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Wikispaces>genewardsmith **Imported revision 247446889 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 247703671 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-08- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-22 12:52:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>247703671</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> | ||
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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">By a //projection pair// is meant a pair of two rational intervals which can be employed by the [[Scala]] "project" command to reduce a JI scale to a scale in a [[JI subgroup]] of the group generated by the scale, in such a way that tempered versions of each are equivalent. This is particularly useful for analyzing [[planar temperaments]], as the projection can then be viewed in lattice form by Scala's "lattice" or "lattice and player" command. | <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">By a //projection pair// is meant a pair of two rational intervals which can be employed by the [[Scala]] "project" command to reduce a JI scale to a scale in a [[JI subgroup]] of the group generated by the scale, in such a way that tempered versions of each are equivalent. This is particularly useful for analyzing [[planar temperaments]], as the projection can then be viewed in lattice form by Scala's "lattice" or "lattice and player" command. | ||
An example of a projection pair is "7 225/32", which when applied by Scala's "project" to a 7-limit scale produces a 5-limit scale, which when tempered by marvel (225/224) temperament gives exactly the same result as the original scale does when also tempered. More than one such pair may be required to reduce to the desired subgroup; for instance "7 225/32 11 4096/375" reduces an 11-limit JI scale to a 5-limit JI scale equivalent under (unidecimal) marvel. This can happen even when only one comma is involved (codimension one temperaments.) For instance, to project a 7-limit scale in the hemimean (3136/3125) reduction to the 2.5.7 subgroup requires "5 3136/625 7 68841472/9765625".</pre></div> | An example of a projection pair is "7 225/32", which when applied by Scala's "project" to a 7-limit scale produces a 5-limit scale, which when tempered by marvel (225/224) temperament gives exactly the same result as the original scale does when also tempered. More than one such pair may be required to reduce to the desired subgroup; for instance "7 225/32 11 4096/375" reduces an 11-limit JI scale to a 5-limit JI scale equivalent under (unidecimal) marvel. This can happen even when only one comma is involved (codimension one temperaments.) For instance, to project a 7-limit scale in the hemimean (3136/3125) reduction to the 2.5.7 subgroup requires "5 3136/625 7 68841472/9765625". | ||
Many projection pairs are given on the pages for various planar temperaments. When no subgroup is indicated, the default 2.3.5 5-limit subgroup is presumed. These lists of pairs can be copied and pasted into Scala and applied to any suitable JI scale.</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>Projection pair</title></head><body>By a <em>projection pair</em> is meant a pair of two rational intervals which can be employed by the <a class="wiki_link" href="/Scala">Scala</a> &quot;project&quot; command to reduce a JI scale to a scale in a <a class="wiki_link" href="/JI%20subgroup">JI subgroup</a> of the group generated by the scale, in such a way that tempered versions of each are equivalent. This is particularly useful for analyzing <a class="wiki_link" href="/planar%20temperaments">planar temperaments</a>, as the projection can then be viewed in lattice form by Scala's &quot;lattice&quot; or &quot;lattice and player&quot; command. <br /> | <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>Projection pair</title></head><body>By a <em>projection pair</em> is meant a pair of two rational intervals which can be employed by the <a class="wiki_link" href="/Scala">Scala</a> &quot;project&quot; command to reduce a JI scale to a scale in a <a class="wiki_link" href="/JI%20subgroup">JI subgroup</a> of the group generated by the scale, in such a way that tempered versions of each are equivalent. This is particularly useful for analyzing <a class="wiki_link" href="/planar%20temperaments">planar temperaments</a>, as the projection can then be viewed in lattice form by Scala's &quot;lattice&quot; or &quot;lattice and player&quot; command. <br /> | ||
<br /> | <br /> | ||
An example of a projection pair is &quot;7 225/32&quot;, which when applied by Scala's &quot;project&quot; to a 7-limit scale produces a 5-limit scale, which when tempered by marvel (225/224) temperament gives exactly the same result as the original scale does when also tempered. More than one such pair may be required to reduce to the desired subgroup; for instance &quot;7 225/32 11 4096/375&quot; reduces an 11-limit JI scale to a 5-limit JI scale equivalent under (unidecimal) marvel. This can happen even when only one comma is involved (codimension one temperaments.) For instance, to project a 7-limit scale in the hemimean (3136/3125) reduction to the 2.5.7 subgroup requires &quot;5 3136/625 7 68841472/9765625&quot;.</body></html></pre></div> | An example of a projection pair is &quot;7 225/32&quot;, which when applied by Scala's &quot;project&quot; to a 7-limit scale produces a 5-limit scale, which when tempered by marvel (225/224) temperament gives exactly the same result as the original scale does when also tempered. More than one such pair may be required to reduce to the desired subgroup; for instance &quot;7 225/32 11 4096/375&quot; reduces an 11-limit JI scale to a 5-limit JI scale equivalent under (unidecimal) marvel. This can happen even when only one comma is involved (codimension one temperaments.) For instance, to project a 7-limit scale in the hemimean (3136/3125) reduction to the 2.5.7 subgroup requires &quot;5 3136/625 7 68841472/9765625&quot;.<br /> | ||
<br /> | |||
Many projection pairs are given on the pages for various planar temperaments. When no subgroup is indicated, the default 2.3.5 5-limit subgroup is presumed. These lists of pairs can be copied and pasted into Scala and applied to any suitable JI scale.</body></html></pre></div> | |||
Revision as of 12:52, 22 August 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-08-22 12:52:27 UTC.
- The original revision id was 247703671.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
By a //projection pair// is meant a pair of two rational intervals which can be employed by the [[Scala]] "project" command to reduce a JI scale to a scale in a [[JI subgroup]] of the group generated by the scale, in such a way that tempered versions of each are equivalent. This is particularly useful for analyzing [[planar temperaments]], as the projection can then be viewed in lattice form by Scala's "lattice" or "lattice and player" command. An example of a projection pair is "7 225/32", which when applied by Scala's "project" to a 7-limit scale produces a 5-limit scale, which when tempered by marvel (225/224) temperament gives exactly the same result as the original scale does when also tempered. More than one such pair may be required to reduce to the desired subgroup; for instance "7 225/32 11 4096/375" reduces an 11-limit JI scale to a 5-limit JI scale equivalent under (unidecimal) marvel. This can happen even when only one comma is involved (codimension one temperaments.) For instance, to project a 7-limit scale in the hemimean (3136/3125) reduction to the 2.5.7 subgroup requires "5 3136/625 7 68841472/9765625". Many projection pairs are given on the pages for various planar temperaments. When no subgroup is indicated, the default 2.3.5 5-limit subgroup is presumed. These lists of pairs can be copied and pasted into Scala and applied to any suitable JI scale.
Original HTML content:
<html><head><title>Projection pair</title></head><body>By a <em>projection pair</em> is meant a pair of two rational intervals which can be employed by the <a class="wiki_link" href="/Scala">Scala</a> "project" command to reduce a JI scale to a scale in a <a class="wiki_link" href="/JI%20subgroup">JI subgroup</a> of the group generated by the scale, in such a way that tempered versions of each are equivalent. This is particularly useful for analyzing <a class="wiki_link" href="/planar%20temperaments">planar temperaments</a>, as the projection can then be viewed in lattice form by Scala's "lattice" or "lattice and player" command. <br /> <br /> An example of a projection pair is "7 225/32", which when applied by Scala's "project" to a 7-limit scale produces a 5-limit scale, which when tempered by marvel (225/224) temperament gives exactly the same result as the original scale does when also tempered. More than one such pair may be required to reduce to the desired subgroup; for instance "7 225/32 11 4096/375" reduces an 11-limit JI scale to a 5-limit JI scale equivalent under (unidecimal) marvel. This can happen even when only one comma is involved (codimension one temperaments.) For instance, to project a 7-limit scale in the hemimean (3136/3125) reduction to the 2.5.7 subgroup requires "5 3136/625 7 68841472/9765625".<br /> <br /> Many projection pairs are given on the pages for various planar temperaments. When no subgroup is indicated, the default 2.3.5 5-limit subgroup is presumed. These lists of pairs can be copied and pasted into Scala and applied to any suitable JI scale.</body></html>