Ragismic microtemperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 150559487 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 172932383 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2010- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-10-22 23:06:34 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>172932383</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">The ragisma is 4375/4374, the smallest 7-limit superparticular ratio. Since (10/9)^4 = 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low cmplexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal. | <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 ragisma is 4375/4374, the smallest 7-limit superparticular ratio. Since (10/9)^4 = 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low cmplexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal. | ||
Comma: 4375/4374 | |||
7-limit | |||
[|1 0 0 0>, |-1/7 0 4/7 1/7>, |0 0 1 0>, |0 0 0 1>] | |||
Eigenmonzos: 2, 8/7, 5/4 | |||
9-limit | |||
[|1 0 0 0>, |0 1 0 0>, |1/5 7/5 1/5 -1/5>, | |||
|1/5 7/5 -4/5 4/5>] | |||
Eigenmonzos: 2, 4/3, 7/5 | |||
Lattice basis: 10/9 length=0.789 6/5 length=0.921 | |||
Angle(10/9, 6/5) = 105.299 | |||
Map to lattice: [<0 -1 -1 -3|, <0 -1 -2 1|] | |||
Map: [<1 0 0 1|, <0 1 0 7|, <0 0 1 -4|] | |||
Generators: 2, 3, 5 | |||
Edos: 9, 19, 26, 27, 45, 46, 53, 72, 80, 91, 99, 171, 270, 441, 494, 612, 665, 935, 1106, 1277, 1376, 1718, 1889, 6279 | |||
===Ennealimmal=== | ===Ennealimmal=== | ||
| Line 37: | Line 56: | ||
<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>Ragismic microtemperaments</title></head><body>The ragisma is 4375/4374, the smallest 7-limit superparticular ratio. Since (10/9)^4 = 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word &quot;relatively&quot; should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low cmplexity, with the same caveat about &quot;relatively&quot;; however 27/25 is the period for ennealimmal.<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>Ragismic microtemperaments</title></head><body>The ragisma is 4375/4374, the smallest 7-limit superparticular ratio. Since (10/9)^4 = 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word &quot;relatively&quot; should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low cmplexity, with the same caveat about &quot;relatively&quot;; however 27/25 is the period for ennealimmal.<br /> | ||
<br /> | |||
Comma: 4375/4374<br /> | |||
<br /> | |||
7-limit<br /> | |||
[|1 0 0 0&gt;, |-1/7 0 4/7 1/7&gt;, |0 0 1 0&gt;, |0 0 0 1&gt;]<br /> | |||
Eigenmonzos: 2, 8/7, 5/4<br /> | |||
<br /> | |||
9-limit<br /> | |||
[|1 0 0 0&gt;, |0 1 0 0&gt;, |1/5 7/5 1/5 -1/5&gt;, <br /> | |||
|1/5 7/5 -4/5 4/5&gt;]<br /> | |||
Eigenmonzos: 2, 4/3, 7/5<br /> | |||
<br /> | |||
Lattice basis: 10/9 length=0.789 6/5 length=0.921<br /> | |||
Angle(10/9, 6/5) = 105.299<br /> | |||
Map to lattice: [&lt;0 -1 -1 -3|, &lt;0 -1 -2 1|]<br /> | |||
<br /> | |||
Map: [&lt;1 0 0 1|, &lt;0 1 0 7|, &lt;0 0 1 -4|]<br /> | |||
Generators: 2, 3, 5<br /> | |||
Edos: 9, 19, 26, 27, 45, 46, 53, 72, 80, 91, 99, 171, 270, 441, 494, 612, 665, 935, 1106, 1277, 1376, 1718, 1889, 6279 <br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Ennealimmal"></a><!-- ws:end:WikiTextHeadingRule:0 -->Ennealimmal</h3> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Ennealimmal"></a><!-- ws:end:WikiTextHeadingRule:0 -->Ennealimmal</h3> | ||