rh!P%SrSSKJr SSKrSSKJr SSKJr SSKJr SSKJr SSKJ r S r S r S#S jr \R"S 54S jrS$Sjr\\\R\R\R\R4\4r0rS\S'0rS\S'0rS\S'0rS\S'SrSrSrSrSrS$SjrSrS$Sjr S%Sjr!Sr"\ \ \ \/r#\\\\\\\\!/r$/\#Q\"P\$Qr%"SS\RL5r'"S S!\RP5r)\*S":XaSSKr\RV"\)5 gg)&a A possibility is a tuple with pitches, and is intended to encapsulate a possible solution to a :class:`~music21.figuredBass.segment.Segment`. Unlike a :class:`~music21.chord.Chord`, the ordering of a possibility does matter. The assumption throughout fbRealizer is that a possibility is always in order from the highest part to the lowest part, and the last element of each possibility is the bass. .. note:: fbRealizer supports voice crossing, so the order of pitches from lowest to highest may not correspond to the ordering of parts. Here, a possibility is created. G5 is in the highest part, and C4 is the bass. The highest part contains the highest Pitch, and the lowest part contains the lowest Pitch. No voice crossing is present. >>> G5 = pitch.Pitch('G5') >>> C5 = pitch.Pitch('C5') >>> E4 = pitch.Pitch('E4') >>> C4 = pitch.Pitch('C4') >>> p1 = (G5, C5, E4, C4) Here, another possibility is created with the same pitches, but this time, with voice crossing present. C5 is in the highest part, but the highest Pitch G5 is in the second highest part. >>> p2 = (C5, G5, E4, C4) The methods in this module are applied to possibilities, and fall into three main categories: 1) Single Possibility Methods. These methods are applied in finding correct possibilities in :meth:`~music21.figuredBass.segment.Segment.allCorrectSinglePossibilities`. 2) Consecutive Possibility Methods. These methods are applied to (possibA, possibB) pairs in :meth:`~music21.figuredBass.segment.Segment.allCorrectConsecutivePossibilities`, possibA being any correct possibility in segmentA and possibB being any correct possibility in segmentB. 3) Special Resolution Methods. These methods are applied in :meth:`~music21.figuredBass.segment.Segment.allCorrectConsecutivePossibilities` as applicable if the pitch names of a Segment correctly spell out an augmented sixth, dominant seventh, or diminished seventh chord. They are located in :mod:`~music21.figuredBass.resolution`. The application of these methods is controlled by corresponding instance variables in a :class:`~music21.figuredBass.rules.Rules` object provided to a Segment. .. note:: The number of parts and maxPitch are universal for a :class:`~music21.figuredBass.realizer.FiguredBassLine`. ) annotationsN)chord) exceptions21)interval)pitch) voiceLeadingcSn[[U55H7nXn[US-[U55HnXnX5:dMSnUs s $ M9 U$)a Returns True if there is voice crossing present between any two parts in possibA. The parts from the lowest part to the highest part (right to left) must correspond to increasingly higher pitches in order for there to be no voice crossing. Comparisons between pitches are done using pitch comparison methods, which are based on pitch space values (see :class:`~music21.pitch.Pitch`). >>> from music21.figuredBass import possibility >>> C4 = pitch.Pitch('C4') >>> E4 = pitch.Pitch('E4') >>> C5 = pitch.Pitch('C5') >>> G5 = pitch.Pitch('G5') >>> possibA1 = (C5, G5, E4) >>> possibility.voiceCrossing(possibA1) # G5 > C5 True >>> possibA2 = (C5, E4, C4) >>> possibility.voiceCrossing(possibA2) False FT)rangelen)possibAhasVoiceCrossing part1Index higherPitch part2Index lowerPitchs Y/home/james-whalen/.local/lib/python3.13/site-packages/music21/figuredBass/possibility.py voiceCrossingrRs`*CL) )  QG =J ,J'#' '' >* cSn/nUH0nURU;dMURUR5 M2 UH nXS;dM SnM U(d[U5[U5:aSnU$)a# Returns True if possibA is incomplete, if it doesn't contain at least one of every pitch name in pitchNamesToContain. For a Segment, pitchNamesToContain is :attr:`~music21.figuredBass.segment.Segment.pitchNamesInChord`. If possibA contains excessive pitch names, a PossibilityException is raised, although this is not a concern with the current implementation of fbRealizer. >>> from music21.figuredBass import possibility >>> C3 = pitch.Pitch('C3') >>> E4 = pitch.Pitch('E4') >>> G4 = pitch.Pitch('G4') >>> C5 = pitch.Pitch('C5') >>> Bb5 = pitch.Pitch('B-5') >>> possibA1 = (C5, G4, E4, C3) >>> pitchNamesA1 = ['C', 'E', 'G', 'B-'] >>> possibility.isIncomplete(possibA1, pitchNamesA1) # Missing B- True >>> pitchNamesA2 = ['C', 'E', 'G'] >>> possibility.isIncomplete(possibA1, pitchNamesA2) False FT)nameappendr )r pitchNamesToContain isIncompleteVpitchNamesContained givenPitch pitchNames r isIncompletersst4M ??"5 5  & &z 7)  / M) c"56=P9QQ  rcSnUcU$US[U5S- n[[U55HXnX4n[US-[U55H5nX6n[URUR- 5U:dM/SnUs s $ MZ U$)aS Returns True if the pitches in the upper parts of possibA are found within maxSemitoneSeparation of each other. The upper parts of possibA are all the pitches except the last. The default value of maxSemitoneSeparation is 12 semitones, enharmonically equivalent to a perfect octave. If this method returns True for this default value, then all the notes in the upper parts can be played by most adult pianists using just the right hand. >>> from music21.figuredBass import possibility >>> C3 = pitch.Pitch('C3') >>> E3 = pitch.Pitch('E3') >>> E4 = pitch.Pitch('E4') >>> G4 = pitch.Pitch('G4') >>> C5 = pitch.Pitch('C5') >>> possibA1 = (C5, G4, E4, C3) >>> possibility.upperPartsWithinLimit(possibA1) True Here, C5 and E3 are separated by almost two octaves. >>> possibA2 = (C5, G4, E3, C3) >>> possibility.upperPartsWithinLimit(possibA2) False Trr F)r r absps)r maxSemitoneSeparationareUpperPartsWithinLimit upperPartsrrrrs rupperPartsWithinLimitr%s< $$''3w>JMM125JJ+0(// A- $#rB5c$UH nX!:dM g g)a Returns True if all pitches in possibA are less than or equal to the maxPitch provided. Comparisons between pitches are done using pitch comparison methods, which are based on pitch space values (see :class:`~music21.pitch.Pitch`). Used in :class:`~music21.figuredBass.segment.Segment` to filter resolutions of special Segments which can have pitches exceeding the universal maxPitch of a :class:`~music21.figuredBass.realizer.FiguredBassLine`. >>> from music21.figuredBass import possibility >>> from music21.figuredBass import resolution >>> G2 = pitch.Pitch('G2') >>> D4 = pitch.Pitch('D4') >>> F5 = pitch.Pitch('F5') >>> B5 = pitch.Pitch('B5') >>> domPossib = (B5, F5, D4, G2) >>> possibility.pitchesWithinLimit(domPossib) True >>> resPossib = resolution.dominantSeventhToMajorTonic(domPossib) >>> resPossib # Contains C6 > B5 (, , , ) >>> possibility.pitchesWithinLimit(resPossib) False FT)r maxPitchrs rpitchesWithinLimitr*s>   rcZUc0nUR5Hup#XS- U:XaM g g)a Takes in a dict, partPitchLimits containing (partNumber, partPitch) pairs, each of which limits a part in possibA to a certain :class:`~music21.pitch.Pitch`. Returns True if all limits are followed in possibA, False otherwise. >>> from music21.figuredBass import possibility >>> C4 = pitch.Pitch('C4') >>> E4 = pitch.Pitch('E4') >>> G4 = pitch.Pitch('G4') >>> C5 = pitch.Pitch('C5') >>> G5 = pitch.Pitch('G5') >>> sopranoPitch = pitch.Pitch('G5') >>> possibA1 = (C5, G4, E4, C4) >>> possibility.limitPartToPitch(possibA1, {1: sopranoPitch}) False >>> possibA2 = (G5, G4, E4, C4) >>> possibility.limitPartToPitch(possibA2, {1: sopranoPitch}) True r FT)items)r partPitchLimits partNumber partPitchs rlimitPartToPitchr0s<(#2#8#8#:Q'94$; rPITCH_QUARTET_TO_BOOL_TYPEparallelFifthsTableparallelOctavesTablehiddenFifthsTablehiddenOctavesTablec Sn[X5n[[U55HnX4upV[US-[U55HnX7up[URUR- 5S-S:XdM4[URU R- 5S-S:XdM_XXV4n U [ ;a[ U nU(aUs s $[ R"U 6n U R5(aSnU[ U 'U(dMUs s $ M U$)a Returns True if there are parallel fifths between any two shared parts of possibA and possibB. If pitchA1 and pitchA2 in possibA are separated by a simple interval of a perfect fifth, and they move to a pitchB1 and pitchB2 in possibB also separated by the simple interval of a perfect fifth, then this constitutes parallel fifths between these two parts. If the method returns False, then no two shared parts have parallel fifths. The method returns True as soon as two shared parts with parallel fifths are found. >>> from music21.figuredBass import possibility >>> C3 = pitch.Pitch('C3') >>> D3 = pitch.Pitch('D3') >>> G3 = pitch.Pitch('G3') >>> A3 = pitch.Pitch('A3') >>> A4 = pitch.Pitch('A4') >>> B4 = pitch.Pitch('B4') Here, the bass moves from C3 to D3 and the tenor moves from G3 to A3. The interval between C3 and G3, as well as between D3 and A3, is a perfect fifth. These two parts, and therefore the two possibilities, have parallel fifths. >>> possibA1 = (B4, G3, C3) >>> possibB1 = (A4, A3, D3) >>> possibility.parallelFifths(possibA1, possibB1) True Now, the tenor moves instead to F3. The interval between D3 and F3 is a minor third. The bass and tenor parts don't form parallel fifths. The soprano part forms parallel fifths with neither the bass nor tenor parts. The two possibilities, therefore, have no parallel fifths. >>> F3 = pitch.Pitch('F3') >>> possibA2 = (B4, G3, C3) >>> possibB2 = (A4, F3, D3) >>> possibility.parallelFifths(possibA2, possibB2) False Fr T) partPairsr r r r!r2rVoiceLeadingQuartet parallelFifth) r possibBhasParallelFifths pairsList pair1Index higherPitchA higherPitchB pair2Index lowerPitchA lowerPitchB pitchQuartetvlqs rparallelFifthsrGsj'+IC N+ '0'<$ QI?J)2)> &[|782=B|782=B'lQL22$7 $E!$,,22LAC  ""$(!0A  -  ((#@,* rc Sn[X5n[[U55HnX4upV[US-[U55HnX7up[URUR- 5S-S:XdM4[URU R- 5S-S:XdM_XXV4n U [ ;a[ U nU(aUs s $[ R"U 6n U R5(aSnU[ U 'U(dMUs s $ M U$)a! Returns True if there are parallel octaves between any two shared parts of possibA and possibB. If pitchA1 and pitchA2 in possibA are separated by a simple interval of a perfect octave, and they move to a pitchB1 and pitchB2 in possibB also separated by the simple interval of a perfect octave, then this constitutes parallel octaves between these two parts. If the method returns False, then no two shared parts have parallel octaves. The method returns True as soon as two shared parts with parallel octaves are found. >>> from music21.figuredBass import possibility >>> C3 = pitch.Pitch('C3') >>> D3 = pitch.Pitch('D3') >>> G3 = pitch.Pitch('G3') >>> A3 = pitch.Pitch('A3') >>> C4 = pitch.Pitch('C4') >>> D4 = pitch.Pitch('D4') Here, the soprano moves from C4 to D4 and the bass moves from C3 to D3. The interval between C3 and C4, as well as between D3 and D4, is a parallel octave. The two parts, and therefore the two possibilities, have parallel octaves. >>> possibA1 = (C4, G3, C3) >>> possibB1 = (D4, A3, D3) >>> possibility.parallelOctaves(possibA1, possibB1) True Now, the soprano moves down to B3. The interval between D3 and B3 is a major sixth. The soprano and bass parts no longer have parallel octaves. The tenor part forms a parallel octave with neither the bass nor soprano, so the two possibilities do not have parallel octaves. (Notice, however, the parallel fifth between the bass and tenor!) >>> B3 = pitch.Pitch('B3') >>> possibA2 = (C4, G3, C3) >>> possibB2 = (B3, A3, D3) >>> possibility.parallelOctaves(possibA2, possibB2) False Fr r7rT) r9r r r r!r3rr:parallelOctave) r r<hasParallelOctavesr>r?r@rArBrCrDrErFs rparallelOctavesrKksj'+IC N+ '0'<$ QI?J)2)> &[|782=B|782=B'lQL33%9,%G"%--22LAC!!##%)"1C  .!!))#@,* rc&Sn[X5nUSupEUSupg[URUR- 5S-S:XaLXgXE4nU[;a [UnU$[R "U6n U R 5(aSnU[U'U$)a^ Returns True if there is a hidden fifth between shared outer parts of possibA and possibB. The outer parts here are the first and last elements of each possibility. If sopranoPitchA and bassPitchA in possibA move to a sopranoPitchB and bassPitchB in possibB in similar motion, and the simple interval between sopranoPitchB and bassPitchB is that of a perfect fifth, then this constitutes a hidden octave between the two possibilities. >>> from music21.figuredBass import possibility >>> C3 = pitch.Pitch('C3') >>> D3 = pitch.Pitch('D3') >>> E3 = pitch.Pitch('E3') >>> F3 = pitch.Pitch('F3') >>> E5 = pitch.Pitch('E5') >>> A5 = pitch.Pitch('A5') Here, the bass part moves up from C3 to D3 and the soprano part moves up from E5 to A5. The simple interval between D3 and A5 is a perfect fifth. Therefore, there is a hidden fifth between the two possibilities. >>> possibA1 = (E5, E3, C3) >>> possibB1 = (A5, F3, D3) >>> possibility.hiddenFifth(possibA1, possibB1) True Here, the soprano and bass parts also move in similar motion, but the simple interval between D3 and Ab5 is a diminished fifth. Consequently, there is no hidden fifth. >>> Ab5 = pitch.Pitch('A-5') >>> possibA2 = (E5, E3, C3) >>> possibB2 = (Ab5, F3, D3) >>> possibility.hiddenFifth(possibA2, possibB2) False Now, we have the soprano and bass parts again moving to A5 and D3, whose simple interval is a perfect fifth. However, the bass moves up while the soprano moves down. Therefore, there is no hidden fifth. >>> E6 = pitch.Pitch('E6') >>> possibA3 = (E6, E3, C3) >>> possibB3 = (A5, F3, D3) >>> possibility.hiddenFifth(possibA3, possibB3) False Frr7r8T)r9r r!r4rr: hiddenFifth) r r<hasHiddenFifthr> highestPitchA highestPitchB lowestPitchA lowestPitchBrErFs rrNrNsnN'+I%.q\"]#,R= \ =  loo -.3q8$MQ , ,.|