New in version 2.0.
Given prolated_duration_1 governed by tempo_mark_1, return prolated_duration_2 governed by tempo_mark_2 such that prolated_duration_1 and prolated_duration_2 consume exactly the same amount of time in seconds.
Consider the two tempo indications below.
abjad> from abjad.tools import durationtools
abjad> tempo_mark_1 = contexttools.TempoMark(Duration(1, 4), 60)
abjad> tempo_mark_2 = contexttools.TempoMark(Duration(1, 4), 90)
The first tempo indication specifies quarter = 60 MM. The second tempo indication specifies quarter = 90 MM.
The second tempo is 1 1/2 times as fast as the first.
abjad> tempo_mark_2 / tempo_mark_1
Duration(3, 2)
An triplet eighth note at tempo 1 equals a regular eighth note at tempo 2.
abjad> durationtools.rewrite_rational_under_new_tempo(Duration(1, 12), tempo_mark_1, tempo_mark_2)
Duration(1, 8)
Conversely, a regular eighth not at tempo 1 equals a dotted sixteenth at tempo 2.
abjad> durationtools.rewrite_rational_under_new_tempo(Duration(1, 8), tempo_mark_1, tempo_mark_2)
Duration(3, 16)
Return fraction.