|
|
| (13 intermediate revisions by 8 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-28 10:13:49 UTC</tt>.<br>
| | |
| : The original revision id was <tt>597384934</tt>.<br>
| | 223edo contains an excellent proportion of [[hornbostel]] temperament (via [[7L 2s]]), between square root of π (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is in[[consistent]] to the [[5-odd-limit]] and higher limit, with three mappings possible for the 5-limit: |
| : The revision comment was: <tt></tt><br>
| | * {{val| 223 353 518 }} ([[patent val]]), |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | * {{val| 223 '''354''' 518 }} (223b), |
| <h4>Original Wikitext content:</h4>
| | * {{val| 223 353 '''517''' }} (223c). |
| <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">=<span style="color: #2230ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">223 equal divisions per 2/1</span>=
| | |
| Divides the 2/1 ratio in 5.38117 Cents each step. Contains an excellent proportion of Hornbostel Temperament (via 7L2s), between Square root of Pi (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223).</pre></div>
| | Using the patent val, it tempers out 393216/390625 ([[würschmidt comma]]) and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit; 243/242, 441/440, 5632/5625, and 1449459/1433600 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit. |
| <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>223edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x223 equal divisions per 2/1"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #2230ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">223 equal divisions per 2/1</span></h1>
| | Using the 223be val, it tempers out 15625/15552 ([[kleisma]]) and {{monzo| 58 -38 1 }} in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit; 3025/3024, 3388/3375, 4375/4356, and 65536/65219 in the 11-limit; 352/351, 1001/1000, 2197/2178, and 2704/2695 in the 13-limit. Using the 223bef val, it tempers out 196/195, 325/324, 364/363, 625/624, and 49152/49049 in the 13-limit. |
| Divides the 2/1 ratio in 5.38117 Cents each step. Contains an excellent proportion of Hornbostel Temperament (via 7L2s), between Square root of Pi (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223).</body></html></pre></div>
| | |
| | Using the 223c val, it tempers out the 129140163/128000000 ([[graviton]]) and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, and 4000/3993 in the 11-limit; 1188/1183, 1573/1568, 1625/1617, 1716/1715, and 3159/3136 in the 13-limit. |
| | |
| | Using the 223e val, it tempers out 1944/1925, 2835/2816, and 4000/3993 in the 11-limit; 364/363, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit. |
| | |
| | === Odd harmonics === |
| | {{Harmonics in equal|223|columns=11}} |
| | |
| | === Subsets and supersets === |
| | 223edo is the 48th [[prime edo]]. |