User’s Guide: Chapter 14: Time Signatures and Beats

Up until now almost all the music we’ve been working with has been in 4/4. That’s not because we love common time so much, but simply because as we noted in Chapter 4 it’s because 4/4 is the default time signature for music21 Stream objects that don’t have another time signature applied to them.

In general, TimeSignature objects are found within Measure objects (a Stream subclass). However, in some cases TimeSignature objects can exist directly on a Stream.

TimeSignature objects, as a subclass of the Music21Object, have an offset and can be positioned anywhere on a Stream. When placed in a Measure, TimeSignature objects are often placed at the start, or zero offset position. The Measure property timeSignature can be used to set or get a TimeSignature at the zero offset position. If a Measure does not have a TimeSignature, the timeSignature property returns None.

Everything that we need to use other time signatures is contained in the meter module, which is imported when you type from music21 import *. There are lots of things in that module, but the one that we care about most is the TimeSignature object. Let’s create a couple of notes and a TimeSignature object.

from music21 import *

noteC = note.Note('C4', type='half')
noteD = note.Note('D4', type='quarter')
noteE = note.Note('E4', type='quarter')
noteF = note.Note('F4', type='half')

tsThreeFour = meter.TimeSignature('3/4')

print(tsThreeFour.numerator, '/',  tsThreeFour.denominator)

 3 / 4

There’s also an easy way of getting this string, call .ratioString:

tsThreeFour.ratioString

 '3/4'

Now that we have our objects, let’s create a Stream object that uses these notes and the TimeSignature object. We’ll append each object in order using a for loop:

stream1 = stream.Stream()

for thisThing in [tsThreeFour, noteC, noteD, noteE, noteF]:
    stream1.append(thisThing)

Let’s look at stream1 using .show('text'):

stream1.show('text')

 {0.0} <music21.meter.TimeSignature 3/4>
 {0.0} <music21.note.Note C>
 {2.0} <music21.note.Note D>
 {3.0} <music21.note.Note E>
 {4.0} <music21.note.Note F>

Wondering why both the time signature and the first note begin at offset 0.0 in the Stream? That’s because by default TimeSignature objects have no length:

tsThreeFour.duration.quarterLength

 0.0

If we show() the Stream without using show('text'), we see that there are two measures of 3/4:

stream1.show()

The TimeSignature object helps the display module known how to divide the Stream into Measure objects. We can see this process directly if we create a new Stream from stream1 that has measures using the makeMeasures() command:

stream2 = stream1.makeMeasures()
stream2.show('text')

 {0.0} <music21.stream.Measure 1 offset=0.0>
     {0.0} <music21.clef.TrebleClef>
     {0.0} <music21.meter.TimeSignature 3/4>
     {0.0} <music21.note.Note C>
     {2.0} <music21.note.Note D>
 {3.0} <music21.stream.Measure 2 offset=3.0>
     {0.0} <music21.note.Note E>
     {1.0} <music21.note.Note F>
     {3.0} <music21.bar.Barline type=final>

The makeMeasures command, by the way, also put a TrebleClef into the Stream and set the last barline to “final”, which makes its output a little prettier in Lilypond (which is what the documentation uses; you are probably using MusicXML if you’re following along, which gets it right…)

stream2.show()

Time signatures have a .symbol setting that can be used to change the display of certain common duple signatures:

s = stream.Stream()
ts0 = meter.TimeSignature('4/4')
ts1 = meter.TimeSignature('4/4')
ts1.symbol = 'common'
ts2 = meter.TimeSignature('2/2')
ts3 = meter.TimeSignature('2/2')
ts3.symbol = 'cut'
s.append(ts0)
s.append(note.Note('C5', type='whole'))
s.append(ts1)
s.append(note.Note('B4', type='whole'))
s.append(ts2)
s.append(note.Note('A4', type='whole'))
s.append(ts3)
s.append(note.Note('G4', type='whole'))
s.makeMeasures(inPlace=True)
s.show()

Working with Beats in TimeSignatures

Beyond just getting nicely formed measures, TimeSignature objects let us figure out information about what beat each Note (or Rest or Chord, etc.) is on. Let’s return to our Stream without measures and look at each note’s beat:

stream1.notes[0]

 <music21.note.Note C>

stream1.notes[0].beat

 1.0

Okay, so the first note is on beat 1 (represented as 1.0 here). That’s different from its offset which is 0.0. Remember that the offset is the number of quarter notes from the beginning of the containing Stream. The beat on the other hand uses notation that is more familiar to musicians. Let’s look at the beat of all the notes in the Stream:

for n in stream1.notes:
    print(n, n.beat)

 <music21.note.Note C> 1.0
 <music21.note.Note D> 3.0
 <music21.note.Note E> 1.0
 <music21.note.Note F> 2.0

If we only wanted to find notes that were on the downbeat we could filter on beats like so:

for n in stream1.notes:
    if n.beat == 1.0:
        print(n)

 <music21.note.Note C>
 <music21.note.Note E>

What would happen if the time signature were different? We can find out by changing the TimeSignature object already in the Stream:

tsThreeFour.ratioString

 '3/4'

tsThreeFour.ratioString = '2/4'

Now the variable name of the TimeSignature object makes little sense, but we do find that the first, second, and fourth notes are on the downbeat.

for n in stream1.notes:
    print(n, n.beat)

 <music21.note.Note C> 1.0
 <music21.note.Note D> 1.0
 <music21.note.Note E> 2.0
 <music21.note.Note F> 1.0

If we change the TimeSignature again to 6/8 then the same notes will be on the downbeat as in the original 3/4 Stream, but they will have different beat numbers. This time we’ll use the numerator and denominator to change the meter. (Remember that all these different tricks are documented in full at music21.meter.TimeSignature.

tsThreeFour.numerator = 6
tsThreeFour.denominator = 8
tsThreeFour

 <music21.meter.TimeSignature 6/8>

stream1.show()

for n in stream1.notes:
    print(n, n.beat)

 <music21.note.Note C> 1.0
 <music21.note.Note D> 7/3
 <music21.note.Note E> 1.0
 <music21.note.Note F> 5/3

There is also a variation of .beat on every Music21Object called .beatStr which returns a string which might look more normal to a musician.

for n in stream1.notes:
    print(n, n.beatStr)

 <music21.note.Note C> 1
 <music21.note.Note D> 2 1/3
 <music21.note.Note E> 1
 <music21.note.Note F> 1 2/3

Notice that by default 6/8 is assumed to be a “fast” 6/8, that is, having two beats and not six per measure. That’s because there’s no easy way to specify the former. We can see how many beats there are per measure by requesting the beatCount of a TimeSignature:

tsThreeFour.beatCount

 2

And we can change that and see how it affects the results:

tsThreeFour.beatCount = 6

for n in stream1.notes:
    print(n, n.beat)

 <music21.note.Note C> 1.0
 <music21.note.Note D> 5.0
 <music21.note.Note E> 1.0
 <music21.note.Note F> 3.0

Using the terminology most musicians use, you can create TimeSignatures of 6/8 with either beat count directly:

tsFast68 = meter.TimeSignature('fast 6/8')
tsSlow68 = meter.TimeSignature('slow 6/8')

tsFast68.beatCount, tsSlow68.beatCount

 (2, 6)

Working with TimeSignatures in scores

We have been dealing with TimeSignature objects that are in a single Stream. However, in general, TimeSignature objects are found within Measure objects inside a Part object. Both Measure and Part are subclasses of Stream. Let’s get a Bach chorale with some nice eighth-note runs from the music21.corpus module’s parse() function. It returns a Score, which is also a Stream subclass.

myBach = corpus.parse('bach/bwv57.8')

print(myBach.__class__)

 <class 'music21.stream.base.Score'>

We will get the Alto part using the Score object’s parts list:

alto = myBach.parts['Alto']

alto

 <music21.stream.Part Alto>

When we call .show() on this Part (or on myBach itself), we can see that this is one of the few chorales that Bach wrote that is in 3/4:

alto.show()

To examine the TimeSignature object active for this part, there are a few approaches. One method is to simply search for the class within all objects in the Part, or the flattened Part Stream representation. Remember that a Part is generally built of Measures, or Stream-embedded containers. To get all the elements in the Stream we can use the flatten property, and then search for a class with the getElementsByClass() method. This returns a new Stream containing all found classes. The first element in this Stream is the TimeSignature.

alto.recurse().getElementsByClass(meter.TimeSignature)[0]

 <music21.meter.TimeSignature 3/4>

len(alto.recurse().getElementsByClass(meter.TimeSignature))

 1

We see that there is exactly one TimeSignatures in the Part.

Alternatively, we can look at the first Measure in the Stream, and examine the timeSignature property.

alto.measure(1).timeSignature

 <music21.meter.TimeSignature 3/4>

Other measures don’t have TimeSignature objects:

alto.measure(7).timeSignature is None

 True

Let’s change that!

alto.measure(7).timeSignature = meter.TimeSignature('6/8')

Now we’ll rebeam according to the new TimeSignatures:

alto.makeBeams(inPlace=True)

We’ll clear all the stem directions so that we don’t get really screwy beams, and then show the new score.

for n in alto.recurse().notes:
    n.stemDirection = None

alto.show()

We’ve sort of cheated by changing the TimeSignature to something that kept all the measure lengths the same. Let’s rebar everything. First we’ll flatten the alto part and then get everything that is NOT a TimeSignature. We will use getElementsNotOfClass() and can either pass it the string “TimeSignature” as we did with “getElementsByClass” above, or for either method we can pass in a class object, which we’ll do here:

newAlto = alto.flatten().getElementsNotOfClass([meter.TimeSignature,
                                                layout.LayoutBase]
                                              ).stream()
newAlto.insert(0, meter.TimeSignature('2/4'))

If we make some measures from this, we’ll see that there are problems around mm. 2-3

newAlto.makeMeasures(inPlace=True)
newAlto.measures(1, 4).show('text', addEndTimes=True)

 {0.0 - 2.0} <music21.stream.Measure 1 offset=0.0>
     {0.0 - 0.0} <music21.instrument.Instrument 'P2: Alto: '>
     {0.0 - 0.0} <music21.clef.TrebleClef>
     {0.0 - 0.0} <music21.key.Key of B- major>
     {0.0 - 0.0} <music21.meter.TimeSignature 2/4>
     {0.0 - 1.0} <music21.note.Note F>
     {1.0 - 2.0} <music21.note.Note F>
 {2.0 - 4.5} <music21.stream.Measure 2 offset=2.0>
     {0.0 - 1.0} <music21.note.Note F>
     {1.0 - 2.5} <music21.note.Note F>
 {4.0 - 6.0} <music21.stream.Measure 3 offset=4.0>
     {0.5 - 1.0} <music21.note.Note F>
     {1.0 - 2.0} <music21.note.Note G>
 {6.0 - 8.0} <music21.stream.Measure 4 offset=6.0>
     {0.0 - 1.0} <music21.note.Note C>
     {1.0 - 2.0} <music21.note.Note C>

Whoops! The last F of measure 2 is actually too long, and the next measure’s first F begins half a beat later. Let’s run the powerful command makeNotation() first before showing:

newAltoFixed = newAlto.makeNotation()
newAltoFixed.show()

We can continue to add multiple TimeSignature objects to this Stream of Notes. First, we will replace the 2/4 bar previously added with a new TimeSignature, using the Stream replace() method. Then, we will insert a number of additional TimeSignature objects at offsets further into the Stream. We will use a flat stream that has no measures, so temporary Measures are automatically created when calling the show()method.

newFlatAlto = newAlto.flatten()
ts = newFlatAlto.getTimeSignatures()[0]
ts

 <music21.meter.TimeSignature 2/4>

newFlatAlto.replace(ts, meter.TimeSignature('5/8'))
newFlatAlto.getTimeSignatures()[0]

 <music21.meter.TimeSignature 5/8>

newFlatAlto.insert(10.0, meter.TimeSignature('7/8'))
newFlatAlto.insert(17.0, meter.TimeSignature('9/8'))
newFlatAlto.insert(26.0, meter.TimeSignature('3/8'))

Now we can makeNotation() again and show this wacky interpretation of Bach:

newFlatAlto.makeNotation().show()

A quick note: If you only want to gather Notes, Rests, or other subclasses of GeneralNote, but don’t mind losing other information as such the KeySignature and Instrument objects, then you achieve the same change in time signature using the notesAndRests property. (Otherwise, it’s best to stick with the getElementsNotOfClass() method).

newAlto = alto.flatten().notesAndRests.stream()
newAlto.insert(0.0, meter.TimeSignature('5/8'))
newAlto.insert(10.0, meter.TimeSignature('7/8'))
newAlto.insert(17.0, meter.TimeSignature('9/8'))
newAlto.insert(26.0, meter.TimeSignature('3/8'))
newAlto.makeNotation().show()

Let’s see how that looks in all the parts by putting the time signatures in their “proper” place in every Part. First, lets get all the TimeSignature objects in the score with .getElementsByClass('TimeSignature') or, even better, the shortcut, getTimeSignatures(). This only works because we already flattened Alto to make newAlto

tsList = newAlto.getTimeSignatures()

tsList is a Part object so we can show it:

print(tsList.__class__)
tsList.show('text')

 <class 'music21.stream.base.Part'>
 {0.0} <music21.meter.TimeSignature 5/8>
 {10.0} <music21.meter.TimeSignature 7/8>
 {17.0} <music21.meter.TimeSignature 9/8>
 {26.0} <music21.meter.TimeSignature 3/8>

Now we’ll create a new Score object and flatten all the parts from the original myBach and get everything but the TimeSignature objects, run .makeNotation() and put it in the new score:

newScore = stream.Score()

for part in myBach.parts:
    flatPart = part.flatten()
    noTSPart = flatPart.getElementsNotOfClass('TimeSignature').stream()
    for ts in tsList:
        noTSPart.insert(ts.offset, ts)
    noTSPart.makeNotation(inPlace=True)
    newScore.insert(0, noTSPart)

newScore.measures(1, 10).show()

Working with Beats in a score

If a Note is in a Measure, and that Measure or a preceding Measure has a TimeSignature, it is possible to find the beat, or the position of the Note in terms of the count of whole or fractional subdivisions of top-level beat partitions.

The Note beat property will return, if available, a numerical representation of the beat, with a floating point value corresponding to the proportional position through the beat. The Note beatStr property returns a string representation, replacing floating point values with fractions when available.

Let’s see what we can do with beats in our same Bach score. Let’s use the beatStr for “beat string” tag to get a nicely formatted measure of the beat for each note in the Soprano part:

sopr = myBach.parts['Soprano'].measures(1,2)

for n in sopr.recurse().notes:
    print(n, n.beatStr)

 <music21.note.Note B-> 1
 <music21.note.Note B-> 2
 <music21.note.Note F> 3
 <music21.note.Note D> 1
 <music21.note.Note C> 2 1/2
 <music21.note.Note B-> 3

Instead of just printing that though, let’s put the beatStr as a lyric on each note:

for n in sopr.recurse().notes:
    n.addLyric(n.beatStr)

sopr.show()

If we change the TimeSignature in a Part, the beat counts will reflect this change. For example, if the Bass part of the same chorale is re-barred in 6/8, new, syncopated beat counts will be given.

bass = myBach.getElementById('Bass')
newBass = bass.flatten().getElementsNotOfClass(meter.TimeSignature).stream()
newMeasures = newBass.makeMeasures(meter.TimeSignature('6/8'))
newMeasures.makeTies(inPlace=True)
for n in newMeasures.recurse().notesAndRests:
    n.addLyric(n.beatStr)
newMeasures.show()

Each note also has a particular beatStrength that shows how metrically accented music21 thinks it is, with 1.0 being most accented and 0 being least.

for n in sopr.recurse().notes:
    print(n, n.beatStrength)

 <music21.note.Note B-> 1.0
 <music21.note.Note B-> 0.5
 <music21.note.Note F> 0.5
 <music21.note.Note D> 1.0
 <music21.note.Note C> 0.25
 <music21.note.Note B-> 0.5

This chapter gives a solid introduction to the types of things you can do with TimeSignatures and beats. We will return again to this topic later in the User’s Guide to show how beaming, accentuation, and other elements can be controlled through meter and TimeSignature objects. But time is not the only thing to have a signature. Chapter 15, Keys and Key Signatures will guide you through working with KeySignature and Key objects.