|
|
| (15 intermediate revisions by 9 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-08-17 14:06:38 UTC</tt>.<br>
| | |
| : The original revision id was <tt>556819417</tt>.<br>
| | 2190edo is a very strong [[13-limit]] system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and nothing beats it until [[2684edo|2684]]. It is closely related to [[730edo]], the Woolhouse unit system, with which it shares the same tuning in the [[5-limit]], but the [[harmonic]]s [[7/1|7]], [[11/1|11]], and [[13/1|13]] are all mapped differently. A basis for the 13-limit [[comma]]s is {[[9801/9800]], [[10648/10647]], 105644/105625, [[140625/140608]], 196625/196608}; also [[tempering out|tempered out]] are [[123201/123200]], [[151263/151250]], and [[250047/250000]]. |
| : 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>
| | It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19 [[subgroup]], where it holds the record of lowest relative error until [[6079edo|6079]], and the 2.3.5.7.11.13.19.29 subgroup, where it holds the record of lowest relative error until [[14618edo|14618]]. |
| <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 2190 equal division divides the octave into 2190 equal parts of 0.5479 cents each. It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]], and nothing beats it until [[2684edo|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250.</pre></div>
| | === Prime harmonics === |
| <h4>Original HTML content:</h4>
| | {{Harmonics in equal|2190|columns=11}} |
| <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>2190edo</title></head><body>The 2190 equal division divides the octave into 2190 equal parts of 0.5479 cents each. It is is a very strong 13-limit system; no smaller division has a smaller 13-limit <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a>, and nothing beats it until <a class="wiki_link" href="/2684edo">2684</a>. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250.</body></html></pre></div>
| | {{Harmonics in equal|2190|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 2190edo (continued)}} |
| | |
| | === Subsets and supersets === |
| | Since 2190 factors into primes as {{nowrap| 2 × 3 × 5 × 73 }}, 2190edo has subset edos {{EDOs| 2, 3, 5, 6, 10, 12, 15, 30, 73, 146, 219, 365, 438, 730, and 1095 }}. A step of 2190edo is exactly {{frac|1|3}} Woolhouse unit. |
| | |
| | [[4380edo]], which doubles 2190edo, provides a good correction to the harmonics [[17/1|17]] and [[23/1|23]]. |