50/49: Difference between revisions

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'''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~~|441/440 = S21~~]], (50/49)/([[55/54]]) = [[540/539~~|540/539 = S12/S14~~]], (50/49)/([[56/55]]) = [[1375/1372]], (50/49)/([[64/63]]) = [[225/224~~|225/224 = S15~~]], (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~~|4000/3969 = S19 * S20<sup>2</sup>~~]].

'''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]].

== Temperaments ==

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 {{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|441/440 = S21]], (50/49)/([[55/54]]) = [[540/539|540/539 = S12/S14]], (50/49)/([[56/55]]) = [[1375/1372]], (50/49)/([[64/63]]) = [[225/224|225/224 = S15]], (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|4000/3969 = S19 * S20<sup>2</sup>]].
+'''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]].
 == Temperaments ==