36/35: Difference between revisions

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**Imported revision 244870561 - Original comment: **
 
→Notation: expand on Johnston notation
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox Interval
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Name = septimal quartertone, mint comma
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-08 14:13:12 UTC</tt>.<br>
| Color name = rg1, rugu unison
: The original revision id was <tt>244870561</tt>.<br>
| Sound = ji-36-35-csound-foscil-220hz.mp3
: The revision comment was: <tt></tt><br>
| Comma = yes
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
}}
<h4>Original Wikitext content:</h4>
{{Wikipedia|Septimal quarter tone}}
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //septimal quarter tone//, 36/35, 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 and 128/125 * 225/224.


[[http://en.wikipedia.org/wiki/Septimal_quarter_tone]] </pre></div>
'''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]].
<h4>Original HTML content:</h4>
 
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;36_35&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;septimal quarter tone&lt;/em&gt;, 36/35, 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 and 128/125 * 225/224. &lt;br /&gt;
== Temperaments ==
&lt;br /&gt;
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.
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_quarter_tone" rel="nofollow"&gt;http://en.wikipedia.org/wiki/Septimal_quarter_tone&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== 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]]
<!-- interwiki -->
[[de:36/35]]

Latest revision as of 11:24, 13 November 2024

Interval information
Ratio 36/35
Factorization 22 × 32 × 5-1 × 7-1
Monzo [2 2 -1 -1⟩
Size in cents 48.77038¢
Names septimal quartertone,
mint comma
Color name rg1, rugu unison
FJS name [math]\displaystyle{ \text{P1}_{5,7} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 10.2992
Weil height (log2 max(n, d)) 10.3399
Wilson height (sopfr(nd)) 22
Comma size medium
S-expressions S6,
S8 × S9

[sound info]
Open this interval in xen-calc
English Wikipedia has an article on:

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

Notes

  1. ↑ Yahoo! Tuning Group | Quartonic
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