36/35: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal | | Name = septimal quartertone, mint comma | ||
| Color name = rg1, rugu unison | | Color name = rg1, rugu unison | ||
| Sound = ji-36-35-csound-foscil-220hz.mp3 | | Sound = ji-36-35-csound-foscil-220hz.mp3 | ||
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{{Wikipedia|Septimal quarter tone}} | {{Wikipedia|Septimal quarter tone}} | ||
'''36/35''', the '''septimal | '''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]]. | ||
[[Ben Johnston's notation]] denotes this interval with "<span style="display: inline-block; transform: rotate(180deg)">7</span>" ( | [[Ben Johnston's notation]] denotes this interval with "<span style="display: inline-block; transform: rotate(180deg)">7</span>" (a turned 7), and the reciprocal 35/36 with an ordinary 7. | ||
== 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>. | |||
== See also == | == See also == | ||
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* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
== Notes == | |||
[[Category:Quartertone]] | [[Category:Quartertone]] | ||
Revision as of 07:19, 20 July 2023
| 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.
Ben Johnston's notation denotes this interval with "7" (a turned 7), and the reciprocal 35/36 with an ordinary 7.
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].
See also
- 35/18 – its octave complement
- 35/24 – its fifth complement
- Gallery of just intervals
- List of superparticular intervals