Tour of regular temperaments: Difference between revisions

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<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:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-17 11:11:38 UTC</tt>.<br>

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-17 11:22:18 UTC</tt>.<br>

: The original revision id was <tt>~~602402660~~</tt>.<br>

: The original revision id was <tt>602404746</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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===[[Würschmidt family]]===

The würschmidt (or wuerschmidt) family tempers out Würschmidt's comma, ~~[[tel:393216/390625|393216/390625]] =~~ |17 1 -8>. Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a perfect 5th two octaves up); that is, (5/4)^8 * ~~([[tel:393216/390625~~|~~393216/390625]])~~ = 6. It tends to generate the same MOS's as [[magic family|magic temperament]], but is tuned slightly more accurately. Both [[31edo]] and [[34edo]] can be used as würschmidt tunings, as can [[65edo]], which is quite accurate.

The würschmidt (or wuerschmidt) family tempers out Würschmidt's comma, |17 1 -8>. Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a perfect 5th two octaves up); that is, (5/4)^8 * |17 1 -8> = 6. It tends to generate the same MOS's as [[magic family|magic temperament]], but is tuned slightly more accurately. Both [[31edo]] and [[34edo]] can be used as würschmidt tunings, as can [[65edo]], which is quite accurate.

===[[Augmented family]]===

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===[[Semicomma family|Orwell and the semicomma family]]===

The semicomma (also known as **Fokker's comma)** ~~[[tel:2109375/2097152|2109375/2097152]] =~~ |-21 3 7> is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to [[orwell]] temperament.

The semicomma (also known as **Fokker's comma),** |-21 3 7> is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to [[orwell]] temperament.

===[[Pythagorean family]]===

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<br />

<h3 id="toc13"><a name="Rank 2 (including &quot;linear&quot;) temperaments-Families-Würschmidt family"></a><a class="wiki_link" href="/W%C3%BCrschmidt%20family">Würschmidt family</a></h3>

The würschmidt (or wuerschmidt) family tempers out Würschmidt's comma, ~~[[tel:393216/390625|393216/390625]] =~~ |17 1 -8&gt;. Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a perfect 5th two octaves up); that is, (5/4)^8 * ~~([[tel:393216/390625~~|~~393216/390625]])~~ = 6. It tends to generate the same MOS's as <a class="wiki_link" href="/magic%20family">magic temperament</a>, but is tuned slightly more accurately. Both <a class="wiki_link" href="/31edo">31edo</a> and <a class="wiki_link" href="/34edo">34edo</a> can be used as würschmidt tunings, as can <a class="wiki_link" href="/65edo">65edo</a>, which is quite accurate.<br />

The würschmidt (or wuerschmidt) family tempers out Würschmidt's comma, |17 1 -8&gt;. Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a perfect 5th two octaves up); that is, (5/4)^8 * |17 1 -8&gt; = 6. It tends to generate the same MOS's as <a class="wiki_link" href="/magic%20family">magic temperament</a>, but is tuned slightly more accurately. Both <a class="wiki_link" href="/31edo">31edo</a> and <a class="wiki_link" href="/34edo">34edo</a> can be used as würschmidt tunings, as can <a class="wiki_link" href="/65edo">65edo</a>, which is quite accurate.<br />

<br />

<h3 id="toc14"><a name="Rank 2 (including &quot;linear&quot;) temperaments-Families-Augmented family"></a><a class="wiki_link" href="/Augmented%20family">Augmented family</a></h3>

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<br />

<h3 id="toc19"><a name="Rank 2 (including &quot;linear&quot;) temperaments-Families-Orwell and the semicomma family"></a><a class="wiki_link" href="/Semicomma%20family">Orwell and the semicomma family</a></h3>

The semicomma (also known as <strong>Fokker's comma)</strong> ~~[[tel:2109375/2097152|2109375/2097152]] =~~ |-21 3 7&gt; is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to <a class="wiki_link" href="/orwell">orwell</a> temperament.<br />

The semicomma (also known as <strong>Fokker's comma),</strong> |-21 3 7&gt; is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to <a class="wiki_link" href="/orwell">orwell</a> temperament.<br />

<br />

<h3 id="toc20"><a name="Rank 2 (including &quot;linear&quot;) temperaments-Families-Pythagorean family"></a><a class="wiki_link" href="/Pythagorean%20family">Pythagorean family</a></h3>

@@ 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-17 11:11:38 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-17 11:22:18 UTC</tt>.<br>
-: The original revision id was <tt>602402660</tt>.<br>
+: The original revision id was <tt>602404746</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 65: / Line 65: @@
 ===[[Würschmidt family]]===
-The würschmidt (or wuerschmidt) family tempers out Würschmidt's comma, [[tel:393216/390625|393216/390625]] = |17 1 -8&gt;. Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a perfect 5th two octaves up); that is, (5/4)^8 * ([[tel:393216/390625|393216/390625]]) = 6. It tends to generate the same MOS's as [[magic family|magic temperament]], but is tuned slightly more accurately. Both [[31edo]] and [[34edo]] can be used as würschmidt tunings, as can [[65edo]], which is quite accurate.
+The würschmidt (or wuerschmidt) family tempers out Würschmidt's comma, |17 1 -8&gt;. Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a perfect 5th two octaves up); that is, (5/4)^8 * |17 1 -8&gt; = 6. It tends to generate the same MOS's as [[magic family|magic temperament]], but is tuned slightly more accurately. Both [[31edo]] and [[34edo]] can be used as würschmidt tunings, as can [[65edo]], which is quite accurate.
 ===[[Augmented family]]===
@@ Line 83: / Line 83: @@
 ===[[Semicomma family|Orwell and the semicomma family]]===
-The semicomma (also known as **Fokker's comma)** [[tel:2109375/2097152|2109375/2097152]] = |-21 3 7&gt; is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to [[orwell]] temperament.
+The semicomma (also known as **Fokker's comma),** |-21 3 7&gt; is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to [[orwell]] temperament.
 ===[[Pythagorean family]]===
@@ Line 459: / Line 459: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Würschmidt family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family"&gt;Würschmidt family&lt;/a&gt;&lt;/h3&gt;
-  The würschmidt (or wuerschmidt) family tempers out Würschmidt's comma, [[tel:393216/390625|393216/390625]] = |17 1 -8&amp;gt;. Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a perfect 5th two octaves up); that is, (5/4)^8 * ([[tel:393216/390625|393216/390625]]) = 6. It tends to generate the same MOS's as &lt;a class="wiki_link" href="/magic%20family"&gt;magic temperament&lt;/a&gt;, but is tuned slightly more accurately. Both &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; and &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; can be used as würschmidt tunings, as can &lt;a class="wiki_link" href="/65edo"&gt;65edo&lt;/a&gt;, which is quite accurate.&lt;br /&gt;
+  The würschmidt (or wuerschmidt) family tempers out Würschmidt's comma, |17 1 -8&amp;gt;. Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a perfect 5th two octaves up); that is, (5/4)^8 * |17 1 -8&amp;gt; = 6. It tends to generate the same MOS's as &lt;a class="wiki_link" href="/magic%20family"&gt;magic temperament&lt;/a&gt;, but is tuned slightly more accurately. Both &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; and &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; can be used as würschmidt tunings, as can &lt;a class="wiki_link" href="/65edo"&gt;65edo&lt;/a&gt;, which is quite accurate.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Augmented family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;&lt;a class="wiki_link" href="/Augmented%20family"&gt;Augmented family&lt;/a&gt;&lt;/h3&gt;
@@ Line 477: / Line 477: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc19"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Orwell and the semicomma family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;&lt;a class="wiki_link" href="/Semicomma%20family"&gt;Orwell and the semicomma family&lt;/a&gt;&lt;/h3&gt;
-  The semicomma (also known as &lt;strong&gt;Fokker's comma)&lt;/strong&gt; [[tel:2109375/2097152|2109375/2097152]] = |-21 3 7&amp;gt; is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to &lt;a class="wiki_link" href="/orwell"&gt;orwell&lt;/a&gt; temperament.&lt;br /&gt;
+  The semicomma (also known as &lt;strong&gt;Fokker's comma),&lt;/strong&gt; |-21 3 7&amp;gt; is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to &lt;a class="wiki_link" href="/orwell"&gt;orwell&lt;/a&gt; temperament.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc20"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Pythagorean family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;&lt;a class="wiki_link" href="/Pythagorean%20family"&gt;Pythagorean family&lt;/a&gt;&lt;/h3&gt;