Porcupine: Difference between revisions
Wikispaces>hstraub **Imported revision 615953209 - Original comment: ** |
Wikispaces>hstraub **Imported revision 615953235 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2017-07-27 10:00: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2017-07-27 10:00:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>615953235</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html"><span style="display: block; text-align: right;"> | <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="display: block; text-align: right;">[[xenharmonie/Porcupine|Deutsch]] | ||
</span> | </span> | ||
**Porcupine** is a [[Regular Temperaments|linear temperament]] in the [[porcupine family]] that tempers out 250/243, the porcupine [[Comma|comma]], and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-[[Harmonic Limit|limit]], 7-limit, or 11-limit temperament, or a 2.3.5.11 [[Subgroup temperaments|subgroup temperament]]. It is one of the best temperaments in the 2.3.5.11 subgroup, with a unique combination of efficiency and accuracy. | **Porcupine** is a [[Regular Temperaments|linear temperament]] in the [[porcupine family]] that tempers out 250/243, the porcupine [[Comma|comma]], and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-[[Harmonic Limit|limit]], 7-limit, or 11-limit temperament, or a 2.3.5.11 [[Subgroup temperaments|subgroup temperament]]. It is one of the best temperaments in the 2.3.5.11 subgroup, with a unique combination of efficiency and accuracy. | ||
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The basic 5-limit harmonic structure of porcupine can be understood simply by noting that tempering out 250/243 makes (4/3)^2 equivalent to (6/5)^3. In perhaps more familiar musical terms, this means two "perfect fourths" equals three "minor thirds". As a consequence of this, 4/3 is divided into 3 equal parts, and 6/5 is divided into 2 of those same equal parts. This is obviously in stark contrast to [[12edo]], and to meantone, in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The "equal tetrachord" formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales. | The basic 5-limit harmonic structure of porcupine can be understood simply by noting that tempering out 250/243 makes (4/3)^2 equivalent to (6/5)^3. In perhaps more familiar musical terms, this means two "perfect fourths" equals three "minor thirds". As a consequence of this, 4/3 is divided into 3 equal parts, and 6/5 is divided into 2 of those same equal parts. This is obviously in stark contrast to [[12edo]], and to meantone, in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The "equal tetrachord" formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales. | ||
[[media type="file" key="porcupinesymmetricminor22edo.mp3"]] | [[media type="file" key="porcupinesymmetricminor22edo.mp3" width="240" height="20"]] | ||
Porcupine symmetric minor scale, containing two equal tetrachords with a major wholetone between them. (Tuning in 22edo) | Porcupine symmetric minor scale, containing two equal tetrachords with a major wholetone between them. (Tuning in [[22edo]]) | ||
[[image:porcupine.png]] | [[image:porcupine.png]] | ||
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[[image:porcupine8.jpg]]</pre></div> | [[image:porcupine8.jpg]]</pre></div> | ||
<h4>Original HTML content:</h4> | <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>Porcupine</title></head><body><span style="display: block; text-align: right;"> | <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>Porcupine</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/Porcupine">Deutsch</a><br /> | ||
</span><br /> | </span><br /> | ||
<strong>Porcupine</strong> is a <a class="wiki_link" href="/Regular%20Temperaments">linear temperament</a> in the <a class="wiki_link" href="/porcupine%20family">porcupine family</a> that tempers out 250/243, the porcupine <a class="wiki_link" href="/Comma">comma</a>, and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-<a class="wiki_link" href="/Harmonic%20Limit">limit</a>, 7-limit, or 11-limit temperament, or a 2.3.5.11 <a class="wiki_link" href="/Subgroup%20temperaments">subgroup temperament</a>. It is one of the best temperaments in the 2.3.5.11 subgroup, with a unique combination of efficiency and accuracy.<br /> | <strong>Porcupine</strong> is a <a class="wiki_link" href="/Regular%20Temperaments">linear temperament</a> in the <a class="wiki_link" href="/porcupine%20family">porcupine family</a> that tempers out 250/243, the porcupine <a class="wiki_link" href="/Comma">comma</a>, and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-<a class="wiki_link" href="/Harmonic%20Limit">limit</a>, 7-limit, or 11-limit temperament, or a 2.3.5.11 <a class="wiki_link" href="/Subgroup%20temperaments">subgroup temperament</a>. It is one of the best temperaments in the 2.3.5.11 subgroup, with a unique combination of efficiency and accuracy.<br /> | ||
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The basic 5-limit harmonic structure of porcupine can be understood simply by noting that tempering out 250/243 makes (4/3)^2 equivalent to (6/5)^3. In perhaps more familiar musical terms, this means two &quot;perfect fourths&quot; equals three &quot;minor thirds&quot;. As a consequence of this, 4/3 is divided into 3 equal parts, and 6/5 is divided into 2 of those same equal parts. This is obviously in stark contrast to <a class="wiki_link" href="/12edo">12edo</a>, and to meantone, in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The &quot;equal tetrachord&quot; formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales.<br /> | The basic 5-limit harmonic structure of porcupine can be understood simply by noting that tempering out 250/243 makes (4/3)^2 equivalent to (6/5)^3. In perhaps more familiar musical terms, this means two &quot;perfect fourths&quot; equals three &quot;minor thirds&quot;. As a consequence of this, 4/3 is divided into 3 equal parts, and 6/5 is divided into 2 of those same equal parts. This is obviously in stark contrast to <a class="wiki_link" href="/12edo">12edo</a>, and to meantone, in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The &quot;equal tetrachord&quot; formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales.<br /> | ||
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Porcupine symmetric minor scale, containing two equal tetrachords with a major wholetone between them. (Tuning in 22edo)<br /> | Porcupine symmetric minor scale, containing two equal tetrachords with a major wholetone between them. (Tuning in <a class="wiki_link" href="/22edo">22edo</a>)<br /> | ||
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