Clipper: Difference between revisions
Wikispaces>genewardsmith **Imported revision 298043012 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 298043896 - 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>2012-02-02 23: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-02 23:33:59 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>298043896</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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Euler(Benedetti(c)) generates a JI group, which can be found by reducing it to a [[Normal lists#x-Normal interval lists|normal interval list]]. This group is characteristic of the comma, and is the group on which tempering by the comma takes place. For instance, Euler(Benedetti(225/224)) generates 2.3.5.7, the full 7-limit group, and tempering it out leads to a rank three temperament, marvel. However, Euler(Benedeti(3136/3125)) generates 2.5.7, and tempering it out generates a rank-two temperament of the 2.5.7 [[Just intonation subgroups|JI subgroup]], with mapping [<1 0 -3|, <0 2 5|] and an approximate 28/25 generator, which might be called 7-limit [[Chromatic pairs#Roulette|roulette]] temperament. | Euler(Benedetti(c)) generates a JI group, which can be found by reducing it to a [[Normal lists#x-Normal interval lists|normal interval list]]. This group is characteristic of the comma, and is the group on which tempering by the comma takes place. For instance, Euler(Benedetti(225/224)) generates 2.3.5.7, the full 7-limit group, and tempering it out leads to a rank three temperament, marvel. However, Euler(Benedeti(3136/3125)) generates 2.5.7, and tempering it out generates a rank-two temperament of the 2.5.7 [[Just intonation subgroups|JI subgroup]], with mapping [<1 0 -3|, <0 2 5|] and an approximate 28/25 generator, which might be called 7-limit [[Chromatic pairs#Roulette|roulette]] temperament. | ||
=Scales= | =Scales= | ||
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Euler(Benedetti(c)) generates a JI group, which can be found by reducing it to a <a class="wiki_link" href="/Normal%20lists#x-Normal interval lists">normal interval list</a>. This group is characteristic of the comma, and is the group on which tempering by the comma takes place. For instance, Euler(Benedetti(225/224)) generates 2.3.5.7, the full 7-limit group, and tempering it out leads to a rank three temperament, marvel. However, Euler(Benedeti(3136/3125)) generates 2.5.7, and tempering it out generates a rank-two temperament of the 2.5.7 <a class="wiki_link" href="/Just%20intonation%20subgroups">JI subgroup</a>, with mapping [&lt;1 0 -3|, &lt;0 2 5|] and an approximate 28/25 generator, which might be called 7-limit <a class="wiki_link" href="/Chromatic%20pairs#Roulette">roulette</a> temperament.<br /> | Euler(Benedetti(c)) generates a JI group, which can be found by reducing it to a <a class="wiki_link" href="/Normal%20lists#x-Normal interval lists">normal interval list</a>. This group is characteristic of the comma, and is the group on which tempering by the comma takes place. For instance, Euler(Benedetti(225/224)) generates 2.3.5.7, the full 7-limit group, and tempering it out leads to a rank three temperament, marvel. However, Euler(Benedeti(3136/3125)) generates 2.5.7, and tempering it out generates a rank-two temperament of the 2.5.7 <a class="wiki_link" href="/Just%20intonation%20subgroups">JI subgroup</a>, with mapping [&lt;1 0 -3|, &lt;0 2 5|] and an approximate 28/25 generator, which might be called 7-limit <a class="wiki_link" href="/Chromatic%20pairs#Roulette">roulette</a> temperament.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->Scales</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->Scales</h1> | ||