50/49: Difference between revisions
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<span style="display: block; text-align: right;">[[:de:50/49 Deutsch]]</span> | <span style="display: block; text-align: right;">[[:de:50/49|Deutsch]]</span> | ||
The '''septimal sixth-tone''' or '''jubilisma''', 50/49, is the only [[superparticular|superparticular]] [[Comma|comma]] aside from [[126/125|126/125]] which has a numerator which is neither square nor triangular, meaning it is not the difference between septimal superparticular rations with numerators differing by either one or two; instead, 50/49 = ([[10/7|10/7]])/([[7/5|7/5]]). [[tempering_out|Tempering it out]] equates the two, leading to temperaments where the square root of two does service for both. Equal temperaments tempering out 50/49 include [[12edo|12]], [[22edo|22]], [[26edo|26]], [[38edo|38]], [[48edo|48]] and [[54edo|54edo]]. | The '''septimal sixth-tone''' or '''jubilisma''', 50/49, is the only [[superparticular|superparticular]] [[Comma|comma]] aside from [[126/125|126/125]] which has a numerator which is neither square nor triangular, meaning it is not the difference between septimal superparticular rations with numerators differing by either one or two; instead, 50/49 = ([[10/7|10/7]])/([[7/5|7/5]]). [[tempering_out|Tempering it out]] equates the two, leading to temperaments where the square root of two does service for both. Equal temperaments tempering out 50/49 include [[12edo|12]], [[22edo|22]], [[26edo|26]], [[38edo|38]], [[48edo|48]] and [[54edo|54edo]]. | ||
Revision as of 00:09, 17 September 2018
The septimal sixth-tone or jubilisma, 50/49, is the only superparticular comma aside from 126/125 which has a numerator which is neither square nor triangular, meaning it is not the difference between septimal superparticular rations with numerators differing by either one or two; instead, 50/49 = (10/7)/(7/5). Tempering it out equates the two, leading to temperaments where the square root of two does service for both. Equal temperaments tempering out 50/49 include 12, 22, 26, 38, 48 and 54edo.