36/35: Difference between revisions
Dave Keenan (talk | contribs) →Sagittal notation: Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Gave the truly-simplest (2,3-free) interval in addition to the octave-reduced interval. Replaced hair-space with nbhsp template call. |
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'''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''', 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 == | == Temperaments == | ||
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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. | 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. | ||
== Sagittal notation == | == Notation == | ||
=== Ben Johnston's notation === | |||
[[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. | |||
=== 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| /|) }}. | 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| /|) }}. | ||
Revision as of 09:02, 10 October 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
Ben Johnston's notation denotes this interval with "7" (a turned 7), and the reciprocal 35/36 with an ordinary 7.
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