36/35: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal quartertone, mint comma | | Name = septimal quartertone, mint comma | ||
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{{Wikipedia|Septimal quarter tone}} | {{Wikipedia|Septimal quarter tone}} | ||
'''36/35''', the '''septimal quartertone''' | '''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 == | == 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 | 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 [[ | 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. | ||
== Etymology == | == Etymology == | ||
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* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
== | == References == | ||
[[Category:Quartertone]] | [[Category:Quartertone]] | ||
[[Category:Mint]] | [[Category:Mint]] | ||
[[Category:Commas named for the intervals they stack]] | [[Category:Commas named for the intervals they stack]] | ||
Latest revision as of 12:21, 1 May 2026
| Interval information |
mint comma
reduced
S8⋅S9
[sound info]
36/35, the septimal quartertone is a 7-limit interval with a size of about 48.8 cents. It arises as the difference between various 7-limit 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.
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"[1]. 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 "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 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 . The upward version is called 1/35M or 35M up and is represented by .
See also
- 35/18 – its octave complement
- 35/24 – its fifth complement
- Gallery of just intervals
- List of superparticular intervals