Xenharmonic Wiki

1817edo: Difference between revisions

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**Imported revision 556767053 - Original comment: **
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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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>2015-08-16 16:09:25 UTC</tt>.<br>
 
: The original revision id was <tt>556767053</tt>.<br>
1817edo is distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system. Past that, adding the mapping for [[29/16|29]] is worth considering.
: 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>
In the 5-limit, it is a strong tuning for [[alphatricot]]. It also [[tempering out|tempers out]] {{monzo| 128 13 -64 }}, corresponding to the 323 & 1171 temperament, which divides the [[3/1|third harmonic]] into 64 equal parts, as well as {{monzo| -89 -42 67 }} and {{monzo| -50 -71 70 }}. In the 7-limit, it tempers out [[4375/4374]] (ragisma). In the 11-limit it tempers out 117649/117612, 2097152/2096325, and tunes rank-3 temperaments [[heimdall]] and [[bragi]]. In the 13-limit, it tempers out [[4096/4095]], [[6656/6655]], and in the 17-limit, [[12376/12375]] and [[14400/14399]].
<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">The 1817 division is distinctly consistent in the 17-limit, and a fairly strong 17-limit system.</pre></div>
In the 17-limit and the 2.3.5.7.11.13.17.37 subgroup (17-limit add-37), the [[patent val]] tunes the [[gold]] temperament which divides the octave into 79 parts, though it is worth noting that the error on the 37th harmonic is quite large.
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;1817edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 1817 division is distinctly consistent in the 17-limit, and a fairly strong 17-limit system.&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Prime harmonics ===
{{Harmonics in equal|1817}}
 
=== Subsets and supersets ===
Since 1817 factors into primes as {{nowrap| 23 × 79 }}, 1817edo contains [[23edo]] and [[79edo]] as subsets.
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