music21.tree.verticality¶

Object for dealing with vertical simultaneities in a fast way w/o Chord’s overhead.

Verticality¶

class music21.tree.verticality.Verticality(offset=None, overlapTimespans=(), startTimespans=(), stopTimespans=(), timespanTree=None)¶

A collection of information about elements that are sounding at a given offset or just finished at that offset or are continuing from before, etc..

Create a timespan-stream from a score:

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...        classList=(note.Note, chord.Chord))

Find the verticality at offset 6.5, or beat 2.5 of measure 2 (there’s a one beat pickup)

>>> verticality = scoreTree.getVerticalityAt(6.5)
>>> verticality
<music21.tree.verticality.Verticality 6.5 {E3 D4 G#4 B4}>

The representation of a verticality gives the pitches from lowest to highest (in sounding notes).

A verticality knows its offset, but because elements might end at different times, it doesn’t know its endTime

>>> verticality.offset
6.5
>>> verticality.endTime
Traceback (most recent call last):
AttributeError: 'Verticality' object has no attribute 'endTime'

However, we can find when the next verticality starts by looking at the nextVerticality

>>> nv = verticality.nextVerticality
>>> nv
<music21.tree.verticality.Verticality 7.0 {A2 C#4 E4 A4}>
>>> nv.offset
7.0

Or more simply:

>>> verticality.nextStartOffset
7.0

(There is also a previousVerticality, but not a previousStartOffset)

What we just demonstrated is actually very powerful: a Verticality keeps a record of exactly where it is in the timespanTree – scores can be recreated with this information.

Getting back to the task at hand, we can find all the PitchedTimespans (and from there the elements) that start at exactly 6.5. There’s one, it’s a passing tone D in the tenor. It lasts from offset 6.5 to offset 7.0, with respect to the beginning of the score, not to the beginning of the measure. That is to say, it’s an eighth note.

>>> verticality.startTimespans
(<PitchedTimespan (6.5 to 7.0) <music21.note.Note D>>,)

And we can get all the PitchedTimespans that were already sounding at the moment (that is to say, the non-passing tones):

>>> verticality.overlapTimespans
(<PitchedTimespan (6.0 to 7.0) <music21.note.Note B>>,
 <PitchedTimespan (6.0 to 7.0) <music21.note.Note G#>>,
 <PitchedTimespan (6.0 to 7.0) <music21.note.Note E>>)

And we can get all the things that stop right at this moment. It’s the E in the tenor preceding the passing tone D:

>>> verticality.stopTimespans
(<PitchedTimespan (6.0 to 6.5) <music21.note.Note E>>,)

Verticality bases

ProtoM21Object

Verticality read-only properties

Verticality.bassTimespan¶

Gets the bass timespan in this verticality.

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality = scoreTree.getVerticalityAt(1.0)
>>> verticality
<music21.tree.verticality.Verticality 1.0 {F#3 C#4 F#4 A4}>

>>> verticality.bassTimespan
<PitchedTimespan (1.0 to 2.0) <music21.note.Note F#>>

Verticality.beatStrength¶

Gets the beat strength of a verticality.

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality = scoreTree.getVerticalityAt(1.0)
>>> verticality.beatStrength
1.0

Note that it will return None if there are no startTimespans at this point:

>>> verticality = scoreTree.getVerticalityAt(1.25)
>>> verticality
<music21.tree.verticality.Verticality 1.25 {F#3 C#4 F#4 A4}>
>>> verticality.startTimespans
()
>>> verticality.beatStrength is None
True

Verticality.measureNumber¶

Gets the measure number of the verticality’s starting elements.

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality = scoreTree.getVerticalityAt(7.0)
>>> verticality.measureNumber
2

Verticality.nextStartOffset¶

Gets the next start-offset in the verticality’s offset-tree.

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality = scoreTree.getVerticalityAt(1.0)
>>> verticality.nextStartOffset
2.0

If a verticality has no tree attached, then it will return None

Verticality.nextVerticality¶

Gets the next verticality after a verticality.

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality = scoreTree.getVerticalityAt(1.0)
>>> print(verticality)
<music21.tree.verticality.Verticality 1.0 {F#3 C#4 F#4 A4}>

>>> nextVerticality = verticality.nextVerticality
>>> print(nextVerticality)
<music21.tree.verticality.Verticality 2.0 {G#3 B3 E4 B4}>

Verticality objects created by an offset-tree hold a reference back to that offset-tree. This means that they determine their next or previous verticality dynamically based on the state of the offset-tree only when asked. Because of this, it is safe to mutate the offset-tree by inserting or removing timespans while iterating over it.

>>> scoreTree.removeTimespanList(nextVerticality.startTimespans)
>>> verticality.nextVerticality
<music21.tree.verticality.Verticality 3.0 {A3 E4 C#5}>

Verticality.pitchClassSet¶

Gets a set of all pitches in a verticality with distinct pitchClasses

>>> n1 = note.Note('C4')
>>> n2 = note.Note('B#5')
>>> s = stream.Stream()
>>> s.insert(4.0, n1)
>>> s.insert(4.0, n2)
>>> scoreTree = s.asTimespans()
>>> verticality = scoreTree.getVerticalityAt(4.0)
>>> pitchSet = verticality.pitchSet
>>> list(sorted(pitchSet))
[<music21.pitch.Pitch C4>, <music21.pitch.Pitch B#5>]

PitchClassSet will return only one pitch. Which of these is returned is arbitrary.

>>> pitchClassSet = verticality.pitchClassSet
>>> list(sorted(pitchClassSet))
[<music21.pitch.Pitch B#5>]

Verticality.pitchSet¶

Gets the pitch set of all elements in a verticality.

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality = scoreTree.getVerticalityAt(1.0)
>>> for pitch in sorted(verticality.pitchSet):
...     pitch
...
<music21.pitch.Pitch F#3>
<music21.pitch.Pitch C#4>
<music21.pitch.Pitch F#4>
<music21.pitch.Pitch A4>

Verticality.previousVerticality¶

Gets the previous verticality before a verticality.

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality = scoreTree.getVerticalityAt(1.0)
>>> print(verticality)
<music21.tree.verticality.Verticality 1.0 {F#3 C#4 F#4 A4}>

>>> previousVerticality = verticality.previousVerticality
>>> print(previousVerticality)
<music21.tree.verticality.Verticality 0.5 {G#3 B3 E4 B4}>

Continue it:

>>> v = scoreTree.getVerticalityAt(1.0)
>>> while v is not None:
...     print(v)
...     v = v.previousVerticality
<music21.tree.verticality.Verticality 1.0 {F#3 C#4 F#4 A4}>
<music21.tree.verticality.Verticality 0.5 {G#3 B3 E4 B4}>
<music21.tree.verticality.Verticality 0.0 {A3 E4 C#5}>

Verticality objects created by an offset-tree hold a reference back to that offset-tree. This means that they determine their next or previous verticality dynamically based on the state of the offset-tree only when asked. Because of this, it is safe to mutate the offset-tree by inserting or removing timespans while iterating over it.

>>> scoreTree.removeTimespanList(previousVerticality.startTimespans)
>>> verticality.previousVerticality
<music21.tree.verticality.Verticality 0.0 {A3 E4 C#5}>

Verticality.startAndOverlapTimespans¶

Return a tuple adding the start and overlap timespans into one.

>>> n1 = note.Note('C4')
>>> n2 = note.Note('D4')
>>> s = stream.Stream()
>>> s.insert(4.0, n1)
>>> s.insert(4.5, n2)
>>> scoreTree = s.asTimespans()
>>> verticality = scoreTree.getVerticalityAt(4.5)
>>> verticality.startTimespans
(<PitchedTimespan (4.5 to 5.5) <music21.note.Note D>>,)

>>> verticality.overlapTimespans
(<PitchedTimespan (4.0 to 5.0) <music21.note.Note C>>,)

>>> verticality.startAndOverlapTimespans
(<PitchedTimespan (4.5 to 5.5) <music21.note.Note D>>,
 <PitchedTimespan (4.0 to 5.0) <music21.note.Note C>>)

>>> verticality = scoreTree.getVerticalityAt(4.0)
>>> verticality.startAndOverlapTimespans
(<PitchedTimespan (4.0 to 5.0) <music21.note.Note C>>,)

Verticality.timeToNextEvent¶

Returns a float or Fraction of the quarterLength to the next event (usually the next Verticality, but also to the end of the piece).

Returns None if there is no next event, such as when the verticality is divorced from its tree.

Read-only properties inherited from ProtoM21Object:

classSet

classes

Verticality methods

Verticality.getAllVoiceLeadingQuartets(*, includeRests=True, includeOblique=True, includeNoMotion=False, returnObjects=True, partPairNumbers=None)¶

>>> c = corpus.parse('luca/gloria').measures(1, 8)
>>> tsCol = tree.fromStream.asTimespans(c, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality22 = tsCol.getVerticalityAt(22.0)

>>> from pprint import pprint as pp
>>> for vlq in verticality22.getAllVoiceLeadingQuartets():
...     pp(vlq)
<music21.voiceLeading.VoiceLeadingQuartet
    v1n1=G4, v1n2=C4, v2n1=E4, v2n2=F4>
<music21.voiceLeading.VoiceLeadingQuartet
    v1n1=G4, v1n2=C4, v2n1=A3, v2n2=A3>
<music21.voiceLeading.VoiceLeadingQuartet
    v1n1=E4, v1n2=F4, v2n1=A3, v2n2=A3>

>>> for vlq in verticality22.getAllVoiceLeadingQuartets(includeRests=False):
...     pp(vlq)
<music21.voiceLeading.VoiceLeadingQuartet
    v1n1=E4, v1n2=F4, v2n1=A3, v2n2=A3>
>>> for vlq in verticality22.getAllVoiceLeadingQuartets(includeOblique=False):
...     pp(vlq)
<music21.voiceLeading.VoiceLeadingQuartet
    v1n1=G4, v1n2=C4, v2n1=E4, v2n2=F4>
>>> verticality22.getAllVoiceLeadingQuartets(includeOblique=False, includeRests=False)
[]

Raw output

>>> for vlqRaw in verticality22.getAllVoiceLeadingQuartets(returnObjects=False):
...     pp(vlqRaw)
((<PitchedTimespan (19.5 to 21.0) <music21.note.Note G>>,
  <PitchedTimespan (22.0 to 22.5) <music21.note.Note C>>),
 (<PitchedTimespan (21.0 to 22.0) <music21.note.Note E>>,
  <PitchedTimespan (22.0 to 23.0) <music21.note.Note F>>))
((<PitchedTimespan (19.5 to 21.0) <music21.note.Note G>>,
  <PitchedTimespan (22.0 to 22.5) <music21.note.Note C>>),
 (<PitchedTimespan (21.5 to 22.5) <music21.note.Note A>>,
  <PitchedTimespan (21.5 to 22.5) <music21.note.Note A>>))
((<PitchedTimespan (21.0 to 22.0) <music21.note.Note E>>,
  <PitchedTimespan (22.0 to 23.0) <music21.note.Note F>>),
 (<PitchedTimespan (21.5 to 22.5) <music21.note.Note A>>,
  <PitchedTimespan (21.5 to 22.5) <music21.note.Note A>>))

>>> for vlq in verticality22.getAllVoiceLeadingQuartets(partPairNumbers=[(0, 1)]):
...     pp(vlq)
<music21.voiceLeading.VoiceLeadingQuartet
    v1n1=G4, v1n2=C4, v2n1=E4, v2n2=F4>

>>> for vlq in verticality22.getAllVoiceLeadingQuartets(partPairNumbers=[(0, 2), (1, 2)]):
...     pp(vlq)
<music21.voiceLeading.VoiceLeadingQuartet
    v1n1=G4, v1n2=C4, v2n1=A3, v2n2=A3>
<music21.voiceLeading.VoiceLeadingQuartet
    v1n1=E4, v1n2=F4, v2n1=A3, v2n2=A3>

Changed in v8: all parameters are keyword only.

Verticality.getPairedMotion(includeRests=True, includeOblique=True)¶

Get a list of two-element tuples that are in the same part [TODO: or containing stream??] and which move at this verticality.

>>> c = corpus.parse('luca/gloria').measures(1, 8)
>>> tsCol = tree.fromStream.asTimespans(c, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality22 = tsCol.getVerticalityAt(22.0)
>>> for pm in verticality22.getPairedMotion():
...     print(pm)
(<PitchedTimespan (19.5 to 21.0) <music21.note.Note G>>,
 <PitchedTimespan (22.0 to 22.5) <music21.note.Note C>>)
(<PitchedTimespan (21.0 to 22.0) <music21.note.Note E>>,
 <PitchedTimespan (22.0 to 23.0) <music21.note.Note F>>)
(<PitchedTimespan (21.5 to 22.5) <music21.note.Note A>>,
 <PitchedTimespan (21.5 to 22.5) <music21.note.Note A>>)

Note that the second pair contains a one-beat rest at 21.0-22.0; so includeRests=False will get rid of that:

>>> for pm in verticality22.getPairedMotion(includeRests=False):
...     print(pm)
(<PitchedTimespan (21.0 to 22.0) <music21.note.Note E>>,
 <PitchedTimespan (22.0 to 23.0) <music21.note.Note F>>)
(<PitchedTimespan (21.5 to 22.5) <music21.note.Note A>>,
 <PitchedTimespan (21.5 to 22.5) <music21.note.Note A>>)

Oblique here means a pair that does not move (it could be called noMotion, because there’s no motion here in a two-note pair, but we still call it includeOblique so it’s consistent with getAllVoiceLeadingQuartets).

>>> for pm in verticality22.getPairedMotion(includeOblique=False):
...     print(pm)
(<PitchedTimespan (19.5 to 21.0) <music21.note.Note G>>,
 <PitchedTimespan (22.0 to 22.5) <music21.note.Note C>>)
(<PitchedTimespan (21.0 to 22.0) <music21.note.Note E>>,
 <PitchedTimespan (22.0 to 23.0) <music21.note.Note F>>)

>>> for pm in verticality22.getPairedMotion(includeOblique=False, includeRests=False):
...     print(pm)
(<PitchedTimespan (21.0 to 22.0) <music21.note.Note E>>,
 <PitchedTimespan (22.0 to 23.0) <music21.note.Note F>>)

Verticality.makeElement(quarterLength: int | float | Fraction | None = None, *, addTies=True, addPartIdAsGroup=False, removeRedundantPitches=True, gatherArticulations='single', gatherExpressions='single', copyPitches=True) → Rest | Chord¶

Makes a Chord or Rest from this verticality and quarterLength.

>>> score = tree.makeExampleScore()
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality = scoreTree.getVerticalityAt(4.0)
>>> verticality
<music21.tree.verticality.Verticality 4.0 {E#3 G3}>
>>> verticality.startTimespans
(<PitchedTimespan (4.0 to 5.0) <music21.note.Note G>>,
 <PitchedTimespan (4.0 to 6.0) <music21.note.Note E#>>)

>>> el = verticality.makeElement(2.0)
>>> el
<music21.chord.Chord E#3 G3>
>>> el.duration.quarterLength
2.0
>>> el.duration.type
'half'

If there is nothing there, then a Rest is created

>>> verticality = scoreTree.getVerticalityAt(400.0)
>>> verticality
<music21.tree.verticality.Verticality 400.0 {}>
>>> el = verticality.makeElement(1/3)
>>> el
<music21.note.Rest 1/3ql>
>>> el.duration.fullName
'Eighth Triplet (1/3 QL)'

>>> n1 = note.Note('C4')
>>> n2 = note.Note('C4')
>>> s = stream.Score()
>>> s.insert(0, n1)
>>> s.insert(0.5, n2)
>>> scoreTree = s.asTimespans()
>>> verticality = scoreTree.getVerticalityAt(0.5)
>>> c = verticality.makeElement(0.5)
>>> c
<music21.chord.Chord C4>

>>> c = verticality.makeElement(0.5, removeRedundantPitches=False)
>>> c
<music21.chord.Chord C4 C4>

Generally the pitches of the new element are not connected to the original pitch:

>>> c[0].pitch.name = 'E'
>>> c[1].pitch.name = 'F'
>>> (n1.name, n2.name)
('C', 'C')

But if copyPitches is False then the original pitch will be used:

>>> n1.name = 'D'
>>> n2.name = 'E'
>>> c = verticality.makeElement(0.5, removeRedundantPitches=False, copyPitches=False)
>>> c
<music21.chord.Chord D4 E4>

>>> c[0].pitch.name = 'F'
>>> c[1].pitch.name = 'G'
>>> (n1.name, n2.name)
('F', 'G')

gatherArticulations and gatherExpressions can be True, False, or (default) ‘single’.

If False, no articulations (or expressions) are transferred to the chord.
If True, all articulations are transferred to the chord.
If ‘single’, then no more than one articulation of each class (chosen from the lowest note) will be added. This way, the chord does not get 4 fermatas, etc.

>>> n1 = note.Note('C4')
>>> n2 = note.Note('D4')
>>> s = stream.Stream()
>>> s.insert(0, n1)
>>> s.insert(0.5, n2)

>>> class AllAttachArticulation(articulations.Articulation):
...     def __init__(self):
...         super().__init__()
...         self.tieAttach = 'all'

>>> class OtherAllAttachArticulation(articulations.Articulation):
...     def __init__(self):
...         super().__init__()
...         self.tieAttach = 'all'

>>> n1.articulations.append(articulations.Accent())
>>> n1.articulations.append(AllAttachArticulation())
>>> n1.expressions.append(expressions.Fermata())

>>> n2.articulations.append(articulations.Staccato())
>>> n2.articulations.append(AllAttachArticulation())
>>> n2.articulations.append(OtherAllAttachArticulation())
>>> n2.expressions.append(expressions.Fermata())

>>> scoreTree = s.asTimespans()

>>> verticality = scoreTree.getVerticalityAt(0.0)
>>> c = verticality.makeElement(1.0)
>>> c.expressions
[<music21.expressions.Fermata>]
>>> c.articulations
[<music21.articulations.Accent>, <...AllAttachArticulation>]

>>> verticality = scoreTree.getVerticalityAt(0.5)

Here there will be no expressions, because there is no note ending at 0.75 and Fermatas attach to the last note:

>>> c = verticality.makeElement(0.25)
>>> c.expressions
[]

>>> c = verticality.makeElement(0.5)
>>> c.expressions
[<music21.expressions.Fermata>]

Only two articulations, since accent attaches to beginning and staccato attaches to last and we are beginning after the start of the first note (with an accent) and cutting right through the second note (with a staccato)

>>> c.articulations
[<...AllAttachArticulation>,
 <...OtherAllAttachArticulation>]

>>> c = verticality.makeElement(0.5, gatherArticulations=True)
>>> c.articulations
[<...AllAttachArticulation>,
 <...AllAttachArticulation>,
 <...OtherAllAttachArticulation>]

>>> c = verticality.makeElement(0.5, gatherArticulations=False)
>>> c.articulations
[]

>>> verticality = scoreTree.getVerticalityAt(1.0)
>>> c = verticality.makeElement(0.5)
>>> c.expressions
[<music21.expressions.Fermata>]
>>> c.articulations
[<music21.articulations.Staccato>,
 <...AllAttachArticulation>,
 <...OtherAllAttachArticulation>]

New in v6.3: copyPitches option

Verticality.toChord()¶

Creates a chord.Chord object of default length (1.0 or the duration of some note object) from the verticality.

Does nothing about ties, etc. – it’s a very dumb chord, but useful for querying consonance, etc. See makeElement() for the smart version.

It may be a zero- or one-pitch chord.

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = score.asTimespans()
>>> verticality = scoreTree.getVerticalityAt(4.0)
>>> verticality.toChord()
<music21.chord.Chord G#3 B3 E4 E5>

Methods inherited from ProtoM21Object:

isClassOrSubclass()

Verticality instance variables

Verticality.offset¶

Gets the start offset of a verticality.

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality = scoreTree.getVerticalityAt(1.0)
>>> verticality
<music21.tree.verticality.Verticality 1.0 {F#3 C#4 F#4 A4}>
>>> verticality.offset
1.0

Verticality.overlapTimespans¶

Gets timespans overlapping the start offset of a verticality.

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality = scoreTree.getVerticalityAt(0.5)
>>> verticality
<music21.tree.verticality.Verticality 0.5 {G#3 B3 E4 B4}>
>>> verticality.overlapTimespans
(<PitchedTimespan (0.0 to 1.0) <music21.note.Note E>>,)

Verticality.startTimespans¶

Gets the timespans starting at a verticality’s start offset.

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...            classList=(note.Note, chord.Chord))
>>> verticality = scoreTree.getVerticalityAt(1.0)
>>> verticality
<music21.tree.verticality.Verticality 1.0 {F#3 C#4 F#4 A4}>
>>> for timespan in verticality.startTimespans:
...     timespan
...
<PitchedTimespan (1.0 to 2.0) <music21.note.Note A>>
<PitchedTimespan (1.0 to 2.0) <music21.note.Note F#>>
<PitchedTimespan (1.0 to 2.0) <music21.note.Note C#>>
<PitchedTimespan (1.0 to 2.0) <music21.note.Note F#>>

Verticality.stopTimespans¶

Gets the timespans stopping at a verticality’s start offset.

>>> score = corpus.parse('bwv66.6')
>>> scoreTree = tree.fromStream.asTimespans(score, flatten=True,
...                classList=(note.Note, chord.Chord))
>>> verticality = scoreTree.getVerticalityAt(1.0)
>>> verticality
<music21.tree.verticality.Verticality 1.0 {F#3 C#4 F#4 A4}>

Note that none of the elements in the stopTimespans are listed in the repr for the Verticality

>>> for timespan in verticality.stopTimespans:
...     timespan
...
<PitchedTimespan (0.0 to 1.0) <music21.note.Note E>>
<PitchedTimespan (0.5 to 1.0) <music21.note.Note B>>
<PitchedTimespan (0.5 to 1.0) <music21.note.Note B>>
<PitchedTimespan (0.5 to 1.0) <music21.note.Note G#>>