Wikispaces>Stephen_Weigel |
|
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2> | | <span style="display: block; text-align: right;">Other languages: [[:de:64/63 Deutsch]]</span> |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | |
| : This revision was by author [[User:Stephen_Weigel|Stephen_Weigel]] and made on <tt>2017-03-19 14:04:54 UTC</tt>.<br>
| | The interval 64/63, called '''septimal comma''' or '''Archytas' comma''' or (in German) '''[http://de.wikipedia.org/wiki/Komma_%28Musik%29#Leipziger_Komma Leipziger Komma]''', is a [[superparticular|superparticular ratio]] which equates [[9/8|9/8]] and [[8/7|8/7]] if tempered out and has the eighth square number as a numerator. It also equates [[7/4|7/4]] with [[16/9|16/9]], so that the just dominant seventh chord, 1-5/4-3/2-16/9, and the otonal tetrad, 1-5/4-3/2-7/4, are equated to the same chord when 64/63 is tempered out. Equal divisions of the octave tempering out 64/63 include 12, 15, 22, 27, 37, 49 and 59. |
| : The original revision id was <tt>609093675</tt>.<br>
| |
| : The revision comment was: <tt></tt><br>
| |
| 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>
| |
| <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"><span style="display: block; text-align: right;">Other languages: [[xenharmonie/64_63|Deutsch]]
| |
| </span>
| |
| The interval 64/63, called **septimal comma** or **Archytas' comma** or (in German) **[[@http://de.wikipedia.org/wiki/Komma_%28Musik%29#Leipziger_Komma|Leipziger Komma]]**, is a [[xenharmonic/superparticular|superparticular ratio]] which equates [[xenharmonic/9_8|9/8]] and [[xenharmonic/8_7|8/7]] if tempered out and has the eighth square number as a numerator. It also equates [[xenharmonic/7_4|7/4]] with [[xenharmonic/16_9|16/9]], so that the just dominant seventh chord, 1-5/4-3/2-16/9, and the otonal tetrad, 1-5/4-3/2-7/4, are equated to the same chord when 64/63 is tempered out. Equal divisions of the octave tempering out 64/63 include 12, 15, 22, 27, 37, 49 and 59. | |
|
| |
|
| The Archytas comma is a 7-limit comma with monzo | 6 -2 0 -1 >. It is | | The Archytas comma is a 7-limit comma with monzo | 6 -2 0 -1 >. It is |
| | |
| 27.264092 cents in size. | | 27.264092 cents in size. |
|
| |
|
| It is similar to the Didymus or syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Archytas comma, the major third is 9/7. (Note that [[Porcupine family|Porcupine]], which tempers out 64/63, uses a minor tone as a generator and generally is considered to have 5/4 major thirds, so it doesn't depend on this equivalency.) | | It is similar to the Didymus or syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Archytas comma, the major third is 9/7. (Note that [[Porcupine_family|Porcupine]], which tempers out 64/63, uses a minor tone as a generator and generally is considered to have 5/4 major thirds, so it doesn't depend on this equivalency.) |
|
| |
|
| If you are using 9/7 major thirds, this also implies that the major third is split into two equal steps that represent both 9/8 and 8/7: If a stack of four fifths gets you to (octave-equivalent) 9/7, and a stack of two fifths gets you to 9/8, then the difference must be (9/7)/(9/8) = 8/7. The 8/7 and 9/8 intervals are equal, however, as a result of the generation process. | | If you are using 9/7 major thirds, this also implies that the major third is split into two equal steps that represent both 9/8 and 8/7: If a stack of four fifths gets you to (octave-equivalent) 9/7, and a stack of two fifths gets you to 9/8, then the difference must be (9/7)/(9/8) = 8/7. The 8/7 and 9/8 intervals are equal, however, as a result of the generation process. |
|
| |
|
| | | [http://en.wikipedia.org/wiki/Septimal_comma http://en.wikipedia.org/wiki/Septimal_comma] [[Category:7-limit]] |
| [[http://en.wikipedia.org/wiki/Septimal_comma]]</pre></div>
| | [[Category:comma]] |
| <h4>Original HTML content:</h4>
| | [[Category:definition]] |
| <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>64_63</title></head><body><span style="display: block; text-align: right;">Other languages: <a class="wiki_link" href="http://xenharmonie.wikispaces.com/64_63">Deutsch</a><br />
| | [[Category:interval]] |
| </span><br />
| | [[Category:ratio]] |
| The interval 64/63, called <strong>septimal comma</strong> or <strong>Archytas' comma</strong> or (in German) <strong><a class="wiki_link_ext" href="http://de.wikipedia.org/wiki/Komma_%28Musik%29#Leipziger_Komma" rel="nofollow" target="_blank">Leipziger Komma</a></strong>, is a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/superparticular">superparticular ratio</a> which equates <a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_8">9/8</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/8_7">8/7</a> if tempered out and has the eighth square number as a numerator. It also equates <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7_4">7/4</a> with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/16_9">16/9</a>, so that the just dominant seventh chord, 1-5/4-3/2-16/9, and the otonal tetrad, 1-5/4-3/2-7/4, are equated to the same chord when 64/63 is tempered out. Equal divisions of the octave tempering out 64/63 include 12, 15, 22, 27, 37, 49 and 59.<br />
| | [[Category:septimal]] |
| <br />
| |
| The Archytas comma is a 7-limit comma with monzo | 6 -2 0 -1 &gt;. It is <br />
| |
| 27.264092 cents in size.<br />
| |
| <br />
| |
| It is similar to the Didymus or syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Archytas comma, the major third is 9/7. (Note that <a class="wiki_link" href="/Porcupine%20family">Porcupine</a>, which tempers out 64/63, uses a minor tone as a generator and generally is considered to have 5/4 major thirds, so it doesn't depend on this equivalency.)<br />
| |
| <br />
| |
| If you are using 9/7 major thirds, this also implies that the major third is split into two equal steps that represent both 9/8 and 8/7: If a stack of four fifths gets you to (octave-equivalent) 9/7, and a stack of two fifths gets you to 9/8, then the difference must be (9/7)/(9/8) = 8/7. The 8/7 and 9/8 intervals are equal, however, as a result of the generation process.<br />
| |
| <br />
| |
| <br />
| |
| <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow">http://en.wikipedia.org/wiki/Septimal_comma</a></body></html></pre></div>
| |