36/35: Difference between revisions
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{{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''' (~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]] | |||
* [[Gallery of just intervals]] | |||
* [[List of superparticular intervals]] | |||
== Notes == | |||
[[Category:Quartertone]] | |||
[[Category:Mint]] | |||
[[Category:Commas named for the intervals they stack]] | |||
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[[de:36/35]] | [[de:36/35]] | ||
Latest revision as of 11:24, 13 November 2024
| Interval information |
mint comma
reduced
S8 × S9
[sound info]
36/35, the septimal quartertone (~48.8 ¢) 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"[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