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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-29 15:45:11 UTC</tt>.<br>
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| : The original revision id was <tt>597455206</tt>.<br>
| | == Theory == |
| : The revision comment was: <tt></tt><br>
| | 120edo shares the [[perfect fifth]] with 12edo, [[tempering out]] the [[Pythagorean comma]]. 120edo is an excellent tuning in the 2.3.7.11.13.23.29 [[subgroup]]. In the no-5's 11-limit, it tempers out [[243/242]]. In the patent val 120edo is also a tuning for the 7-limit [[decoid]] temperament. |
| 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>
| | The 120bdd val is a tuning for [[superpyth]] where 3/2 is tuned to exactly 710{{c}}. It may be used as a ''de facto'' dual fifth in [[Substitute harmonic#Newcome|newcome]] temperament. |
| <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">120edo means division of the octave into equal parts of 10 cents each. Its patent val is contorted only through the 3-limit and does not temper out 81/80 in the 5-limit or 64/63 and 5120/5103 in the 7-limit. However, 5120/5103 is done about as badly as this interval can be done relative to an equal division, falling close to exactly in the middle of a step (1\120 is ~42.42 relative cents sharp of it). Being the simplest division of the octave by the Germanic [[https://en.wikipedia.org/wiki/Long_hundred|long hundred]], it has a unit step which is the fine relative cent of [[1edo]]</pre></div>
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| <h4>Original HTML content:</h4>
| | === Prime harmonics === |
| <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>120edo</title></head><body>120edo means division of the octave into equal parts of 10 cents each. Its patent val is contorted only through the 3-limit and does not temper out 81/80 in the 5-limit or 64/63 and 5120/5103 in the 7-limit. However, 5120/5103 is done about as badly as this interval can be done relative to an equal division, falling close to exactly in the middle of a step (1\120 is ~42.42 relative cents sharp of it). Being the simplest division of the octave by the Germanic <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Long_hundred" rel="nofollow">long hundred</a>, it has a unit step which is the fine relative cent of <a class="wiki_link" href="/1edo">1edo</a></body></html></pre></div>
| | {{Harmonics in equal|120}} |
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| | === Subsets and supersets === |
| | 120edo is the 10th highly composite edo and the 5th factorial edo (since {{nowrap|120 {{=}} 5!}} {{nowrap|{{=}} 1 × 2 × 3 × 4 × 5}}). It has many subsets: {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, and 60 }}. |
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| | === Miscellaneous properties === |
| | 120edo also has a [[concoctic]] generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes. |
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| | == JI approximation == |
| | {{Q-odd-limit intervals|120}} |
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| | == Intervals == |
| | {{Interval table}} |
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| | == Notation == |
| | === Ups and downs notation === |
| | 120edo can be notated using [[ups and downs notation]] using [[Helmholtz–Ellis]] accidentals and Stein–Zimmerman [[24edo#Notation|quarter-tone]] accidentals: |
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| | {{Sharpness-sharp10-qt1|120}} |