EDT: 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:

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-28 18:15:45 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-28 18:18:10 UTC</tt>.

: The original revision id was <tt>~~600679064~~</tt>.

: The original revision id was <tt>600679238</tt>.

: The revision comment was: <tt></tt>

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The other no twos rank two temperament which 13edt "supports" is [[Arcturus]], which takes an ~5:3 as a generator. I speak advisedly of 13edt supporting this temperament because the lowest-error proper MOS of it is a 2L 11s triskaidecatonic scale. However, if you do not mind having a smeary 5, you will need only a 2L 7s (nonatonic) scale to make an understandable rendition of it.

The named but not necessarily no twos rank two temperament which 13edt "supports" is [[Sirius]], which takes a generator between ~7:6 and ~6:5. Like Arcturus, I speak advisedly of 13edt supporting it because the most proper small MOS of it is triskaidecatonic. Unlike Arcturus, there is a smaller MOS of it than this which is technically proper. However, this MOS is the Grumpy heptatonic scale the use of which is made problematic by the uniqueness of the step of the second size. It is problematic to have the step of the second size be unique in a subscale of an ~~edX~~ because it creates a strong sense of a second equal division of a Y strictly less than X, and this sense of two different equal divisions a trying to happen in the same scale causes ordinary concepts of equivalence to break down in spectacular ways.

The named but not necessarily no twos rank two temperament which 13edt "supports" is [[Sirius]], which takes a generator between ~7:6 and ~6:5. Like Arcturus, I speak advisedly of 13edt supporting it because the most proper small MOS of it is triskaidecatonic. Unlike Arcturus, there is a smaller MOS of it than this which is technically proper. However, this MOS is the Grumpy heptatonic scale the use of which is made problematic by the uniqueness of the step of the second size. It is problematic to have the step of the second size be unique in a subscale of an edx because it creates a strong sense of a second equal division of a y strictly less than x, and this sense of two different equal divisions trying to happen in the same scale causes ordinary concepts of equivalence to break down in spectacular ways.

The final interval which 13edt can reasonably use to generate a rank two temperament is its false 3\2 of 5 degrees. By a weird coincidence, it will generate the [[5L 3s]] unfair father octatonic scale just as if it were an interval of an edo, except that the scale will not always contain a false 4\3 as it must in an edo. This means, most importantly, that 16\15 cannot be assumed to be a "comma" tempered out by this false Father temperament when it is taken as a temperament of full just intonation. By a second, and totally separate, weird coincidence, the well-known Bohlen-Pierce temperament is its index-2 subtemperament.

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The other no twos rank two temperament which 13edt &quot;supports&quot; is <a class="wiki_link" href="/Arcturus">Arcturus</a>, which takes an ~5:3 as a generator. I speak advisedly of 13edt supporting this temperament because the lowest-error proper MOS of it is a 2L 11s triskaidecatonic scale. However, if you do not mind having a smeary 5, you will need only a 2L 7s (nonatonic) scale to make an understandable rendition of it.

The named but not necessarily no twos rank two temperament which 13edt &quot;supports&quot; is <a class="wiki_link" href="/Sirius">Sirius</a>, which takes a generator between ~7:6 and ~6:5. Like Arcturus, I speak advisedly of 13edt supporting it because the most proper small MOS of it is triskaidecatonic. Unlike Arcturus, there is a smaller MOS of it than this which is technically proper. However, this MOS is the Grumpy heptatonic scale the use of which is made problematic by the uniqueness of the step of the second size. It is problematic to have the step of the second size be unique in a subscale of an ~~edX~~ because it creates a strong sense of a second equal division of a Y strictly less than X, and this sense of two different equal divisions a trying to happen in the same scale causes ordinary concepts of equivalence to break down in spectacular ways.

The named but not necessarily no twos rank two temperament which 13edt &quot;supports&quot; is <a class="wiki_link" href="/Sirius">Sirius</a>, which takes a generator between ~7:6 and ~6:5. Like Arcturus, I speak advisedly of 13edt supporting it because the most proper small MOS of it is triskaidecatonic. Unlike Arcturus, there is a smaller MOS of it than this which is technically proper. However, this MOS is the Grumpy heptatonic scale the use of which is made problematic by the uniqueness of the step of the second size. It is problematic to have the step of the second size be unique in a subscale of an edx because it creates a strong sense of a second equal division of a y strictly less than x, and this sense of two different equal divisions trying to happen in the same scale causes ordinary concepts of equivalence to break down in spectacular ways.

The final interval which 13edt can reasonably use to generate a rank two temperament is its false 3\2 of 5 degrees. By a weird coincidence, it will generate the <a class="wiki_link" href="/5L%203s">5L 3s</a> unfair father octatonic scale just as if it were an interval of an edo, except that the scale will not always contain a false 4\3 as it must in an edo. This means, most importantly, that 16\15 cannot be assumed to be a &quot;comma&quot; tempered out by this false Father temperament when it is taken as a temperament of full just intonation. By a second, and totally separate, weird coincidence, the well-known Bohlen-Pierce temperament is its index-2 subtemperament.

@@ 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>2016-11-28 18:15:45 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-28 18:18:10 UTC</tt>.<br>
-: The original revision id was <tt>600679064</tt>.<br>
+: The original revision id was <tt>600679238</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 25: / Line 25: @@
 The other no twos rank two temperament which 13edt "supports" is [[Arcturus]], which takes an ~5:3 as a generator. I speak advisedly of 13edt supporting this temperament because the lowest-error proper MOS of it is a 2L 11s triskaidecatonic scale. However, if you do not mind having a smeary 5, you will need only a 2L 7s (nonatonic) scale to make an understandable rendition of it.
-The named but not necessarily no twos rank two temperament which 13edt "supports" is [[Sirius]], which takes a generator between ~7:6 and ~6:5. Like Arcturus, I speak advisedly of 13edt supporting it because the most proper small MOS of it is triskaidecatonic. Unlike Arcturus, there is a smaller MOS of it than this which is technically proper. However, this MOS is the Grumpy heptatonic scale the use of which is made problematic by the uniqueness of the step of the second size. It is problematic to have the step of the second size be unique in a subscale of an edX because it creates a strong sense of a second equal division of a Y strictly less than X, and this sense of two different equal divisions a trying to happen in the same scale causes ordinary concepts of equivalence to break down in spectacular ways.
+The named but not necessarily no twos rank two temperament which 13edt "supports" is [[Sirius]], which takes a generator between ~7:6 and ~6:5. Like Arcturus, I speak advisedly of 13edt supporting it because the most proper small MOS of it is triskaidecatonic. Unlike Arcturus, there is a smaller MOS of it than this which is technically proper. However, this MOS is the Grumpy heptatonic scale the use of which is made problematic by the uniqueness of the step of the second size. It is problematic to have the step of the second size be unique in a subscale of an edx because it creates a strong sense of a second equal division of a y strictly less than x, and this sense of two different equal divisions trying to happen in the same scale causes ordinary concepts of equivalence to break down in spectacular ways.
 The final interval which 13edt can reasonably use to generate a rank two temperament is its false 3\2 of 5 degrees. By a weird coincidence, it will generate the [[5L 3s]] unfair father octatonic scale just as if it were an interval of an edo, except that the scale will not always contain a false 4\3 as it must in an edo. This means, most importantly, that 16\15 cannot be assumed to be a "comma" tempered out by this false Father temperament when it is taken as a temperament of full just intonation. By a second, and totally separate, weird coincidence, the well-known Bohlen-Pierce temperament is its index-2 subtemperament.
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 The other no twos rank two temperament which 13edt &amp;quot;supports&amp;quot; is &lt;a class="wiki_link" href="/Arcturus"&gt;Arcturus&lt;/a&gt;, which takes an ~5:3 as a generator. I speak advisedly of 13edt supporting this temperament because the lowest-error proper MOS of it is a 2L 11s triskaidecatonic scale. However, if you do not mind having a smeary 5, you will need only a 2L 7s (nonatonic) scale to make an understandable rendition of it.&lt;br /&gt;
 &lt;br /&gt;
-The named but not necessarily no twos rank two temperament which 13edt &amp;quot;supports&amp;quot; is &lt;a class="wiki_link" href="/Sirius"&gt;Sirius&lt;/a&gt;, which takes a generator between ~7:6 and ~6:5. Like Arcturus, I speak advisedly of 13edt supporting it because the most proper small MOS of it is triskaidecatonic. Unlike Arcturus, there is a smaller MOS of it than this which is technically proper. However, this MOS is the Grumpy heptatonic scale the use of which is made problematic by the uniqueness of the step of the second size. It is problematic to have the step of the second size be unique in a subscale of an edX because it creates a strong sense of a second equal division of a Y strictly less than X, and this sense of two different equal divisions a trying to happen in the same scale causes ordinary concepts of equivalence to break down in spectacular ways.&lt;br /&gt;
+The named but not necessarily no twos rank two temperament which 13edt &amp;quot;supports&amp;quot; is &lt;a class="wiki_link" href="/Sirius"&gt;Sirius&lt;/a&gt;, which takes a generator between ~7:6 and ~6:5. Like Arcturus, I speak advisedly of 13edt supporting it because the most proper small MOS of it is triskaidecatonic. Unlike Arcturus, there is a smaller MOS of it than this which is technically proper. However, this MOS is the Grumpy heptatonic scale the use of which is made problematic by the uniqueness of the step of the second size. It is problematic to have the step of the second size be unique in a subscale of an edx because it creates a strong sense of a second equal division of a y strictly less than x, and this sense of two different equal divisions trying to happen in the same scale causes ordinary concepts of equivalence to break down in spectacular ways.&lt;br /&gt;
 &lt;br /&gt;
 The final interval which 13edt can reasonably use to generate a rank two temperament is its false 3\2 of 5 degrees. By a weird coincidence, it will generate the &lt;a class="wiki_link" href="/5L%203s"&gt;5L 3s&lt;/a&gt; unfair father octatonic scale just as if it were an interval of an edo, except that the scale will not always contain a false 4\3 as it must in an edo. This means, most importantly, that 16\15 cannot be assumed to be a &amp;quot;comma&amp;quot; tempered out by this false Father temperament when it is taken as a temperament of full just intonation. By a second, and totally separate, weird coincidence, the well-known Bohlen-Pierce temperament is its index-2 subtemperament.&lt;br /&gt;