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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | '''Nicolic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the nicola, [[1575/1573]]. |
| 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:xenwolf|xenwolf]] and made on <tt>2011-10-19 17:27:20 UTC</tt>.<br>
| | Nicolic chords are of [[dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the [[15-odd-limit]]. There are 3 triads, 6 tetrads and 2 pentads for a total of 11 distinct chord structures. |
| : The original revision id was <tt>266566564</tt>.<br>
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| : The revision comment was: <tt></tt><br>
| | The nicolic triads include the following palindromic form since it identifies [[13/7]] by a stack of two [[15/11]]'s: |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | * 1–15/11–13/7 with steps of 15/11, 15/11, [[14/13]]. |
| <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 **nicolic tetrad** in close position is a [[Unisone|1]]-[[15_13|15/13]]-[[15_11|15/11]]-[[11_7|11/7]] in a temperament where the [[nicola]], 1575/1573, is [[tempering out|tempered out]]. It therefore has steps of 15/13-[[13_11|13/11]]-15/13-[[14_11|14/11]], and is a [[15-limit]] chord. [[Equal]] divisions with nicolic tetrads include [[58edo]], [[72edo]], [[87edo]], [[103edo]], [[121edo]], [[130edo]], [[190edo]], [[217edo]], [[224edo]], [[311edo]], [[414edo]], [[441edo]], [[665edo]] and [[855edo]].</pre></div>
| | And a pair in inverse relationship: |
| <h4>Original HTML content:</h4>
| | * 1–15/11–[[11/7]] with steps of 15/11, [[15/13]], [[14/11]], and its inverse |
| <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>nicolic tetrad</title></head><body>The <strong>nicolic tetrad</strong> in close position is a <a class="wiki_link" href="/Unisone">1</a>-<a class="wiki_link" href="/15_13">15/13</a>-<a class="wiki_link" href="/15_11">15/11</a>-<a class="wiki_link" href="/11_7">11/7</a> in a temperament where the <a class="wiki_link" href="/nicola">nicola</a>, 1575/1573, is <a class="wiki_link" href="/tempering%20out">tempered out</a>. It therefore has steps of 15/13-<a class="wiki_link" href="/13_11">13/11</a>-15/13-<a class="wiki_link" href="/14_11">14/11</a>, and is a <a class="wiki_link" href="/15-limit">15-limit</a> chord. <a class="wiki_link" href="/Equal">Equal</a> divisions with nicolic tetrads include <a class="wiki_link" href="/58edo">58edo</a>, <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a>, <a class="wiki_link" href="/103edo">103edo</a>, <a class="wiki_link" href="/121edo">121edo</a>, <a class="wiki_link" href="/130edo">130edo</a>, <a class="wiki_link" href="/190edo">190edo</a>, <a class="wiki_link" href="/217edo">217edo</a>, <a class="wiki_link" href="/224edo">224edo</a>, <a class="wiki_link" href="/311edo">311edo</a>, <a class="wiki_link" href="/414edo">414edo</a>, <a class="wiki_link" href="/441edo">441edo</a>, <a class="wiki_link" href="/665edo">665edo</a> and <a class="wiki_link" href="/855edo">855edo</a>.</body></html></pre></div>
| | * 1–15/11–[[26/15]] with steps of 15/11, 14/11, 15/13. |
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| | For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are |
| | * 1–15/13–15/11–11/7 with steps of 15/13, [[13/11]], 15/13, 14/11; |
| | * 1–15/13–[[22/15]]–11/7 with steps of 15/13, 14/11, [[15/14]], 14/11. |
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| | The inversely related pairs of chords are |
| | * 1–15/11–11/7–13/7 with steps of 15/11, 15/13, 13/11, 14/13, and its inverse |
| | * 1–15/11–22/15–26/15 with steps of 15/11, 14/13, 13/11, 15/13; |
| | * 1–15/11–26/15–13/7 with steps of 15/11, 14/11, 15/14, 14/13, and its inverse |
| | * 1–15/11–22/15–11/7 with steps of 15/11, 14/13, 15/14, 14/11. |
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| | They can be extended to pentads: |
| | * 1–15/14–15/13–15/11–11/7 with steps of 15/14, 14/13, 13/11, 15/13, 14/11, and its inverse |
| | * 1–15/13–15/11–22/15–11/7 with steps of 15/13, 13/11, 14/13, 15/14, 14/11. |
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| | [[Equal temperament]]s with nicolic chords include {{Optimal ET sequence| 29, 31, 43, 58, 72, 87, 94, 103, 121, 130, 159, 190, 217, 224, 311, 414, 441, 665 and 855 }}. |
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| | Here is a listening sample, tempered to TE tuning of nicolic. |
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| | {| class="wikitable center-all" |
| | ! Ratio |
| | ! [[1/1]] || [[15/13]] || [[15/11]] || [[11/7]] |
| | |- |
| | ! [[Cent]]s |
| | | 0.000 || 247.099 || 536.086 || 783.185 |
| | |- |
| | ! Sound <br> <small>[[:File:Nicolic tetrad.mp3|[info]]]</small> |
| | | colspan="4" | [[File:Nicolic tetrad.mp3]] |
| | |} |
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| | [[Category:15-odd-limit chords]] |
| | [[Category:Essentially tempered chords]] |
| | [[Category:Triads]] |
| | [[Category:Tetrads]] |
| | [[Category:Pentads]] |
| | [[Category:Nicolic]] |
| | [[Category:Listen]] |