Diaschismic family: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>~~2012~~-05-~~17 17~~:04:03 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-08-24 21:33:59 UTC</tt>.<br>

: The original revision id was <tt>~~336795458~~</tt>.<br>

: The original revision id was <tt>519497090</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>

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<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">[[toc]]

The 5-limit parent comma for the **diaschismic family** is 2048/2025, the [[diaschisma]]. Its monzo is |11 -4 -2>, and flipping that yields <<2 -4 -11|| for the wedgie for 5-limit diaschismic, or **srutal**, temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. [[34edo]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]] or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities.

[[Tuning Ranges of Regular Temperaments|valid range]]: [600.000 to 720.000] (2 to 5)

nice range: [701.955, 706.843]

strict range: [701.955, 706.843]

[[POTE tuning|POTE generator]]: ~3/2 = 704.898

Line 19:

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=Srutal=

Commas: 2048/2025, 4375/4374

valid range: [703.448, 705.882] (58 to 34d)

nice range: [701.955, 706.843]

strict range: [703.448, 705.882]

POTE generator: ~3/2 = 704.814

Line 29:

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==11-limit==

Commas: 176/175, 896/891, 1331/1323

valid range: [704.348, 705.882] (46 to 34d)

nice range: [701.955, 706.843]

strict range: [704.348, 705.882]

POTE generator: ~3/2 = 704.856

Line 38:

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==13-limit==

Commas: 169/168, 176/175, 325/324, 364/363

valid range: [704.348, 705.882] (46 to 34d)

nice range: [701.955, 706.843]

strict range: [704.348, 705.882]

POTE generator: ~3/2 = 704.881

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Commas: 50/49, 64/63

valid range: [700.000, 720.000] (12 to 10)

nice range: [701.955, 715.587]

strict range: [701.955, 715.587]

[[POTE tuning|POTE generator]]: 707.048

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==11-limit==

Commas: 50/49, 64/63, 99/98

valid range: [700.000, 709.091] (12 to 22)

nice range: [701.955, 715.587]

strict range: [701.955, 709.091]

[[POTE tuning|POTE generator]]: 706.885

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Commas: 50/49, 64/63, 65/63, 99/98

valid range: []

nice range: [701.955, 738.573]

strict range: []

POTE generator: ~3/2 = 708.919

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==Pajarous==

Commas: 50/49, 55/54, 64/63

valid range: 709.091 (22)

nice range: [701.955, 715.803]

strict range: 709.091

POTE generator: ~3/2 = 709.578

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===13-limit===

Commas: 50/49, 55/54, 64/63, 65/63

valid range: []

nice range: [701.955, 738.573]

strict range: []

POTE generator: ~3/2 = 710.240

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</div>

The 5-limit parent comma for the <strong>diaschismic family</strong> is 2048/2025, the <a class="wiki_link" href="/diaschisma">diaschisma</a>. Its monzo is |11 -4 -2&gt;, and flipping that yields &lt;&lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or <strong>srutal</strong>, temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. <a class="wiki_link" href="/34edo">34edo</a> is a good tuning choice, with <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/56edo">56edo</a>, <a class="wiki_link" href="/58edo">58edo</a> or <a class="wiki_link" href="/80edo">80edo</a> being other possibilities. Both <a class="wiki_link" href="/12edo">12edo</a> and <a class="wiki_link" href="/22edo">22edo</a> support it, and retuning them to a MOS of diaschismic gives two scale possibilities.<br />

<br />

<a class="wiki_link" href="/Tuning%20Ranges%20of%20Regular%20Temperaments">valid range</a>: [600.000 to 720.000] (2 to 5)<br />

nice range: [701.955, 706.843]<br />

strict range: [701.955, 706.843]<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 704.898<br />

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<h1 id="toc1"><a name="Srutal"></a>Srutal</h1>

Commas: 2048/2025, 4375/4374<br />

<br />

valid range: [703.448, 705.882] (58 to 34d)<br />

nice range: [701.955, 706.843]<br />

strict range: [703.448, 705.882]<br />

<br />

POTE generator: ~3/2 = 704.814<br />

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<h2 id="toc2"><a name="Srutal-11-limit"></a>11-limit</h2>

Commas: 176/175, 896/891, 1331/1323<br />

<br />

valid range: [704.348, 705.882] (46 to 34d)<br />

nice range: [701.955, 706.843]<br />

strict range: [704.348, 705.882]<br />

<br />

POTE generator: ~3/2 = 704.856<br />

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<h2 id="toc3"><a name="Srutal-13-limit"></a>13-limit</h2>

Commas: 169/168, 176/175, 325/324, 364/363<br />

<br />

valid range: [704.348, 705.882] (46 to 34d)<br />

nice range: [701.955, 706.843]<br />

strict range: [704.348, 705.882]<br />

<br />

POTE generator: ~3/2 = 704.881<br />

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<br />

Commas: 50/49, 64/63<br />

<br />

valid range: [700.000, 720.000] (12 to 10)<br />

nice range: [701.955, 715.587]<br />

strict range: [701.955, 715.587]<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 707.048<br />

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<h2 id="toc5"><a name="Pajara-11-limit"></a>11-limit</h2>

Commas: 50/49, 64/63, 99/98<br />

<br />

valid range: [700.000, 709.091] (12 to 22)<br />

nice range: [701.955, 715.587]<br />

strict range: [701.955, 709.091]<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 706.885<br />

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<h2 id="toc6"><a name="Pajara-13-limit"></a>13-limit</h2>

Commas: 50/49, 64/63, 65/63, 99/98<br />

<br />

valid range: []<br />

nice range: [701.955, 738.573]<br />

strict range: []<br />

<br />

POTE generator: ~3/2 = 708.919<br />

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<h2 id="toc7"><a name="Pajara-Pajarous"></a>Pajarous</h2>

Commas: 50/49, 55/54, 64/63<br />

<br />

valid range: 709.091 (22)<br />

nice range: [701.955, 715.803]<br />

strict range: 709.091<br />

<br />

POTE generator: ~3/2 = 709.578<br />

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<h3 id="toc8"><a name="Pajara-Pajarous-13-limit"></a>13-limit</h3>

Commas: 50/49, 55/54, 64/63, 65/63<br />

<br />

valid range: []<br />

nice range: [701.955, 738.573]<br />

strict range: []<br />

<br />

POTE generator: ~3/2 = 710.240<br />

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Compositions:<br />

<br />

<a class="wiki_link_ext" href="http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3" rel="nofollow">http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3</a><br />

<a class="wiki_link_ext" href="http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3" rel="nofollow">http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3</a><br />

(the description says &quot;lemba&quot; which has a similar sale structure but different mapping for 5)<br />

<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2012-05-17 17:04:03 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-08-24 21:33:59 UTC</tt>.<br>
-: The original revision id was <tt>336795458</tt>.<br>
+: The original revision id was <tt>519497090</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>
@@ Line 8: / Line 8: @@
 <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">[[toc]]
 The 5-limit parent comma for the **diaschismic family** is 2048/2025, the [[diaschisma]]. Its monzo is |11 -4 -2&gt;, and flipping that yields &lt;&lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or **srutal**, temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. [[34edo]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]] or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities.
+[[Tuning Ranges of Regular Temperaments|valid range]]: [600.000 to 720.000] (2 to 5)
+nice range: [701.955, 706.843]
+strict range: [701.955, 706.843]
 [[POTE tuning|POTE generator]]: ~3/2 = 704.898
@@ Line 19: / Line 23: @@
 =Srutal=
 Commas: 2048/2025, 4375/4374
+valid range: [703.448, 705.882] (58 to 34d)
+nice range: [701.955, 706.843]
+strict range: [703.448, 705.882]
 POTE generator: ~3/2 = 704.814
@@ Line 29: / Line 37: @@
 ==11-limit==
 Commas: 176/175, 896/891, 1331/1323
+valid range: [704.348, 705.882] (46 to 34d)
+nice range: [701.955, 706.843]
+strict range: [704.348, 705.882]
 POTE generator: ~3/2 = 704.856
@@ Line 38: / Line 50: @@
 ==13-limit==
 Commas: 169/168, 176/175, 325/324, 364/363
+valid range: [704.348, 705.882] (46 to 34d)
+nice range: [701.955, 706.843]
+strict range: [704.348, 705.882]
 POTE generator: ~3/2 = 704.881
@@ Line 52: / Line 68: @@
 Commas: 50/49, 64/63
+valid range: [700.000, 720.000] (12 to 10)
+nice range: [701.955, 715.587]
+strict range:  [701.955, 715.587]
 [[POTE tuning|POTE generator]]: 707.048
@@ Line 61: / Line 81: @@
 ==11-limit==
 Commas: 50/49, 64/63, 99/98
+valid range: [700.000, 709.091] (12 to 22)
+nice range: [701.955, 715.587]
+strict range: [701.955, 709.091]
 [[POTE tuning|POTE generator]]: 706.885
@@ Line 71: / Line 95: @@
 Commas: 50/49, 64/63, 65/63, 99/98
+valid range: []
+nice range: [701.955, 738.573]
+strict range: []
 POTE generator: ~3/2 = 708.919
@@ Line 79: / Line 107: @@
 ==Pajarous==
 Commas: 50/49, 55/54, 64/63
+valid range: 709.091 (22)
+nice range: [701.955, 715.803]
+strict range: 709.091
 POTE generator: ~3/2 = 709.578
@@ Line 88: / Line 120: @@
 ===13-limit===
 Commas: 50/49, 55/54, 64/63, 65/63
+valid range: []
+nice range: [701.955, 738.573]
+strict range: []
 POTE generator: ~3/2 = 710.240
@@ Line 472: / Line 508: @@
 &lt;!-- ws:end:WikiTextTocRule:129 --&gt;&lt;!-- ws:start:WikiTextTocRule:130: --&gt;&lt;/div&gt;
 &lt;!-- ws:end:WikiTextTocRule:130 --&gt;The 5-limit parent comma for the &lt;strong&gt;diaschismic family&lt;/strong&gt; is 2048/2025, the &lt;a class="wiki_link" href="/diaschisma"&gt;diaschisma&lt;/a&gt;. Its monzo is |11 -4 -2&amp;gt;, and flipping that yields &amp;lt;&amp;lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or &lt;strong&gt;srutal&lt;/strong&gt;, temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; is a good tuning choice, with &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/56edo"&gt;56edo&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; or &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; being other possibilities. Both &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; and &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; support it, and retuning them to a MOS of diaschismic gives two scale possibilities.&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/Tuning%20Ranges%20of%20Regular%20Temperaments"&gt;valid range&lt;/a&gt;: [600.000 to 720.000] (2 to 5)&lt;br /&gt;
+nice range: [701.955, 706.843]&lt;br /&gt;
+strict range: [701.955, 706.843]&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 704.898&lt;br /&gt;
@@ Line 483: / Line 523: @@
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Srutal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Srutal&lt;/h1&gt;
 Commas: 2048/2025, 4375/4374&lt;br /&gt;
+&lt;br /&gt;
+valid range: [703.448, 705.882] (58 to 34d)&lt;br /&gt;
+nice range: [701.955, 706.843]&lt;br /&gt;
+strict range: [703.448, 705.882]&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~3/2 = 704.814&lt;br /&gt;
@@ Line 493: / Line 537: @@
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Srutal-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
 Commas: 176/175, 896/891, 1331/1323&lt;br /&gt;
+&lt;br /&gt;
+valid range: [704.348, 705.882] (46 to 34d)&lt;br /&gt;
+nice range: [701.955, 706.843]&lt;br /&gt;
+strict range: [704.348, 705.882]&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~3/2 = 704.856&lt;br /&gt;
@@ Line 502: / Line 550: @@
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Srutal-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
 Commas: 169/168, 176/175, 325/324, 364/363&lt;br /&gt;
+&lt;br /&gt;
+valid range: [704.348, 705.882] (46 to 34d)&lt;br /&gt;
+nice range: [701.955, 706.843]&lt;br /&gt;
+strict range: [704.348, 705.882]&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~3/2 = 704.881&lt;br /&gt;
@@ Line 516: / Line 568: @@
 &lt;br /&gt;
 Commas: 50/49, 64/63&lt;br /&gt;
+&lt;br /&gt;
+valid range: [700.000, 720.000] (12 to 10)&lt;br /&gt;
+nice range: [701.955, 715.587]&lt;br /&gt;
+strict range:  [701.955, 715.587]&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 707.048&lt;br /&gt;
@@ Line 525: / Line 581: @@
 &lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Pajara-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;11-limit&lt;/h2&gt;
   Commas: 50/49, 64/63, 99/98&lt;br /&gt;
+&lt;br /&gt;
+valid range: [700.000, 709.091] (12 to 22)&lt;br /&gt;
+nice range: [701.955, 715.587]&lt;br /&gt;
+strict range: [701.955, 709.091]&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 706.885&lt;br /&gt;
@@ Line 534: / Line 594: @@
 &lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Pajara-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
 Commas: 50/49, 64/63, 65/63, 99/98&lt;br /&gt;
+&lt;br /&gt;
+valid range: []&lt;br /&gt;
+nice range: [701.955, 738.573]&lt;br /&gt;
+strict range: []&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~3/2 = 708.919&lt;br /&gt;
@@ Line 543: / Line 607: @@
 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Pajara-Pajarous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Pajarous&lt;/h2&gt;
   Commas: 50/49, 55/54, 64/63&lt;br /&gt;
+&lt;br /&gt;
+valid range: 709.091 (22)&lt;br /&gt;
+nice range: [701.955, 715.803]&lt;br /&gt;
+strict range: 709.091&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~3/2 = 709.578&lt;br /&gt;
@@ Line 552: / Line 620: @@
 &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Pajara-Pajarous-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h3&gt;
 Commas: 50/49, 55/54, 64/63, 65/63&lt;br /&gt;
+&lt;br /&gt;
+valid range: []&lt;br /&gt;
+nice range: [701.955, 738.573]&lt;br /&gt;
+strict range: []&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~3/2 = 710.240&lt;br /&gt;
@@ Line 754: / Line 826: @@
 Compositions:&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextUrlRule:545:http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3 --&gt;&lt;a class="wiki_link_ext" href="http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3" rel="nofollow"&gt;http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:545 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextUrlRule:582:http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3 --&gt;&lt;a class="wiki_link_ext" href="http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3" rel="nofollow"&gt;http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:582 --&gt;&lt;br /&gt;
 (the description says &amp;quot;lemba&amp;quot; which has a similar sale structure but different mapping for 5)&lt;br /&gt;
 &lt;br /&gt;