50/49: Difference between revisions
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{{Wikipedia|Septimal third tone#Septimal sixth tone}} | {{Wikipedia|Septimal third tone#Septimal sixth tone}} | ||
'''50/49''', the ''' | '''50/49''', also known as the '''small septimal sixth-tone''', '''small septimal diesis''', '''septimal tritonic diesis''', or '''jubilisma''', is a [[7-limit]] [[medium comma]]. It is the only [[superparticular]] [[comma]] in the 7-limit aside from [[126/125]] and [[4375/4374]] which has a numerator which is neither square nor [[triangular number|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]]). | ||
It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct, however, it ''can'' be equated with other commas; for example: | |||
* ([[36/35]])/(50/49) = [[126/125]] | * ([[36/35]])/(50/49) = [[126/125]] | ||
* ([[45/44]])/(50/49) = [[441/440]] | * ([[45/44]])/(50/49) = [[441/440]] | ||
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== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma equates the | [[Tempering out]] this comma equates the two septimal tritones (i.e. [[7/5]] and [[10/7]]) with each other, leading to temperaments where the square root of two approximates both. See [[Jubilismic family]] for the rank-3 family where it is tempered out, and [[Jubilismic clan]] for the rank-2 clan where it is tempered out. | ||
Equal temperaments tempering out 50/49 include [[12edo]], [[22edo]], [[26edo]], [[38edo]], [[48edo]] and [[54edo]]. | Equal temperaments tempering out 50/49 include [[12edo]], [[22edo]], [[26edo]], [[38edo]], [[48edo]], and [[54edo]]. | ||
== See also == | == See also == | ||
Revision as of 14:16, 1 January 2025
| Interval information |
small septimal sixth-tone,
(septimal) tritonic diesis
Biruyo comma
reduced
50/49, also known as the small septimal sixth-tone, small septimal diesis, septimal tritonic diesis, or jubilisma, is a 7-limit medium comma. It is the only superparticular comma in the 7-limit aside from 126/125 and 4375/4374 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).
It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct, however, it can be equated with other commas; for example:
- (36/35)/(50/49) = 126/125
- (45/44)/(50/49) = 441/440
- (50/49)/(55/54) = 540/539
- (50/49)/(56/55) = 1375/1372
- (50/49)/(64/63) = 225/224
- (50/49)/(65/64) = 640/637
- (50/49)/(66/65) = 1625/1617
- (50/49)/(78/77) = 275/273
- (50/49)/(81/80) = 4000/3969
Temperaments
Tempering out this comma equates the two septimal tritones (i.e. 7/5 and 10/7) with each other, leading to temperaments where the square root of two approximates both. See Jubilismic family for the rank-3 family where it is tempered out, and Jubilismic clan for the rank-2 clan where it is tempered out.
Equal temperaments tempering out 50/49 include 12edo, 22edo, 26edo, 38edo, 48edo, and 54edo.
See also
- List of superparticular intervals
- 49/48 – the large septimal sixth-tone