36/35: Difference between revisions
m Text replacement - "(\[\[\:(dev|es|purdal|de|en):[^[:space:]\|]*) (.*])" to "$1|$3" |
Re-organize following 15/14 |
||
| (30 intermediate revisions by 14 users not shown) | |||
| Line 1: | Line 1: | ||
{{Interwiki | |||
| en = 36/35 | |||
| de = 36/35 | |||
}} | |||
{{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}} | |||
'''36/35''', the '''septimal quartertone''' is a [[7-limit]] interval with a size of about 48.8 [[cent]]s. It arises as the difference between various 7-limit [[interval quality|qualities]] of seconds, thirds, sixths, and sevenths: between supermajor and classical major, and between subminor and classical minor. These are the pairs of intervals separated by 36/35: | |||
* [[28/27]] and [[16/15]] | |||
* [[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]] | |||
* [[7/4]] and [[9/5]] | |||
* [[15/8]] and [[27/14]] | |||
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 generator, it is almost a fourth of the septimal whole tone [[28/25]], differing by a [[wizma]]. This allows it to be used as a generator for a temperament of [[hemimean]] called [[sengagen]], where 5/4, 7/5 and 7/4 map to 8, 12 and 20 quartertones respectively. | |||
[[ | 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]] for the family of rank-3 temperaments where it is tempered out, and [[Mint temperaments]] for the collection of rank-2 temperaments where it is tempered out. | ||
The ''' | == 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 == | ||
[[Category: | === Ben Johnston's notation === | ||
[[Category: | 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. | ||
[[Category: | |||
=== 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]] | |||
* [[Gallery of just intervals]] | |||
* [[List of superparticular intervals]] | |||
== References == | |||
[[Category:Quartertone]] | |||
[[Category:Mint]] | |||
[[Category:Commas named for the intervals they stack]] | |||