36/35: Difference between revisions

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~~'''[[:de:~~36/35|~~Deutsch]]'''~~

{{Infobox Interval

| Name = septimal quartertone, mint comma

| Color name = rg1, rugu unison

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

| Comma = yes

}}

</~~span>~~

'''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]].

'''~~36/35~~'''

== Temperaments ==

~~|2 2~~ -1 -~~1>~~

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.

48.~~77038 cents~~

== 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.

[[~~File:ji-36-35-csound-foscil-220hz.mp3~~]] ~~[[:File:ji-~~36~~-35-csound-foscil-220hz~~.~~mp3|sound sample]]~~ [[~~:File:ji-36-35-csound-foscil-220hz.mp3|details~~]]

== 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.

~~The '''septimal quarter tone''' (ratio: 36/35, size: 48.77038~~ [[~~cent|cents~~]]) is the ~~difference between [[10/9~~|~~10/9]]~~ and ~~[[8/7|8/7]]~~, ~~[[7/6|7/6]] and [[6/5|6/5]]~~, ~~[[5~~/~~4|5~~/~~4]] and [[9/7|9/7]]~~, ~~[[14/9~~|~~14/9]] and [[8/5|8/5]], [[5/3|5/3]] and [[12/7|12/7]], and [[7/4|7/4]] and [[9/5|9/5]]~~. ~~It has a numerator which~~ is ~~both the sixth square number and the eighth [[triangular_number|triangular number]], leading to it being the product of two [[superparticular|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 and 128/125 * 225/224~~.

=== 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| /|) }}.

[~~http:~~//~~en.wikipedia.org/wiki/Septimal_quarter_tone http://en.wikipedia.org/wiki/Septimal_quarter_tone~~] [[Category:~~definition~~]]

== See also ==

[[Category:~~interval~~]]

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

[[Category:~~quartertone~~]]

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

[[~~Category~~:~~septimal~~]]

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

== Notes ==

[[Category:Quartertone]]

[[Category:Mint]]

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

[[de:36/35]]

@@ Line 1: / Line 1: @@
-<span style="display: block; text-align: right;">'''[[:de:36/35|Deutsch]]'''
+{{Infobox Interval
+| Name = septimal quartertone, mint comma
+| Color name = rg1, rugu unison
+| Sound = ji-36-35-csound-foscil-220hz.mp3
+| Comma = yes
+}}
+{{Wikipedia|Septimal quarter tone}}
-</span>
+'''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]].
-'''36/35'''
+== Temperaments ==
-|2 2 -1 -1&gt;
+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.
-.77038 cents
+== 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.
-[[File:ji-36-35-csound-foscil-220hz.mp3]] [[:File:ji-36-35-csound-foscil-220hz.mp3|sound sample]] [[:File:ji-36-35-csound-foscil-220hz.mp3|details]]
+== 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.
-The '''septimal quarter tone''' (ratio: 36/35, size: 48.77038 [[cent|cents]]) is the difference between [[10/9|10/9]] and [[8/7|8/7]], [[7/6|7/6]] and [[6/5|6/5]], [[5/4|5/4]] and [[9/7|9/7]], [[14/9|14/9]] and [[8/5|8/5]], [[5/3|5/3]] and [[12/7|12/7]], and [[7/4|7/4]] and [[9/5|9/5]]. It has a numerator which is both the sixth square number and the eighth [[triangular_number|triangular number]], leading to it being the product of two [[superparticular|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 and 128/125 * 225/224.
+=== 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| /|) }}.
-[http://en.wikipedia.org/wiki/Septimal_quarter_tone http://en.wikipedia.org/wiki/Septimal_quarter_tone]      [[Category:definition]]
+== See also ==
-[[Category:interval]]
+* [[35/18]] – its [[octave complement]]
-[[Category:quartertone]]
+* [[35/24]] – its [[fifth complement]]
-[[Category:septimal]]
+* [[Gallery of just intervals]]
+* [[List of superparticular intervals]]
+== Notes ==
+[[Category:Quartertone]]
+[[Category:Mint]]
+[[Category:Commas named for the intervals they stack]]
+<!-- interwiki -->
+[[de:36/35]]