Gammic family: Difference between revisions

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:~~hstraub~~|~~hstraub~~]] and made on <tt>2010-08-18 04:10:44 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-17 04:32:24 UTC</tt>.<br>

: The original revision id was <tt>~~157093555~~</tt>.<br>

: The original revision id was <tt>188883039</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>

<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">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 microtemperament tempering out |-29 -11 20>. This temperament, gammic, takes ~~five~~ generator steps to reach 5/4, and 20 to reach 3/2.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 [[171edo]], [[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 if used for it.

<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 microtemperament tempering out |-29 -11 20>. This temperament, gammic, takes 11 generator steps to reach 5/4, and 20 to reach 3/2.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 [[171edo]], [[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 if used for it.

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.

[[POTE tuning|POTE generator]]: 35.096

Map: [<1 1 2|, <0 20 11|]

EDOs: 34, 103, 137, 171, 547, 718, 889, 1607

7-limit

Commas: 4375/4374, 6591796875/6576668672

[[POTE tuning|POTE generator]]: 35.090

Map: [<1 1 2 0|, <0 20 11 96|]

EDOs: 171, 1402, 1573, 1744, 1915

===Neptune===

Line 15:

Line 28:

Adding 385/384 or 1375/1372 to the list of commas allows for an extension to the 11-limit, where (7/5)^3 equates to 11/4. This may be described as <<40 22 21 -3 ...|| or 68&103, and 171 can still be used as a tuning, with val <171 271 397 480 591|.

An article on Neptune as an analog of miracle can be found [[http://tech.groups.yahoo.com/group/tuning-math/message/6001|here]].</pre></div>

An article on Neptune as an analog of miracle can be found [[http://tech.groups.yahoo.com/group/tuning-math/message/6001|here]].

[[POTE tuning|POTE generator]]: 582.452

Map: [<1 21 13 13|, <0 -40 -22 -21|]

Generators: 2, 7/5

EDOs: 35, 68, 103, 171, 1094, 1265, 1436, 1607, 1778

11-limit

Commas: 385/384, 1375/1372, 2465529759/2441406250

[[POTE tuning|POTE generator]]: 582.475

Map: [1 21 13 13 2|, <0 -40 -22 -21 3|]

Generators: 2, 7/5

EDOs: 35, 68, 103, 171, 274, 445</pre></div>

<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>Gammic family</title></head><body>The <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a> 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 microtemperament tempering out |-29 -11 20&gt;. This temperament, gammic, takes ~~five~~ generator steps to reach 5/4, and 20 to reach 3/2.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 <a class="wiki_link" href="/171edo">171edo</a>, <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 if used for it.<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>Gammic family</title></head><body>The <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a> 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 microtemperament tempering out |-29 -11 20&gt;. This temperament, gammic, takes 11 generator steps to reach 5/4, and 20 to reach 3/2.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 <a class="wiki_link" href="/171edo">171edo</a>, <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 if used for it.<br />

<br />

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.<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 35.096<br />

<br />

Map: [&lt;1 1 2|, &lt;0 20 11|]<br />

EDOs: 34, 103, 137, 171, 547, 718, 889, 1607<br />

<br />

7-limit<br />

Commas: 4375/4374, 6591796875/6576668672<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 35.090<br />

<br />

Map: [&lt;1 1 2 0|, &lt;0 20 11 96|]<br />

EDOs: 171, 1402, 1573, 1744, 1915<br />

<br />

<h3 id="toc0"><a name="x--Neptune"></a>Neptune</h3>

Line 26:

Line 67:

Adding 385/384 or 1375/1372 to the list of commas allows for an extension to the 11-limit, where (7/5)^3 equates to 11/4. This may be described as &lt;&lt;40 22 21 -3 ...|| or 68&amp;103, and 171 can still be used as a tuning, with val &lt;171 271 397 480 591|.<br />

<br />

An article on Neptune as an analog of miracle can be found <a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/6001" rel="nofollow">here</a>.</body></html></pre></div>

An article on Neptune as an analog of miracle can be found <a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/6001" rel="nofollow">here</a>.<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 582.452<br />

<br />

Map: [&lt;1 21 13 13|, &lt;0 -40 -22 -21|]<br />

Generators: 2, 7/5<br />

EDOs: 35, 68, 103, 171, 1094, 1265, 1436, 1607, 1778<br />

<br />

11-limit<br />

Commas: 385/384, 1375/1372, 2465529759/2441406250<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 582.475<br />

<br />

Map: [1 21 13 13 2|, &lt;0 -40 -22 -21 3|]<br />

Generators: 2, 7/5<br />

EDOs: 35, 68, 103, 171, 274, 445</body></html></pre></div>

@@ 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:hstraub|hstraub]] and made on <tt>2010-08-18 04:10:44 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-17 04:32:24 UTC</tt>.<br>
-: The original revision id was <tt>157093555</tt>.<br>
+: The original revision id was <tt>188883039</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>
 <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">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 microtemperament tempering out |-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.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 [[171edo]], [[Schismatic family|schismatic]] 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 [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.
+<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 microtemperament tempering out |-29 -11 20&gt;. This temperament, gammic, takes 11 generator steps to reach 5/4, and 20 to reach 3/2.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 [[171edo]], [[Schismatic family|schismatic]] 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 [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.
 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.
+[[POTE tuning|POTE generator]]: 35.096
+Map: [&lt;1 1 2|, &lt;0 20 11|]
+EDOs: 34, 103, 137, 171, 547, 718, 889, 1607
+-limit
+Commas: 4375/4374, 6591796875/6576668672
+[[POTE tuning|POTE generator]]: 35.090
+Map: [&lt;1 1 2 0|, &lt;0 20 11 96|]
+EDOs: 171, 1402, 1573, 1744, 1915
 ===Neptune===
@@ Line 15: / Line 28: @@
 Adding 385/384 or 1375/1372 to the list of commas allows for an extension to the 11-limit, where (7/5)^3 equates to 11/4. This may be described as &lt;&lt;40 22 21 -3 ...|| or 68&amp;103, and 171 can still be used as a tuning, with val &lt;171 271 397 480 591|.
-An article on Neptune as an analog of miracle can be found [[http://tech.groups.yahoo.com/group/tuning-math/message/6001|here]].</pre></div>
+An article on Neptune as an analog of miracle can be found [[http://tech.groups.yahoo.com/group/tuning-math/message/6001|here]].
+[[POTE tuning|POTE generator]]: 582.452
+Map: [&lt;1 21 13 13|, &lt;0 -40 -22 -21|]
+Generators: 2, 7/5
+EDOs: 35, 68, 103, 171, 1094, 1265, 1436, 1607, 1778
+-limit
+Commas: 385/384, 1375/1372, 2465529759/2441406250
+[[POTE tuning|POTE generator]]: 582.475
+Map: [1 21 13 13 2|, &lt;0 -40 -22 -21 3|]
+Generators: 2, 7/5
+EDOs: 35, 68, 103, 171, 274, 445</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Gammic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;a class="wiki_link" href="/Carlos%20Gamma"&gt;Carlos Gamma&lt;/a&gt; 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 microtemperament tempering out |-29 -11 20&amp;gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = |13 5 -9&amp;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 &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt;, &lt;a class="wiki_link" href="/Schismatic%20family"&gt;schismatic&lt;/a&gt; temperament makes for a natural comparison. Schismatic, with a wedgie of &amp;lt;&amp;lt;1 -8 -15|| is plainly much less complex than gammic with wedgie &amp;lt;&amp;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 &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.&lt;br /&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Gammic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;a class="wiki_link" href="/Carlos%20Gamma"&gt;Carlos Gamma&lt;/a&gt; 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 microtemperament tempering out |-29 -11 20&amp;gt;. This temperament, gammic, takes 11 generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = |13 5 -9&amp;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 &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt;, &lt;a class="wiki_link" href="/Schismatic%20family"&gt;schismatic&lt;/a&gt; temperament makes for a natural comparison. Schismatic, with a wedgie of &amp;lt;&amp;lt;1 -8 -15|| is plainly much less complex than gammic with wedgie &amp;lt;&amp;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 &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.&lt;br /&gt;
 &lt;br /&gt;
 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 &amp;lt;&amp;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.&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 35.096&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 1 2|, &amp;lt;0 20 11|]&lt;br /&gt;
+EDOs: 34, 103, 137, 171, 547, 718, 889, 1607&lt;br /&gt;
+&lt;br /&gt;
+-limit&lt;br /&gt;
+Commas: 4375/4374, 6591796875/6576668672&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 35.090&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 1 2 0|, &amp;lt;0 20 11 96|]&lt;br /&gt;
+EDOs: 171, 1402, 1573, 1744, 1915&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Neptune"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Neptune&lt;/h3&gt;
@@ Line 26: / Line 67: @@
 Adding 385/384 or 1375/1372 to the list of commas allows for an extension to the 11-limit, where (7/5)^3 equates to 11/4. This may be described as &amp;lt;&amp;lt;40 22 21 -3 ...|| or 68&amp;amp;103, and 171 can still be used as a tuning, with val &amp;lt;171 271 397 480 591|.&lt;br /&gt;
 &lt;br /&gt;
-An article on Neptune as an analog of miracle can be found &lt;a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/6001" rel="nofollow"&gt;here&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
+An article on Neptune as an analog of miracle can be found &lt;a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/6001" rel="nofollow"&gt;here&lt;/a&gt;.&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 582.452&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 21 13 13|, &amp;lt;0 -40 -22 -21|]&lt;br /&gt;
+Generators: 2, 7/5&lt;br /&gt;
+EDOs: 35, 68, 103, 171, 1094, 1265, 1436, 1607, 1778&lt;br /&gt;
+&lt;br /&gt;
+-limit&lt;br /&gt;
+Commas: 385/384, 1375/1372, 2465529759/2441406250&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 582.475&lt;br /&gt;
+&lt;br /&gt;
+Map: [1 21 13 13 2|, &amp;lt;0 -40 -22 -21 3|]&lt;br /&gt;
+Generators: 2, 7/5&lt;br /&gt;
+EDOs: 35, 68, 103, 171, 274, 445&lt;/body&gt;&lt;/html&gt;</pre></div>