This module defines various types of interval objects. Fundamental classes are Interval, DiatonicInterval, and ChromaticInterval. Numerous utility functions are provided for processing and generating intervals. module authors: Michael Scott Cuthbert, Jackie Rogoff, Amy Hailes, and Christopher Ariza
Given two Note objects, returns a ChromaticInterval object.
>>> from music21 import note
>>> aNote = note.Note('c4')
>>> bNote = note.Note('g#5')
>>> notesToChromatic(aNote, bNote)
<music21.interval.ChromaticInterval 20>
Given a GenericInterval and a ChromaticInterval object, return a DiatonicInterval.
>>> aInterval = GenericInterval('descending fifth')
>>> bInterval = ChromaticInterval(-7)
>>> cInterval = intervalsToDiatonic(aInterval, bInterval)
>>> cInterval
<music21.interval.DiatonicInterval P5>
Given two Note objects, returns an Interval object. The same functionality is available by calling the Interval class with two Notes as arguments.
>>> from music21 import note
>>> aNote = note.Note('c4')
>>> bNote = note.Note('g5')
>>> aInterval = notesToInterval(aNote, bNote)
>>> aInterval
<music21.interval.Interval P12>
>>> bInterval = Interval(noteStart=aNote, noteEnd=bNote)
>>> aInterval.niceName == bInterval.niceName
True
Convert a diatonic number to a step name and a octave integer.
>>> convertDiatonicNumberToStep(15)
('C', 2)
>>> convertDiatonicNumberToStep(23)
('D', 3)
>>> convertDiatonicNumberToStep(0)
('C', 0)
>>> convertDiatonicNumberToStep(1)
('C', 0)
>>> convertDiatonicNumberToStep(2)
('D', 0)
>>> convertDiatonicNumberToStep(3)
('E', 0)
>>> convertDiatonicNumberToStep(4)
('F', 0)
>>> convertDiatonicNumberToStep(5)
('G', 0)
Convert an interval specified in terms of its name (second, third) into an integer. If integers are passed, assume the are correct.
>>> convertGeneric(3)
3
>>> convertGeneric('third')
3
>>> convertGeneric('3rd')
3
>>> convertGeneric('octave')
8
>>> convertGeneric('twelfth')
12
>>> convertGeneric('descending twelfth')
-12
>>> convertGeneric(12)
12
>>> convertGeneric(-12)
-12
Given a number of semitones, return a default diatonic specifier.
>>> convertSemitoneToSpecifierGeneric(0)
('P', 1)
>>> convertSemitoneToSpecifierGeneric(-2)
('M', -2)
>>> convertSemitoneToSpecifierGeneric(1)
('m', 2)
>>> convertSemitoneToSpecifierGeneric(7)
('P', 5)
>>> convertSemitoneToSpecifierGeneric(11)
('M', 7)
>>> convertSemitoneToSpecifierGeneric(12)
('P', 8)
>>> convertSemitoneToSpecifierGeneric(13)
('m', 9)
>>> convertSemitoneToSpecifierGeneric(-15)
('m', -10)
>>> convertSemitoneToSpecifierGeneric(24)
('P', 15)
Given an integer or a string, return the integer for the appropriate specifier. This permits specifiers to specified in a flexible manner.
>>> convertSpecifier(3)
(3, 'm')
>>> convertSpecifier('p')
(1, 'P')
>>> convertSpecifier('P')
(1, 'P')
>>> convertSpecifier('M')
(2, 'M')
>>> convertSpecifier('major')
(2, 'M')
>>> convertSpecifier('m')
(3, 'm')
>>> convertSpecifier('Augmented')
(4, 'A')
>>> convertSpecifier('a')
(4, 'A')
>>> convertSpecifier(None)
(None, None)
Returns the interval number from the given staff distance.
>>> convertStaffDistanceToInterval(3)
4
>>> convertStaffDistanceToInterval(7)
8
Given two Note objects, returns the higher note based on actual pitch. If both pitches are the same, returns the first note given.
>>> from music21 import note
>>> aNote = note.Note('c#3')
>>> bNote = note.Note('d--3')
>>> getAbsoluteHigherNote(aNote, bNote)
<music21.note.Note C#>
Given two Note objects, returns the lower note based on actual pitch. If both pitches are the same, returns the first note given.
>>> from music21 import note
>>> aNote = note.Note('c#3')
>>> bNote = note.Note('d--3')
>>> getAbsoluteLowerNote(aNote, bNote)
<music21.note.Note D-->
Given two Note or Pitch objects, this function returns the higher object based on diatonic note numbers. Returns the note higher in pitch if the diatonic number is the same, or the first note if pitch is also the same.
>>> from music21 import pitch
>>> cis = pitch.Pitch("C#")
>>> deses = pitch.Pitch("D--")
>>> higher = getWrittenHigherNote(cis, deses)
>>> higher is deses
True
>>> from music21 import note
>>> aNote = note.Note('c#3')
>>> bNote = note.Note('d-3')
>>> getWrittenHigherNote(aNote, bNote)
<music21.note.Note D->
>>> aNote = note.Note('c#3')
>>> bNote = note.Note('d--3')
>>> getWrittenHigherNote(aNote, bNote)
<music21.note.Note D-->
Given two Note objects, returns the lower note based on diatonic note number. Returns the note lower in pitch if the diatonic number is the same, or the first note if pitch is also the same.
>>> from music21 import note
>>> aNote = note.Note('c#3')
>>> bNote = note.Note('d--3')
>>> getWrittenLowerNote(aNote, bNote)
<music21.note.Note C#>
>>> from music21 import note
>>> aNote = note.Note('c#3')
>>> bNote = note.Note('d-3')
>>> getWrittenLowerNote(aNote, bNote)
<music21.note.Note C#>
Given two Note objects, returns a GenericInterval object.
>>> from music21 import note
>>> aNote = note.Note('c4')
>>> bNote = note.Note('g5')
>>> aInterval = notesToGeneric(aNote, bNote)
>>> aInterval
<music21.interval.GenericInterval 12>
Given an interval string (such as “P5”, “m3”, “A2”) return a Interval object.
>>> aInterval = stringToInterval('P5')
>>> aInterval
<music21.interval.Interval P5>
>>> aInterval = stringToInterval('m3')
>>> aInterval
<music21.interval.Interval m3>
Given a Note and a interval string (such as ‘P5’) or an Interval object, return a new Note object at the appropriate pitch level.
>>> from music21 import note
>>> aNote = note.Note('c4')
>>> bNote = transposeNote(aNote, 'p5')
>>> bNote
<music21.note.Note G>
>>> aNote = note.Note('f#4')
>>> bNote = transposeNote(aNote, 'm2')
>>> bNote
<music21.note.Note G>
Given a Pitch and a Interval object, return a new Pitch object at the appropriate pitch level.
>>> from music21 import pitch
>>> aPitch = pitch.Pitch('C4')
>>> aInterval = Interval('P5')
>>> bPitch = transposePitch(aPitch, aInterval)
>>> bPitch
G4
>>> bInterval = stringToInterval('P-5')
>>> cPitch = transposePitch(aPitch, bInterval)
>>> cPitch
F3
Inherits from: Music21Object
An Interval class that encapsulates both a chromatic and diatonic intervals all in one model. The interval is specified either as named arguments, a DiatonicInterval and a ChromaticInterval, or two Note objects, from which both a ChromaticInterval and DiatonicInterval are derived.
>>> from music21 import note
>>> n1 = note.Note('c3')
>>> n2 = note.Note('c5')
>>> aInterval = Interval(noteStart=n1, noteEnd=n2)
>>> aInterval
<music21.interval.Interval P15>
>>> from music21 import note
>>> n1 = note.Note('c3')
>>> n2 = note.Note('g3')
>>> aInterval = Interval(noteStart=n1, noteEnd=n2)
>>> aInterval
<music21.interval.Interval P5>
>>> aInterval = Interval(noteStart=n1, noteEnd=None)
Traceback (most recent call last):
IntervalException: two or zero Note classes must be defined
>>> aInterval = DiatonicInterval('major', 'third')
>>> bInterval = ChromaticInterval(4)
>>> cInterval = Interval(diatonic=aInterval, chromatic=bInterval)
>>> cInterval
<music21.interval.Interval M3>
>>> cInterval = Interval(diatonic=aInterval, chromatic=None)
Traceback (most recent call last):
IntervalException: either both or zero diatonic and chromatic classes must be defined
>>> aInterval = Interval('m3')
>>> aInterval
<music21.interval.Interval m3>
>>> aInterval = Interval('M3')
>>> aInterval
<music21.interval.Interval M3>
>>> aInterval = Interval('p5')
>>> aInterval
<music21.interval.Interval P5>
>>> aInterval = Interval('half')
>>> aInterval
<music21.interval.Interval m2>
>>> aInterval = Interval('-h')
>>> aInterval
<music21.interval.Interval m-2>
>>> aInterval = Interval(3)
>>> aInterval
<music21.interval.Interval m3>
>>> aInterval = Interval(7)
>>> aInterval
<music21.interval.Interval P5>
Interval attributes
Attributes without Documentation: chromatic, diatonic, diatonicType, direction, generic, niceName, type
Attributes inherited from Music21Object: classSortOrder, id, groups
Interval properties
- complement¶
Return a new Interval object that is the complement of this Interval.
>>> aInterval = Interval('M3') >>> bInterval = aInterval.complement >>> bInterval <music21.interval.Interval m6>
- intervalClass¶
Return the interval class from the chromatic interval.
>>> aInterval = Interval('M3') >>> aInterval.intervalClass 4
- noteEnd¶
Assuming this Interval has been defined, set the end note (_noteEnd) to a new value; this will adjust the value of the start note (_noteStart).
>>> from music21 import note >>> aInterval = Interval('M3') >>> aInterval.noteEnd = note.Note('e4') >>> aInterval.noteStart.nameWithOctave 'C4' >>> aInterval = Interval('m2') >>> aInterval.noteEnd = note.Note('A#3') >>> aInterval.noteStart.nameWithOctave 'G##3' >>> n1 = note.Note('g#3') >>> n2 = note.Note('c3') >>> aInterval = Interval(n1, n2) >>> aInterval.directedName # downward augmented fifth 'A-5' >>> aInterval.noteEnd = note.Note('c4') >>> aInterval.noteStart.nameWithOctave 'G#4' >>> aInterval = Interval('M3') >>> aInterval.noteEnd = note.Note('A-3') >>> aInterval.noteStart.nameWithOctave 'F-3'
- noteStart¶
Assuming this Interval has been defined, set the start note (_noteStart) to a new value; this will adjust the value of the end note (_noteEnd).
>>> from music21 import note >>> aInterval = Interval('M3') >>> aInterval.noteStart = note.Note('c4') >>> aInterval.noteEnd.nameWithOctave 'E4' >>> n1 = note.Note('c3') >>> n2 = note.Note('g#3') >>> aInterval = Interval(n1, n2) >>> aInterval.name 'A5' >>> aInterval.noteStart = note.Note('g4') >>> aInterval.noteEnd.nameWithOctave 'D#5' >>> aInterval = Interval('-M3') >>> aInterval.noteStart = note.Note('c4') >>> aInterval.noteEnd.nameWithOctave 'A-3' >>> aInterval = Interval('M-2') >>> aInterval.noteStart = note.Note('A#3') >>> aInterval.noteEnd.nameWithOctave 'G#3' >>> aInterval = Interval('h') >>> aInterval.directedName 'm2' >>> aInterval.noteStart = note.Note('F#3') >>> aInterval.noteEnd.nameWithOctave 'G3'Properties inherited from Music21Object: classes, duration, offset, parent, priority
Interval methods
- reinit()¶
- Reinitialize the internal interval objects in case something has changed. Called during __init__ to assign attributes.
- reverse()¶
Return an reversed version of this interval. If given Notes, these notes are reversed.
>>> from music21 import note >>> n1 = note.Note('c3') >>> n2 = note.Note('g3') >>> aInterval = Interval(noteStart=n1, noteEnd=n2) >>> aInterval <music21.interval.Interval P5> >>> bInterval = aInterval.reverse() >>> bInterval <music21.interval.Interval P-5> >>> bInterval.noteStart == aInterval.noteEnd True >>> aInterval = Interval('m3') >>> aInterval.reverse() <music21.interval.Interval m-3>
- transposePitch(p, reverse=False, clearAccidentalDisplay=True)¶
Given a Pitch, return a new, transposed Pitch, that is transformed according to this Interval. This is the main public interface to all transposition routines found on higher-level objects.
>>> from music21 import pitch >>> p1 = pitch.Pitch('a#') >>> i = Interval('m3') >>> p2 = i.transposePitch(p1) >>> p2 C#5 >>> p2 = i.transposePitch(p1, reverse=True) >>> p2 F##4Methods inherited from Music21Object: searchParentByAttr(), getContextAttr(), setContextAttr(), addContext(), addLocation(), addLocationAndParent(), freezeIds(), getContextByClass(), getOffsetBySite(), getSiteIds(), getSites(), hasContext(), isClass(), purgeLocations(), removeLocationBySite(), removeLocationBySiteId(), setOffsetBySite(), show(), unfreezeIds(), unwrapWeakref(), wrapWeakref(), write()
Inherits from: Music21Object
Chromatic interval class. Unlike a Diatonic interval, this Interval class treats interval spaces in half-steps.
>>> aInterval = ChromaticInterval(-14)
>>> aInterval.semitones
-14
>>> aInterval.undirected
14
>>> aInterval.mod12
10
>>> aInterval.intervalClass
2
ChromaticInterval attributes
Attributes inherited from Music21Object: classSortOrder, id
ChromaticInterval properties
Properties inherited from Music21Object: classes, duration, offset, parent, priority
ChromaticInterval methods
- getDiatonic()¶
Given a Chromatic interval, return a Diatonic interval object. While there is more than one Generic Interval for any given chromatic interval, this is needed to to permit easy chromatic specification of Interval objects.
>>> aInterval = ChromaticInterval(5) >>> aInterval.getDiatonic() <music21.interval.DiatonicInterval P4> >>> aInterval = ChromaticInterval(7) >>> aInterval.getDiatonic() <music21.interval.DiatonicInterval P5> >>> aInterval = ChromaticInterval(11) >>> aInterval.getDiatonic() <music21.interval.DiatonicInterval M7>
- reverse()¶
Return an inverted interval, that is, reversing the direction.
>>> aInterval = ChromaticInterval(-14) >>> aInterval.reverse() <music21.interval.ChromaticInterval 14> >>> aInterval = ChromaticInterval(3) >>> aInterval.reverse() <music21.interval.ChromaticInterval -3>Methods inherited from Music21Object: searchParentByAttr(), getContextAttr(), setContextAttr(), addContext(), addLocation(), addLocationAndParent(), freezeIds(), getContextByClass(), getOffsetBySite(), getSiteIds(), getSites(), hasContext(), isClass(), purgeLocations(), removeLocationBySite(), removeLocationBySiteId(), setOffsetBySite(), show(), unfreezeIds(), unwrapWeakref(), wrapWeakref(), write()
Inherits from: Music21Object
A class representing a diatonic interval. Two required arguments are a specifier (such as perfect, major, or minor) and a generic, an interval size (such as 2, 2nd, or second). A DiatonicInterval contains and encapsulates a GenericInterval
The specifier is an integer specifying a value in the prefixSpecs and niceSpecNames lists. The generic is an integer or GenericInterval instance.
>>> aInterval = DiatonicInterval(1, 1)
>>> aInterval.simpleName
'P1'
>>> aInterval = DiatonicInterval('p', 1)
>>> aInterval.simpleName
'P1'
>>> aInterval = DiatonicInterval('major', 3)
>>> aInterval.simpleName
'M3'
>>> aInterval.niceName
'Major Third'
>>> aInterval.semiSimpleName
'M3'
>>> aInterval.directedSimpleName
'M3'
>>> aInterval.invertedOrderedSpecifier
'm'
>>> aInterval.mod7
'M3'
>>> aInterval = DiatonicInterval('major', 'third')
>>> aInterval.niceName
'Major Third'
>>> aInterval = DiatonicInterval('perfect', 'octave')
>>> aInterval.niceName
'Perfect Octave'
>>> aInterval = DiatonicInterval('minor', 10)
>>> aInterval.mod7
'm3'
DiatonicInterval attributes
Attributes inherited from Music21Object: classSortOrder, id
DiatonicInterval properties
Properties inherited from Music21Object: classes, duration, offset, parent, priority
DiatonicInterval methods
- getChromatic()¶
Return a Chromatic interval based on the size of this Interval.
>>> aInterval = DiatonicInterval('major', 'third') >>> aInterval.niceName 'Major Third' >>> aInterval.getChromatic() <music21.interval.ChromaticInterval 4> >>> aInterval = DiatonicInterval('augmented', -5) >>> aInterval.niceName 'Augmented Fifth' >>> aInterval.getChromatic() <music21.interval.ChromaticInterval -8> >>> aInterval = DiatonicInterval('minor', 'second') >>> aInterval.niceName 'Minor Second' >>> aInterval.getChromatic() <music21.interval.ChromaticInterval 1>
- reverse()¶
Return a DiatonicInterval that is an inversion of this Interval.
>>> aInterval = DiatonicInterval('major', 3) >>> aInterval.reverse().directedName 'M-3' >>> aInterval = DiatonicInterval('augmented', 5) >>> aInterval.reverse().directedName 'A-5'Methods inherited from Music21Object: searchParentByAttr(), getContextAttr(), setContextAttr(), addContext(), addLocation(), addLocationAndParent(), freezeIds(), getContextByClass(), getOffsetBySite(), getSiteIds(), getSites(), hasContext(), isClass(), purgeLocations(), removeLocationBySite(), removeLocationBySiteId(), setOffsetBySite(), show(), unfreezeIds(), unwrapWeakref(), wrapWeakref(), write()
Inherits from: Music21Object
A GenericInterval is an interval such as Third, Seventh, Octave, or Tenth. Constructor takes an integer or string specifying the interval and direction. The interval is not specified in half-steps, but in numeric values derived from interval names: a Third is 3; a Seventh is 7, etc. String values for interval names (‘3rd’ or ‘third’) are accepted. staffDistance: the number of lines or spaces apart; E.g. C4 to C4 = 0; C4 to D4 = 1; C4 to B3 = -1
>>> aInterval = GenericInterval(3)
>>> aInterval.direction
1
>>> aInterval.perfectable
False
>>> aInterval.staffDistance
2
>>> aInterval = GenericInterval('Third')
>>> aInterval.staffDistance
2
>>> aInterval = GenericInterval(-12)
>>> aInterval.niceName
'Twelfth'
>>> aInterval.perfectable
True
>>> aInterval.staffDistance
-11
>>> aInterval.mod7
4
>>> bInterval = aInterval.complement()
>>> bInterval.staffDistance
3
>>> aInterval = GenericInterval('descending twelfth')
>>> aInterval.perfectable
True
>>> aInterval.staffDistance
-11
>>> aInterval = GenericInterval(0)
Traceback (most recent call last):
IntervalException: The Zeroth is not an interval
>>> aInterval = GenericInterval(24)
>>> aInterval.niceName
'24'
GenericInterval attributes
Attributes inherited from Music21Object: classSortOrder, id
GenericInterval properties
Properties inherited from Music21Object: classes, duration, offset, parent, priority
GenericInterval methods
- complement()¶
Returns a new GenericInterval object where descending 3rds are 6ths, etc.
>>> aInterval = GenericInterval('Third') >>> aInterval.complement() <music21.interval.GenericInterval 6>
- getDiatonic(specifier)¶
Given a specifier, return a DiatonicInterval object. Specifier should be provided as a string name, such as ‘dd’, ‘M’, or ‘perfect’.
>>> aInterval = GenericInterval('Third') >>> aInterval.getDiatonic('major') <music21.interval.DiatonicInterval M3> >>> aInterval.getDiatonic('minor') <music21.interval.DiatonicInterval m3> >>> aInterval.getDiatonic('d') <music21.interval.DiatonicInterval d3> >>> aInterval.getDiatonic('a') <music21.interval.DiatonicInterval A3> >>> aInterval.getDiatonic(2) <music21.interval.DiatonicInterval M3> >>> bInterval = GenericInterval('fifth') >>> bInterval.getDiatonic('perfect') <music21.interval.DiatonicInterval P5>
- reverse()¶
Returns a new GenericInterval object that is inverted.
>>> aInterval = GenericInterval('Third') >>> aInterval.reverse() <music21.interval.GenericInterval -3> >>> aInterval = GenericInterval(-13) >>> aInterval.direction -1 >>> aInterval.reverse() <music21.interval.GenericInterval 13>Methods inherited from Music21Object: searchParentByAttr(), getContextAttr(), setContextAttr(), addContext(), addLocation(), addLocationAndParent(), freezeIds(), getContextByClass(), getOffsetBySite(), getSiteIds(), getSites(), hasContext(), isClass(), purgeLocations(), removeLocationBySite(), removeLocationBySiteId(), setOffsetBySite(), show(), unfreezeIds(), unwrapWeakref(), wrapWeakref(), write()