49/48: Difference between revisions

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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-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]].

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

== See also ==

* [[Semiphore family]]

* [[Semiphore family]], the rank-3 family where it is tempered out

* [[Slendro clan]]

* [[Slendro clan]], the rank-2 clan where it is tempered out

* [[Medium comma]]

* [[List of superparticular intervals]]

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[[Category:Medium comma]]

[[Category:Superparticular]]

[[Category:Slendro]]

[[Category:Listen]]

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 }}
-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-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]].
 In classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo]].
 == See also ==
-* [[Semiphore family]]
+* [[Semiphore family]], the rank-3 family where it is tempered out
-* [[Slendro clan]]
+* [[Slendro clan]], the rank-2 clan where it is tempered out
 * [[Medium comma]]
 * [[List of superparticular intervals]]
@@ Line 32: / Line 32: @@
 [[Category:Medium comma]]
 [[Category:Superparticular]]
+[[Category:Slendro]]
 [[Category:Listen]]