Wikispaces>RicardoMatosinhos |
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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | '''1/2-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a half of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor sevenths being exactly [[9/5]] (and major seconds being exactly [[10/9]]). |
| 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:RicardoMatosinhos|RicardoMatosinhos]] and made on <tt>2015-12-09 15:38:44 UTC</tt>.<br>
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| : The original revision id was <tt>569631497</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">In 1/2-comma [[meantone]] temperament, each perfect fifth is tempered by a half of a [[Syntonic Comma|syntonic comma]] from its just value of [[3_2|3/2]]. This results in minor sevenths being exactly 9/5 (and major seconds being exactly 10/9).
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| In this system, the "major thirds" are exactly 100/81 or approximately 365 cents, thus bordering on neutral thirds. The fifths of this temperament are even narrower than those of [[26edo]], which is the most likely candidate for a closed system approximating this meantime. </pre></div> | | In this system, the major thirds are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo]], but closer to 33, which is the best small number candidate for a closed system approximating this meantone. If you want more precision, [[125edo]] using the bb [[val]] flat 5th is audibly indistinguishable from a closed system of half-comma meantone, with an error measured in thousandths of a cent. |
| <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>1-2 syntonic comma meantone</title></head><body>In 1/2-comma <a class="wiki_link" href="/meantone">meantone</a> temperament, each perfect fifth is tempered by a half of a <a class="wiki_link" href="/Syntonic%20Comma">syntonic comma</a> from its just value of <a class="wiki_link" href="/3_2">3/2</a>. This results in minor sevenths being exactly 9/5 (and major seconds being exactly 10/9).<br />
| | For a tuning with so flat a fifth, the 7-limit [[extension]] that preserves [[7-odd-limit]] [[diamond monotone]] is [[flattertone]]. Otherwise the septimal meantone mapping has the sizes of [[7/6]] and [[8/7]] swapped, and the flattone mapping has the sizes of [[7/5]] and [[10/7]] swapped. |
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| In this system, the &quot;major thirds&quot; are exactly 100/81 or approximately 365 cents, thus bordering on neutral thirds. The fifths of this temperament are even narrower than those of <a class="wiki_link" href="/26edo">26edo</a>, which is the most likely candidate for a closed system approximating this meantime.</body></html></pre></div>
| | == Tuning profile == |
| | [[Projection map]]: |
| | |
| | {| class="right-all" |
| | |- |
| | | [⟨ || 1 || 2 || 4 || 10 || ] |
| | |- |
| | | ⟨ || 0 || -1 || -4 || -17 || ] |
| | |- |
| | | ⟨ || 0 || 1/2 || 2 || 17/2 || ] |
| | |- |
| | | ⟨ || 0 || 0 || 0 || 0 || ]] |
| | |} |
| | |
| | [[Tuning map]]: {{val| 1200 1891.2019 2764.8074 3350.4316 }} |
| | |
| | [[Error map]]: {{val| 0 -10.7531 -21.5063 -18.3944 }} |
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| | [[Category:Meantone]] |
| | [[Category:Historical]] |