49/48: Difference between revisions

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
	[[File:Ji-{{#regex:49/48\|/(\S+)\/(\S+)/\|\1-\2}}-csound-foscil-220hz.mp3\|270px]]; [[:File:Ji-{{#regex:49/48\|/(\S+)\/(\S+)/\|\1-\2}}-csound-foscil-220hz.mp3\|[sound info]]]
	Open this interval in xen-calc

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Revision as of 11:47, 13 September 2020

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.

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-The large septimal or slendro diesis, 49/48 (35.6968 [[cent|cents]]), is a [[superparticular|superparticular]] ratio spanning the small distance between a subminor third of [[7/6|7/6]] and a supermajor second of [[8/7]]. 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.
+{{Infobox Interval
+| Icon =
+| Ratio = 49/48
+| Monzo = -4 -1 0 2
+| Cents = 35.69681
+| Name = large septimal diesis <br> slendro diesis
+| Color name = zz2, zozo comma
+| Sound = Ji-{{#regex:{{PAGENAME}}|/(\S+)\/(\S+)/|\1-\2}}-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.
-[http://en.wikipedia.org/wiki/Septimal_diesis http://en.wikipedia.org/wiki/Septimal_diesis]
+In classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo]].
-[[Category:interval]]
+== See also ==
-[[Category:septimal]]
+* [[Medium comma]]
+* [[Gallery of just intervals]]
+* [https://en.wikipedia.org/wiki/Septimal_diesis Septimal diesis &#45; Wikipedia]
+[[Category:7-limit]]
+[[Category:Septimal]]
+[[Category:Interval ratio]]
+[[Category:Medium comma]]
+[[Category:Superparticular]]
+[[Category:Listen]]

49/48: Difference between revisions

Revision as of 11:47, 13 September 2020

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