music21.serial¶
This module defines objects for defining and manipulating structures
common to serial and/or twelve-tone music,
including ToneRow
subclasses.
Serial searching methods that were previously here have been moved to alpha.search.serial
Functions¶
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music21.serial.
getHistoricalRowByName
(rowName)¶ Given the name referring to a twelve-tone row used in the historical literature, returns a
HistoricalTwelveToneRow
object with attributes describing the row.The names of the rows with stored attributes are below (each must be passed as a string, in single quotes).
>>> for r in sorted(list(serial.historicalDict)): ... print(r) RowBergChamberConcerto RowBergDerWein RowBergLulu RowBergLuluActIIScene1 RowBergLuluActIScene20 RowBergLyricSuite RowBergLyricSuitePerm RowBergViolinConcerto RowBergWozzeckPassacaglia RowSchoenbergFragOrganSonata RowSchoenbergFragPiano RowSchoenbergFragPianoPhantasia RowSchoenbergIsraelExists RowSchoenbergJakobsleiter RowSchoenbergMosesAron RowSchoenbergOp23No5 RowSchoenbergOp24Mvmt4 RowSchoenbergOp24Mvmt5 RowSchoenbergOp25 RowSchoenbergOp26 RowSchoenbergOp27No1 RowSchoenbergOp27No2 RowSchoenbergOp27No3 RowSchoenbergOp27No4 RowSchoenbergOp28No1 RowSchoenbergOp28No3 RowSchoenbergOp29 RowSchoenbergOp30 RowSchoenbergOp31 RowSchoenbergOp32 RowSchoenbergOp33A RowSchoenbergOp33B RowSchoenbergOp34 RowSchoenbergOp35No1 RowSchoenbergOp35No2 RowSchoenbergOp35No3 RowSchoenbergOp35No5 RowSchoenbergOp36 RowSchoenbergOp37 RowSchoenbergOp41 RowSchoenbergOp42 RowSchoenbergOp44 RowSchoenbergOp45 RowSchoenbergOp46 RowSchoenbergOp47 RowSchoenbergOp48No1 RowSchoenbergOp48No2 RowSchoenbergOp48No3 RowSchoenbergOp50A RowSchoenbergOp50B RowSchoenbergOp50C RowWebernOp17No2 RowWebernOp17No3 RowWebernOp18No1 RowWebernOp18No2 RowWebernOp18No3 RowWebernOp19No1 RowWebernOp19No2 RowWebernOp20 RowWebernOp21 RowWebernOp22 RowWebernOp23 RowWebernOp24 RowWebernOp25 RowWebernOp26 RowWebernOp27 RowWebernOp28 RowWebernOp29 RowWebernOp30 RowWebernOp31 RowWebernOpNo17No1
>>> a = serial.getHistoricalRowByName('RowWebernOp29') >>> a.row [3, 11, 2, 1, 5, 4, 7, 6, 10, 9, 0, 8] >>> a.composer 'Webern' >>> a.opus 'Op. 29' >>> a.title 'Cantata I' >>> a.isLinkChord() False
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music21.serial.
pcToToneRow
(pcSet)¶ A convenience function that, given a list of pitch classes represented as integers and turns it in to a
ToneRow
object.>>> a = serial.pcToToneRow(range(12)) >>> a.show('text') {0.0} <music21.note.Note C> {1.0} <music21.note.Note C#> {2.0} <music21.note.Note D> {3.0} <music21.note.Note E-> {4.0} <music21.note.Note E> {5.0} <music21.note.Note F> {6.0} <music21.note.Note F#> {7.0} <music21.note.Note G> {8.0} <music21.note.Note G#> {9.0} <music21.note.Note A> {10.0} <music21.note.Note B-> {11.0} <music21.note.Note B> >>> matrixObj = a.matrix() >>> print(matrixObj) 0 1 2 3 4 5 6 7 8 9 A B B 0 1 2 3 4 5 6 7 8 9 A ...
>>> a = serial.pcToToneRow([4,5,0,6,7,2,'a',8,9,1,'b',3]) >>> matrixObj = a.matrix() >>> print(matrixObj) 0 1 8 2 3 A 6 4 5 9 7 B B 0 7 1 2 9 5 3 4 8 6 A ...
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music21.serial.
rowToMatrix
(p)¶ takes a row of numbers of converts it to a 12-tone matrix.
HistoricalTwelveToneRow¶
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class
music21.serial.
HistoricalTwelveToneRow
(composer=None, opus=None, title=None, row=None)¶ Subclass of
TwelveToneRow
storing additional attributes of a twelve-tone row used in the historical literature.
HistoricalTwelveToneRow
bases
HistoricalTwelveToneRow
read-only properties
Read-only properties inherited from Stream
:
Read-only properties inherited from StreamCoreMixin
:
Read-only properties inherited from Music21Object
:
HistoricalTwelveToneRow
read/write properties
Read/write properties inherited from Stream
:
Read/write properties inherited from Music21Object
:
HistoricalTwelveToneRow
methods
Methods inherited from TwelveToneRow
:
Methods inherited from ToneRow
:
Methods inherited from Stream
:
Methods inherited from StreamCoreMixin
:
Methods inherited from Music21Object
:
HistoricalTwelveToneRow
instance variables
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HistoricalTwelveToneRow.
composer
¶ The name of the composer.
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HistoricalTwelveToneRow.
opus
¶ The opus of the work, or None.
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HistoricalTwelveToneRow.
title
¶ The title of the work.
Instance variables inherited from ToneRow
:
Instance variables inherited from Stream
:
Instance variables inherited from Music21Object
:
ToneRow¶
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class
music21.serial.
ToneRow
¶ A Stream representation of a tone row, or an ordered sequence of pitches; can most importantly be used to deal with serial transformations.
ToneRow
bases
ToneRow
read-only properties
Read-only properties inherited from Stream
:
Read-only properties inherited from StreamCoreMixin
:
Read-only properties inherited from Music21Object
:
ToneRow
read/write properties
Read/write properties inherited from Stream
:
Read/write properties inherited from Music21Object
:
ToneRow
methods
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ToneRow.
findOriginalCenteredTransformations
(otherRow)¶ Gives the list of original-centered serial transformations taking one
ToneRow
to another, the second specified in the argument. Each transformation is given as a tuple of the transformation type and index.See
originalCenteredTransformation()
for an explanation of this convention.>>> chromatic = serial.pcToToneRow([2, 3, 4, 5, 6, 7, 8, 9, 'A', 'B', 0, 1]) >>> reversechromatic = serial.pcToToneRow([8, 7, 6, 5, 4, 3, 2, 1, 0, 'B', 'A', 9]) >>> chromatic.findOriginalCenteredTransformations(reversechromatic) [('I', 6), ('R', 7)] >>> schoenberg25 = serial.getHistoricalRowByName('RowSchoenbergOp25') >>> schoenberg26 = serial.getHistoricalRowByName('RowSchoenbergOp26') >>> schoenberg25.findOriginalCenteredTransformations(schoenberg26) [] >>> schoenberg26.findOriginalCenteredTransformations( ... schoenberg26.originalCenteredTransformation('RI',8)) [('RI', 8)]
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ToneRow.
findZeroCenteredTransformations
(otherRow)¶ Gives the list of zero-centered serial transformations taking one
ToneRow
to another, the second specified in the argument. Each transformation is given as a tuple of the transformation type and index.See
zeroCenteredTransformation()
for an explanation of this convention.>>> chromatic = serial.pcToToneRow([2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1]) >>> reversechromatic = serial.pcToToneRow([8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9]) >>> chromatic.findZeroCenteredTransformations(reversechromatic) [('I', 8), ('R', 9)] >>> schoenberg25 = serial.getHistoricalRowByName('RowSchoenbergOp25') >>> schoenberg26 = serial.pcToToneRow(serial.getHistoricalRowByName( ... 'RowSchoenbergOp26').row) >>> schoenberg25.findZeroCenteredTransformations(schoenberg26) [] >>> schoenberg26.findZeroCenteredTransformations( ... schoenberg26.zeroCenteredTransformation('RI',8)) [('RI', 8)]
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ToneRow.
getIntervalsAsString
()¶ Returns the string of intervals between consecutive pitch classes of a
ToneRow
. ‘T’ = 10, ‘E’ = 11.>>> cRow = serial.pcToToneRow([0]) >>> cRow.getIntervalsAsString() '' >>> reversechromatic = serial.pcToToneRow([11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) >>> reversechromatic.getIntervalsAsString() 'EEEEEEEEEEE'
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ToneRow.
isSameRow
(row)¶ Convenience function describing if two rows are the same.
>>> row1 = serial.pcToToneRow([6, 7, 8]) >>> row2 = serial.pcToToneRow([-6, 19, 128]) >>> row3 = serial.pcToToneRow([6, 7, -8]) >>> row1.isSameRow(row2) True >>> row2.isSameRow(row1) True >>> row1.isSameRow(row3) False
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ToneRow.
isTwelveToneRow
()¶ Describes whether or not a
ToneRow
constitutes a twelve-tone row. Note that aTwelveToneRow
object might not be a twelve-tone row.>>> serial.pcToToneRow(range(0,12)).isTwelveToneRow() True >>> serial.pcToToneRow(range(0,10)).isTwelveToneRow() False >>> serial.pcToToneRow([3,3,3,3,3,3,3,3,3,3,3,3]).isTwelveToneRow() False
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ToneRow.
makeTwelveToneRow
()¶ Convenience function returning a
TwelveToneRow
with the same pitches. Note that aToneRow
may be created without being a true twelve tone row.>>> a = serial.pcToToneRow(range(0,11)) >>> type(a) <class 'music21.serial.ToneRow'> >>> n = note.Note() >>> n.pitch.pitchClass = 11 >>> a.append(n) >>> a = a.makeTwelveToneRow() ... >>> type(a) <class 'music21.serial.TwelveToneRow'>
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ToneRow.
noteNames
()¶ Convenience function showing the note names of a
ToneRow
as a list.>>> chromatic = serial.pcToToneRow(range(0,12)) >>> chromatic.noteNames() ['C', 'C#', 'D', 'E-', 'E', 'F', 'F#', 'G', 'G#', 'A', 'B-', 'B'] >>> halfStep = serial.pcToToneRow([0,1]) >>> halfStep.noteNames() ['C', 'C#']
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ToneRow.
originalCenteredTransformation
(transformationType, index)¶ Returns a
ToneRow
giving a transformation of a tone row. Admissible transformations are ‘T’ (transposition), ‘I’ (inversion), ‘R’ (retrograde), and ‘RI’ (retrograde inversion).In the “original-centered” convention, which is less common than the “zero-centered” convention, the original row is not initially transposed to start on the pitch class 0. Thus, the transformation Tn transposes the original row up by n semitones, and the transformations In, Rn, and RIn first transform the row appropriately (without transposition), then transpose the resulting row by n semitones.
>>> chromatic = serial.pcToToneRow(range(0,12)) >>> chromatic.pitchClasses() [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] >>> chromaticP3 = chromatic.originalCenteredTransformation('T',3) >>> chromaticP3.pitchClasses() [3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2] >>> chromaticI6 = chromatic.originalCenteredTransformation('I',6) >>> chromaticI6.pitchClasses() [6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7] >>> schoenberg = serial.getHistoricalRowByName('RowSchoenbergOp26') >>> schoenberg.pitchClasses() [3, 7, 9, 11, 1, 0, 10, 2, 4, 6, 8, 5] >>> schoenbergR8 = schoenberg.originalCenteredTransformation('R',8) >>> schoenbergR8.pitchClasses() [1, 4, 2, 0, 10, 6, 8, 9, 7, 5, 3, 11] >>> schoenbergRI9 = schoenberg.originalCenteredTransformation('RI',9) >>> schoenbergRI9.noteNames() ['B-', 'G', 'A', 'B', 'C#', 'F', 'E-', 'D', 'E', 'F#', 'G#', 'C']
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ToneRow.
pitchClasses
()¶ Convenience function showing the pitch classes of a
ToneRow
as a list.>>> L = [5*i for i in range(0,12)] >>> quintupleRow = serial.pcToToneRow(L) >>> quintupleRow <music21.serial.TwelveToneRow 0x104760780> >>> quintupleRow.pitchClasses() [0, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7] >>> halfStep = serial.pcToToneRow([0, 1]) >>> halfStep.pitchClasses() [0, 1]
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ToneRow.
zeroCenteredTransformation
(transformationType, index)¶ Returns a
ToneRow
giving a transformation of a tone row. Admissible transformationTypes are ‘P’ (prime), ‘I’ (inversion), ‘R’ (retrograde), and ‘RI’ (retrograde inversion).In the “zero-centered” convention, the transformations Pn and In start on the pitch class n, and the transformations Rn and RIn end on the pitch class n.
>>> chromatic = serial.pcToToneRow(range(0,12)) >>> chromatic.pitchClasses() [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] >>> chromaticP3 = chromatic.zeroCenteredTransformation('P',3) >>> chromaticP3.pitchClasses() [3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2] >>> chromaticI6 = chromatic.zeroCenteredTransformation('I',6) >>> chromaticI6.pitchClasses() [6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7] >>> schoenberg = serial.getHistoricalRowByName('RowSchoenbergOp26') >>> schoenberg.pitchClasses() [3, 7, 9, 11, 1, 0, 10, 2, 4, 6, 8, 5] >>> schoenbergR8 = schoenberg.zeroCenteredTransformation('R',8) >>> schoenbergR8.pitchClasses() [10, 1, 11, 9, 7, 3, 5, 6, 4, 2, 0, 8] >>> schoenbergRI9 = schoenberg.zeroCenteredTransformation('RI',9) >>> schoenbergRI9.noteNames() ['G', 'E', 'F#', 'G#', 'B-', 'D', 'C', 'B', 'C#', 'E-', 'F', 'A']
Methods inherited from Stream
:
Methods inherited from StreamCoreMixin
:
Methods inherited from Music21Object
:
ToneRow
instance variables
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ToneRow.
row
¶ A list representing the pitch class values of the row.
Instance variables inherited from Stream
:
Instance variables inherited from Music21Object
:
TwelveToneMatrix¶
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class
music21.serial.
TwelveToneMatrix
(*arguments, **keywords)¶ An object representation of a 2-dimensional array of 12 pitches. Internal representation is as a
Stream
, which stores 12 Streams, each Stream a horizontal row of pitches in the matrix.This object is commonly used by calling the
matrix()
method ofTwelveToneRow()
(or a subclass).
TwelveToneMatrix
bases
TwelveToneMatrix
read-only properties
Read-only properties inherited from Stream
:
Read-only properties inherited from StreamCoreMixin
:
Read-only properties inherited from Music21Object
:
TwelveToneMatrix
read/write properties
Read/write properties inherited from Stream
:
Read/write properties inherited from Music21Object
:
TwelveToneMatrix
methods
Methods inherited from Stream
:
Methods inherited from StreamCoreMixin
:
Methods inherited from Music21Object
:
TwelveToneMatrix
instance variables
Instance variables inherited from Stream
:
Instance variables inherited from Music21Object
:
TwelveToneRow¶
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class
music21.serial.
TwelveToneRow
¶ A Stream representation of a twelve-tone row, capable of producing a 12-tone matrix.
TwelveToneRow
bases
TwelveToneRow
read-only properties
Read-only properties inherited from Stream
:
Read-only properties inherited from StreamCoreMixin
:
Read-only properties inherited from Music21Object
:
TwelveToneRow
read/write properties
Read/write properties inherited from Stream
:
Read/write properties inherited from Music21Object
:
TwelveToneRow
methods
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TwelveToneRow.
areCombinatorial
(transType1, index1, transType2, index2, convention)¶ Describes whether or not two transformations of a twelve-tone row are combinatorial.
The first and second arguments describe one transformation, while the third and fourth describe another. One of the zero-centered or original-centered conventions for tone row transformations must be specified in the last argument; see
zeroCenteredTransformation()
andoriginalCenteredTransformation()
explanations of these conventions.>>> moses = serial.getHistoricalRowByName('RowSchoenbergMosesAron') >>> moses.pitchClasses() [9, 10, 4, 2, 3, 1, 7, 5, 6, 8, 11, 0] >>> moses.areCombinatorial('P', 1, 'I', 4, 'zero') True >>> moses.areCombinatorial('R', 5, 'RI', 6, 'original') False
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TwelveToneRow.
findHistorical
()¶ Checks if a given
music21.serial.TwelveToneRow
is the same as any of the historical twelve-tone rows stored by music21: seemusic21.serial.getHistoricalRowByName()
. Returns a list of names of historical rows to which the input row is identical.>>> row = serial.pcToToneRow([2, 3, 9, 1, 11, 5, 8, 7, 4, 0, 10, 6]) >>> row.findHistorical() ['RowSchoenbergOp32'] >>> chromatic = serial.pcToToneRow(range(0,12)) >>> chromatic.findHistorical() []
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TwelveToneRow.
findTransformedHistorical
(convention)¶ Checks if a given
music21.serial.TwelveToneRow
is a transformation of any of the historical twelve-tone rows stored by music21: seemusic21.serial.getHistoricalRowByName()
. Returns a list of tuples, the tuple consisting of the name of a historical row, and a list of transformations relating the input row to the historical row.The convention for serial transformations must also be specified as ‘zero’ or ‘original’, as explained in
findZeroCenteredTransformations()
andfindOriginalCenteredTransformations()
.>>> row = serial.pcToToneRow([5, 9, 11, 3, 6, 7, 4, 10, 0, 8, 2, 1]) >>> row.findTransformedHistorical('original') [('RowSchoenbergOp32', [('R', 11)])]
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TwelveToneRow.
getLinkClassification
()¶ Gives the classification number of a Link Chord (as given in http://www.johnlinkmusic.com/LinkChords.pdf), that is, is an all-interval twelve-tone row containing a voicing of the all-trichord hexachord: [0, 1, 2, 4, 7, 8]. In addition, gives a list of sets of five contiguous intervals within the row representing a voicing of the all-trichord hexachord. Note that the interval sets may be transformed.
Named for John Link who discovered them.
>>> bergLyric = serial.getHistoricalRowByName('RowBergLyricSuite') >>> bergLyric.pitchClasses() [5, 4, 0, 9, 7, 2, 8, 1, 3, 6, 10, 11] >>> bergLyric.isAllInterval() True >>> bergLyric.getLinkClassification() (None, []) >>> link = serial.pcToToneRow([0, 3, 8, 2, 10, 11, 9, 4, 1, 5, 7, 6]) >>> link.getLinkClassification() (62, ['8352E']) >>> doubleLink = serial.pcToToneRow([0, 1, 8, 5, 7, 10, 4, 3, 11, 9, 2, 6]) >>> doubleLink.getLinkClassification() (33, ['236E8', '36E8T'])
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TwelveToneRow.
isAllInterval
()¶ Describes whether or not a
TwelveToneRow
is an all-interval row.>>> chromatic = serial.pcToToneRow(range(0,12)) >>> chromatic.pitchClasses() [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] >>> chromatic.isAllInterval() False >>> bergLyric = serial.getHistoricalRowByName('RowBergLyricSuite') >>> bergLyric.pitchClasses() [5, 4, 0, 9, 7, 2, 8, 1, 3, 6, 10, 11] >>> bergLyric.isAllInterval() True
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TwelveToneRow.
isLinkChord
()¶ Describes whether or not a
TwelveToneRow
is a Link Chord.>>> bergLyric = serial.getHistoricalRowByName('RowBergLyricSuite') >>> bergLyric.pitchClasses() [5, 4, 0, 9, 7, 2, 8, 1, 3, 6, 10, 11] >>> bergLyric.isAllInterval() True >>> bergLyric.isLinkChord() False >>> link = serial.pcToToneRow([0, 3, 8, 2, 10, 11, 9, 4, 1, 5, 7, 6]) >>> link.isLinkChord() True >>> doubleLink = serial.pcToToneRow([0, 1, 8, 5, 7, 10, 4, 3, 11, 9, 2, 6]) >>> doubleLink.isLinkChord() True
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TwelveToneRow.
matrix
()¶ Returns a
TwelveToneMatrix
object for the row. That object can just be printed (or displayed via .show())>>> src = serial.getHistoricalRowByName('RowSchoenbergOp37') >>> [p.name for p in src] ['D', 'C#', 'A', 'B-', 'F', 'E-', 'E', 'C', 'G#', 'G', 'F#', 'B'] >>> len(src) 12 >>> s37 = serial.getHistoricalRowByName('RowSchoenbergOp37').matrix() >>> print(s37) 0 B 7 8 3 1 2 A 6 5 4 9 1 0 8 9 4 2 3 B 7 6 5 A 5 4 0 1 8 6 7 3 B A 9 2 4 3 B 0 7 5 6 2 A 9 8 1 ... >>> [str(e.pitch) for e in s37[0]] ['C', 'B', 'G', 'G#', 'E-', 'C#', 'D', 'B-', 'F#', 'F', 'E', 'A']
Methods inherited from ToneRow
:
Methods inherited from Stream
:
Methods inherited from StreamCoreMixin
:
Methods inherited from Music21Object
:
TwelveToneRow
instance variables
Instance variables inherited from ToneRow
:
Instance variables inherited from Stream
:
Instance variables inherited from Music21Object
: