and pitches): self._abstract = AbstractScale() self._abstract.buildNetworkFromPitches(pitches) if self.tonic in pitches: self._abstract.tonicDegree = pitches.index(self.tonic) + 1 @property def isConcrete(self): ''' Return True if the scale is Concrete, that is, it has a defined Tonic. >>> sc1 = scale.MajorScale('c') >>> sc1.isConcrete True >>> sc2 = scale.MajorScale() >>> sc2.isConcrete False To be concrete, a Scale must have a defined tonic. An abstract Scale is not Concrete ''' if self.tonic is None: return False else: return True def __eq__(self, other): ''' For concrete equality, the stored abstract objects must evaluate as equal, as well as local attributes. >>> sc1 = scale.MajorScale('c') >>> sc2 = scale.MajorScale('c') >>> sc3 = scale.MinorScale('c') >>> sc4 = scale.MajorScale('g') >>> sc5 = scale.MajorScale() # an abstract scale, as no tonic defined >>> sc1 == sc2 True >>> sc1 == sc3 False >>> sc1 == sc4 False >>> sc1.abstract == sc4.abstract # can compare abstract forms True >>> sc4 == sc5 # implicit abstract comparison True >>> sc5 == sc2 # implicit abstract comparison True >>> sc5 == sc3 # implicit abstract comparison False ''' if not super().__eq__(other): return False if not self.isConcrete or not other.isConcrete: # if tonic is none, then we automatically do an abstract comparison return self._abstract == other._abstract else: if (isinstance(other, self.__class__) and isinstance(self, other.__class__) and self._abstract == other._abstract and self.boundRange == other.boundRange and self.tonic == other.tonic): return True else: return False def __hash__(self): return id(self) >> 4 @property def name(self): ''' Return or construct the name of this scale >>> sc = scale.DiatonicScale() # abstract, as no defined tonic >>> sc.name 'Abstract diatonic' ''' if self.tonic is None: return ' '.join(['Abstract', self.type]) else: return ' '.join([self.tonic.name, self.type]) def _reprInternal(self): return self.name # -------------------------------------------------------------------------- def getTonic(self): ''' Return the tonic. >>> sc = scale.ConcreteScale(tonic='e-4') >>> sc.getTonic() ''' return self.tonic @property def abstract(self): ''' Return the AbstractScale instance governing this ConcreteScale. >>> sc1 = scale.MajorScale('d') >>> sc2 = scale.MajorScale('b-') >>> sc1 == sc2 False >>> sc1.abstract == sc2.abstract True Abstract scales can also be set afterwards: >>> scVague = scale.ConcreteScale() >>> scVague.abstract = scale.AbstractDiatonicScale('major') >>> scVague.tonic = pitch.Pitch('D') >>> [p.name for p in scVague.getPitches()] ['D', 'E', 'F#', 'G', 'A', 'B', 'C#', 'D'] >>> scVague.abstract = scale.AbstractOctatonicScale() >>> [p.name for p in scVague.getPitches()] ['D', 'E', 'F', 'G', 'A-', 'B-', 'C-', 'D-', 'D'] * Changed in v6: changing `.abstract` is now allowed. ''' # copy before returning? (No, it is too slow) return self._abstract @abstract.setter def abstract(self, newAbstract: AbstractScale): if not isinstance(newAbstract, AbstractScale): raise TypeError(f'abstract must be an AbstractScale, not {type(newAbstract)}') self._abstract = newAbstract def getDegreeMaxUnique(self): ''' Convenience routine to get this from the AbstractScale. ''' return self._abstract.getDegreeMaxUnique() def transpose(self, value, *, inPlace=False): ''' Transpose this Scale by the given interval Note: It does not make sense to transpose an abstract scale, since it is merely a collection of intervals. Thus, only concrete scales can be transposed. >>> sc1 = scale.MajorScale('C') >>> sc2 = sc1.transpose('p5') >>> sc2 >>> sc3 = sc2.transpose('p5') >>> sc3 >>> sc3.transpose('p5', inPlace=True) >>> sc3 ''' if inPlace: post = self else: post = copy.deepcopy(self) if self.tonic is None: # could raise an error; just assume a 'c' post.tonic = pitch.Pitch('C4') post.tonic.transpose(value, inPlace=True) else: post.tonic.transpose(value, inPlace=True) # may need to clear cache here if not inPlace: return post def tune( self, streamObj, minPitch=None, maxPitch=None, direction=None ) -> None: ''' Given a Stream object containing Pitches, match all pitch names and or pitch space values and replace the target pitch with copies of pitches stored in this scale. This is always applied recursively to all sub-Streams. ''' from music21 import chord # we may use a directed or subset of the scale to tune # in the future, we might even match contour or direction # bug in PyCharm # noinspection PyArgumentList pitchColl = self.getPitches(minPitch=minPitch, maxPitch=maxPitch, direction=direction ) pitchCollNames = [p.name for p in pitchColl] def tuneOnePitch(p, dst: list[pitch.Pitch]): # some pitches might be quarter / 3/4 tones; need to convert # these to microtonal representations so that we can directly # compare pitch names pAlt = p.convertQuarterTonesToMicrotones(inPlace=False) # need to permit enharmonic comparisons: G# and A- should # in most cases match testEnharmonics = pAlt.getAllCommonEnharmonics(alterLimit=2) testEnharmonics.append(pAlt) for pEnh in testEnharmonics: if pEnh.name not in pitchCollNames: continue # get the index from the names and extract the pitch by # index pDst = pitchColl[pitchCollNames.index(pEnh.name)] # get a deep copy for each note pDstNew = copy.deepcopy(pDst) pDstNew.octave = pEnh.octave # copy octave # need to adjust enharmonic pDstNewEnh = pDstNew.getAllCommonEnharmonics(alterLimit=2) match: pitch.Pitch|None = None for x in pDstNewEnh: # try to match enharmonic with original alt if x.name == pAlt.name: match = x if match is None: # get original dst.append(pDstNew) else: dst.append(match) # for p in streamObj.pitches: # this is always recursive for e in streamObj.recurse().notes: # get notes and chords if e.isChord: elementPitches = e.pitches else: # simulate a list elementPitches = [e.pitch] # store a list of reset chord pitches outerDestination: list[pitch.Pitch] = [] for p in elementPitches: tuneOnePitch(p, outerDestination) # reassign the changed pitch if outerDestination: if isinstance(e, chord.Chord): # note: we may not have matched all pitches e.pitches = tuple(outerDestination) else: # only one e.pitch = outerDestination[0] def romanNumeral(self, degree): ''' Return a RomanNumeral object built on the specified scale degree. >>> sc1 = scale.MajorScale('a-4') >>> h1 = sc1.romanNumeral(1) >>> h1.root() >>> h5 = sc1.romanNumeral(5) >>> h5.root() >>> h5 ''' from music21 import roman return roman.RomanNumeral(degree, self) def getPitches( self, minPitch: str|pitch.Pitch|None = None, maxPitch: str|pitch.Pitch|None = None, direction: Direction|None = None ) -> list[pitch.Pitch]: ''' Return a list of Pitch objects, using a deepcopy of a cached version if available. ''' # get from interval network of abstract scale if self._abstract is None: return [] # TODO: get and store in cache; return a copy # or generate from network stored in abstract if self.tonic is None: # note: could raise an error here, but instead will # use a pseudo-tonic pitchObj = pitch.Pitch('C4') else: pitchObj = self.tonic stepOfPitch = self._abstract.tonicDegree minPitchObj: pitch.Pitch|None if isinstance(minPitch, str): minPitchObj = pitch.Pitch(minPitch) else: minPitchObj = minPitch maxPitchObj: pitch.Pitch|None if isinstance(maxPitch, str): maxPitchObj = pitch.Pitch(maxPitch) else: maxPitchObj = maxPitch if (minPitchObj is not None and maxPitchObj is not None and minPitchObj > maxPitchObj and direction is None): reverse = True (minPitchObj, maxPitchObj) = (maxPitchObj, minPitchObj) elif direction == Direction.DESCENDING: reverse = True # reverse presentation so pitches go high to low else: reverse = False if direction is None: direction = Direction.ASCENDING # this creates new pitches on each call return self._abstract.getRealization(pitchObj, stepOfPitch, minPitch=minPitchObj, maxPitch=maxPitchObj, direction=direction, reverse=reverse) # raise ScaleException('Cannot generate a scale from a DiatonicScale class') # this needs to stay separate from getPitches; both are needed pitches = property(getPitches, doc=''' Get a default pitch list from this scale. ''') def getChord( self, minPitch=None, maxPitch=None, direction=Direction.ASCENDING, **keywords ) -> 'music21.chord.Chord': ''' Return a realized chord containing all the pitches in this scale within a particular inclusive range defined by two pitches. All keyword arguments are passed on to the Chord, permitting specification of `quarterLength` and similar parameters. ''' from music21 import chord # bug in PyCharm # noinspection PyArgumentList myPitches = self.getPitches(minPitch=minPitch, maxPitch=maxPitch, direction=direction) return chord.Chord(myPitches, **keywords) # this needs to stay separate from getChord chord = property(getChord, doc=''' Return a Chord object from this harmony over a default range. Use the `getChord()` method if you need greater control over the parameters of the chord. ''') def pitchFromDegree( self, degree: int, minPitch=None, maxPitch=None, direction: Direction = Direction.ASCENDING, equateTermini: bool = True): ''' Given a scale degree, return a deepcopy of the appropriate pitch. >>> sc = scale.MajorScale('e-') >>> sc.pitchFromDegree(2) >>> sc.pitchFromDegree(7) OMIT_FROM_DOCS Test deepcopy >>> d = sc.pitchFromDegree(7) >>> d.accidental = pitch.Accidental('sharp') >>> d >>> sc.pitchFromDegree(7) ''' if self._abstract is None: # pragma: no cover raise ScaleException('Abstract scale underpinning this scale is not defined.') cacheKey: _PitchDegreeCacheKey|None = None if (self.usePitchDegreeCache and self.tonic and not minPitch and not maxPitch and getattr(self, 'type', None)): tonicCacheKey = self.tonic.nameWithOctave cacheKey = ( self.__class__, self.type, tonicCacheKey, degree, direction, equateTermini ) if cacheKey in _pitchDegreeCache: return pitch.Pitch(_pitchDegreeCache[cacheKey]) post = self._abstract.getPitchFromNodeDegree( pitchReference=self.tonic, # pitch defined here nodeName=self._abstract.tonicDegree, # defined in abstract class nodeDegreeTarget=degree, # target looking for direction=direction, minPitch=minPitch, maxPitch=maxPitch, equateTermini=equateTermini) if cacheKey: _pitchDegreeCache[cacheKey] = post.nameWithOctave return post # if 0 < degree <= self._abstract.getDegreeMaxUnique(): # return self.getPitches()[degree - 1] # else: # raise('Scale degree is out of bounds: must be between 1 and %s.' % ( # self._abstract.getDegreeMaxUnique())) def pitchesFromScaleDegrees( self, degreeTargets, minPitch=None, maxPitch=None, direction=Direction.ASCENDING): ''' Given one or more scale degrees, return a list of all matches over the entire range. >>> sc = scale.MajorScale('e-') >>> sc.pitchesFromScaleDegrees([3, 7]) [, ] >>> [str(p) for p in sc.pitchesFromScaleDegrees([3, 7], 'c2', 'c6')] ['D2', 'G2', 'D3', 'G3', 'D4', 'G4', 'D5', 'G5'] >>> sc = scale.HarmonicMinorScale('a') >>> [str(p) for p in sc.pitchesFromScaleDegrees([3, 7], 'c2', 'c6')] ['C2', 'G#2', 'C3', 'G#3', 'C4', 'G#4', 'C5', 'G#5', 'C6'] ''' # TODO: rely here on intervalNetwork for caching post = self._abstract.realizePitchByDegree( pitchReference=self.tonic, # pitch defined here nodeId=self._abstract.tonicDegree, # defined in abstract class nodeDegreeTargets=degreeTargets, # target looking for direction=direction, minPitch=minPitch, maxPitch=maxPitch) return post def intervalBetweenDegrees( self, degreeStart, degreeEnd, direction=Direction.ASCENDING, equateTermini=True): ''' Given two degrees, provide the interval as an interval.Interval object. >>> sc = scale.MajorScale('e-') >>> sc.intervalBetweenDegrees(3, 7) ''' # get pitches for each degree pStart = self.pitchFromDegree(degreeStart, direction=direction, equateTermini=equateTermini) pEnd = self.pitchFromDegree(degreeEnd, direction=direction, equateTermini=equateTermini) if pStart is None: raise ScaleException(f'cannot get a pitch for scale degree: {pStart}') if pEnd is None: raise ScaleException(f'cannot get a pitch for scale degree: {pEnd}') return interval.Interval(pStart, pEnd) def getScaleDegreeFromPitch(self, pitchTarget, direction=Direction.ASCENDING, comparisonAttribute='name'): ''' For a given pitch, return the appropriate scale degree. If no scale degree is available, None is returned. Note: by default it will use a find algorithm that is based on the note's `.name` not on `.pitchClass` because this is used so commonly by tonal functions. So if it's important that D# and E- are the same, set the comparisonAttribute to `pitchClass` >>> sc = scale.MajorScale('e-') >>> sc.getScaleDegreeFromPitch('e-2') 1 >>> sc.getScaleDegreeFromPitch('d') 7 >>> sc.getScaleDegreeFromPitch('d#', comparisonAttribute='name') is None True >>> sc.getScaleDegreeFromPitch('d#', comparisonAttribute='pitchClass') 1 >>> sc.getScaleDegreeFromPitch('e') is None True >>> sc.getScaleDegreeFromPitch('e', comparisonAttribute='step') 1 >>> sc = scale.HarmonicMinorScale('a') >>> sc.getScaleDegreeFromPitch('c') 3 >>> sc.getScaleDegreeFromPitch('g#') 7 >>> sc.getScaleDegreeFromPitch('g') is None True >>> cMaj = key.Key('C') >>> cMaj.getScaleDegreeFromPitch(pitch.Pitch('E-'), ... direction=scale.Direction.ASCENDING, ... comparisonAttribute='step') 3 ''' post = self._abstract.getRelativeNodeDegree(pitchReference=self.tonic, nodeName=self._abstract.tonicDegree, pitchTarget=pitchTarget, comparisonAttribute=comparisonAttribute, direction=direction) return post def getScaleDegreeAndAccidentalFromPitch(self, pitchTarget, direction=Direction.ASCENDING, comparisonAttribute='name'): ''' Given a scale (or :class:`~music21.key.Key` object) and a pitch, return a two-element tuple of the degree of the scale and an accidental (or None) needed to get this pitch. >>> cMaj = key.Key('C') >>> cMaj.getScaleDegreeAndAccidentalFromPitch(pitch.Pitch('E')) (3, None) >>> cMaj.getScaleDegreeAndAccidentalFromPitch(pitch.Pitch('E-')) (3, ) The Direction of a melodic minor scale is significant >>> aMin = scale.MelodicMinorScale('a') >>> aMin.getScaleDegreeAndAccidentalFromPitch(pitch.Pitch('G'), ... direction=scale.Direction.DESCENDING) (7, None) >>> aMin.getScaleDegreeAndAccidentalFromPitch(pitch.Pitch('G'), ... direction=scale.Direction.ASCENDING) (7, ) >>> aMin.getScaleDegreeAndAccidentalFromPitch(pitch.Pitch('G-'), ... direction=scale.Direction.ASCENDING) (7, ) Returns (None, None) if for some reason this scale does not have this step (a whole-tone scale, for instance) ''' scaleStep = self.getScaleDegreeFromPitch(pitchTarget, direction, comparisonAttribute) if scaleStep is not None: return (scaleStep, None) else: scaleStepNormal = self.getScaleDegreeFromPitch(pitchTarget, direction, comparisonAttribute='step') if scaleStepNormal is None: raise ScaleException( 'Cannot get any scale degree from getScaleDegreeFromPitch for pitchTarget ' + f"{pitchTarget}, direction {direction}, comparisonAttribute='step'") pitchesFound = self.pitchesFromScaleDegrees([scaleStepNormal]) if not pitchesFound: return (None, None) else: foundPitch = pitchesFound[0] if foundPitch.accidental is None: foundAlter = 0 else: foundAlter = foundPitch.accidental.alter if pitchTarget.accidental is None: pitchAlter = 0 else: pitchAlter = pitchTarget.accidental.alter alterDiff = pitchAlter - foundAlter if alterDiff == 0: # should not happen return (scaleStepNormal, None) else: alterAccidental = pitch.Accidental(alterDiff) return (scaleStepNormal, alterAccidental) # uses "traditional" chromatic solfeg and mostly Shearer Hullah (if needed) # noinspection SpellCheckingInspection _solfegSyllables = {1: {-2: 'def', -1: 'de', 0: 'do', 1: 'di', 2: 'dis', }, 2: {-2: 'raf', -1: 'ra', 0: 're', 1: 'ri', 2: 'ris', }, 3: {-2: 'mef', -1: 'me', 0: 'mi', 1: 'mis', 2: 'mish', }, 4: {-2: 'fef', -1: 'fe', 0: 'fa', 1: 'fi', 2: 'fis', }, 5: {-2: 'sef', -1: 'se', 0: 'sol', 1: 'si', 2: 'sis', }, 6: {-2: 'lef', -1: 'le', 0: 'la', 1: 'li', 2: 'lis', }, 7: {-2: 'tef', -1: 'te', 0: 'ti', 1: 'tis', 2: 'tish', }, } # TOO SLOW! # _humdrumSolfegSyllables = copy.deepcopy(_solfegSyllables) # _humdrumSolfegSyllables[3][1] = 'my' # _humdrumSolfegSyllables[5] = {-2: 'sef', -1: 'se', 0: 'so', 1:'si', 2:'sis'} # _humdrumSolfegSyllables[7][1] = 'ty' # noinspection SpellCheckingInspection _humdrumSolfegSyllables = { 1: {-2: 'def', -1: 'de', 0: 'do', 1: 'di', 2: 'dis', }, 2: {-2: 'raf', -1: 'ra', 0: 're', 1: 'ri', 2: 'ris', }, 3: {-2: 'mef', -1: 'me', 0: 'mi', 1: 'my', 2: 'mish', }, 4: {-2: 'fef', -1: 'fe', 0: 'fa', 1: 'fi', 2: 'fis', }, 5: {-2: 'sef', -1: 'se', 0: 'so', 1: 'si', 2: 'sis', }, 6: {-2: 'lef', -1: 'le', 0: 'la', 1: 'li', 2: 'lis', }, 7: {-2: 'tef', -1: 'te', 0: 'ti', 1: 'ty', 2: 'tish', }, } def solfeg(self, pitchTarget=None, direction=Direction.ASCENDING, variant='music21', chromatic=True): ''' Returns the chromatic solfeg (or diatonic if chromatic is False) for a given pitch in a given scale. The `variant` method lets one specify either the default `music21` or `humdrum` solfeg representation for altered notes. >>> eflatMaj = key.Key('E-') >>> eflatMaj.solfeg(pitch.Pitch('G')) 'mi' >>> eflatMaj.solfeg('A') 'fi' >>> eflatMaj.solfeg('A', chromatic=False) 'fa' >>> eflatMaj.solfeg(pitch.Pitch('G#'), variant='music21') # default 'mis' >>> eflatMaj.solfeg(pitch.Pitch('G#'), variant='humdrum') 'my' ''' if isinstance(pitchTarget, str): pitchTarget = pitch.Pitch(pitchTarget) (scaleDeg, accidental) = self.getScaleDegreeAndAccidentalFromPitch(pitchTarget, direction) if variant == 'music21': syllableDict = self._solfegSyllables elif variant == 'humdrum': syllableDict = self._humdrumSolfegSyllables else: raise ScaleException(f'Unknown solfeg variant {variant}') if scaleDeg > 7: raise ScaleException('Cannot call solfeg on non-7-degree scales') if scaleDeg is None: raise ScaleException('Unknown scale degree for this pitch') if chromatic is True: if accidental is None: return syllableDict[scaleDeg][0] else: return syllableDict[scaleDeg][accidental.alter] else: return syllableDict[scaleDeg][0] # no type checking as a deprecated call that shadows superclass. @t.no_type_check @deprecated('v9', 'v10', 'use nextPitch instead') def next( self, pitchOrigin=None, direction: 'music21.scale.intervalNetwork.Direction'|int = Direction.ASCENDING, stepSize=1, getNeighbor: 'music21.scale.intervalNetwork.Direction'|bool = True, ): # pragma: no cover ''' See :meth:`~music21.scale.ConcreteScale.nextPitch`. This function is a deprecated alias for that method. This routine was named and created before music21 aspired to have full subclass substitution. Thus, is shadows the `.next()` function of Music21Object without performing similar functionality. The routine is formally deprecated in v9 and will be removed in v10. ''' return self.nextPitch( pitchOrigin=pitchOrigin, direction=direction, stepSize=stepSize, getNeighbor=getNeighbor ) def nextPitch( self, pitchOrigin=None, direction: Direction|int = Direction.ASCENDING, stepSize=1, getNeighbor: Direction|bool = True, ): ''' Get the next pitch above (or below if direction is Direction.DESCENDING) a `pitchOrigin` or None. If the `pitchOrigin` is None, the tonic pitch is returned. This is useful when starting a chain of iterative calls. The `direction` attribute may be either ascending or descending. Default is `ascending`. Optionally, positive or negative integers may be provided as directional stepSize scalars. An optional `stepSize` argument can be used to set the number of scale steps that are stepped through. Thus, .nextPitch(stepSize=2) will give not the next pitch in the scale, but the next after this one. The `getNeighbor` will return a pitch from the scale if `pitchOrigin` is not in the scale. This value can be True, Direction.ASCENDING, or Direction.DESCENDING. >>> sc = scale.MajorScale('e-') >>> print(sc.nextPitch('e-5')) F5 >>> print(sc.nextPitch('e-5', stepSize=2)) G5 >>> print(sc.nextPitch('e-6', stepSize=3)) A-6 This uses the getNeighbor attribute to find the next note above f#5 in the E-flat major scale: >>> sc.nextPitch('f#5') >>> sc = scale.HarmonicMinorScale('g') >>> sc.nextPitch('g4', scale.Direction.DESCENDING) >>> sc.nextPitch('F#4', scale.Direction.DESCENDING) >>> sc.nextPitch('E-4', scale.Direction.DESCENDING) >>> sc.nextPitch('E-4', scale.Direction.ASCENDING, 1) >>> sc.nextPitch('E-4', scale.Direction.ASCENDING, 2) ''' if pitchOrigin is None: return self.tonic if self._abstract is None: # pragma: no cover raise ScaleException('Abstract scale underpinning this scale is not defined.') directionEnum: Direction # allow numerical directions if isinstance(direction, int): if direction != 0: # treat as a positive or negative step scalar if direction > 0: stepScalar = direction directionEnum = Direction.ASCENDING else: # negative non-zero stepScalar = abs(direction) directionEnum = Direction.DESCENDING else: raise ScaleException('direction cannot be zero') else: # when direction is a string, use scalar of 1 stepScalar = 1 # stepSize is still used directionEnum = direction # pick reverse direction for neighbor if getNeighbor is True: if directionEnum == Direction.ASCENDING: getNeighbor = Direction.DESCENDING elif directionEnum == Direction.DESCENDING: getNeighbor = Direction.ASCENDING post = self._abstract.nextPitch( pitchReference=self.tonic, nodeName=self._abstract.tonicDegree, pitchOrigin=pitchOrigin, direction=directionEnum, stepSize=stepSize * stepScalar, # multiplied getNeighbor=getNeighbor ) return post def isNext(self, other, pitchOrigin, direction: Direction = Direction.ASCENDING, stepSize=1, getNeighbor: Direction|bool = True, comparisonAttribute='name'): ''' Given another pitch, as well as an origin and a direction, determine if this other pitch is in the next in the scale. >>> sc1 = scale.MajorScale('g') >>> sc1.isNext('d4', 'c4', scale.Direction.ASCENDING) True ''' if isinstance(other, str): # convert to pitch other = pitch.Pitch(other) elif hasattr(other, 'pitch'): # possibly a note other = other.pitch # just get pitch component elif not isinstance(other, pitch.Pitch): return False # cannot compare to non-pitch nPitch = self.nextPitch(pitchOrigin, direction=direction, stepSize=stepSize, getNeighbor=getNeighbor) if nPitch is None: return None if (getattr(nPitch, comparisonAttribute) == getattr(other, comparisonAttribute)): return True else: return False # -------------------------------------------------------------------------- # comparison and evaluation def match(self, other, comparisonAttribute='name'): ''' Given another object of the forms that `extractPitchList` can take, (e.g., a :class:`~music21.stream.Stream`, a :class:`~music21.scale.ConcreteScale`, a list of :class:`~music21.pitch.Pitch` objects), return a named dictionary of pitch lists with keys 'matched' and 'notMatched'. >>> sc1 = scale.MajorScale('g') >>> sc2 = scale.MajorScale('d') >>> sc3 = scale.MajorScale('a') >>> sc4 = scale.MajorScale('e') >>> from pprint import pprint as pp >>> pp(sc1.match(sc2)) {'matched': [, , , , , ], 'notMatched': []} >>> pp(sc2.match(sc3)) {'matched': [, , , , , ], 'notMatched': []} >>> pp(sc1.match(sc4)) {'matched': [, , , ], 'notMatched': [, , ]} ''' # strip out unique pitches in a list otherPitches = self.extractPitchList(other, comparisonAttribute=comparisonAttribute) # need to deal with direction here? or get an aggregate scale matched, notMatched = self._abstract._net.match( pitchReference=self.tonic, nodeId=self._abstract.tonicDegree, pitchTarget=otherPitches, # can supply a list here comparisonAttribute=comparisonAttribute) post = { 'matched': matched, 'notMatched': notMatched, } return post def findMissing(self, other, comparisonAttribute='pitchClass', minPitch=None, maxPitch=None, direction=Direction.ASCENDING, alteredDegrees=None): ''' Given another object of the forms that `extractPitches` takes (e.g., a :class:`~music21.stream.Stream`, a :class:`~music21.scale.ConcreteScale`, a list of :class:`~music21.pitch.Pitch` objects), return a list of pitches that are found in this Scale but are not found in the provided object. >>> sc1 = scale.MajorScale('g4') >>> [str(p) for p in sc1.findMissing(['d'])] ['G4', 'A4', 'B4', 'C5', 'E5', 'F#5', 'G5'] ''' # strip out unique pitches in a list otherPitches = self.extractPitchList(other, comparisonAttribute=comparisonAttribute) post = self._abstract._net.findMissing( pitchReference=self.tonic, nodeId=self._abstract.tonicDegree, pitchTarget=otherPitches, # can supply a list here comparisonAttribute=comparisonAttribute, minPitch=minPitch, maxPitch=maxPitch, direction=direction, alteredDegrees=alteredDegrees, ) return post def deriveRanked(self, other, resultsReturned=4, comparisonAttribute='pitchClass', removeDuplicates=False): # noinspection PyShadowingNames ''' Return a list of closest-matching :class:`~music21.scale.ConcreteScale` objects based on this :class:`~music21.scale.AbstractScale`, provided as a :class:`~music21.stream.Stream`, a :class:`~music21.scale.ConcreteScale`, or a list of :class:`~music21.pitch.Pitch` objects. Returned integer values represent the number of matches. If you are working with Diatonic Scales, you will probably want to change the `comparisonAttribute` to `name`. >>> sc1 = scale.MajorScale() >>> sc1.deriveRanked(['C', 'E', 'B']) [(3, ), (3, ), (2, ), (2, )] With the default of comparing by pitchClass, D- is fine for B major because C# is in the B major scale. >>> sc1.deriveRanked(['D-', 'E', 'B']) [(3, ), (3, ), (3, ), (3, )] Comparing based on enharmonic-sensitive spelling, has fewer hits for all of these scales: >>> sc1.deriveRanked(['D-', 'E', 'B'], comparisonAttribute='name') [(2, ), (2, ), (2, ), (2, )] Notice that we check how many of the pitches are in the scale and do not de-duplicate pitches. >>> sc1.deriveRanked(['C', 'E', 'E', 'E', 'B']) [(5, ), (5, ), (4, ), (4, )] If removeDuplicates is given, the E's will get less weight: >>> sc1.deriveRanked(['C', 'E', 'E', 'E', 'B'], removeDuplicates=True) [(3, ), (3, ), (2, ), (2, )] >>> sc1.deriveRanked(['C#', 'E', 'G#']) [(3, ), (3, ), (3, ), (3, )] A Concrete Scale created from pitches still has similar characteristics to the original. Here we create a scale like a Harmonic minor but with flat 2 and sharp 4. >>> e = scale.ConcreteScale(pitches=['A4', 'B-4', 'C5', 'D#5', 'E5', 'F5', 'G#5', 'A5']) Notice the G# is allowed to be chosen even though we are specifically looking for scales with a G natural in them. Once no scale matched all three pitches, which scale that matches two pitches is arbitrary. >>> bestScales = e.deriveRanked(['C', 'E', 'G'], resultsReturned=6) >>> bestScales [(3, ), (3, ), (3, ), (2, ), (2, ), (2, )] >>> eConcrete = bestScales[0][1] >>> ' '.join([str(p) for p in eConcrete.pitches]) 'E4 F4 G4 A#4 B4 C5 D#5 E5' ''' # possibly return dictionary with named parameters # default return all scales that match all provided pitches # instead of results returned, define how many matched pitches necessary otherPitches = self.extractPitchList(other, comparisonAttribute=comparisonAttribute, removeDuplicates=removeDuplicates) pairs = self._abstract._net.find(pitchTarget=otherPitches, resultsReturned=resultsReturned, comparisonAttribute=comparisonAttribute, alteredDegrees=self._abstract._alteredDegrees) post = [] for weight, p in pairs: sc = self.__class__(tonic=p) if sc.abstract is None: sc.abstract = copy.deepcopy(self._abstract) post.append((weight, sc)) return post def derive(self, other, comparisonAttribute='pitchClass'): ''' Return the closest-matching :class:`~music21.scale.ConcreteScale` based on the pitch collection provided as a :class:`~music21.stream.Stream`, a :class:`~music21.scale.ConcreteScale`, or a list of :class:`~music21.pitch.Pitch` objects. How the "closest-matching" scale is defined still needs to be refined and has changed in the past and will probably change in the future. >>> sc1 = scale.MajorScale() >>> sc1.derive(['C#', 'E', 'G#']) >>> sc1.derive(['E-', 'B-', 'D'], comparisonAttribute='name') ''' otherPitches = self.extractPitchList(other, comparisonAttribute=comparisonAttribute) # weight target membership pairs = self._abstract._net.find(pitchTarget=otherPitches, comparisonAttribute=comparisonAttribute) newScale = self.__class__(tonic=pairs[0][1]) if newScale.abstract is None: newScale.abstract = copy.deepcopy(self._abstract) return newScale def deriveAll(self, other, comparisonAttribute='pitchClass'): # noinspection PyShadowingNames ''' Return a list of all Scales of the same class as `self` where all the pitches in `other` are contained. Similar to "deriveRanked" but only returns those scales no matter how many which contain all the pitches. Just returns a list in order. If you are working with Diatonic Scales, you will probably want to change the `comparisonAttribute` to `name`. >>> sc1 = scale.MajorScale() >>> sc1.deriveAll(['C', 'E', 'B']) [, ] >>> [sc.name for sc in sc1.deriveAll(['D-', 'E', 'B'])] ['B major', 'A major', 'E major', 'D major', 'C- major'] >>> sc1.deriveAll(['D-', 'E', 'B'], comparisonAttribute='name') [] Find all instances of this pentatonic scale in major scales: >>> scList = sc1.deriveAll(['C#', 'D#', 'F#', 'G#', 'A#'], comparisonAttribute='name') >>> [sc.name for sc in scList] ['B major', 'F# major', 'C# major'] ''' # possibly return dictionary with named parameters # default return all scales that match all provided pitches # instead of results returned, define how many matched pitches necessary otherPitches = self.extractPitchList(other, comparisonAttribute=comparisonAttribute) pairs = self._abstract._net.find(pitchTarget=otherPitches, resultsReturned=None, comparisonAttribute=comparisonAttribute, alteredDegrees=self._abstract._alteredDegrees) post = [] numPitches = len(otherPitches) for weight, p in pairs: if weight == numPitches: # only want matches where all notes match sc = self.__class__(tonic=p) if sc.abstract is None: sc.abstract = copy.deepcopy(self._abstract) post.append(sc) return post def deriveByDegree(self, degree, pitchRef): ''' Given a scale degree and a pitch, return a new :class:`~music21.scale.ConcreteScale` that satisfies that condition. Find a major scale with C as the 7th degree: >>> sc1 = scale.MajorScale() >>> sc1.deriveByDegree(7, 'c') TODO: Does not yet work for directional scales ''' p = self._abstract.getNewTonicPitch( pitchReference=pitchRef, nodeName=degree, ) # except intervalNetwork.IntervalNetworkException: # p = self._abstract.getNewTonicPitch( # pitchReference=pitchRef, # nodeName=degree, # direction=Direction.DESCENDING, # ) if p is None: raise ScaleException('cannot derive new tonic') newScale = self.__class__(tonic=p) if newScale.abstract is None: newScale.abstract = copy.deepcopy(self._abstract) return newScale # -------------------------------------------------------------------------- # alternative outputs def getScalaData(self): ''' Return a configured :class:`~music21.scala.ScalaData` Object for this scale. It can be used to find interval distances in cents between degrees. ''' ss = self.abstract.getScalaData() # customize with more specific representation ss.description = repr(self) return ss def write(self, fmt=None, fp=None, direction=Direction.ASCENDING): ''' Write the scale in a format. Here, prepare scala format if requested. ''' if fmt is not None: fileFormat, unused_ext = common.findFormat(fmt) if fileFormat == 'scala': return self.abstract.write(fmt=fmt, fp=fp, direction=direction) return Scale.write(self, fmt=fmt, fp=fp) def show(self, fmt=None, app=None, direction=Direction.ASCENDING): ''' Show the scale in a format. Here, prepare scala format if requested. ''' if fmt is not None: fileFormat, unused_ext = common.findFormat(fmt) if fileFormat == 'scala': self.abstract.show(fmt=fmt, app=app, direction=direction) return Scale.show(self, fmt=fmt, app=app) # ------------------------------------------------------------------------------ # concrete scales and subclasses class DiatonicScale(ConcreteScale): ''' A concrete diatonic scale. Each DiatonicScale has one instance of a :class:`~music21.scale.AbstractDiatonicScale`. ''' usePitchDegreeCache = True def __init__(self, tonic: str|pitch.Pitch|note.Note|None = None, **keywords): super().__init__(tonic=tonic, **keywords) self._abstract: AbstractDiatonicScale = AbstractDiatonicScale(**keywords) self.type = 'diatonic' def getTonic(self): ''' Return the tonic of the diatonic scale. >>> sc = scale.MajorScale('e-') >>> sc.getTonic() >>> sc = scale.MajorScale('F#') >>> sc.getTonic() If no tonic has been defined, it will return an Exception. (same is true for `getDominant`, `getLeadingTone`, etc.) >>> sc = scale.DiatonicScale() >>> sc.getTonic() Traceback (most recent call last): music21.scale.intervalNetwork.IntervalNetworkException: pitchReference cannot be None ''' # NOTE: override method on ConcreteScale that simply returns _tonic return self.pitchFromDegree(self._abstract.tonicDegree) def getDominant(self): ''' Return the dominant. >>> sc = scale.MajorScale('e-') >>> sc.getDominant() >>> sc = scale.MajorScale('F#') >>> sc.getDominant() ''' return self.pitchFromDegree(self._abstract.dominantDegree) def getLeadingTone(self): ''' Return the leading tone. >>> sc = scale.MinorScale('c') >>> sc.getLeadingTone() Note that the leading tone isn't necessarily the same as the 7th scale degree in minor: >>> sc.pitchFromDegree(7) ''' # NOTE: must adjust for modes that do not have a proper leading tone seventhDegree = self.pitchFromDegree(7) distanceInSemitones = seventhDegree.midi - self.tonic.midi if distanceInSemitones != 11: # if not a major seventh, raise/lower the seventh degree alterationInSemitones = 11 - distanceInSemitones seventhDegree.accidental = pitch.Accidental( seventhDegree.alter + alterationInSemitones ) return seventhDegree def getParallelMinor(self): ''' Return a parallel minor scale based on this concrete scale. >>> sc1 = scale.MajorScale(pitch.Pitch('a')) >>> [str(p) for p in sc1.pitches] ['A4', 'B4', 'C#5', 'D5', 'E5', 'F#5', 'G#5', 'A5'] >>> sc2 = sc1.getParallelMinor() >>> [str(p) for p in sc2.pitches] ['A4', 'B4', 'C5', 'D5', 'E5', 'F5', 'G5', 'A5'] Running getParallelMinor() again doesn't change anything >>> sc3 = sc2.getParallelMinor() >>> [str(p) for p in sc3.pitches] ['A4', 'B4', 'C5', 'D5', 'E5', 'F5', 'G5', 'A5'] ''' return MinorScale(self.tonic) def getParallelMajor(self): ''' Return a concrete relative major scale >>> sc1 = scale.MinorScale(pitch.Pitch('g')) >>> [str(p) for p in sc1.pitches] ['G4', 'A4', 'B-4', 'C5', 'D5', 'E-5', 'F5', 'G5'] >>> sc2 = sc1.getParallelMajor() >>> [str(p) for p in sc2.pitches] ['G4', 'A4', 'B4', 'C5', 'D5', 'E5', 'F#5', 'G5'] ''' return MajorScale(self.tonic) def getRelativeMinor(self): ''' Return a relative minor scale based on this concrete scale. >>> sc1 = scale.MajorScale(pitch.Pitch('a')) >>> [str(p) for p in sc1.pitches] ['A4', 'B4', 'C#5', 'D5', 'E5', 'F#5', 'G#5', 'A5'] >>> sc2 = sc1.getRelativeMinor() >>> [str(p) for p in sc2.pitches] ['F#5', 'G#5', 'A5', 'B5', 'C#6', 'D6', 'E6', 'F#6'] ''' return MinorScale(self.pitchFromDegree(self.abstract.relativeMinorDegree)) def getRelativeMajor(self): ''' Return a concrete relative major scale >>> sc1 = scale.MinorScale(pitch.Pitch('g')) >>> [str(p) for p in sc1.pitches] ['G4', 'A4', 'B-4', 'C5', 'D5', 'E-5', 'F5', 'G5'] >>> sc2 = sc1.getRelativeMajor() >>> [str(p) for p in sc2.pitches] ['B-4', 'C5', 'D5', 'E-5', 'F5', 'G5', 'A5', 'B-5'] Though it's unlikely you would want to do it, `getRelativeMajor` works on other diatonic scales than just Major and Minor. >>> sc2 = scale.DorianScale('d') >>> [str(p) for p in sc2.pitches] ['D4', 'E4', 'F4', 'G4', 'A4', 'B4', 'C5', 'D5'] >>> [str(p) for p in sc2.getRelativeMajor().pitches] ['C5', 'D5', 'E5', 'F5', 'G5', 'A5', 'B5', 'C6'] ''' return MajorScale(self.pitchFromDegree(self.abstract.relativeMajorDegree)) # ------------------------------------------------------------------------------ # diatonic scales and modes class MajorScale(DiatonicScale): ''' A Major Scale >>> sc = scale.MajorScale(pitch.Pitch('d')) >>> sc.pitchFromDegree(7).name 'C#' ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'major' # build the network for the appropriate scale self._abstract.buildNetwork(self.type) # N.B. do not subclass methods, since generally RomanNumerals use Keys # and Key is a subclass of DiatonicScale not MajorScale or MinorScale class MinorScale(DiatonicScale): ''' A natural minor scale, or the Aeolian mode. >>> sc = scale.MinorScale(pitch.Pitch('g')) >>> [str(p) for p in sc.pitches] ['G4', 'A4', 'B-4', 'C5', 'D5', 'E-5', 'F5', 'G5'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'minor' self._abstract.buildNetwork(self.type) class DorianScale(DiatonicScale): ''' A scale built on the Dorian (D-D white-key) mode. >>> sc = scale.DorianScale(pitch.Pitch('d')) >>> [str(p) for p in sc.pitches] ['D4', 'E4', 'F4', 'G4', 'A4', 'B4', 'C5', 'D5'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'dorian' self._abstract.buildNetwork(self.type) class PhrygianScale(DiatonicScale): ''' A Phrygian scale (E-E white key) >>> sc = scale.PhrygianScale(pitch.Pitch('e')) >>> [str(p) for p in sc.pitches] ['E4', 'F4', 'G4', 'A4', 'B4', 'C5', 'D5', 'E5'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'phrygian' self._abstract.buildNetwork(self.type) class LydianScale(DiatonicScale): ''' A Lydian scale (that is, the F-F white-key scale; does not have the probability of B- emerging as in a historical Lydian collection). >>> sc = scale.LydianScale(pitch.Pitch('f')) >>> [str(p) for p in sc.pitches] ['F4', 'G4', 'A4', 'B4', 'C5', 'D5', 'E5', 'F5'] >>> sc = scale.LydianScale(pitch.Pitch('c')) >>> [str(p) for p in sc.pitches] ['C4', 'D4', 'E4', 'F#4', 'G4', 'A4', 'B4', 'C5'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'lydian' self._abstract.buildNetwork(self.type) class MixolydianScale(DiatonicScale): ''' A mixolydian scale >>> sc = scale.MixolydianScale(pitch.Pitch('g')) >>> [str(p) for p in sc.pitches] ['G4', 'A4', 'B4', 'C5', 'D5', 'E5', 'F5', 'G5'] >>> sc = scale.MixolydianScale(pitch.Pitch('c')) >>> [str(p) for p in sc.pitches] ['C4', 'D4', 'E4', 'F4', 'G4', 'A4', 'B-4', 'C5'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'mixolydian' self._abstract.buildNetwork(self.type) class HypodorianScale(DiatonicScale): ''' A hypodorian scale: a dorian scale where the given pitch is scale degree 4. >>> sc = scale.HypodorianScale(pitch.Pitch('d')) >>> [str(p) for p in sc.pitches] ['A3', 'B3', 'C4', 'D4', 'E4', 'F4', 'G4', 'A4'] >>> sc = scale.HypodorianScale(pitch.Pitch('c')) >>> [str(p) for p in sc.pitches] ['G3', 'A3', 'B-3', 'C4', 'D4', 'E-4', 'F4', 'G4'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'hypodorian' self._abstract.buildNetwork(self.type) class HypophrygianScale(DiatonicScale): ''' A hypophrygian scale >>> sc = scale.HypophrygianScale(pitch.Pitch('e')) >>> sc.abstract.octaveDuplicating True >>> [str(p) for p in sc.pitches] ['B3', 'C4', 'D4', 'E4', 'F4', 'G4', 'A4', 'B4'] >>> sc.getTonic() >>> sc.getDominant() >>> sc.pitchFromDegree(1) # scale degree 1 is treated as lowest ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'hypophrygian' self._abstract.buildNetwork(self.type) class HypolydianScale(DiatonicScale): ''' A hypolydian scale >>> sc = scale.HypolydianScale(pitch.Pitch('f')) >>> [str(p) for p in sc.pitches] ['C4', 'D4', 'E4', 'F4', 'G4', 'A4', 'B4', 'C5'] >>> sc = scale.HypolydianScale(pitch.Pitch('c')) >>> [str(p) for p in sc.pitches] ['G3', 'A3', 'B3', 'C4', 'D4', 'E4', 'F#4', 'G4'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'hypolydian' self._abstract.buildNetwork(self.type) class HypomixolydianScale(DiatonicScale): ''' A hypomixolydian scale >>> sc = scale.HypomixolydianScale(pitch.Pitch('g')) >>> [str(p) for p in sc.pitches] ['D4', 'E4', 'F4', 'G4', 'A4', 'B4', 'C5', 'D5'] >>> sc = scale.HypomixolydianScale(pitch.Pitch('c')) >>> [str(p) for p in sc.pitches] ['G3', 'A3', 'B-3', 'C4', 'D4', 'E4', 'F4', 'G4'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'hypomixolydian' self._abstract.buildNetwork(self.type) class LocrianScale(DiatonicScale): ''' A so-called "locrian" scale >>> sc = scale.LocrianScale(pitch.Pitch('b')) >>> [str(p) for p in sc.pitches] ['B4', 'C5', 'D5', 'E5', 'F5', 'G5', 'A5', 'B5'] >>> sc = scale.LocrianScale(pitch.Pitch('c')) >>> [str(p) for p in sc.pitches] ['C4', 'D-4', 'E-4', 'F4', 'G-4', 'A-4', 'B-4', 'C5'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'locrian' self._abstract.buildNetwork(self.type) class HypolocrianScale(DiatonicScale): ''' A hypolocrian scale >>> sc = scale.HypolocrianScale(pitch.Pitch('b')) >>> [str(p) for p in sc.pitches] ['F4', 'G4', 'A4', 'B4', 'C5', 'D5', 'E5', 'F5'] >>> sc = scale.HypolocrianScale(pitch.Pitch('c')) >>> [str(p) for p in sc.pitches] ['G-3', 'A-3', 'B-3', 'C4', 'D-4', 'E-4', 'F4', 'G-4'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'hypolocrian' self._abstract.buildNetwork(self.type) class HypoaeolianScale(DiatonicScale): ''' A hypoaeolian scale >>> sc = scale.HypoaeolianScale(pitch.Pitch('a')) >>> [str(p) for p in sc.pitches] ['E4', 'F4', 'G4', 'A4', 'B4', 'C5', 'D5', 'E5'] >>> sc = scale.HypoaeolianScale(pitch.Pitch('c')) >>> [str(p) for p in sc.pitches] ['G3', 'A-3', 'B-3', 'C4', 'D4', 'E-4', 'F4', 'G4'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'hypoaeolian' self._abstract.buildNetwork(self.type) # ------------------------------------------------------------------------------ # other diatonic scales class HarmonicMinorScale(DiatonicScale): ''' The harmonic minor collection, realized as a scale. (The usage of this collection as a scale, is quite ahistorical for Western European classical music, but it is common in other parts of the world, but where the term "HarmonicMinor" would not be appropriate). >>> sc = scale.HarmonicMinorScale('e4') >>> [str(p) for p in sc.pitches] ['E4', 'F#4', 'G4', 'A4', 'B4', 'C5', 'D#5', 'E5'] >>> sc.getTonic() >>> sc.getDominant() >>> sc.pitchFromDegree(1) # scale degree 1 is treated as lowest >>> sc = scale.HarmonicMinorScale() >>> sc >>> sc.deriveRanked(['C', 'E', 'G'], comparisonAttribute='name') [(3, ), (3, ), (2, ), (2, )] Note that G and D are also equally good as B and A, but the system arbitrarily chooses among ties. ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'harmonic minor' # note: this changes the previously assigned AbstractDiatonicScale # from the DiatonicScale base class self._abstract = AbstractHarmonicMinorScale() # network building happens on object creation # self._abstract.buildNetwork() class MelodicMinorScale(DiatonicScale): ''' A melodic minor scale, which is not the same ascending or descending >>> sc = scale.MelodicMinorScale('e4') ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self.type = 'melodic minor' # note: this changes the previously assigned AbstractDiatonicScale # from the DiatonicScale base class self._abstract = AbstractMelodicMinorScale() # ------------------------------------------------------------------------------ # other scales class OctatonicScale(ConcreteScale): ''' A concrete Octatonic scale in one of two modes ''' usePitchDegreeCache = True def __init__(self, tonic=None, mode=None, **keywords): super().__init__(tonic=tonic, **keywords) self._abstract = AbstractOctatonicScale(mode=mode) self.type = 'Octatonic' class OctaveRepeatingScale(ConcreteScale): ''' A concrete cyclical scale, based on a cycle of intervals. >>> sc = scale.OctaveRepeatingScale('c4', ['m3', 'M3']) >>> sc.pitches [, , , ] >>> [str(p) for p in sc.getPitches('g2', 'g6')] ['G2', 'C3', 'E-3', 'G3', 'C4', 'E-4', 'G4', 'C5', 'E-5', 'G5', 'C6', 'E-6', 'G6'] >>> sc.getScaleDegreeFromPitch('c4') 1 >>> sc.getScaleDegreeFromPitch('e-') 2 No `intervalList` defaults to a single minor second: >>> sc2 = scale.OctaveRepeatingScale() >>> sc2.pitches [, , ] ''' def __init__(self, tonic=None, intervalList: list|None = None, **keywords): super().__init__(tonic=tonic, **keywords) mode = intervalList if intervalList else ['m2'] self._abstract = AbstractOctaveRepeatingScale(mode=mode) self.type = 'Octave Repeating' class CyclicalScale(ConcreteScale): ''' A concrete cyclical scale, based on a cycle of intervals. >>> sc = scale.CyclicalScale('c4', ['P5']) # can give one list >>> sc.pitches [, ] >>> [str(p) for p in sc.getPitches('g2', 'g6')] ['B-2', 'F3', 'C4', 'G4', 'D5', 'A5', 'E6'] >>> sc.getScaleDegreeFromPitch('g4') # as single interval cycle, all are 1 1 >>> sc.getScaleDegreeFromPitch('b-2', direction=scale.Direction.BI) 1 No `intervalList` defaults to a single minor second: >>> sc2 = scale.CyclicalScale() >>> sc2.pitches [, ] ''' def __init__(self, tonic: str|pitch.Pitch|note.Note|None = None, intervalList: list|None = None, **keywords): super().__init__(tonic=tonic, **keywords) mode = intervalList if intervalList else ['m2'] self._abstract = AbstractCyclicalScale(mode=mode) self.type = 'Cyclical' class ChromaticScale(ConcreteScale): ''' A concrete cyclical scale, based on a cycle of half steps. >>> sc = scale.ChromaticScale('g2') >>> [str(p) for p in sc.pitches] ['G2', 'A-2', 'A2', 'B-2', 'B2', 'C3', 'C#3', 'D3', 'E-3', 'E3', 'F3', 'F#3', 'G3'] >>> [str(p) for p in sc.getPitches('g2', 'g6')] ['G2', 'A-2', ..., 'F#3', 'G3', 'A-3', ..., 'F#4', 'G4', 'A-4', ..., 'G5', ..., 'F#6', 'G6'] >>> sc.abstract.getDegreeMaxUnique() 12 >>> sc.pitchFromDegree(1) >>> sc.pitchFromDegree(2) >>> sc.pitchFromDegree(3) >>> sc.pitchFromDegree(8) >>> sc.pitchFromDegree(12) >>> sc.getScaleDegreeFromPitch('g2', comparisonAttribute='pitchClass') 1 >>> sc.getScaleDegreeFromPitch('F#6', comparisonAttribute='pitchClass') 12 ''' usePitchDegreeCache = True def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self._abstract = AbstractCyclicalScale(mode=[ 'm2', 'm2', 'm2', 'm2', 'm2', 'm2', 'm2', 'm2', 'm2', 'm2', 'm2', 'm2']) self._abstract._net.pitchSimplification = 'mostCommon' self.type = 'Chromatic' class WholeToneScale(ConcreteScale): ''' A concrete whole-tone scale. >>> sc = scale.WholeToneScale('g2') >>> [str(p) for p in sc.pitches] ['G2', 'A2', 'B2', 'C#3', 'D#3', 'E#3', 'G3'] >>> [str(p) for p in sc.getPitches('g2', 'g5')] ['G2', 'A2', 'B2', 'C#3', 'D#3', 'E#3', 'G3', 'A3', 'B3', 'C#4', 'D#4', 'E#4', 'G4', 'A4', 'B4', 'C#5', 'D#5', 'E#5', 'G5'] >>> sc.abstract.getDegreeMaxUnique() 6 >>> sc.pitchFromDegree(1) >>> sc.pitchFromDegree(2) >>> sc.pitchFromDegree(6) >>> sc.getScaleDegreeFromPitch('g2', comparisonAttribute='pitchClass') 1 >>> sc.getScaleDegreeFromPitch('F6', comparisonAttribute='pitchClass') 6 ''' usePitchDegreeCache = True def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self._abstract = AbstractCyclicalScale(mode=['M2', 'M2', 'M2', 'M2', 'M2', 'M2']) self.type = 'Whole tone' class SieveScale(ConcreteScale): ''' A scale created from a Xenakis sieve logical string, based on the :class:`~music21.sieve.Sieve` object definition. The complete period of the sieve is realized as intervals and used to create a scale. >>> sc = scale.SieveScale('c4', '3@0') >>> sc.pitches [, ] >>> sc = scale.SieveScale('d4', '3@0') >>> sc.pitches [, ] >>> sc = scale.SieveScale('c2', '(-3@2 & 4) | (-3@1 & 4@1) | (3@2 & 4@2) | (-3 & 4@3)') >>> [str(p) for p in sc.pitches] ['C2', 'D2', 'E2', 'F2', 'G2', 'A2', 'B2', 'C3'] OMIT_FROM_DOCS Test that an empty SieveScale can be created: >>> sc = scale.SieveScale() ''' def __init__(self, tonic=None, sieveString='2@0', eld: int|float = 1, **keywords): super().__init__(tonic=tonic, **keywords) # self.tonic is a Pitch if self.tonic is not None: tonic = self.tonic else: tonic = pitch.Pitch('C4') self._pitchSieve = sieve.PitchSieve(sieveString, pitchLower=str(tonic), pitchUpper=str(tonic.transpose(48)), eld=eld) # four octave default # environLocal.printDebug([self._pitchSieve.sieveObject.represent(), # self._pitchSieve.getIntervalSequence()]) # mode here is a list of intervals intervalSequence = self._pitchSieve.getIntervalSequence() self._abstract = AbstractCyclicalScale(mode=intervalSequence) self.type = 'Sieve' class ScalaScale(ConcreteScale): ''' A scale created from a Scala scale .scl file. Any file in the Scala archive can be given by name. Additionally, a file path to a Scala .scl file, or a raw string representation, can be used. >>> sc = scale.ScalaScale('g4', 'mbira banda') >>> [str(p) for p in sc.pitches] ['G4', 'A4(-15c)', 'B4(-11c)', 'C#5(-7c)', 'D~5(+6c)', 'E5(+14c)', 'F~5(+1c)', 'G#5(+2c)'] If only a single string is given, and it's too long to be a tonic, or it ends in .scl, assume it's the name of a scala scale and set the tonic to C4 >>> sc = scale.ScalaScale('pelog_9') >>> [str(p) for p in sc.pitches] ['C4', 'C#~4(-17c)', 'D~4(+17c)', 'F~4(-17c)', 'F#~4(+17c)', 'G#4(-0c)', 'A~4(-17c)', 'C5(-0c)'] If no scale with that name can be found then it raises an exception: >>> sc = scale.ScalaScale('badFileName.scl') Traceback (most recent call last): music21.scale.ScaleException: Could not find a file named badFileName.scl in the scala database ''' def __init__(self, tonic=None, scalaString=None, **keywords): if (tonic is not None and scalaString is None and isinstance(tonic, str) and (len(tonic) >= 4 or tonic.endswith('scl'))): # just a scale was wanted scalaString = tonic tonic = 'C4' super().__init__(tonic=tonic, **keywords) self._scalaData = None self.description = None # this might be a raw scala file list if scalaString is not None and scalaString.count('\n') > 3: # if no match, this might be a complete Scala string self._scalaData = scala.ScalaData(scalaString) self._scalaData.parse() elif scalaString is not None: # try to load a named scale from a file path or stored # on the scala archive # returns None or a scala storage object readFile = scala.parse(scalaString) if readFile is None: raise ScaleException( f'Could not find a file named {scalaString} in the scala database') self._scalaData = readFile else: # grab a default self._scalaData = scala.parse('fj-12tet.scl') intervalSequence = self._scalaData.getIntervalSequence() self._abstract = AbstractCyclicalScale(mode=intervalSequence) self._abstract._net.pitchSimplification = 'mostCommon' self.type = f'Scala: {self._scalaData.fileName}' self.description = self._scalaData.description class RagAsawari(ConcreteScale): ''' A concrete pseudo-raga scale. >>> sc = scale.RagAsawari('c2') >>> [str(p) for p in sc.pitches] ['C2', 'D2', 'F2', 'G2', 'A-2', 'C3'] >>> [str(p) for p in sc.getPitches(direction=scale.Direction.DESCENDING)] ['C3', 'B-2', 'A-2', 'G2', 'F2', 'E-2', 'D2', 'C2'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self._abstract = AbstractRagAsawari() self.type = 'Rag Asawari' class RagMarwa(ConcreteScale): ''' A concrete pseudo-raga scale. >>> sc = scale.RagMarwa('c2') this gets a pitch beyond the terminus b/c of descending form max >>> [str(p) for p in sc.pitches] ['C2', 'D-2', 'E2', 'F#2', 'A2', 'B2', 'A2', 'C3', 'D-3'] ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self._abstract = AbstractRagMarwa() self.type = 'Rag Marwa' # >>> sc.getPitches(direction=Direction.DESCENDING) # [C2, D2, E2, G2, A2, C3] class WeightedHexatonicBlues(ConcreteScale): ''' A concrete scale based on a dynamic mixture of a minor pentatonic and the hexatonic blues scale. ''' def __init__(self, tonic=None, **keywords): super().__init__(tonic=tonic, **keywords) self._abstract = AbstractWeightedHexatonicBlues() self.type = 'Weighted Hexatonic Blues' # TODO: decide whether to store implicit tonic. # if not set, then comparisons fall to abstract # ------------------------------------------------------------------------------ # define presented order in documentation _DOC_ORDER = [ConcreteScale, AbstractScale] if __name__ == '__main__': import music21 music21.mainTest()