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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | A '''keemic chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in the [[keemic]] temperament. Since [[100/99]] is [[tempering out|tempered out]], [[ptolemismic chords]] are also keemic chords; since [[385/384]] is tempered out, [[keenanismic chords]] are also keemic chords. Aside from these, there are also essentially keemic tempered chords. |
| 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:genewardsmith|genewardsmith]] and made on <tt>2011-10-25 18:02:53 UTC</tt>.<br>
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| : The original revision id was <tt>268530672</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">A //magical seventh// is an 11-limit essentially tempered dyadic chord consisting of three sharp minor thirds and an 8/7, in other words a 6/5-6/5-6/5-8/7 chord, which closes at the octave since both 99/98 and 385/384 (and therefore 875/864) are tempered out. This means that in the 11-limit 4&7&15 planar temperament tempering these out, the chord is the tempering of 1-6/5-16/11-7/4. In an optimized tuning for the 4&7&15 temperament, the marvel comma 225/224 shrinks in size and may reverse direction, and adding it to the list of commas does little tuning damage; this results in 11-limit magic temperament, which has the same optimal patent val ([[104edo]].) Hence while it by definition it merely requires the 4&7&15 temperament, it can for the most part be regarded as a chord of [[magic]] (19&22) temperament.
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| However, this chord also exists and has low complexity in 11-limit [[Superpyth#Suprapyth|suprapyth]] temperament. One is found in the 7-note MOS.</pre></div>
| | The most basic of these is the '''magical seventh chord''', consisting of three sharp [[6/5|classical minor thirds]] and a [[8/7|septimal whole tone]], which closes at the [[octave]] since both [[100/99]] and [[385/384]] (and therefore [[875/864]]) are [[tempering out|tempered out]]. This means the chord is the tempering of |
| <h4>Original HTML content:</h4>
| | * 1–6/5–16/11–7/4 with steps 6/5, 6/5, 6/5, 8/7. |
| <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>magical seventh chord</title></head><body>A <em>magical seventh</em> is an 11-limit essentially tempered dyadic chord consisting of three sharp minor thirds and an 8/7, in other words a 6/5-6/5-6/5-8/7 chord, which closes at the octave since both 99/98 and 385/384 (and therefore 875/864) are tempered out. This means that in the 11-limit 4&amp;7&amp;15 planar temperament tempering these out, the chord is the tempering of 1-6/5-16/11-7/4. In an optimized tuning for the 4&amp;7&amp;15 temperament, the marvel comma 225/224 shrinks in size and may reverse direction, and adding it to the list of commas does little tuning damage; this results in 11-limit magic temperament, which has the same optimal patent val (<a class="wiki_link" href="/104edo">104edo</a>.) Hence while it by definition it merely requires the 4&amp;7&amp;15 temperament, it can for the most part be regarded as a chord of <a class="wiki_link" href="/magic">magic</a> (19&amp;22) temperament.<br />
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| | In an optimized tuning for the keemic temperament, the [[marvel]] comma [[225/224]] shrinks in size and may reverse direction, and adding it to the list of commas does little tuning [[damage]]; this results in 11-limit [[magic]] temperament, which has the same [[optimal patent val]] ([[104edo]]). Hence [[magic]] (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a [[Graham complexity]] of 12, so it does not appear that often. |
| However, this chord also exists and has low complexity in 11-limit <a class="wiki_link" href="/Superpyth#Suprapyth">suprapyth</a> temperament. One is found in the 7-note MOS.</body></html></pre></div>
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| | Other temperaments that feature this chord prominently include 11-limit [[keemun]], [[superkleismic]], [[porcupine]] and [[doublewide]]. |
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| | For other tetrads, there are |
| | * 1–5/4–16/11–9/5 with steps 5/4, 7/6, 5/4, 10/9; |
| | * 1–12/11–5/4–9/5 with steps 12/11, 8/7, 16/11, 10/9, and its inverse |
| | * 1–12/11–6/5–7/4 with steps 12/11, 10/9, 16/11, 8/7. |
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| | For pentads, there are |
| | * 1–12/11–5/4–3/2–9/5 with steps 12/11, 8/7, 6/5, 6/5, 10/9, and its inverse |
| | * 1–6/5–11/8–3/2–5/3 with steps 6/5, 8/7, 12/11, 10/9, 6/5; |
| | * 1–5/4–11/8–3/2–12/7 with steps 5/4, 11/10, 12/11, 8/7, 7/6, and its inverse |
| | * 1–12/11–6/5–3/2–7/4 with steps 12/11, 11/10, 5/4, 7/6, 8/7. |
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| | The count of keemic chords is therefore tetrads: 4, and pentads: 4, for a total of 8. |
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| | [[Category:11-odd-limit chords]] |
| | [[Category:Essentially tempered chords]] |
| | [[Category:Tetrads]] |
| | [[Category:Pentads]] |
| | [[Category:Keemic]] |