TemporalUnit

TemporalUnit(count: int, base: Measurable)

A length of musical time defined as n number of a Measurable Duration. This is used to represent (among other things) time signatures and tuple definitions.

Example: WSMN Time Signatures

A time signature has: - a numerator (top number), which defines “how many” of some MetricalDuration. - a denominator (bottom number), which defines some MetricalDuration.

So 4/4 time is 4 quarter notes and is expressed as:

>>> from openmusickit.systems.wsmn.temporal.metrical_duration import MetricalDuration
>>> TemporalUnit(4, MetricalDuration(1, 4)).rational_length
Fraction(1, 1)

Compound meters such as 6/8 can be expressed using the dotted duration or the base duration:

>>> TemporalUnit(6, MetricalDuration(1, 8)) == TemporalUnit(2, MetricalDuration(1, 4, dots=1))
True

More exotic time signatures can be achieved by using tupleted durations as the denominator.

Tuplets

Musically, a tuplet is defined as a ratio of notated notes (expressed as nominal Durations) to the amount of time those notes take up as expressed in the surrounding musical context.

A standard quarter note triplet, then, is: - three quarter notes, which take up the time of - two quarter notes.

Each of these (nominal and actual) is defined as a TemporalUnit, and combined into a tuplet definition using a TemporalRatio.

Attributes

Name	Description
`__slots__`
count
base
temporal_system
rational_length	The count times the base: three eighths are three eighths of a whole note.

Methods

Name	Description
`__eq__`
`__lt__`	Shorter than `other`, by rational length, within compatible systems.
`__hash__`
scale	Scale the Temporal Unit.
`__repr__`

`eq`

__eq__(other)

`lt`

__lt__(other)

Shorter than other, by rational length, within compatible systems.

>>> from openmusickit.systems.wsmn.temporal.symbols import quarter, dotted_quarter
>>> quarter < dotted_quarter, dotted_quarter < quarter
(True, False)

`hash`

__hash__()

scale

scale(scalar: int | Fraction)

Scale the Temporal Unit.

The count is scaled whenever the result is a whole number (4 quarters * 2 = 8 quarters; 6 eighths / 2 = 3 eighths). Otherwise the remaining factor is pushed into the base duration (3 eighths / 2 = 3 sixteenths; 1 quarter * 3/2 = 3 eighths; 4 quarters / 3 = 4 triplet eighths, if the base supports tuplets).

>>> from openmusickit.systems.wsmn.temporal.symbols import quarter, eighth
>>> TemporalUnit(4, quarter).scale(2)
TemporalUnit(8, MetricalDuration(1, 4))
>>> TemporalUnit(3, eighth).scale(Fraction(1, 2))
TemporalUnit(3, MetricalDuration(1, 16))
>>> TemporalUnit(4, quarter).scale(Fraction(1, 3)).base.rational_length
Fraction(1, 12)

Raises

Name	Type	Description
	ScalingError	if the scalar is not positive, or if the base cannot absorb the leftover factor.

`repr`

__repr__()