36/35: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = septimal quartertone, mint comma

~~| Ratio = 36/35~~

~~| Monzo = 2 2 -1 -1~~

~~| Cents = 48.77038~~

| Name = septimal ~~quarter tone~~

| Color name = rg1, rugu unison

~~| FJS name = P135~~

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

| Comma = yes

}}

~~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 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]].

== 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>. Before that, it had been known as the ''quartonic comma'', which refers to another comma today.

== Notation ==

=== Ben Johnston's notation ===

In [[Ben Johnston's notation]], this interval is denoted with "{{invert|7}}" (a turned "7"), and the reciprocal 35/36 with an ordinary "7". If the base note is C, then [[7/4]] is reprented by C–Bb7.

=== Sagittal notation ===

In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal | \!) }} and is called the '''35 medium diesis''', or '''35M''' for short, because the simplest interval it notates is 35/1 = 5×7 (equiv. 35/16), as for example in C-D{{nbhsp}}{{sagittal | \!) }}. The upward version is called '''1/35M''' or '''35M up''' and is represented by {{sagittal| /|) }}.

== See also ==

* [[35/18]] – its [[octave complement]]

* [[35/24]] – its [[fifth complement]]

* [[~~Wikipedia: Septimal quarter tone~~]]

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

== Notes ==

~~[[Category:7-limit]]~~

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

[[Category:Quartertone]]

[[Category:~~Listen~~]]

[[Category:Mint]]

[[Category:Commas named for the intervals they stack]]

[[de:36/35]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = septimal quartertone, mint comma
-| Ratio = 36/35
-| Monzo = 2 2 -1 -1
-| Cents = 48.77038
-| Name = septimal quarter tone
 | Color name = rg1, rugu unison
-| FJS name = P1<sub>35</sub>
 | Sound = ji-36-35-csound-foscil-220hz.mp3
+| Comma = yes
 }}
+{{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 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]].
+== 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>. Before that, it had been known as the ''quartonic comma'', which refers to another comma today.
+== Notation ==
+=== Ben Johnston's notation ===
+In [[Ben Johnston's notation]], this interval is denoted with "{{invert|7}}" (a turned "7"), and the reciprocal 35/36 with an ordinary "7". If the base note is C, then [[7/4]] is reprented by C–Bb7.
+=== Sagittal notation ===
+In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal | \!) }} and is called the '''35 medium diesis''', or '''35M''' for short, because the simplest interval it notates is 35/1 = 5×7 (equiv. 35/16), as for example in C-D{{nbhsp}}{{sagittal | \!) }}. The upward version is called '''1/35M''' or '''35M up''' and is represented by {{sagittal| /|) }}.
 == See also ==
 * [[35/18]] – its [[octave complement]]
 * [[35/24]] – its [[fifth complement]]
-* [[Wikipedia: Septimal quarter tone]]
+* [[Gallery of just intervals]]
+* [[List of superparticular intervals]]
+== Notes ==
-[[Category:7-limit]]
-[[Category:Interval ratio]]
 [[Category:Quartertone]]
-[[Category:Listen]]
+[[Category:Mint]]
+[[Category:Commas named for the intervals they stack]]
 <!-- interwiki -->
 [[de:36/35]]