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 '''jubilisma''' (also '''small septimal sixth-tone''' or '''septimal tritonic diesis''') is a [[7-limit]] [[medium comma]]. It is the only [[superparticular]] [[comma]] in the 7-limit aside from [[126/125]] 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]], ([[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]] and (50/49)/([[81/80]]) = [[4000/3969]].
'''50/49''', the '''jubilisma''' (also '''small septimal sixth-tone''' or '''septimal tritonic diesis''') is a [[7-limit]] [[medium comma]]. It is the only [[superparticular]] [[comma]] in the 7-limit aside from [[126/125]] 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]]
* ([[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 ==
== Temperaments ==

Revision as of 02:16, 14 October 2024

Interval information
Ratio 50/49
Factorization 2 × 52 × 7-2
Monzo [1 0 2 -2⟩
Size in cents 34.97561¢
Names jubilisma,
small septimal sixth-tone,
(septimal) tritonic diesis
Color name rryy-2, biruyo negative 2nd,
Biruyo comma
FJS name [math]\displaystyle{ \text{d}{-2}^{5,5}_{7,7} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 11.2586
Weil norm (log2 max(n, d)) 11.2877
Wilson norm (sopfr(nd)) 26
Comma size medium
S-expression S5/S7
Open this interval in xen-calc
English Wikipedia has an article on:

50/49, the jubilisma (also small septimal sixth-tone or septimal tritonic diesis) is a 7-limit medium comma. It is the only superparticular comma in the 7-limit 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).

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:

Temperaments

Tempering out this comma equates the 7/5 with 10/7, its octave complement, leading to temperaments where the square root of two does service for both. See Jubilismic family for the rank-3 family where it is tempered out. See 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

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