Kite's thoughts on pergens: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-01-13 04:38:08 UTC</tt>.<br>

: The original revision id was <tt>~~624814191~~</tt>.<br>

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For example, small triple amber tempers out (12,-1,0,0,-3) from 2.3.11, making a third-11th pergen. The generator is 11/8. If 11/8 is notated as ^P4, the enharmonic is v<span style="vertical-align: super;">3</span>M2, but if 11/8 is notated as vA4, the enharmonic is ^<span style="vertical-align: super;">3</span>dd2.

This is all for single-comma temperaments. Each comma of a multiple-comma temperament also implies an enharmonic, and they may conflict. True double pergens, which are always multi-comma, tend to have multiple notations. For example, the half-everything pergen has 3 possible notations, all equally valid. Even single-split pergens can have multiple commas that imply different enharmonics. ~~So alternate enharmonics are needed sometimes~~.

This is all for single-comma temperaments. Each comma of a multiple-comma temperament also implies an enharmonic, and they may conflict. True double pergens, which are always multi-comma, tend to have multiple notations. For example, the half-everything pergen has 3 possible notations, all equally valid. Even single-split pergens can have multiple commas that imply different enharmonics.

Sometimes the temperament implies an enharmonic that isn't even a 2nd. For example, liese is (P8, P11/3), with G = 7/5 = d5. E = 3·d5 - P11 = descending dd3.

==Alternate keyspans and stepspans==

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||= 8L 2s ||= (P8/2, P4/4) [10] ||= half-8ve quarter-4th decatonic ||< half-8ve quarter-12th ||

||= 9L 1s ||= (P8, P4/2) [10] ||= quarter-4th decatonic ||< ||

4L 2s can be (

==Combining pergens==

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For example, small triple amber tempers out (12,-1,0,0,-3) from 2.3.11, making a third-11th pergen. The generator is 11/8. If 11/8 is notated as ^P4, the enharmonic is v<span style="vertical-align: super;">3</span>M2, but if 11/8 is notated as vA4, the enharmonic is ^<span style="vertical-align: super;">3</span>dd2.<br />

<br />

This is all for single-comma temperaments. Each comma of a multiple-comma temperament also implies an enharmonic, and they may conflict. True double pergens, which are always multi-comma, tend to have multiple notations. For example, the half-everything pergen has 3 possible notations, all equally valid. Even single-split pergens can have multiple commas that imply different enharmonics. ~~So alternate enharmonics are needed sometimes~~.<br />

This is all for single-comma temperaments. Each comma of a multiple-comma temperament also implies an enharmonic, and they may conflict. True double pergens, which are always multi-comma, tend to have multiple notations. For example, the half-everything pergen has 3 possible notations, all equally valid. Even single-split pergens can have multiple commas that imply different enharmonics. <br />

<br />

Sometimes the temperament implies an enharmonic that isn't even a 2nd. For example, liese is (P8, P11/3), with G = 7/5 = d5. E = 3·d5 - P11 = descending dd3.<br />

<br />

<h2 id="toc11"><a name="Further Discussion-Alternate keyspans and stepspans"></a>Alternate keyspans and stepspans</h2>

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</table>

<br />

4L 2s can be (<br />

<br />

<h2 id="toc13"><a name="Further Discussion-Combining pergens"></a>Combining pergens</h2>

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<h2 id="toc16"><a name="Further Discussion-Misc notes"></a>Misc notes</h2>

<br />

Pergens were discovered by Kite Giedraitis in 2017, and developed with the help of Praveen Venkataramana. Earlier drafts of this article can be found at <a href="http://xenharmonic.wikispaces.com/pergen+names">http://xenharmonic.wikispaces.com/pergen+names</a><br />

Pergens were discovered by Kite Giedraitis in 2017, and developed with the help of Praveen Venkataramana. Earlier drafts of this article can be found at <a href="http://xenharmonic.wikispaces.com/pergen+names">http://xenharmonic.wikispaces.com/pergen+names</a><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:TallKite|TallKite]] and made on <tt>2018-01-13 03:54:52 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-01-13 04:38:08 UTC</tt>.<br>
-: The original revision id was <tt>624814191</tt>.<br>
+: The original revision id was <tt>624814715</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 416: / Line 416: @@
 For example, small triple amber tempers out (12,-1,0,0,-3) from 2.3.11, making a third-11th pergen. The generator is 11/8. If 11/8 is notated as ^P4, the enharmonic is v&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;M2, but if 11/8 is notated as vA4, the enharmonic is ^&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;dd2.
-This is all for single-comma temperaments. Each comma of a multiple-comma temperament also implies an enharmonic, and they may conflict. True double pergens, which are always multi-comma, tend to have multiple notations. For example, the half-everything pergen has 3 possible notations, all equally valid. Even single-split pergens can have multiple commas that imply different enharmonics. So alternate enharmonics are needed sometimes.
+This is all for single-comma temperaments. Each comma of a multiple-comma temperament also implies an enharmonic, and they may conflict. True double pergens, which are always multi-comma, tend to have multiple notations. For example, the half-everything pergen has 3 possible notations, all equally valid. Even single-split pergens can have multiple commas that imply different enharmonics.
+Sometimes the temperament implies an enharmonic that isn't even a 2nd. For example, liese is (P8, P11/3), with G = 7/5 = d5. E = 3·d5 - P11 = descending dd3.
 ==Alternate keyspans and stepspans==
@@ Line 485: / Line 487: @@
 ||= 8L 2s ||= (P8/2, P4/4) [10] ||= half-8ve quarter-4th decatonic ||&lt; half-8ve quarter-12th ||
 ||= 9L 1s ||= (P8, P4/2) [10] ||= quarter-4th decatonic ||&lt;   ||
+L 2s can be (
 ==Combining pergens==
@@ Line 2,264: / Line 2,268: @@
 For example, small triple amber tempers out (12,-1,0,0,-3) from 2.3.11, making a third-11th pergen. The generator is 11/8. If 11/8 is notated as ^P4, the enharmonic is v&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;M2, but if 11/8 is notated as vA4, the enharmonic is ^&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;dd2.&lt;br /&gt;
 &lt;br /&gt;
-This is all for single-comma temperaments. Each comma of a multiple-comma temperament also implies an enharmonic, and they may conflict. True double pergens, which are always multi-comma, tend to have multiple notations. For example, the half-everything pergen has 3 possible notations, all equally valid. Even single-split pergens can have multiple commas that imply different enharmonics. So alternate enharmonics are needed sometimes.&lt;br /&gt;
+This is all for single-comma temperaments. Each comma of a multiple-comma temperament also implies an enharmonic, and they may conflict. True double pergens, which are always multi-comma, tend to have multiple notations. For example, the half-everything pergen has 3 possible notations, all equally valid. Even single-split pergens can have multiple commas that imply different enharmonics. &lt;br /&gt;
+&lt;br /&gt;
+Sometimes the temperament implies an enharmonic that isn't even a 2nd. For example, liese is (P8, P11/3), with G = 7/5 = d5. E = 3·d5 - P11 = descending dd3.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:63:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Further Discussion-Alternate keyspans and stepspans"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:63 --&gt;Alternate keyspans and stepspans&lt;/h2&gt;
@@ Line 2,751: / Line 2,757: @@
 &lt;/table&gt;
+&lt;br /&gt;
+L 2s can be (&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:67:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Further Discussion-Combining pergens"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:67 --&gt;Combining pergens&lt;/h2&gt;
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 &lt;!-- ws:start:WikiTextHeadingRule:73:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Further Discussion-Misc notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:73 --&gt;Misc notes&lt;/h2&gt;
   &lt;br /&gt;
-Pergens were discovered by Kite Giedraitis in 2017, and developed with the help of Praveen Venkataramana. Earlier drafts of this article can be found at &lt;!-- ws:start:WikiTextUrlRule:3829:http://xenharmonic.wikispaces.com/pergen+names --&gt;&lt;a href="http://xenharmonic.wikispaces.com/pergen+names"&gt;http://xenharmonic.wikispaces.com/pergen+names&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:3829 --&gt;&lt;br /&gt;
+Pergens were discovered by Kite Giedraitis in 2017, and developed with the help of Praveen Venkataramana. Earlier drafts of this article can be found at &lt;!-- ws:start:WikiTextUrlRule:3833:http://xenharmonic.wikispaces.com/pergen+names --&gt;&lt;a href="http://xenharmonic.wikispaces.com/pergen+names"&gt;http://xenharmonic.wikispaces.com/pergen+names&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:3833 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;