TimeSignature.simplify_ratio

TimeSignature.simplify_ratio(*, min_denominator: int = 4) → None

Simplifies the ratio of an abjad.TimeSignature according to a minimum denominator value. Mutates the ratio in place and has no return value. Note that Auxjad adds this function as an extension method to abjad.TimeSignature (see usage below).

Basic usage:

By default, this method simplifies the ratio of numerator / denominator using a minimum denominator value of 4 (that is, the denominator will not get smaller than 4). In the case below, (2, 4) is the simplest representation of the ratio (4, 8) with a denominator equal to or larger than 4.

>>> time_signature = abjad.TimeSignature((4, 8))
>>> time_signature.simplify_ratio()
>>> time_signature
abjad.TimeSignature((2, 4))
>>> time_signature = abjad.TimeSignature((1, 1))
>>> time_signature.simplify_ratio()
>>> time_signature
abjad.TimeSignature((4, 4))

If a ratio cannot be simplified at all, the function returns a time signature with the original ratio.

>>> time_signature = abjad.TimeSignature((7, 8))
>>> time_signature.simplify_ratio()
>>> time_signature
abjad.TimeSignature((7, 8))

It also simplifies ratios even if the minimum denominator cannot be reached.

>>> time_signature = abjad.TimeSignature((10, 16))
>>> time_signature.simplify_ratio()
>>> time_signature
abjad.TimeSignature((5, 8))

min_denominator:

The min_denominator can be set to values other than 4. If set to 2, the simplest representaion of the ratio (4, 8) becomes (1, 2).

>>> time_signature = abjad.TimeSignature((4, 8))
>>> time_signature.simplify_ratio(min_denominator=2)
>>> time_signature
abjad.TimeSignature((1, 2))
>>> time_signature = abjad.TimeSignature((1, 1))
>>> time_signature.simplify_ratio(min_denominator=1)
>>> time_signature
abjad.TimeSignature((1, 1))