49/48: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 49/48

| Monzo = -4 -1 0 2

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| Sound = Ji-49-48-csound-foscil-220hz.mp3

}}

'''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]].

~~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]].

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]].

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

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* [[List of superparticular intervals]]

* [[Gallery of just intervals]]

* [[Wikipedia: Septimal diesis]]

[[Category:7-limit]]

~~[[Category:Interval ratio]]~~

[[Category:Medium commas]]

[[Category:Superparticular]]

[[Category:Slendro]]

[[Category:Semiphore]]

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 }}
 {{Infobox Interval
-| Icon =
 | Ratio = 49/48
 | Monzo = -4 -1 0 2
@@ Line 15: / Line 14: @@
 | Sound = Ji-49-48-csound-foscil-220hz.mp3
 }}
+{{Wikipedia|Septimal diesis}}
+'''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]].
-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]].
+/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]].
 In classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo]].
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 * [[List of superparticular intervals]]
 * [[Gallery of just intervals]]
-* [[Wikipedia: Septimal diesis]]
 [[Category:7-limit]]
-[[Category:Interval ratio]]
 [[Category:Medium commas]]
 [[Category:Superparticular]]
 [[Category:Slendro]]
 [[Category:Semiphore]]