36/35: Difference between revisions

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{{Infobox Interval

| Name = septimal ~~quarter tone~~

| Name = septimal quartertone, mint comma

| Color name = rg1, rugu unison

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

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'''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]].

'''36/35''', the '''septimal quartertone''' (~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]].

[[Ben Johnston's notation]] denotes this interval with "7" (an turned 7), and the reciprocal 35/36 with an ordinary 7.

[[Ben Johnston's notation]] denotes this interval with "7" (a turned 7), and the reciprocal 35/36 with an ordinary 7.

== Temperaments ==

When treated as a comma to be tempered out, it is known as the '''mint comma''', and tempering it out leads to the [[mint]] temperament. See [[mint family]], the family of rank-3 temperaments where it is tempered out, and [[mint temperaments]], the collection of rank-2 temperaments where it is tempered out.

== Etymology ==

The name ''mint comma'' was given by [[Mike Battaglia]] in 2012, for minor third because "it mixes 7/6 and 6/5 together into one minty interval"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_103732.html Yahoo! Tuning Group | ''Quartonic'']</ref>.

== See also ==

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* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

* [[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

== Notes ==

[[Category:Quartertone]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = septimal quarter tone
+| Name = septimal quartertone, mint comma
 | Color name = rg1, rugu unison
 | Sound = ji-36-35-csound-foscil-220hz.mp3
@@ Line 7: / Line 7: @@
 {{Wikipedia|Septimal quarter tone}}
-'''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]].
+'''36/35''', the '''septimal quartertone''' (~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]].
-[[Ben Johnston's notation]] denotes this interval with "<span style="display: inline-block; transform: rotate(180deg)">7</span>" (an turned 7), and the reciprocal 35/36 with an ordinary 7.
+[[Ben Johnston's notation]] denotes this interval with "<span style="display: inline-block; transform: rotate(180deg)">7</span>" (a turned 7), and the reciprocal 35/36 with an ordinary 7.
+== Temperaments ==
+When treated as a comma to be tempered out, it is known as the '''mint comma''', and tempering it out leads to the [[mint]] temperament. See [[mint family]], the family of rank-3 temperaments where it is tempered out, and [[mint temperaments]], the collection of rank-2 temperaments where it is tempered out.
+== Etymology ==
+The name ''mint comma'' was given by [[Mike Battaglia]] in 2012, for <u>min</u>or <u>t</u>hird because "it mixes 7/6 and 6/5 together into one minty interval"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_103732.html Yahoo! Tuning Group | ''Quartonic'']</ref>.
 == See also ==
@@ Line 16: / Line 22: @@
 * [[Gallery of just intervals]]
 * [[List of superparticular intervals]]
-* [[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
+== Notes ==
 [[Category:Quartertone]]