music21.figuredBass.resolution

Note

The terminology, V43, viio, iv, etc. are explained more fully in The Music Theory Handbook by Marjorie Merryman.

This module contains methods which can properly resolve dominant seventh, diminished seventh, and augmented sixth chords expressed as possibilities (See possibility). Although these methods can stand alone, they are speed-enhanced for instances of Segment, where there are many possibilities formed around the same chord. If provided with additional arguments, the methods only transpose() each Pitch in a possibility by the appropriate interval.

Functions

music21.figuredBass.resolution.augmentedSixthToDominant(augSixthPossib, augSixthType=None, augSixthChordInfo=None)

Resolves French (augSixthType = 1), German (augSixthType = 2), and Swiss (augSixthType = 3) augmented sixth chords to the root position dominant triad.

Proper Italian augmented sixth resolutions not supported within this method.

>>> from music21.figuredBass import resolution
>>> Bb2 = pitch.Pitch('B-2')
>>> D4 = pitch.Pitch('D4')
>>> E4 = pitch.Pitch('E4')
>>> Es4 = pitch.Pitch('E#4')
>>> F4 = pitch.Pitch('F4')
>>> G4 = pitch.Pitch('G4')
>>> Gs4 = pitch.Pitch('G#4')
>>> iv6 = (G4, D4, D4, Bb2)
>>> itAug6 = (Gs4, D4, D4, Bb2)
>>> frAug6 = (Gs4, E4, D4, Bb2)
>>> grAug6 = (Gs4, F4, D4, Bb2)
>>> swAug6 = (Gs4, Es4, D4, Bb2)

>>> frRes = resolution.augmentedSixthToDominant(frAug6)
>>> frRes
(<music21.pitch.Pitch A4>, <music21.pitch.Pitch E4>,
 <music21.pitch.Pitch C#4>, <music21.pitch.Pitch A2>)
>>> [str(p) for p in frRes]
['A4', 'E4', 'C#4', 'A2']

>>> grRes = resolution.augmentedSixthToDominant(grAug6)
>>> [str(p) for p in grRes]
['A4', 'E4', 'C#4', 'A2']

>>> swRes = resolution.augmentedSixthToDominant(swAug6)
>>> [str(p) for p in swRes]
['A4', 'E4', 'C#4', 'A2']
>>> resolution.showResolutions(frAug6, frRes, grAug6, grRes, swAug6, swRes)
../_images/fbResolution_a6toV.png

Above: French, German, and Swiss resolutions, respectively.

music21.figuredBass.resolution.augmentedSixthToMajorTonic(augSixthPossib, augSixthType=None, augSixthChordInfo=None)

Resolves French (augSixthType = 1), German (augSixthType = 2), and Swiss (augSixthType = 3) augmented sixth chords to the major tonic 6,4.

Proper Italian augmented sixth resolutions not supported within this method.

>>> from music21.figuredBass import resolution
>>> Bb2 = pitch.Pitch('B-2')
>>> D4 = pitch.Pitch('D4')
>>> E4 = pitch.Pitch('E4')
>>> Es4 = pitch.Pitch('E#4')
>>> F4 = pitch.Pitch('F4')
>>> G4 = pitch.Pitch('G4')
>>> Gs4 = pitch.Pitch('G#4')
>>> iv6 = (G4, D4, D4, Bb2)
>>> itAug6 = (Gs4, D4, D4, Bb2)
>>> frAug6 = (Gs4, E4, D4, Bb2)
>>> grAug6 = (Gs4, F4, D4, Bb2)
>>> swAug6 = (Gs4, Es4, D4, Bb2)
>>> frRes = resolution.augmentedSixthToMajorTonic(frAug6)
>>> [str(p) for p in frRes]
['A4', 'F#4', 'D4', 'A2']
>>> grRes = resolution.augmentedSixthToMajorTonic(grAug6)
>>> [str(p) for p in grRes]
['A4', 'F#4', 'D4', 'A2']
>>> swRes = resolution.augmentedSixthToMajorTonic(swAug6)
>>> [str(p) for p in swRes]
['A4', 'F#4', 'D4', 'A2']
>>> resolution.showResolutions(frAug6, frRes, grAug6, grRes, swAug6, swRes)
../_images/fbResolution_a6toI.png

Above: French, German, and Swiss resolutions, respectively.

music21.figuredBass.resolution.augmentedSixthToMinorTonic(augSixthPossib, augSixthType=None, augSixthChordInfo=None)

Resolves French (augSixthType = 1), German (augSixthType = 2), and Swiss (augSixthType = 3) augmented sixth chords to the minor tonic 6,4.

Proper Italian augmented sixth resolutions not supported within this method.

>>> from music21.figuredBass import resolution
>>> Bb2 = pitch.Pitch('B-2')
>>> D4 = pitch.Pitch('D4')
>>> E4 = pitch.Pitch('E4')
>>> Es4 = pitch.Pitch('E#4')
>>> F4 = pitch.Pitch('F4')
>>> G4 = pitch.Pitch('G4')
>>> Gs4 = pitch.Pitch('G#4')
>>> iv6 = (G4, D4, D4, Bb2)
>>> itAug6 = (Gs4, D4, D4, Bb2)
>>> frAug6 = (Gs4, E4, D4, Bb2)
>>> grAug6 = (Gs4, F4, D4, Bb2)
>>> swAug6 = (Gs4, Es4, D4, Bb2)
>>> frRes = resolution.augmentedSixthToMinorTonic(frAug6)
>>> [str(p) for p in frRes]
['A4', 'F4', 'D4', 'A2']
>>> grRes = resolution.augmentedSixthToMinorTonic(grAug6)
>>> [str(p) for p in grRes]
['A4', 'F4', 'D4', 'A2']
>>> swRes = resolution.augmentedSixthToMinorTonic(swAug6)
>>> [str(p) for p in swRes]
['A4', 'F4', 'D4', 'A2']
>>> resolution.showResolutions(frAug6, frRes, grAug6, grRes, swAug6, swRes)
../_images/fbResolution_a6toIm.png

Above: French, German, and Swiss resolutions, respectively.

music21.figuredBass.resolution.dominantSeventhToMajorTonic(domPossib, resolveV43toI6=False, domChordInfo=None)

Resolves a dominant seventh chord in root position or any of its inversions to the major tonic, in root position or first inversion.

The second inversion (4,3) dominant seventh chord can resolve to the tonic in either inversion. This is controlled by resolveV43toI6, and is set to True by resolveDominantSeventhSegment() only when the segmentChord of a Segment spells out a dominant seventh chord in second inversion.

>>> from music21.figuredBass import resolution
>>> G2 = pitch.Pitch('G2')
>>> C3 = pitch.Pitch('C3')
>>> E3 = pitch.Pitch('E3')
>>> G3 = pitch.Pitch('G3')
>>> Bb3 = pitch.Pitch('B-3')
>>> B3 = pitch.Pitch('B3')
>>> C4 = pitch.Pitch('C4')
>>> F4 = pitch.Pitch('F4')
>>> Bb4 = pitch.Pitch('B-4')
>>> D5 = pitch.Pitch('D5')
>>> E5 = pitch.Pitch('E5')
>>> domPossibA1 = (D5, F4, B3, G2)
>>> resPossibA1 = resolution.dominantSeventhToMajorTonic(domPossibA1)
>>> resPossibA1
(<music21.pitch.Pitch C5>, <music21.pitch.Pitch E4>,
 <music21.pitch.Pitch C4>, <music21.pitch.Pitch C3>)
>>> resolution.showResolutions(domPossibA1, resPossibA1)
../_images/fbResolution_V7toI_1.png 
>>> domPossibA2 = (Bb3, G3, E3, C3)
>>> resPossibA2 = resolution.dominantSeventhToMajorTonic(domPossibA2)
>>> [str(p) for p in resPossibA2]
['A3', 'F3', 'F3', 'F3']
>>> resolution.showResolutions(domPossibA2, resPossibA2)
../_images/fbResolution_V7toI_2.png 
>>> domPossibA3 = (E5, Bb4, C4, G3)
>>> resPossibA3a = resolution.dominantSeventhToMajorTonic(domPossibA3, False)
>>> [str(p) for p in resPossibA3a]
['F5', 'A4', 'C4', 'F3']
>>> resPossibA3b = resolution.dominantSeventhToMajorTonic(domPossibA3, True)
>>> [str(p) for p in resPossibA3b]
['F5', 'C5', 'C4', 'A3']
>>> resolution.showResolutions(domPossibA3, resPossibA3a, domPossibA3, resPossibA3b)
../_images/fbResolution_V7toI_3.png
music21.figuredBass.resolution.dominantSeventhToMinorTonic(domPossib, resolveV43toi6=False, domChordInfo=None)

Resolves a dominant seventh chord in root position or any of its inversions to the minor tonic, in root position or first inversion, accordingly.

The second inversion (4,3) dominant seventh chord can resolve to the tonic in either inversion. This is controlled by resolveV43toi6, and is set to True by resolveDominantSeventhSegment() only when the segmentChord of a Segment spells out a dominant seventh chord in second inversion.

>>> from music21.figuredBass import resolution
>>> G2 = pitch.Pitch('G2')
>>> C3 = pitch.Pitch('C3')
>>> E3 = pitch.Pitch('E3')
>>> G3 = pitch.Pitch('G3')
>>> Bb3 = pitch.Pitch('B-3')
>>> B3 = pitch.Pitch('B3')
>>> C4 = pitch.Pitch('C4')
>>> F4 = pitch.Pitch('F4')
>>> Bb4 = pitch.Pitch('B-4')
>>> D5 = pitch.Pitch('D5')
>>> E5 = pitch.Pitch('E5')
>>> domPossibA1 = (D5, F4, B3, G2)
>>> resPossibA1 = resolution.dominantSeventhToMinorTonic(domPossibA1)
>>> [str(p) for p in resPossibA1]
['C5', 'E-4', 'C4', 'C3']
>>> resolution.showResolutions(domPossibA1, resPossibA1)
../_images/fbResolution_V7toIm_1.png 
>>> domPossibA2 = (Bb3, G3, E3, C3)
>>> resPossibA2 = resolution.dominantSeventhToMinorTonic(domPossibA2)
>>> ', '.join([str(p) for p in resPossibA2])
'A-3, F3, F3, F3'
>>> resolution.showResolutions(domPossibA2, resPossibA2)
../_images/fbResolution_V7toIm_2.png 
>>> domPossibA3 = (E5, Bb4, C4, G3)
>>> resPossibA3a = resolution.dominantSeventhToMinorTonic(domPossibA3, False)
>>> [str(p) for p in resPossibA3a]
['F5', 'A-4', 'C4', 'F3']
>>> resPossibA3b = resolution.dominantSeventhToMinorTonic(domPossibA3, True)
>>> [str(p) for p in resPossibA3b]
['F5', 'C5', 'C4', 'A-3']
>>> resolution.showResolutions(domPossibA3, resPossibA3a, domPossibA3, resPossibA3b)
../_images/fbResolution_V7toIm_3.png
music21.figuredBass.resolution.dominantSeventhToMajorSubmediant(domPossib, domChordInfo=None)

Resolves a dominant seventh chord in root position to the major submediant (VI) in root position.

>>> from music21.figuredBass import resolution
>>> G2 = pitch.Pitch('G2')
>>> B3 = pitch.Pitch('B3')
>>> F4 = pitch.Pitch('F4')
>>> D5 = pitch.Pitch('D5')
>>> domPossibA1 = (D5, F4, B3, G2)
>>> resPossibA1 = resolution.dominantSeventhToMajorSubmediant(domPossibA1)
>>> [p.nameWithOctave for p in resPossibA1]
['C5', 'E-4', 'C4', 'A-2']
>>> resolution.showResolutions(domPossibA1, resPossibA1)
../_images/fbResolution_V7toVI.png
music21.figuredBass.resolution.dominantSeventhToMinorSubmediant(domPossib, domChordInfo=None)

Resolves a dominant seventh chord in root position to the minor submediant (vi) in root position.

>>> from music21.figuredBass import resolution
>>> G2 = pitch.Pitch('G2')
>>> B3 = pitch.Pitch('B3')
>>> F4 = pitch.Pitch('F4')
>>> D5 = pitch.Pitch('D5')
>>> domPossibA1 = (D5, F4, B3, G2)
>>> resPossibA1 = resolution.dominantSeventhToMinorSubmediant(domPossibA1)
>>> [p.nameWithOctave for p in resPossibA1]
['C5', 'E4', 'C4', 'A2']
>>> resolution.showResolutions(domPossibA1, resPossibA1)
../_images/fbResolution_V7toVIm.png
music21.figuredBass.resolution.dominantSeventhToMajorSubdominant(domPossib, domChordInfo=None)

Resolves a dominant seventh chord in root position to the major subdominant (IV) in first inversion.

>>> from music21.figuredBass import resolution
>>> G2 = pitch.Pitch('G2')
>>> B3 = pitch.Pitch('B3')
>>> F4 = pitch.Pitch('F4')
>>> D5 = pitch.Pitch('D5')
>>> domPossibA1 = (D5, F4, B3, G2)
>>> resPossibA1 = resolution.dominantSeventhToMajorSubdominant(domPossibA1)
>>> [p.nameWithOctave for p in resPossibA1]
['C5', 'F4', 'C4', 'A2']
>>> resolution.showResolutions(domPossibA1, resPossibA1)
../_images/fbResolution_V7toIV.png
music21.figuredBass.resolution.dominantSeventhToMinorSubdominant(domPossib, domChordInfo=None)

Resolves a dominant seventh chord in root position to the minor subdominant (iv) in first inversion.

>>> from music21.figuredBass import resolution
>>> G2 = pitch.Pitch('G2')
>>> B3 = pitch.Pitch('B3')
>>> F4 = pitch.Pitch('F4')
>>> D5 = pitch.Pitch('D5')
>>> domPossibA1 = (D5, F4, B3, G2)
>>> resPossibA1 = resolution.dominantSeventhToMinorSubdominant(domPossibA1)
>>> [p.nameWithOctave for p in resPossibA1]
['C5', 'F4', 'C4', 'A-2']
>>> resolution.showResolutions(domPossibA1, resPossibA1)
../_images/fbResolution_V7toIVm.png
music21.figuredBass.resolution.diminishedSeventhToMajorTonic(dimPossib, doubledRoot=False, dimChordInfo=None)

Resolves a fully diminished seventh chord to the major tonic, in root position or either inversion.

The resolution of the diminished seventh chord can have a doubled third (standard resolution) or a doubled root (alternate resolution), because the third of the diminished chord can either rise or fall. The desired resolution is attained using doubledRoot, and is set by resolveDiminishedSeventhSegment().

>>> from music21.figuredBass import resolution
>>> Cs3 = pitch.Pitch('C#3')
>>> G3 = pitch.Pitch('G3')
>>> E4 = pitch.Pitch('E4')
>>> Bb4 = pitch.Pitch('B-4')
>>> dimPossibA = (Bb4, E4, G3, Cs3)
>>> resPossibAa = resolution.diminishedSeventhToMajorTonic(dimPossibA, False)
>>> [str(p) for p in resPossibAa]
['A4', 'F#4', 'F#3', 'D3']
>>> resPossibAb = resolution.diminishedSeventhToMajorTonic(dimPossibA, True)
>>> [p.nameWithOctave for p in resPossibAb]
['A4', 'D4', 'F#3', 'D3']
>>> resolution.showResolutions(dimPossibA, resPossibAa, dimPossibA, resPossibAb)
../_images/fbResolution_vii7toI.png
music21.figuredBass.resolution.diminishedSeventhToMinorTonic(dimPossib, doubledRoot=False, dimChordInfo=None)

Resolves a fully diminished seventh chord to the minor tonic, in root position or either inversion.

The resolution of the diminished seventh chord can have a doubled third (standard resolution) or a doubled root (alternate resolution), because the third of the diminished chord can either rise or fall. The desired resolution is attained using doubledRoot, and is set by resolveDiminishedSeventhSegment().

>>> from music21.figuredBass import resolution
>>> Cs3 = pitch.Pitch('C#3')
>>> G3 = pitch.Pitch('G3')
>>> E4 = pitch.Pitch('E4')
>>> Bb4 = pitch.Pitch('B-4')
>>> dimPossibA = (Bb4, E4, G3, Cs3)
>>> resPossibAa = resolution.diminishedSeventhToMinorTonic(dimPossibA, False)
>>> [p.nameWithOctave for p in resPossibAa]
['A4', 'F4', 'F3', 'D3']
>>> resPossibAb = resolution.diminishedSeventhToMinorTonic(dimPossibA, True)
>>> [p.nameWithOctave for p in resPossibAb]
['A4', 'D4', 'F3', 'D3']
>>> resolution.showResolutions(dimPossibA, resPossibAa, dimPossibA, resPossibAb)
../_images/fbResolution_vii7toIm.png
music21.figuredBass.resolution.diminishedSeventhToMajorSubdominant(dimPossib, dimChordInfo=None)

Resolves a fully diminished seventh chord to the major subdominant (IV).

>>> from music21.figuredBass import resolution
>>> Cs3 = pitch.Pitch('C#3')
>>> G3 = pitch.Pitch('G3')
>>> E4 = pitch.Pitch('E4')
>>> Bb4 = pitch.Pitch('B-4')
>>> dimPossibA = (Bb4, E4, G3, Cs3)
>>> resPossibA = resolution.diminishedSeventhToMajorSubdominant(dimPossibA)
>>> [str(p) for p in resPossibA]
['B4', 'D4', 'G3', 'D3']
>>> resolution.showResolutions(dimPossibA, resPossibA)
../_images/fbResolution_vii7toIV.png
music21.figuredBass.resolution.diminishedSeventhToMinorSubdominant(dimPossib, dimChordInfo=None)

Resolves a fully diminished seventh chord to the minor subdominant (iv).

>>> from music21.figuredBass import resolution
>>> Cs3 = pitch.Pitch('C#3')
>>> G3 = pitch.Pitch('G3')
>>> E4 = pitch.Pitch('E4')
>>> Bb4 = pitch.Pitch('B-4')
>>> dimPossibA = (Bb4, E4, G3, Cs3)
>>> resPossibA = resolution.diminishedSeventhToMinorSubdominant(dimPossibA)
>>> [str(p) for p in resPossibA]
['B-4', 'D4', 'G3', 'D3']
>>> resolution.showResolutions(dimPossibA, resPossibA)
../_images/fbResolution_vii7toIVm.png
music21.figuredBass.resolution.showResolutions(*allPossib)

Takes in possibilities as arguments and adds them in order to a Score which is then displayed in external software.