Diaschisma: Difference between revisions

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2048/2025, the diaschisma, an interval of 19.553 [[cent|cents]], it is the difference between four perfect fifths plus two major thirds and three octaves, Tempering it out leads to [[Diaschismic_family|Diaschismic temperament]]. It may also be defined as the difference between a just Pythagorean minor seventh and a just augmented sixth (E.A. [[16/9|16/9]] - 225/128), as the difference between two [[16/15|diatonic semitones]] and the [[9/8|major whole tone]], that is, (9/8)/(16/15)^2, or as the difference between the 5-limit tritone [[45/32|45/32]] and its enharmonic equivalent [[64/45|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 [[Diaschismic_family|diaschismic temperament]]. 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]].
 
[[Category:5-limit]]
[[Category:Small comma]]
[[Category:Diaschismic]]