49/48: Difference between revisions

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'''49/48''', the '''large septimal diesis''' (or '''slendro diesis'''), is a [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo]].
'''49/48''', the '''large septimal diesis''' (or '''slendro diesis'''), is a [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo]].


49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where the two intervals are equated, and the fourth is split in a perfect half. It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct, but it ''can'' be equated with other commas; for example (49/48)/([[81/80]]) = [[245/243]], (49/48)/([[64/63]]) = [[1029/1024]], (49/48)/([[3125/3072]]) = [[3136/3125]], (49/48)/([[50/49]]) = [[2401/2400]], ([[128/125]])/(49/48) = [[6144/6125]], ([[36/35]])/(49/48) = [[1728/1715]].
49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where the two intervals are equated, and the fourth is split in a perfect half. It cannot be tempered out if all of the consonances of the 7-odd-limit are [[consistency|distinct]], but it ''can'' be equated with other commas; for example (49/48)/([[81/80]]) = [[245/243]], (49/48)/([[64/63]]) = [[1029/1024]], (49/48)/([[3125/3072]]) = [[3136/3125]], (49/48)/([[50/49]]) = [[2401/2400]], ([[128/125]])/(49/48) = [[6144/6125]], ([[36/35]])/(49/48) = [[1728/1715]].


== See also ==
== See also ==

Revision as of 00:57, 5 June 2024

Interval information
Ratio 49/48
Factorization 2-4 × 3-1 × 72
Monzo [-4 -1 0 2⟩
Size in cents 35.69681¢
Names large septimal diesis,
slendro diesis
Color name zz2, zozo 2nd,
Zozo comma
FJS name [math]\displaystyle{ \text{m2}^{7,7} }[/math]
Special properties square superparticular,
reduced
Tenney norm (log2 nd) 11.1997
Weil norm (log2 max(n, d)) 11.2294
Wilson norm (sopfr(nd)) 25
Comma size medium
S-expression S7

[sound info]
Open this interval in xen-calc
English Wikipedia has an article on:

49/48, the large septimal diesis (or slendro diesis), is a superparticular ratio spanning the small distance between a subminor third (7/6) and a supermajor second (8/7) or between the supermajor sixth (12/7) and the harmonic seventh (7/4). Measuring about 35.7 ¢, it is a medium comma; however, in classical Western music, this interval is not known as a comma as it is not tempered out in 12edo.

49/48 is tempered out in 15edo and 19edo, where the two intervals are equated, and the fourth is split in a perfect half. It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct, but it can be equated with other commas; for example (49/48)/(81/80) = 245/243, (49/48)/(64/63) = 1029/1024, (49/48)/(3125/3072) = 3136/3125, (49/48)/(50/49) = 2401/2400, (128/125)/(49/48) = 6144/6125, (36/35)/(49/48) = 1728/1715.

See also

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