49/48: Difference between revisions

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| Name = large septimal diesis <br> slendro diesis
| Name = large septimal diesis <br> slendro diesis
| Color name = zz2, zozo comma
| Color name = zz2, zozo comma
| Sound = Ji-{{#regex:{{PAGENAME}}|/(\S+)\/(\S+)/|\1-\2}}-csound-foscil-220hz.mp3
| Sound = Ji-49-48-csound-foscil-220hz.mp3
}}
}}
The '''large septimal diesis''' (or '''slendro diesis'''), '''49/48''' (35.6968 [[cent]]s), 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]]). It 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-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.
The '''large septimal diesis''' (or '''slendro diesis'''), '''49/48''' (35.6968 [[cent]]s), 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]]). It 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-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.

Revision as of 20:40, 16 September 2020

Interval information
Ratio 49/48
Factorization 2-4 × 3-1 × 72
Monzo [-4 -1 0 2
Size in cents 35.69681¢
Name large septimal diesis
slendro diesis
Color name zz2, 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

[sound info]
Open this interval in xen-calc

The large septimal diesis (or slendro diesis), 49/48 (35.6968 cents), 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). It 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-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.

In classical Western music, this interval is not known as a comma as it is not tempered out in 12edo.

See also