|
|
| (10 intermediate revisions by 7 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | '''Huntmic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the huntma, [[640/637]]. |
| 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>2011-08-01 16:38:57 UTC</tt>.<br>
| |
| : The original revision id was <tt>243776417</tt>.<br>
| |
| : The revision comment was: <tt></tt><br>
| |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| |
| <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">//Huntmic chords// are certain 13-limit [[Dyadic chord|essentially tempered chords]] which close at the octave by tempering out the huntma, 640/637. These include triads with steps of size (huntmic tempered) 5/4-16/13-8/7-8/7, 16/13-5/4-8/7-8/7 and 5/4-8/7-16/13-8/7, leading to the huntmic temperings of 5/4-20/13-7/4-2, 16/13-20/13-7/4-2 and 5/4-10/7-7/4-2. Note that the last chord can also be tempered by 441/440 to the [[werckismic chords|werckismic tetrad]]. Aside from tetrads, there are huntmic triads, the huntmic tempered versions of 1-16/13-7/5 and 1-8/7-7/5.
| |
|
| |
|
| The name huntmic comes from the fact that the [[optimal patent val]] for huntmic temperament is [[205edo]], the basis of the Hunt System of [[Aaron Andrew Hunt]]. Other equal temperaments with huntmic chords include 22, 53, 68, 80, 94, 111, 121, 137 and 215.</pre></div>
| | There are three triads, six tetrads and two pentads as 2.5.7.13 [[subgroup]] [[13-odd-limit]] essentially tempered chords. |
| <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>huntmic chords</title></head><body><em>Huntmic chords</em> are certain 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered chords</a> which close at the octave by tempering out the huntma, 640/637. These include triads with steps of size (huntmic tempered) 5/4-16/13-8/7-8/7, 16/13-5/4-8/7-8/7 and 5/4-8/7-16/13-8/7, leading to the huntmic temperings of 5/4-20/13-7/4-2, 16/13-20/13-7/4-2 and 5/4-10/7-7/4-2. Note that the last chord can also be tempered by 441/440 to the <a class="wiki_link" href="/werckismic%20chords">werckismic tetrad</a>. Aside from tetrads, there are huntmic triads, the huntmic tempered versions of 1-16/13-7/5 and 1-8/7-7/5.<br />
| | For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is |
| <br />
| | * 1-8/7-13/10 chord with steps of 8/7-8/7-20/13. |
| The name huntmic comes from the fact that the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for huntmic temperament is <a class="wiki_link" href="/205edo">205edo</a>, the basis of the Hunt System of <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a>. Other equal temperaments with huntmic chords include 22, 53, 68, 80, 94, 111, 121, 137 and 215.</body></html></pre></div> | | |
| | The inversely related pair of chords is |
| | * 1-16/13-7/5 with steps of 16/13-8/7-10/7, and its inverse |
| | * 1-8/7-7/5 with steps of 8/7-16/13-10/7. |
| | |
| | For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are |
| | * 1-16/13-7/5-7/4 chord with steps of 16/13-8/7-5/4-8/7; |
| | * 1-8/7-16/13-7/5 chord with steps of 8/7-14/13-8/7-10/7. |
| | |
| | The inversely related pairs of chords are |
| | * 1-5/4-10/7-13/8 with steps of 5/4-8/7-8/7-16/13, and its inverse |
| | * 1-8/7-13/10-13/8 with steps of 8/7-8/7-5/4-16/13; |
| | * 1-8/7-13/10-13/7 with steps of 8/7-8/7-10/7-14/13, and its inverse |
| | * 1-8/7-13/10-7/5 with steps of 8/7-8/7-14/13-10/7. |
| | |
| | They can be extended to pentads: |
| | * 1-8/7-10/7-13/8-7/4 with steps of 8/7-5/4-8/7-14/13-8/7, and its inverse |
| | * 1-8/7-16/13-7/5-7/4 with steps of 8/7-14/13-8/7-5/4-8/7. |
| | |
| | Equal temperaments with huntmic chords include {{Optimal ET sequence| 22, 53, 68, 80, 94, 111, 121, 137, 205 and 215 }}. The name huntmic comes from the fact that the [[optimal patent val]] for huntmic temperament is [[205edo]], the basis of the [[Hunt System]] of [[Aaron Andrew Hunt]]. |
| | |
| | [[Category:Essentially tempered chords]] |
| | [[Category:Triads]] |
| | [[Category:Tetrads]] |
| | [[Category:Pentads]] |
| | [[Category:Huntmic]] |