divisions

In music, an old method of improvising variations by dividing the basic note values of a theme into smaller fractions representing higher tempi in proportion to the original time values (see diminution).

The medieval extension of harmonic ratios to tempo can be found in the keyboard variations of Mozart, Beethoven, and Brahms; in the late 20th century Karlheinz Stockhausen reinvented the concept by introducing a tempo scale equivalent to equal temperament, with metronomic values graduated within the ‘tempo-octave’ 60-120 beats per minute.