|
|
| (34 intermediate revisions by 17 users not shown) |
| Line 1: |
Line 1: |
| <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:Sarzadoce|Sarzadoce]] and made on <tt>2011-08-09 15:02:03 UTC</tt>.<br>
| | | Color name = rg1, rugu unison |
| : The original revision id was <tt>245077143</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, is the difference between [[10_9|10/9]] and [[8_7|8/7]], [[7_6|7/6]] and [[6_5|6/5]], [[5_4|5/4]] and [[9_7|9/7]], [[14_9|14/9]] and [[8_5|8/5]], [[5_3|5/3]] and [[12_7|12/7]], and [[7_4|7/4]] and [[9_5|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 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"><html><head><title>36_35</title></head><body>The <strong>septimal quarter tone</strong>, 36/35, is the difference between <a class="wiki_link" href="/10_9">10/9</a> and <a class="wiki_link" href="/8_7">8/7</a>, <a class="wiki_link" href="/7_6">7/6</a> and <a class="wiki_link" href="/6_5">6/5</a>, <a class="wiki_link" href="/5_4">5/4</a> and <a class="wiki_link" href="/9_7">9/7</a>, <a class="wiki_link" href="/14_9">14/9</a> and <a class="wiki_link" href="/8_5">8/5</a>, <a class="wiki_link" href="/5_3">5/3</a> and <a class="wiki_link" href="/12_7">12/7</a>, and <a class="wiki_link" href="/7_4">7/4</a> and <a class="wiki_link" href="/9_5">9/5</a>. It has a numerator which is both the sixth square number and the eighth <a class="wiki_link" href="/triangular%20number">triangular number</a>, leading to it being the product of two <a class="wiki_link" href="/superparticular">superparticular</a> 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.<br />
| | == Temperaments == |
| <br />
| | 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. |
| <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_quarter_tone" rel="nofollow">http://en.wikipedia.org/wiki/Septimal_quarter_tone</a></body></html></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]] |