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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | A '''werckismic chord''' is an [[essentially tempered dyadic chord]] tempered by the werckisma, [[441/440]]. |
| 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>2011-12-13 23:34:44 UTC</tt>.<br>
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| : The original revision id was <tt>285750550</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 //werckismic chord// is an [[dyadic chord|essentially tempered dyadic chord]] in werckismic (441/440) tempering in the 2.9.5.7.11 subgroup in the 11-odd-limit.
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| The werckismic triads consist of three pairs of inversely related chords: 1-11/9-7/5 with steps 11/9-8/7-10/7 and 1-11/9-7/4 with steps 11/9-10/7-8/7; 1-11/7-7/4 with steps 11/7-10/9-8/7 and 1-11/7-9/5 with steps 11/7-8/7-10/9; and 1-7/5-11/7 with steps 7/5-9/8-14/11 and 1-14/11-10/7 with steps 14/11-9/8-7/5.
| | Werckismic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the [[11-odd-limit]], meaning that there are 6 [[triad]]s, 15 [[tetrad]]s and 6 [[pentad]]s, for a total of 27 distinct chord structures. |
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| The werckismic tetrads consist of three palindromic (self-inversive) chords and five pairs of chords in an inverse relationship. The palindromic chords are 1-5/4-10/7-7/4 with steps 5/4-8/7-11/9-8/7; 1-9/8-10/7-11/7 with steps 9/8-14/11-11/10-14/11; and 1-14/11-7/5-16/9 with steps 14/11-11/10-14/11-9/8. The pairs of chords are 1-11/9-11/7-7/4 with steps 11/9-9/7-10/9-8/7 and 1-9/7-11/7-9/5 with steps 9/7-11/9-8/7-10/9; 1-10/7-11/7-7/4 with steps 10/7-11/10-10/9-8/7 and 1-8/7-14/11-7/5 with steps 8/7-10/9-11/10-10/7; 1-9/8-10/7-7/4 with steps 9/8-14/11-11/9-8/7 and 1-11/9-14/9-7/4 with steps 11/9-14/11-9/8-8/7; 1-11/9-11/8-7/4 with steps 11/9-9/8-14/11-8/7 and 1-14/11-10/7-7/4 with steps 14/11-9/8-11/9-8/7; 1-9/8-5/4-10/7 with steps 9/8-10/9-8/7-7/5 and 1-10/9-5/4-7/4 with steps 10/9-9/8-7/5-8/7; and 1-9/8-9/7-10/7 with steps 9/8-8/7-10/9-7/5 and 1-9/8-11/7-7/4 with steps 9/8-7/5-10/9-8/7. | | The werckismic triads consist of three pairs of inversely related chords: |
| | * 1–11/9–7/5 with steps 11/9, 8/7, 10/7, and its inverse |
| | * 1–11/9–7/4 with steps 11/9, 10/7, 8/7; |
| | * 1–11/7–7/4 with steps 11/7, 10/9, 8/7, and its inverse |
| | * 1–11/7–9/5 with steps 11/7, 8/7, 10/9; |
| | * 1–7/5–11/7 with steps 7/5, 9/8, 14/11, and its inverse |
| | * 1–14/11–10/7 with steps 14/11, 9/8, 7/5. |
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| The werckismic pentads consist of three pairs of chords in an inverse relationship: 1-9/8-5/4-10/7-7/4 with steps 9/8-10/9-8/7-11/9-8/7 and 1-11/9-7/5-14/9-7/4 with steps 11/9-8/7-10/9-9/8-8/7; 1-11/9-11/8-11/7-7/4 with steps 11/9-9/8-8/7-10/9-8/7 and 1-9/8-11/8-11/7-7/4 with steps 9/8-11/9-8/7-10/9-8/7; 1-9/8-9/7-10/7-11/7 with steps 9/8-8/7-10/9-11/10-14/11 and 1-9/8-10/7-11/7-7/4 with steps 9/8-14/11-11/10-10/9-8/7. | | The werckismic tetrads consist of three palindromic (self-inversive) chords and five pairs of chords in an inverse relationship. The palindromic chords are |
| | * 1–5/4–10/7–7/4 with steps 5/4, 8/7, 11/9, 8/7; |
| | * 1–9/8–10/7–11/7 with steps 9/8, 14/11, 11/10, 14/11; |
| | * 1–14/11–7/5–16/9 with steps 14/11, 11/10, 14/11, 9/8. |
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| Equal temperaments with werckismic chords include 31, 41, 43, 46, 58, 72, 77, 84, 103, 118, 130, 159, 171, 190, 248, 289, 320, 727d, 929d and 1249d.</pre></div>
| | The pairs of chords are: |
| <h4>Original HTML content:</h4>
| | * 1–11/9–11/7–7/4 with steps 11/9, 9/7, 10/9, 8/7, 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>werckismic chords</title></head><body>A <em>werckismic chord</em> is an <a class="wiki_link" href="/dyadic%20chord">essentially tempered dyadic chord</a> in werckismic (441/440) tempering in the 2.9.5.7.11 subgroup in the 11-odd-limit.<br />
| | * 1–9/7–11/7–9/5 with steps 9/7, 11/9, 8/7, 10/9; |
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| | * 1–10/7–11/7–7/4 with steps 10/7, 11/10, 10/9, 8/7, and its inverse |
| The werckismic triads consist of three pairs of inversely related chords: 1-11/9-7/5 with steps 11/9-8/7-10/7 and 1-11/9-7/4 with steps 11/9-10/7-8/7; 1-11/7-7/4 with steps 11/7-10/9-8/7 and 1-11/7-9/5 with steps 11/7-8/7-10/9; and 1-7/5-11/7 with steps 7/5-9/8-14/11 and 1-14/11-10/7 with steps 14/11-9/8-7/5.<br /> | | * 1–8/7–14/11–7/5 with steps 8/7, 10/9, 11/10, 10/7; |
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| | * 1–9/8–10/7–7/4 with steps 9/8, 14/11, 11/9, 8/7, and its inverse |
| The werckismic tetrads consist of three palindromic (self-inversive) chords and five pairs of chords in an inverse relationship. The palindromic chords are 1-5/4-10/7-7/4 with steps 5/4-8/7-11/9-8/7; 1-9/8-10/7-11/7 with steps 9/8-14/11-11/10-14/11; and 1-14/11-7/5-16/9 with steps 14/11-11/10-14/11-9/8. The pairs of chords are 1-11/9-11/7-7/4 with steps 11/9-9/7-10/9-8/7 and 1-9/7-11/7-9/5 with steps 9/7-11/9-8/7-10/9; 1-10/7-11/7-7/4 with steps 10/7-11/10-10/9-8/7 and 1-8/7-14/11-7/5 with steps 8/7-10/9-11/10-10/7; 1-9/8-10/7-7/4 with steps 9/8-14/11-11/9-8/7 and 1-11/9-14/9-7/4 with steps 11/9-14/11-9/8-8/7; 1-11/9-11/8-7/4 with steps 11/9-9/8-14/11-8/7 and 1-14/11-10/7-7/4 with steps 14/11-9/8-11/9-8/7; 1-9/8-5/4-10/7 with steps 9/8-10/9-8/7-7/5 and 1-10/9-5/4-7/4 with steps 10/9-9/8-7/5-8/7; and 1-9/8-9/7-10/7 with steps 9/8-8/7-10/9-7/5 and 1-9/8-11/7-7/4 with steps 9/8-7/5-10/9-8/7.<br />
| | * 1–11/9–14/9–7/4 with steps 11/9, 14/11, 9/8, 8/7; |
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| | * 1–11/9–11/8–7/4 with steps 11/9, 9/8, 14/11, 8/7, and its inverse |
| The werckismic pentads consist of three pairs of chords in an inverse relationship: 1-9/8-5/4-10/7-7/4 with steps 9/8-10/9-8/7-11/9-8/7 and 1-11/9-7/5-14/9-7/4 with steps 11/9-8/7-10/9-9/8-8/7; 1-11/9-11/8-11/7-7/4 with steps 11/9-9/8-8/7-10/9-8/7 and 1-9/8-11/8-11/7-7/4 with steps 9/8-11/9-8/7-10/9-8/7; 1-9/8-9/7-10/7-11/7 with steps 9/8-8/7-10/9-11/10-14/11 and 1-9/8-10/7-11/7-7/4 with steps 9/8-14/11-11/10-10/9-8/7.<br /> | | * 1–14/11–10/7–7/4 with steps 14/11, 9/8, 11/9, 8/7; |
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| | * 1–9/8–5/4–10/7 with steps 9/8, 10/9, 8/7, 7/5, and its inverse |
| Equal temperaments with werckismic chords include 31, 41, 43, 46, 58, 72, 77, 84, 103, 118, 130, 159, 171, 190, 248, 289, 320, 727d, 929d and 1249d.</body></html></pre></div> | | * 1–10/9–5/4–7/4 with steps 10/9, 9/8, 7/5, 8/7; |
| | * 1–9/8–9/7–10/7 with steps 9/8, 8/7, 10/9, 7/5, and its inverse |
| | * 1–9/8–11/7–7/4 with steps 9/8, 7/5, 10/9, 8/7. |
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| | The werckismic pentads consist of three pairs of chords in an inverse relationship: |
| | * 1–9/8–5/4–10/7–7/4 with steps 9/8, 10/9, 8/7, 11/9, 8/7, and its inverse |
| | * 1–11/9–7/5–14/9–7/4 with steps 11/9, 8/7, 10/9, 9/8, 8/7; |
| | * 1–11/9–11/8–11/7–7/4 with steps 11/9, 9/8, 8/7, 10/9, 8/7, and its inverse |
| | * 1–9/8–11/8–11/7–7/4 with steps 9/8, 11/9, 8/7, 10/9, 8/7; |
| | * 1–9/8–9/7–10/7–11/7 with steps 9/8, 8/7, 10/9, 11/10, 14/11, and its inverse |
| | * 1–9/8–10/7–11/7–7/4 with steps 9/8, 14/11, 11/10, 10/9, 8/7. |
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| | [[Equal temperament]]s with werckismic chords include {{EDOs| 31, 41, 43, 46, 58, 72, 77, 84, 103, 118, 130, 159, 171, 190, 248, 289, and 320 }}, with [[320edo]] giving the [[optimal patent val]]. |
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| | [[Category:11-odd-limit chords]] |
| | [[Category:Essentially tempered chords]] |
| | [[Category:Triads]] |
| | [[Category:Tetrads]] |
| | [[Category:Pentads]] |
| | [[Category:Werckismic]] |