36/35: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 36/35

| Monzo = 2 2 -1 -1

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| Sound = ji-36-35-csound-foscil-220hz.mp3

}}

~~The~~ '''septimal quarter tone''' (~~ratio: 36/35, size:~~ 48.~~77038~~ [[cent|~~cents~~]]) is the difference between [[10/9]] and [[8/7]], [[7/6]] and [[6/5]], [[5/4]] and [[9/7]], [[14/9]] and [[8/5]], [[5/3]] and [[12/7]], and [[7/4]] and [[9/5]]. It has a numerator which is both the sixth square number and the eighth [[triangular number]], leading to it being the product of two [[superparticular]] commas both as [[64/63]] × [[81/80]] and as [[66/65]] × [[78/77]]; it is also [[45/44]] × [[176/175]], [[51/50]] × [[120/119]], [[128/125]] × [[225/224]], [[50/49]] × [[126/125]] and [[56/55]] × [[99/98]].

'''36/35''', the '''septimal quarter tone''' (~48.8 [[cent|¢]]) is the difference between [[10/9]] and [[8/7]], [[7/6]] and [[6/5]], [[5/4]] and [[9/7]], [[14/9]] and [[8/5]], [[5/3]] and [[12/7]], and [[7/4]] and [[9/5]]. It has a numerator which is both the sixth square number and the eighth [[triangular number]], leading to it being the product of two [[superparticular]] commas both as [[64/63]] × [[81/80]] and as [[66/65]] × [[78/77]]; it is also [[45/44]] × [[176/175]], [[51/50]] × [[120/119]], [[128/125]] × [[225/224]], [[50/49]] × [[126/125]] and [[56/55]] × [[99/98]].

== See also ==

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* [[Mint family]], the family of rank-3 temperaments where it is tempered out

* [[Mint temperaments]], the collection of rank-2 temperaments where it is tempered out

* [[Wikipedia: Septimal quarter tone]]

[[Category:7-limit]]

[[Category:Medium comma]]

~~[[Category:Interval]]~~

[[Category:Quartertone]]

[[Category:Superparticular]]

[[Category:Mint]]

[[Category:~~Listen~~]]

[[Category:Pages with internal sound examples]]

[[de:36/35]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 36/35
 | Monzo = 2 2 -1 -1
@@ Line 9: / Line 8: @@
 | Sound = ji-36-35-csound-foscil-220hz.mp3
 }}
+{{Wikipedia|Septimal quarter tone}}
-The '''septimal quarter tone''' (ratio: 36/35, size: 48.77038 [[cent|cents]]) is the difference between [[10/9]] and [[8/7]], [[7/6]] and [[6/5]], [[5/4]] and [[9/7]], [[14/9]] and [[8/5]], [[5/3]] and [[12/7]], and [[7/4]] and [[9/5]]. It has a numerator which is both the sixth square number and the eighth [[triangular number]], leading to it being the product of two [[superparticular]] commas both as [[64/63]] × [[81/80]] and as [[66/65]] × [[78/77]]; it is also [[45/44]] × [[176/175]], [[51/50]] × [[120/119]], [[128/125]] × [[225/224]], [[50/49]] × [[126/125]] and [[56/55]] × [[99/98]].
+'''36/35''', the '''septimal quarter tone''' (~48.8 [[cent|¢]]) is the difference between [[10/9]] and [[8/7]], [[7/6]] and [[6/5]], [[5/4]] and [[9/7]], [[14/9]] and [[8/5]], [[5/3]] and [[12/7]], and [[7/4]] and [[9/5]]. It has a numerator which is both the sixth square number and the eighth [[triangular number]], leading to it being the product of two [[superparticular]] commas both as [[64/63]] × [[81/80]] and as [[66/65]] × [[78/77]]; it is also [[45/44]] × [[176/175]], [[51/50]] × [[120/119]], [[128/125]] × [[225/224]], [[50/49]] × [[126/125]] and [[56/55]] × [[99/98]].
 == See also ==
@@ Line 19: / Line 19: @@
 * [[Mint family]], the family of rank-3 temperaments where it is tempered out
 * [[Mint temperaments]], the collection of rank-2 temperaments where it is tempered out
-* [[Wikipedia: Septimal quarter tone]]
 [[Category:7-limit]]
 [[Category:Medium comma]]
-[[Category:Interval]]
 [[Category:Quartertone]]
 [[Category:Superparticular]]
 [[Category:Mint]]
-[[Category:Listen]]
+[[Category:Pages with internal sound examples]]
 <!-- interwiki -->
 [[de:36/35]]