music21.figuredBass.segment

OverlaidSegment

class music21.figuredBass.segment.OverlaidSegment(bassNote: str | Note = 'C3', notationString: str | None = None, fbScale: FiguredBassScale | None = None, fbRules: Rules | None = None, numParts=4, maxPitch: str | Pitch = 'B5', listOfPitches=None)

Class to allow Segments to be overlaid with non-chord notes.

OverlaidSegment bases

OverlaidSegment methods

OverlaidSegment.allSinglePossibilities()

Returns an iterator through a set of naive possibilities for a Segment, using numParts, the pitch of bassNote, and allPitchesAboveBass.

>>> from music21.figuredBass import segment
>>> segmentA = segment.Segment()
>>> allPossib = segmentA.allSinglePossibilities()
>>> allPossib.__class__
<... 'itertools.product'>

The number of naive possibilities is always the length of allPitchesAboveBass raised to the (numParts - 1) power. The power is 1 less than the number of parts because the bass pitch is constant.

>>> allPossibList = list(allPossib)
>>> len(segmentA.allPitchesAboveBass)
9
>>> segmentA.numParts
4
>>> len(segmentA.allPitchesAboveBass) ** (segmentA.numParts-1)
729
>>> len(allPossibList)
729

>>> for i in (81, 275, 426):
...    [str(p) for p in allPossibList[i]]
['E3', 'C3', 'C3', 'C3']
['C4', 'C4', 'G4', 'C3']
['G4', 'G3', 'C4', 'C3']

Methods inherited from Segment:

OverlaidSegment instance variables

Instance variables inherited from Segment:

Segment

class music21.figuredBass.segment.Segment(bassNote: str | Note = 'C3', notationString: str | None = None, fbScale: FiguredBassScale | None = None, fbRules: Rules | None = None, numParts=4, maxPitch: str | Pitch = 'B5', listOfPitches=None)

Segment methods

Segment.allCorrectConsecutivePossibilities(segmentB)

Returns an iterator through correct (possibA, possibB) pairs.

  • If segmentA (self) is a special Segment, meaning that one of the Segment resolution methods in specialResolutionRules() needs to be applied, then this method returns every correct possibility of segmentA matched up with exactly one resolution possibility.

  • If segmentA is an ordinary, non-special Segment, then this method returns every combination of correct possibilities of segmentA and correct possibilities of segmentB which passes all filters in consecutivePossibilityRules().

Two notes on segmentA being a special Segment:

  1. By default, resolution possibilities are not filtered using singlePossibilityRules() rules of segmentB. Filter by setting applySinglePossibRulesToResolution to True.

  2. By default, (possibA, possibB) pairs are not filtered using consecutivePossibilityRules() rules of segmentA. Filter by setting applyConsecutivePossibRulesToResolution to True.

>>> from music21.figuredBass import segment
>>> segmentA = segment.Segment(bassNote=note.Note('C3'), notationString='')
>>> segmentB = segment.Segment(bassNote=note.Note('D3'), notationString='4,3')

Here, an ordinary resolution is being executed, because segmentA is an ordinary Segment.

>>> consecutivePairs1 = segmentA.allCorrectConsecutivePossibilities(segmentB)
>>> consecutivePairsList1 = list(consecutivePairs1)
>>> len(consecutivePairsList1)
31
>>> consecutivePairsList1[29]
((<...G5>, <...G5>, <...E5>, <...C3>), (<...G5>, <...F5>, <...B4>, <...D3>))

Here, a special resolution is being executed, because segmentA below is a special Segment.

>>> segmentA = segment.Segment(bassNote=note.Note('D3'), notationString='4,3')
>>> segmentB = segment.Segment(bassNote=note.Note('C3'), notationString='')
>>> consecutivePairs2 = segmentA.allCorrectConsecutivePossibilities(segmentB)
>>> consecutivePairsList2 = list(consecutivePairs2)
>>> len(consecutivePairsList2)
6
>>> consecutivePairsList2[5]
((<...G5>, <...F5>, <...B4>, <...D3>), (<...G5>, <...E5>, <...C5>, <...C3>))
Segment.allCorrectSinglePossibilities()

Uses allSinglePossibilities() and returns an iterator through a set of correct possibilities for a Segment, all possibilities which pass all filters in singlePossibilityRules().

>>> from music21.figuredBass import segment
>>> segmentA = segment.Segment()
>>> allPossib = segmentA.allSinglePossibilities()
>>> allCorrectPossib = segmentA.allCorrectSinglePossibilities()

Most of the 729 naive possibilities were filtered out using the default rules set, leaving only 21.

>>> allPossibList = list(allPossib)
>>> len(allPossibList)
729
>>> allCorrectPossibList = list(allCorrectPossib)
>>> len(allCorrectPossibList)
21

>>> for i in (5, 12, 20):
...   [str(p) for p in allCorrectPossibList[i]]
['E4', 'G3', 'G3', 'C3']
['C5', 'G4', 'E4', 'C3']
['G5', 'G5', 'E5', 'C3']
Segment.allSinglePossibilities()

Returns an iterator through a set of naive possibilities for a Segment, using numParts, the pitch of bassNote, and allPitchesAboveBass.

>>> from music21.figuredBass import segment
>>> segmentA = segment.Segment()
>>> allPossib = segmentA.allSinglePossibilities()
>>> allPossib.__class__
<... 'itertools.product'>

The number of naive possibilities is always the length of allPitchesAboveBass raised to the (numParts - 1) power. The power is 1 less than the number of parts because the bass pitch is constant.

>>> allPossibList = list(allPossib)
>>> len(segmentA.allPitchesAboveBass)
9
>>> segmentA.numParts
4
>>> len(segmentA.allPitchesAboveBass) ** (segmentA.numParts-1)
729
>>> len(allPossibList)
729

>>> for i in (81, 275, 426):
...    [str(p) for p in allPossibList[i]]
['E3', 'C3', 'C3', 'C3']
['C4', 'C4', 'G4', 'C3']
['G4', 'G3', 'C4', 'C3']
Segment.consecutivePossibilityRules(fbRules=None)

A framework for storing consecutive possibility rules and methods to be applied in allCorrectConsecutivePossibilities(). Takes in a Rules object, fbRules; if None then a new rules.Rules() object is created.

Items are added within this method in the following form:

(willRunOnlyIfTrue, methodToRun, keepSolutionsWhichReturn, optionalArgs)

These items are compiled internally when allCorrectConsecutivePossibilities() is called on a Segment. Here, the compilation of rules and methods bases on a default fbRules is shown.

>>> from music21.figuredBass import segment
>>> segmentA = segment.Segment()
>>> allConsecutiveRules = segmentA.consecutivePossibilityRules()

>>> segment.printRules(allConsecutiveRules)
Will run:  Method:                       Keep solutions which return:  Arguments:
True       partsSame                     True                          []
False      upperPartsSame                True                          None
True       voiceOverlap                  False                         None
True       partMovementsWithinLimits     True                          []
True       parallelFifths                False                         None
True       parallelOctaves               False                         None
True       hiddenFifth                   False                         None
True       hiddenOctave                  False                         None
False      couldBeItalianA6Resolution    True           [<music21.pitch.Pitch C3>,
                                                         <music21.pitch.Pitch C3>,
                                                         <music21.pitch.Pitch E3>,
                                                         <music21.pitch.Pitch G3>], True

Now, a modified fbRules is provided, allowing hidden octaves and voice overlap, and limiting the soprano line to stepwise motion.

>>> from music21.figuredBass import rules
>>> fbRules = rules.Rules()
>>> fbRules.forbidVoiceOverlap = False
>>> fbRules.forbidHiddenOctaves = False
>>> fbRules.partMovementLimits.append((1, 2))
>>> allConsecutiveRules = segmentA.consecutivePossibilityRules(fbRules)
>>> segment.printRules(allConsecutiveRules)
Will run:  Method:                       Keep solutions which return:  Arguments:
True       partsSame                     True                          []
False      upperPartsSame                True                          None
False      voiceOverlap                  False                         None
True       partMovementsWithinLimits     True                          [(1, 2)]
True       parallelFifths                False                         None
True       parallelOctaves               False                         None
True       hiddenFifth                   False                         None
False      hiddenOctave                  False                         None
False      couldBeItalianA6Resolution    True           [<music21.pitch.Pitch C3>,
                                                         <music21.pitch.Pitch C3>,
                                                         <music21.pitch.Pitch E3>,
                                                         <music21.pitch.Pitch G3>], True
Segment.resolveAugmentedSixthSegment(segmentB)

Can resolve a Segment whose segmentChord spells out a French, German, or Swiss augmented sixth chord. Italian augmented sixth Segments are solved as an ordinary Segment using couldBeItalianA6Resolution(). If no applicable method in resolution can be used, the Segment is resolved as an ordinary Segment.

>>> from music21.figuredBass import segment
>>> segmentA = segment.Segment(bassNote=note.Note('A-2'), notationString='#6,b5,3')
>>> segmentA.pitchNamesInChord  # spell out a Gr+6 chord
['A-', 'C', 'E-', 'F#']
>>> allAugSixthPossib = segmentA.allCorrectSinglePossibilities()
>>> allAugSixthPossibList = list(allAugSixthPossib)
>>> len(allAugSixthPossibList)
7

>>> allAugSixthPossibList[1]
(<music21.pitch.Pitch C4>, <music21.pitch.Pitch F#3>, <...E-3>, <...A-2>)
>>> allAugSixthPossibList[4]
(<music21.pitch.Pitch C5>, <music21.pitch.Pitch F#4>, <...E-4>, <...A-2>)

>>> segmentB = segment.Segment(bassNote=note.Note('G2'), notationString='')
>>> allAugResPossibPairs = segmentA.resolveAugmentedSixthSegment(segmentB)
>>> allAugResPossibPairsList = list(allAugResPossibPairs)
>>> len(allAugResPossibPairsList)
7
>>> allAugResPossibPairsList[1]
((<...C4>, <...F#3>, <...E-3>, <...A-2>), (<...B3>, <...G3>, <...D3>, <...G2>))
>>> allAugResPossibPairsList[4]
((<...C5>, <...F#4>, <...E-4>, <...A-2>), (<...B4>, <...G4>, <...D4>, <...G2>))
Segment.resolveDiminishedSeventhSegment(segmentB, doubledRoot=False)

Can resolve a Segment whose segmentChord spells out a diminished seventh chord. If no applicable method in resolution can be used, the Segment is resolved as an ordinary Segment.

>>> from music21.figuredBass import segment
>>> segmentA = segment.Segment(bassNote=note.Note('B2'), notationString='b7')
>>> allDimPossib = segmentA.allCorrectSinglePossibilities()
>>> allDimPossibList = list(allDimPossib)
>>> len(allDimPossibList)
7
>>> [p.nameWithOctave for p in allDimPossibList[4]]
['D5', 'A-4', 'F4', 'B2']
>>> [p.nameWithOctave for p in allDimPossibList[6]]
['A-5', 'F5', 'D5', 'B2']

>>> segmentB = segment.Segment(bassNote=note.Note('C3'), notationString='')
>>> dimResPairs = segmentA.resolveDiminishedSeventhSegment(segmentB)
>>> dimResPairsList = list(dimResPairs)
>>> len(dimResPairsList)
7
>>> dimResPairsList[4]
((<...D5>, <...A-4>, <...F4>, <...B2>), (<...E5>, <...G4>, <...E4>, <...C3>))
>>> dimResPairsList[6]
((<...A-5>, <...F5>, <...D5>, <...B2>), (<...G5>, <...E5>, <...E5>, <...C3>))
Segment.resolveDominantSeventhSegment(segmentB)

Can resolve a Segment whose segmentChord spells out a dominant seventh chord. If no applicable method in resolution can be used, the Segment is resolved as an ordinary Segment.

>>> from music21.figuredBass import segment
>>> segmentA = segment.Segment(bassNote=note.Note('G2'), notationString='7')
>>> allDomPossib = segmentA.allCorrectSinglePossibilities()
>>> allDomPossibList = list(allDomPossib)
>>> len(allDomPossibList)
8
>>> allDomPossibList[2]
(<music21.pitch.Pitch D4>, <music21.pitch.Pitch B3>,
 <music21.pitch.Pitch F3>, <music21.pitch.Pitch G2>)
>>> allDomPossibList[5]
(<music21.pitch.Pitch D5>, <music21.pitch.Pitch B4>,
 <music21.pitch.Pitch F4>, <music21.pitch.Pitch G2>)

Here, the Soprano pitch of resolution (C6) exceeds default maxPitch of B5, so it’s filtered out.

>>> [p.nameWithOctave for p in allDomPossibList[7]]
['B5', 'F5', 'D5', 'G2']

>>> segmentB = segment.Segment(bassNote=note.Note('C3'), notationString='')
>>> domResPairs = segmentA.resolveDominantSeventhSegment(segmentB)
>>> domResPairsList = list(domResPairs)
>>> len(domResPairsList)
7
>>> domResPairsList[2]
((<music21.pitch.Pitch D4>, <...B3>, <...F3>, <...G2>),
 (<...C4>, <...C4>, <...E3>, <...C3>))
>>> domResPairsList[5]
((<...D5>, <...B4>, <...F4>, <...G2>), (<...C5>, <...C5>, <...E4>, <...C3>))
Segment.singlePossibilityRules(fbRules=None)

A framework for storing single possibility rules and methods to be applied in allCorrectSinglePossibilities(). Takes in a Rules object, fbRules. If None then a new rules object is created.

Items are added within this method in the following form:

(willRunOnlyIfTrue, methodToRun, keepSolutionsWhichReturn, optionalArgs)

These items are compiled internally when allCorrectSinglePossibilities() is called on a Segment. Here, the compilation of rules and methods bases on a default fbRules is shown.

>>> from music21.figuredBass import segment
>>> segmentA = segment.Segment()
>>> allSingleRules = segmentA.singlePossibilityRules()
>>> segment.printRules(allSingleRules)
Will run:  Method:                       Keep solutions which return:  Arguments:
True       isIncomplete                  False                         ['C', 'E', 'G']
True       upperPartsWithinLimit         True                          12
True       voiceCrossing                 False                         None

Here, a modified fbRules is provided, which allows for incomplete possibilities.

>>> from music21.figuredBass import rules
>>> fbRules = rules.Rules()
>>> fbRules.forbidIncompletePossibilities = False
>>> allSingleRules = segmentA.singlePossibilityRules(fbRules)
>>> segment.printRules(allSingleRules)
Will run:  Method:                       Keep solutions which return:  Arguments:
False      isIncomplete                  False                         ['C', 'E', 'G']
True       upperPartsWithinLimit         True                          12
True       voiceCrossing                 False                         None
Segment.specialResolutionRules(fbRules=None)

A framework for storing methods which perform special resolutions on Segments. Unlike the methods in singlePossibilityRules() and consecutivePossibilityRules(), these methods deal with the Segment itself, and rely on submethods to resolve the individual possibilities accordingly depending on what the resolution Segment is.

If fbRules is None, then a new rules.Rules() object is created.

Items are added within this method in the following form:

(willRunOnlyIfTrue, methodToRun, optionalArgs)

These items are compiled internally when allCorrectConsecutivePossibilities() is called on a Segment. Here, the compilation of rules and methods based on a default fbRules is shown.

>>> from music21.figuredBass import segment
>>> segmentA = segment.Segment()
>>> allSpecialResRules = segmentA.specialResolutionRules()
>>> segment.printRules(allSpecialResRules, maxLength=3)
Will run:  Method:                          Arguments:
False      resolveDominantSeventhSegment    None
False      resolveDiminishedSeventhSegment  False
False      resolveAugmentedSixthSegment     None

Dominant Seventh Segment:

>>> segmentA = segment.Segment(bassNote=note.Note('B2'), notationString='6,5')
>>> allSpecialResRules = segmentA.specialResolutionRules()
>>> segment.printRules(allSpecialResRules, maxLength=3)
Will run:  Method:                          Arguments:
True       resolveDominantSeventhSegment    None
False      resolveDiminishedSeventhSegment  False
False      resolveAugmentedSixthSegment     None

Fully-Diminished Seventh Segment:

>>> segmentA = segment.Segment(bassNote=note.Note('B2'), notationString='-7')
>>> allSpecialResRules = segmentA.specialResolutionRules()
>>> segment.printRules(allSpecialResRules, maxLength=3)
Will run:  Method:                          Arguments:
False      resolveDominantSeventhSegment    None
True       resolveDiminishedSeventhSegment  False
False      resolveAugmentedSixthSegment     None

Augmented Sixth Segment:

>>> segmentA = segment.Segment(bassNote=note.Note('A-2'), notationString='#6,b5')
>>> allSpecialResRules = segmentA.specialResolutionRules()
>>> segment.printRules(allSpecialResRules, maxLength=3)
Will run:  Method:                          Arguments:
False      resolveDominantSeventhSegment    None
False      resolveDiminishedSeventhSegment  False
True       resolveAugmentedSixthSegment     None

Segment instance variables

Segment.allPitchesAboveBass

A list of allowable pitches in the upper parts of a possibility. This is derived using getPitches(), providing bassNote.pitch, maxPitch from the Rules object, and pitchNamesInChord as arguments.

Segment.bassNote

A Note whose pitch forms the bass of each possibility.

Segment.fbRules

A deepcopy of the Rules object provided.

Segment.numParts

The number of parts (including the bass) that possibilities should contain, which comes directly from numParts in the Rules object.

Segment.pitchNamesInChord

A list of allowable pitch names. This is derived from bassNote.pitch and notationString using getPitchNames().

Segment.segmentChord

allPitchesAboveBass represented as a Chord.

Functions

music21.figuredBass.segment.getPitches(pitchNames=('C', 'E', 'G'), bassPitch: str | Pitch = 'C3', maxPitch: str | Pitch = 'C8')

Given a list of pitchNames, a bassPitch, and a maxPitch, returns a sorted list of pitches between the two limits (inclusive) which correspond to items in pitchNames.

>>> from music21.figuredBass import segment
>>> pitches = segment.getPitches()
>>> print(', '.join([p.nameWithOctave for p in pitches]))
C3, E3, G3, C4, E4, G4, C5, E5, G5, C6, E6, G6, C7, E7, G7, C8

>>> pitches = segment.getPitches(['G', 'B', 'D', 'F'], bassPitch=pitch.Pitch('B2'))
>>> print(', '.join([p.nameWithOctave for p in pitches]))
B2, D3, F3, G3, B3, D4, F4, G4, B4, D5, F5, G5, B5, D6, F6, G6, B6, D7, F7, G7, B7

>>> pitches = segment.getPitches(['F##', 'A#', 'C#'], bassPitch=pitch.Pitch('A#3'))
>>> print(', '.join([p.nameWithOctave for p in pitches]))
A#3, C#4, F##4, A#4, C#5, F##5, A#5, C#6, F##6, A#6, C#7, F##7, A#7

The maxPitch must have an octave:

>>> segment.getPitches(maxPitch=pitch.Pitch('E'))
Traceback (most recent call last):
ValueError: maxPitch must be given an octave
music21.figuredBass.segment.printRules(rulesList, maxLength=4)

Method which can print to the console rules inputted into singlePossibilityRules(), consecutivePossibilityRules(), and specialResolutionRules(). For the first two methods, maxLength is 4. For the third method, maxLength is 3.