49/48: Difference between revisions

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Godtone (talk | contribs)
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distinctly consistent redirects to consistency so arguably that is the error that needs to be fixed as the consistency page is where it's defined but it doesnt have its own section
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Godtone (talk | contribs)
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m consistency is irrelevant here but the principal concern still applies; "distinct" should redirect somewhere more appropriate too
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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 [[distinctly consistent|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 [[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 00:05, 7 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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