Diaschisma: Difference between revisions
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'''2048/2025''', the '''diaschisma''', an interval of 19.553 [[cent|cents]], is the difference between four perfect fifths plus two major thirds and three octaves. Tempering it out leads to the [[diaschismic family]] of temperaments. It may also be defined as the difference between a Pythagorean minor seventh ([[16/9]]) and a just augmented sixth ([[225/128]]), as the difference between two classic diatonic semitones ([[16/15]]) and the major whole tone ([[9/8]]), that is, (9/8)/(16/15)<sup>2</sup>, or as the difference between the 5-limit tritone [[45/32]] and its enharmonic equivalent [[64/45]]. | '''2048/2025''', the '''diaschisma''', an interval of 19.553 [[cent|cents]], is the difference between four perfect fifths plus two major thirds and three octaves. Tempering it out leads to the [[diaschismic family]] of temperaments. It may also be defined as the difference between a Pythagorean minor seventh ([[16/9]]) and a just augmented sixth ([[225/128]]), as the difference between two classic diatonic semitones ([[16/15]]) and the major whole tone ([[9/8]]), that is, (9/8)/(16/15)<sup>2</sup>, or as the difference between the 5-limit tritone [[45/32]] and its enharmonic equivalent [[64/45]]. | ||
== Example == | |||
[http://micro.soonlabel.com/petr_parizek/pp_pump_examples/pump_1.ogg parizek1] A [[comma pump]] progression that assumes that the diaschisma is tempered out (i.e. equates two notes that are separated by a diaschisma). | |||
== See also == | == See also == | ||