|
|
| (12 intermediate revisions by 5 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | A '''valinorsmic chord''' is a [[valinorsma]] (176/175) tempered [[essentially tempered chord]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-10 21:45:42 UTC</tt>.<br>
| | Valinorsmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.5.7.11 [[subgroup]] [[11-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. |
| : The original revision id was <tt>284568832</tt>.<br>
| | |
| : The revision comment was: <tt></tt><br>
| | There are three valinorsmic triads: the valinorsmic version of the augmented triad, |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | * 1–5/4–8/5 with steps 5/4, 14/11, 5/4, |
| <h4>Original Wikitext content:</h4>
| | |
| <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 valinorsmic tetrad is any of five 15-limit [[Dyadic chord|essentially tempered tetrads]] which are tempered by the valinorsma, 176/175. Four of them represent alternative, valinorsmic, temperings of the four 7-limit tetrads with steps 5/4-6/5-8/7-7/6 and 5/4-8/7-6/5-7/6 and their inversions 6/5-5/4-7/6-8/7 and 5/4-7/6-6/5-8/7, leading to 176/175 temperings of 1-5/4-10/7-12/7, 1-5/4-3/2-12/7, 1-6/5-3/2-7/4 and 1-5/4-22/15-7/4. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords. Aside from these, there are many more with smaller step sizes such as 11/10.</pre></div>
| | and an inversely related pair, |
| <h4>Original HTML content:</h4>
| | * 1–8/5–7/4 with steps 8/5, 11/10, 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>valinorsmic chords</title></head><body>A valinorsmic tetrad is any of five 15-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered tetrads</a> which are tempered by the valinorsma, 176/175. Four of them represent alternative, valinorsmic, temperings of the four 7-limit tetrads with steps 5/4-6/5-8/7-7/6 and 5/4-8/7-6/5-7/6 and their inversions 6/5-5/4-7/6-8/7 and 5/4-7/6-6/5-8/7, leading to 176/175 temperings of 1-5/4-10/7-12/7, 1-5/4-3/2-12/7, 1-6/5-3/2-7/4 and 1-5/4-22/15-7/4. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords. Aside from these, there are many more with smaller step sizes such as 11/10.</body></html></pre></div>
| | * 1–8/7–5/4 with steps 8/7, 11/10, 8/5. |
| | |
| | Valinorsmic tetrads are six in number, consisting of two palindromic chords and two pairs of inversely related chords. The palindromes are |
| | * 1–11/10–5/4–7/4 with steps 11/10, 8/7, 7/5, 8/7, and its inverse |
| | * 1–11/10–5/4–11/8 with steps 11/10, 8/7, 11/10, 16/11. |
| | |
| | The rest are |
| | * 1–5/4–8/5–7/4 with steps 5/4, 14/11, 11/10, 8/7, and its inverse |
| | * 1–5/4–10/7–11/7 with steps 5/4, 8/7, 11/10, 14/11; |
| | * 1–5/4–11/8–11/7 with steps 5/4, 11/10, 8/7, 14/11, and its inverse |
| | * 1–11/10–11/8–7/4 with steps 11/10, 5/4, 14/11, 8/7. |
| | |
| | Finally, there are the two inversely related pentads, |
| | * 1–11/10–5/4–8/5–7/4 with steps 11/10, 8/7, 14/11, 11/10, 8/7, and its inverse |
| | * 1–11/10–5/4–11/8–7/4 with steps 11/10, 8/7, 11/10, 14/11, 8/7. |
| | |
| | If we are willing to go to the [[15-odd-limit]], we get four alternative, valinorsmic, temperings of the four [[keenanismic chords|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9, 6/5, 8/7, 6/5, leading to 1–11/9–22/15–5/3 chords. |
| | |
| | [[Equal temperament]]s with valinorsmic chords include {{EDOs| 22, 31, 43, 46, 53, 58, 68, 80, 89, 111 }} with 111edo giving the [[optimal patent val]]. |
| | |
| | [[Category:11-odd-limit chords]] |
| | [[Category:Essentially tempered chords]] |
| | [[Category:Triads]] |
| | [[Category:Tetrads]] |
| | [[Category:Pentads]] |
| | [[Category:Valinorsmic]] |