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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | #REDIRECT [[Gammic_family]] |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-06-22 18:06:53 UTC</tt>.<br>
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| : The original revision id was <tt>150072979</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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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">The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two temperament tempering out |-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.
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| The generator in question is 1990656/1953125 = |13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15|| is plainly much less complex than gammic with wedgie <<20 11 -29||, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.
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| Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192||. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</pre></div>
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| <h4>Original HTML content:</h4>
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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two temperament tempering out |-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.<br />
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| The generator in question is 1990656/1953125 = |13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15|| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29||, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.<br />
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| <br />
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| Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192||. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</body></html></pre></div>
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