2L 5s: Difference between revisions
Wikispaces>keenanpepper **Imported revision 385547970 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 540550588 - 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: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-10 23:19:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>540550588</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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In terms of harmonic entropy, the most significant minimum is at [[Meantone family|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1. | In terms of harmonic entropy, the most significant minimum is at [[Meantone family|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1. | ||
||||||||||||||~ generator in degrees of an [[edo]] ||~ generator in cents ||~ | ||||||||||||||~ generator in degrees of an [[edo]] ||~ generator in cents ||~ tetrachord ||~ L in cents ||~ s in cents ||~ L to s ratio ||~ comments || | ||
||= 3\7 ||= ||= ||= ||= || || ||= 514.3 ||= | ||= 3\7 ||= ||= ||= ||= || || ||= 514.3 ||= 1 1 1 ||= 171.4 ||= 171.4 ||= 1.00 ||= || | ||
||= ||= ||= ||= ||= 13\30 || || ||= 520.0 ||= | ||= ||= ||= ||= ||= 13\30 || || ||= 520.0 ||= 4 4 5 ||= 200.0 ||= 160.0 ||= 1.25 ||= Mavila extends from here... || | ||
||= ||= ||= ||= 10\23 ||= || || ||= 521.7 ||= | ||= ||= ||= ||= 10\23 ||= || || ||= 521.7 ||= 3 3 4 ||= 208.7 ||= 156.5 ||= 1.33 ||= || | ||
||= ||= ||= ||= ||= 17\39 || || ||= 523.1 ||= | ||= ||= ||= ||= ||= 17\39 || || ||= 523.1 ||= 5 5 7 ||= 215.4 ||= 153.8 ||= 1.40 ||= || | ||
||= ||= ||= 7\16 ||= ||= || || ||= 525.0 ||= | ||= ||= ||= 7\16 ||= ||= || || ||= 525.0 ||= 2 2 3 ||= 225.0 ||= 150.0 ||= 1.50 ||= Mavila in Armodue | ||
Optimum rank range (L/s=3/2) || | Optimum rank range (L/s=3/2) || | ||
||= ||= ||= ||= ||= 18\41 || || ||= 526.8 ||= | ||= ||= ||= ||= ||= 18\41 || || ||= 526.8 ||= 5 5 8 ||= 234.1 ||= 146.3 ||= 1.60 ||= || | ||
|| || || || || || || ||= 1200*5/(13-phi) ||= 1 1 phi | || || || || || || || ||= 1200*5/(13-phi) ||= 1 1 phi ||= 235.7 ||= 145.7 ||= phi ||= Golden mavila || | ||
|| || || || || || 29\66 || ||= 527.3 ||= 8 8 13 | || || || || || || 29\66 || ||= 527.3 ||= 8 8 13 ||= 236.4 ||= 145.5 ||= 1.62 ||= || | ||
||= ||= ||= ||= 11\25 ||= || || ||= 528.0 ||= | ||= ||= ||= ||= 11\25 ||= || || ||= 528.0 ||= 3 3 5 ||= 240.0 ||= 144.0 ||= 1.67 ||= || | ||
||= ||= ||= ||= ||= 15\34 || || ||= 529.4 ||= | ||= ||= ||= ||= ||= 15\34 || || ||= 529.4 ||= 4 4 7 ||= 247.1 ||= 141.2 ||= 1.75 ||= ...to somewhere around here || | ||
||= ||= 4\9 ||= ||= ||= || || ||= 533.3 ||= | ||= ||= 4\9 ||= ||= ||= || || ||= 533.3 ||= 1 1 2 ||= 266.7 ||= 133.3 ||= 2.00 ||= Boundary of propriety (generators | ||
smaller than this are proper) || | smaller than this are proper) || | ||
||= ||= ||= ||= ||= 13\29 || || ||= 537.9 ||= | ||= ||= ||= ||= ||= 13\29 || || ||= 537.9 ||= 3 3 7 ||= 289.7 ||= 124.1 ||= 2.33 ||= || | ||
||= ||= ||= ||= 9\20 ||= || || ||= 540.0 ||= | ||= ||= ||= ||= 9\20 ||= || || ||= 540.0 ||= 2 2 5 ||= 300.0 ||= 120.0 ||= 2.50 ||= || | ||
||= ||= ||= ||= ||= 14\31 || || ||= 541.9 ||= | ||= ||= ||= ||= ||= 14\31 || || ||= 541.9 ||= 3 3 8 ||= 309.7 ||= 116.1 ||= 2.66 ||= || | ||
||= ||= ||= 5\11 ||= ||= || || ||= 545.5 ||= | || || || || || || || ||= 545.2 ||= 1 1 2.97 ||= 325.9 ||= 109.6 ||= 2.97 ||= L/s = 3/2^(1/75) || | ||
||= ||= ||= ||= ||= 11\24 || || ||= 550.0 ||= | ||= ||= ||= 5\11 ||= ||= || || ||= 545.5 ||= 1 1 3 ||= 327.3 ||= 109.1 ||= 3.00 ||= L/s = 3 || | ||
||= ||= ||= ||= 6\13 ||= || || ||= 553.8 ||= | || || || || || || || ||= 545.7 ||= 1 1 3.03 ||= 328.65 ||= 108.5 ||= 3.03 ||= <span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span> || | ||
||= ||= ||= ||= ||= 11\24 || || ||= 550.0 ||= 2 2 7 ||= 350.0 ||= 100.0 ||= 3.50 ||= || | |||
||= ||= ||= ||= 6\13 ||= || || ||= 553.8 ||= 1 1 4 ||= 369.2 ||= 92.3 ||= 4.00 ||= Thuja is optimal around here | |||
L/s = 4 || | L/s = 4 || | ||
||= ||= ||= ||= ||= 7\15 || || ||= 560.0 ||= | ||= ||= ||= ||= ||= 7\15 || || ||= 560.0 ||= 1 1 5 ||= 400.0 ||= 80.0 ||= 5.00 ||= ie. (11/8)^5 = 5/1 || | ||
||= ||= ||= ||= ||= ||= 8\17 ||= ||= 564.7 ||= | ||= ||= ||= ||= ||= ||= 8\17 ||= ||= 564.7 ||= 1 1 6 ||= 423.5 ||= 70.6 ||= 6.00 ||= || | ||
||= ||= ||= ||= ||= ||= ||= 9\19 ||= 568.4 ||= | ||= ||= ||= ||= ||= ||= ||= 9\19 ||= 568.4 ||= 1 1 7 ||= 442.1 ||= 63.2 ||= 7.00 ||= Liese/Triton is around here || | ||
||= 1\2 ||= ||= ||= ||= || || ||= 600.0 ||= | ||= 1\2 ||= ||= ||= ||= || || ||= 600.0 ||= 0 0 1 ||= 600.0 ||= 0 ||= — ||= ||</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>2L 5s</title></head><body>2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of <a class="wiki_link" href="/7edo">7edo</a>) and 1\2 (1 degree of <a class="wiki_link" href="/2edo">2edo</a> — the half-octave tritone that appears in every even-numbered edo).<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>2L 5s</title></head><body>2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of <a class="wiki_link" href="/7edo">7edo</a>) and 1\2 (1 degree of <a class="wiki_link" href="/2edo">2edo</a> — the half-octave tritone that appears in every even-numbered edo).<br /> | ||
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<th>generator in cents<br /> | <th>generator in cents<br /> | ||
</th> | </th> | ||
<th> | <th>tetrachord<br /> | ||
</th> | </th> | ||
<th>L in cents<br /> | <th>L in cents<br /> | ||
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<td style="text-align: center;">514.3<br /> | <td style="text-align: center;">514.3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1 1 1<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">171.4<br /> | <td style="text-align: center;">171.4<br /> | ||
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<td style="text-align: center;">520.0<br /> | <td style="text-align: center;">520.0<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">4 4 5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">200.0<br /> | <td style="text-align: center;">200.0<br /> | ||
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<td style="text-align: center;">521.7<br /> | <td style="text-align: center;">521.7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">3 3 4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">208.7<br /> | <td style="text-align: center;">208.7<br /> | ||
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<td style="text-align: center;">523.1<br /> | <td style="text-align: center;">523.1<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">5 5 7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">215.4<br /> | <td style="text-align: center;">215.4<br /> | ||
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<td style="text-align: center;">525.0<br /> | <td style="text-align: center;">525.0<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">2 2 3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">225.0<br /> | <td style="text-align: center;">225.0<br /> | ||
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<td style="text-align: center;">526.8<br /> | <td style="text-align: center;">526.8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">5 5 8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">234.1<br /> | <td style="text-align: center;">234.1<br /> | ||
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<td style="text-align: center;">1200*5/(13-phi)<br /> | <td style="text-align: center;">1200*5/(13-phi)<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1 1 phi | <td style="text-align: center;">1 1 phi<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">235.7<br /> | <td style="text-align: center;">235.7<br /> | ||
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<td style="text-align: center;">527.3<br /> | <td style="text-align: center;">527.3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">8 8 13 | <td style="text-align: center;">8 8 13<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">236.4<br /> | <td style="text-align: center;">236.4<br /> | ||
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<td style="text-align: center;">528.0<br /> | <td style="text-align: center;">528.0<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">3 3 5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">240.0<br /> | <td style="text-align: center;">240.0<br /> | ||
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<td style="text-align: center;">529.4<br /> | <td style="text-align: center;">529.4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">4 4 7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">247.1<br /> | <td style="text-align: center;">247.1<br /> | ||
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<td style="text-align: center;">533.3<br /> | <td style="text-align: center;">533.3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1 1 2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">266.7<br /> | <td style="text-align: center;">266.7<br /> | ||
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<td style="text-align: center;">537.9<br /> | <td style="text-align: center;">537.9<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">3 3 7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">289.7<br /> | <td style="text-align: center;">289.7<br /> | ||
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<td style="text-align: center;">540.0<br /> | <td style="text-align: center;">540.0<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">2 2 5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">300.0<br /> | <td style="text-align: center;">300.0<br /> | ||
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<td style="text-align: center;">541.9<br /> | <td style="text-align: center;">541.9<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">3 3 8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">309.7<br /> | <td style="text-align: center;">309.7<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
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<td style="text-align: center;">545.2<br /> | |||
</td> | |||
<td style="text-align: center;">1 1 2.97<br /> | |||
</td> | |||
<td style="text-align: center;">325.9<br /> | |||
</td> | |||
<td style="text-align: center;">109.6<br /> | |||
</td> | |||
<td style="text-align: center;">2.97<br /> | |||
</td> | |||
<td style="text-align: center;">L/s = 3/2^(1/75)<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">545.5<br /> | <td style="text-align: center;">545.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1 1 3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">327.3<br /> | <td style="text-align: center;">327.3<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">L/s = 3<br /> | <td style="text-align: center;">L/s = 3<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
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<td style="text-align: center;">545.7<br /> | |||
</td> | |||
<td style="text-align: center;">1 1 3.03<br /> | |||
</td> | |||
<td style="text-align: center;">328.65<br /> | |||
</td> | |||
<td style="text-align: center;">108.5<br /> | |||
</td> | |||
<td style="text-align: center;">3.03<br /> | |||
</td> | |||
<td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">550.0<br /> | <td style="text-align: center;">550.0<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">2 2 7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">350.0<br /> | <td style="text-align: center;">350.0<br /> | ||
| Line 528: | Line 586: | ||
<td style="text-align: center;">553.8<br /> | <td style="text-align: center;">553.8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1 1 4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">369.2<br /> | <td style="text-align: center;">369.2<br /> | ||
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<td style="text-align: center;">560.0<br /> | <td style="text-align: center;">560.0<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1 1 5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">400.0<br /> | <td style="text-align: center;">400.0<br /> | ||
| Line 585: | Line 643: | ||
<td style="text-align: center;">564.7<br /> | <td style="text-align: center;">564.7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1 1 6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">423.5<br /> | <td style="text-align: center;">423.5<br /> | ||
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<td style="text-align: center;">568.4<br /> | <td style="text-align: center;">568.4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1 1 7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">442.1<br /> | <td style="text-align: center;">442.1<br /> | ||
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<td style="text-align: center;">600.0<br /> | <td style="text-align: center;">600.0<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">0 0 1<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">600.0<br /> | <td style="text-align: center;">600.0<br /> | ||