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]].