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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | The 78 equal division divides the octave into 78 equal parts of size 15.385 [[cent|cent]]s each. It tempers out 2048/2025 in the [[5-limit|5-limit]]; 875/864 and 2401/2400 in the [[7-limit|7-limit]]; and 100/99, 385/384 and 1375/1372 in the [[11-limit|11-limit]]. It provides the [[Optimal_patent_val|optimal patent val]] for 11-limit [[Diaschismic_family|keen temperament]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-06-18 10:43:29 UTC</tt>.<br>
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| : The original revision id was <tt>585778963</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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 78 equal division divides the octave into 78 equal parts of size 15.385 [[cent]]s each. It tempers out 2048/2025 in the [[5-limit]]; 875/864 and 2401/2400 in the [[7-limit]]; and 100/99, 385/384 and 1375/1372 in the [[11-limit]]. It provides the [[optimal patent val]] for 11-limit [[Diaschismic family|keen temperament]].
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| Much like [[100edo|100bddd]], the 78ddd val can be used to construct an alternative to 22edo for pajara. The large and small step sizes in this case have ratio 4:3. The width of the tempered perfect fifth is 707.7 cents. The major third is 384.6 cents; less than two cents flat of just. The harmonic seventh is 984.6 cents, or about 15.8 cents sharp; hence this tuning prioritizes the 3- and 5-limits over the 7-limit, while still ensuring that no basic 7-limit intervals other than the tritones are more than 16 cents off. The 22-note 2MOS generated in this way could be used to build straight-fretted guitars that would be [[https://en.wikipedia.org/wiki/Augmented-fourths_tuning|tuned in tritones]]. The appeal of this scale is that it is less xenharmonic than [[22edo]] is, for listeners accustomed to 12edo. In particular, the 163.6¢ "flat minor whole tone" of 22edo is now 169.2¢, making it more clearly a //whole// tone (albeit noticeably flat), rather than a neutral second.</pre></div> | | Much like [[100edo|100bddd]], the 78ddd val can be used to construct an alternative to 22edo for pajara. The large and small step sizes in this case have ratio 4:3. The width of the tempered perfect fifth is 707.7 cents. The major third is 384.6 cents; less than two cents flat of just. The harmonic seventh is 984.6 cents, or about 15.8 cents sharp; hence this tuning prioritizes the 3- and 5-limits over the 7-limit, while still ensuring that no basic 7-limit intervals other than the tritones are more than 16 cents off. The 22-note 2MOS generated in this way could be used to build straight-fretted guitars that would be [https://en.wikipedia.org/wiki/Augmented-fourths_tuning tuned in tritones]. The appeal of this scale is that it is less xenharmonic than [[22edo|22edo]] is, for listeners accustomed to 12edo. In particular, the 163.6¢ "flat minor whole tone" of 22edo is now 169.2¢, making it more clearly a ''whole'' tone (albeit noticeably flat), rather than a neutral second. |
| <h4>Original HTML content:</h4>
| | [[Category:edo]] |
| <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>78edo</title></head><body>The 78 equal division divides the octave into 78 equal parts of size 15.385 <a class="wiki_link" href="/cent">cent</a>s each. It tempers out 2048/2025 in the <a class="wiki_link" href="/5-limit">5-limit</a>; 875/864 and 2401/2400 in the <a class="wiki_link" href="/7-limit">7-limit</a>; and 100/99, 385/384 and 1375/1372 in the <a class="wiki_link" href="/11-limit">11-limit</a>. It provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11-limit <a class="wiki_link" href="/Diaschismic%20family">keen temperament</a>.<br />
| | [[Category:keen]] |
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| | [[Category:theory]] |
| Much like <a class="wiki_link" href="/100edo">100bddd</a>, the 78ddd val can be used to construct an alternative to 22edo for pajara. The large and small step sizes in this case have ratio 4:3. The width of the tempered perfect fifth is 707.7 cents. The major third is 384.6 cents; less than two cents flat of just. The harmonic seventh is 984.6 cents, or about 15.8 cents sharp; hence this tuning prioritizes the 3- and 5-limits over the 7-limit, while still ensuring that no basic 7-limit intervals other than the tritones are more than 16 cents off. The 22-note 2MOS generated in this way could be used to build straight-fretted guitars that would be <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Augmented-fourths_tuning" rel="nofollow">tuned in tritones</a>. The appeal of this scale is that it is less xenharmonic than <a class="wiki_link" href="/22edo">22edo</a> is, for listeners accustomed to 12edo. In particular, the 163.6¢ &quot;flat minor whole tone&quot; of 22edo is now 169.2¢, making it more clearly a <em>whole</em> tone (albeit noticeably flat), rather than a neutral second.</body></html></pre></div>
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