2L 3s: Difference between revisions
Wikispaces>keenanpepper **Imported revision 385545782 - Original comment: ** |
Wikispaces>guest **Imported revision 406481786 - Original comment: ** |
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| 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: | : This revision was by author [[User:guest|guest]] and made on <tt>2013-02-12 16:21:32 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>406481786</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> | ||
| Line 13: | Line 13: | ||
|| || || || || || 11\27 || 488.89 || 222.22 || 44.44 || 177.78 || 6 5 5 6 5 ||= Slendro (insofar as it resembles a MOS) | || || || || || || 11\27 || 488.89 || 222.22 || 44.44 || 177.78 || 6 5 5 6 5 ||= Slendro (insofar as it resembles a MOS) | ||
would be in this region || | would be in this region || | ||
|| || || || || 9\22 || || 490.91 || 218.18 || 54. | || || || || || 9\22 || || 490.91 || 218.18 || 54.545 || 163.64 || 5 4 4 5 4 ||= || | ||
|| || || || || || 16\39 || 492.31 || 215.38 || 61.54 || 153.85 || 9 7 7 9 7 ||= No-5's superpyth/dominant is around here || | || || || || || || 16\39 || 492.31 || 215.38 || 61.54 || 153.85 || 9 7 7 9 7 ||= No-5's superpyth/dominant is around here || | ||
|| || || || 7\17 || || || 494.12 || 211.76 || 70.59 || 141.18 || 4 3 3 4 3 ||= || | || || || || 7\17 || || || 494.12 || 211.76 || 70.59 || 141.18 || 4 3 3 4 3 ||= || | ||
|| || || || || || 19\46 || 495.65 || 208.7 || 78.26 || 130.435 || 11 8 8 11 8 || || | |||
|| || || || || 12\29 || || 496.55 || 206.9 || 82.76 || 124.14 || 7 5 5 7 5 ||= || | || || || || || 12\29 || || 496.55 || 206.9 || 82.76 || 124.14 || 7 5 5 7 5 ||= || | ||
|| || || || || || 17\41 || 497.56 || 204.88 || 87.8 || 117.07 || 10 7 7 10 7 ||= Pythagorean pentatonic is around here || | || || || || || || 17\41 || 497.56 || 204.88 || 87.8 || 117.07 || 10 7 7 10 7 ||= Pythagorean pentatonic is around here || | ||
|| || || 5\12 || || || || 500 || 200 || 100 || 100 || 3 2 2 3 2 ||= Familiar 12-equal pentatonic | || || || 5\12 || || || || 500 || 200 || 100 || 100 || 3 2 2 3 2 ||= Familiar 12-equal pentatonic | ||
(also optimum rank range: L/s=3/2) || | (also optimum rank range: L/s=3/2) || | ||
|| || || || || || || || || || || || || | |||
|| || || || || 13\31 || || 503.23 || 193.55 || 116.13 || 77.42 || 8 5 5 8 5 ||= Optimal meantone pentatonic | || || || || || 13\31 || || 503.23 || 193.55 || 116.13 || 77.42 || 8 5 5 8 5 ||= Optimal meantone pentatonic | ||
is around here || | is around here || | ||
| Line 25: | Line 27: | ||
|| || || || || || 21\50 || 504 || 192 || 120 || 72 || 13 8 8 13 8 ||= || | || || || || || || 21\50 || 504 || 192 || 120 || 72 || 13 8 8 13 8 ||= || | ||
|| || || || 8\19 || || || 505.26 || 189.47 || 126.32 || 63.16 || 5 3 3 5 3 ||= || | || || || || 8\19 || || || 505.26 || 189.47 || 126.32 || 63.16 || 5 3 3 5 3 ||= || | ||
|| || || || || || 19\45 || 506.67 || 186.67 || 133.33 || 53.33 || 12 7 12 7 12 7 || || | |||
|| || || || || 11\26 || || 507.69 || 184.615 || 138.46 || 46.15 || 7 4 4 7 4 || || | |||
|| || || || || || 14\33 || 509.09 || 181.82 || 145.455 || 36.36 || 9 5 5 9 5 || || | |||
|| || 3\7 || || || || || 514.29 || 171.43 || 171.43 || 0 || 2 1 1 2 1 ||= (Boundary of propriety: smaller | || || 3\7 || || || || || 514.29 || 171.43 || 171.43 || 0 || 2 1 1 2 1 ||= (Boundary of propriety: smaller | ||
generators than this are strictly proper) || | generators than this are strictly proper) || | ||
|| || || || || || 13\30 || 520 || 160 || 200 || 40 || 9 4 4 9 4 || || | |||
||< ||< ||< ||< ||< 10\23 ||< ||< 521.74 ||< 156.52 ||< 208.7 ||< 52.17 ||< 7 3 3 7 3 ||< || | |||
|| || || || || || 17\39 || 523.08 || 153.84 || 215.385 || 61.54 || 12 5 5 12 5 || || | |||
|| || || || 7\16 || || || 525 || 150 || 225 || 75 || 5 2 2 5 2 ||= 5-note subset of pelog (insofar as it | || || || || 7\16 || || || 525 || 150 || 225 || 75 || 5 2 2 5 2 ||= 5-note subset of pelog (insofar as it | ||
resembles a MOS) would be in this region || | resembles a MOS) would be in this region || | ||
|| || || || || || 18\41 || 526.83 || 146.34 || 234.15 || 87.8 || 13 5 5 13 5 || || | |||
|| || || || || || || 600(25+√5)/31 || 145.7 || 235.75 || 90.05 || phi+1 1 1 phi+1 1 || || | |||
|| || || || || 11\25 || || 528 || 144 || 240 || 96 || 8 3 3 8 3 || || | |||
|| || || || || || 15\34 || 529.41 || 141.18 || 247.06 || 105.88 || 11 4 4 11 4 || || | |||
|| || || 4\9 || || || || 533.33 || 133.33 || 266.67 || 133.33 || 3 1 1 3 1 ||= L/s = 3 || | || || || 4\9 || || || || 533.33 || 133.33 || 266.67 || 133.33 || 3 1 1 3 1 ||= L/s = 3 || | ||
|| || || || || || 13\29 || 537.93 || 124.14 || 289.655 || 165.52 || 10 3 3 10 3 || || | |||
|| || || || || 9\20 || || 540 || 120 || 240 || 180 || 7 2 2 7 2 || || | |||
|| || || || || || 14\31 || 541.935 || 116.13 || 309.68 || 193.55 || 11 3 3 11 3 || || | |||
|| || || || 5\11 || || || 545.45 || 109.09 || 327.27 || 218.18 || 4 1 1 4 1 ||= L/s = 4 || | || || || || 5\11 || || || 545.45 || 109.09 || 327.27 || 218.18 || 4 1 1 4 1 ||= L/s = 4 || | ||
|| || || || || || 11\24 || 550 || 100 || 350 || 250 || 9 2 2 9 2 || || | |||
|| || || || || 6\13 || || 553.85 || 92.31 || 369.23 || 276.92 || 5 1 1 5 1 || || | |||
|| || || || || || 7\15 || 560 || 80 || 480 || 400 || || || | |||
|| 1\2 || || || || || || 600 || 0 || 600 || 600 || 1 0 0 1 0 ||= || | || 1\2 || || || || || || 600 || 0 || 600 || 600 || 1 0 0 1 0 ||= || | ||
| Line 131: | Line 149: | ||
<td>218.18<br /> | <td>218.18<br /> | ||
</td> | </td> | ||
<td>54. | <td>54.545<br /> | ||
</td> | </td> | ||
<td>163.64<br /> | <td>163.64<br /> | ||
| Line 190: | Line 208: | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>19\46<br /> | |||
</td> | |||
<td>495.65<br /> | |||
</td> | |||
<td>208.7<br /> | |||
</td> | |||
<td>78.26<br /> | |||
</td> | |||
<td>130.435<br /> | |||
</td> | |||
<td>11 8 8 11 8<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 269: | Line 313: | ||
<td style="text-align: center;">Familiar 12-equal pentatonic<br /> | <td style="text-align: center;">Familiar 12-equal pentatonic<br /> | ||
(also optimum rank range: L/s=3/2)<br /> | (also optimum rank range: L/s=3/2)<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 374: | Line 444: | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>19\45<br /> | |||
</td> | |||
<td>506.67<br /> | |||
</td> | |||
<td>186.67<br /> | |||
</td> | |||
<td>133.33<br /> | |||
</td> | |||
<td>53.33<br /> | |||
</td> | |||
<td>12 7 12 7 12 7<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>11\26<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>507.69<br /> | |||
</td> | |||
<td>184.615<br /> | |||
</td> | |||
<td>138.46<br /> | |||
</td> | |||
<td>46.15<br /> | |||
</td> | |||
<td>7 4 4 7 4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>14\33<br /> | |||
</td> | |||
<td>509.09<br /> | |||
</td> | |||
<td>181.82<br /> | |||
</td> | |||
<td>145.455<br /> | |||
</td> | |||
<td>36.36<br /> | |||
</td> | |||
<td>9 5 5 9 5<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 401: | Line 549: | ||
<td style="text-align: center;">(Boundary of propriety: smaller<br /> | <td style="text-align: center;">(Boundary of propriety: smaller<br /> | ||
generators than this are strictly proper)<br /> | generators than this are strictly proper)<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>13\30<br /> | |||
</td> | |||
<td>520<br /> | |||
</td> | |||
<td>160<br /> | |||
</td> | |||
<td>200<br /> | |||
</td> | |||
<td>40<br /> | |||
</td> | |||
<td>9 4 4 9 4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: left;"><br /> | |||
</td> | |||
<td style="text-align: left;"><br /> | |||
</td> | |||
<td style="text-align: left;"><br /> | |||
</td> | |||
<td style="text-align: left;"><br /> | |||
</td> | |||
<td style="text-align: left;">10\23<br /> | |||
</td> | |||
<td style="text-align: left;"><br /> | |||
</td> | |||
<td style="text-align: left;">521.74<br /> | |||
</td> | |||
<td style="text-align: left;">156.52<br /> | |||
</td> | |||
<td style="text-align: left;">208.7<br /> | |||
</td> | |||
<td style="text-align: left;">52.17<br /> | |||
</td> | |||
<td style="text-align: left;">7 3 3 7 3<br /> | |||
</td> | |||
<td style="text-align: left;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>17\39<br /> | |||
</td> | |||
<td>523.08<br /> | |||
</td> | |||
<td>153.84<br /> | |||
</td> | |||
<td>215.385<br /> | |||
</td> | |||
<td>61.54<br /> | |||
</td> | |||
<td>12 5 5 12 5<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 428: | Line 654: | ||
<td style="text-align: center;">5-note subset of pelog (insofar as it<br /> | <td style="text-align: center;">5-note subset of pelog (insofar as it<br /> | ||
resembles a MOS) would be in this region<br /> | resembles a MOS) would be in this region<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>18\41<br /> | |||
</td> | |||
<td>526.83<br /> | |||
</td> | |||
<td>146.34<br /> | |||
</td> | |||
<td>234.15<br /> | |||
</td> | |||
<td>87.8<br /> | |||
</td> | |||
<td>13 5 5 13 5<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>600(25+√5)/31<br /> | |||
</td> | |||
<td>145.7<br /> | |||
</td> | |||
<td>235.75<br /> | |||
</td> | |||
<td>90.05<br /> | |||
</td> | |||
<td>phi+1 1 1 phi+1 1<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>11\25<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>528<br /> | |||
</td> | |||
<td>144<br /> | |||
</td> | |||
<td>240<br /> | |||
</td> | |||
<td>96<br /> | |||
</td> | |||
<td>8 3 3 8 3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>15\34<br /> | |||
</td> | |||
<td>529.41<br /> | |||
</td> | |||
<td>141.18<br /> | |||
</td> | |||
<td>247.06<br /> | |||
</td> | |||
<td>105.88<br /> | |||
</td> | |||
<td>11 4 4 11 4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 454: | Line 784: | ||
</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 /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>13\29<br /> | |||
</td> | |||
<td>537.93<br /> | |||
</td> | |||
<td>124.14<br /> | |||
</td> | |||
<td>289.655<br /> | |||
</td> | |||
<td>165.52<br /> | |||
</td> | |||
<td>10 3 3 10 3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>9\20<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>540<br /> | |||
</td> | |||
<td>120<br /> | |||
</td> | |||
<td>240<br /> | |||
</td> | |||
<td>180<br /> | |||
</td> | |||
<td>7 2 2 7 2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>14\31<br /> | |||
</td> | |||
<td>541.935<br /> | |||
</td> | |||
<td>116.13<br /> | |||
</td> | |||
<td>309.68<br /> | |||
</td> | |||
<td>193.55<br /> | |||
</td> | |||
<td>11 3 3 11 3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 480: | Line 888: | ||
</td> | </td> | ||
<td style="text-align: center;">L/s = 4<br /> | <td style="text-align: center;">L/s = 4<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>11\24<br /> | |||
</td> | |||
<td>550<br /> | |||
</td> | |||
<td>100<br /> | |||
</td> | |||
<td>350<br /> | |||
</td> | |||
<td>250<br /> | |||
</td> | |||
<td>9 2 2 9 2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>6\13<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>553.85<br /> | |||
</td> | |||
<td>92.31<br /> | |||
</td> | |||
<td>369.23<br /> | |||
</td> | |||
<td>276.92<br /> | |||
</td> | |||
<td>5 1 1 5 1<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>7\15<br /> | |||
</td> | |||
<td>560<br /> | |||
</td> | |||
<td>80<br /> | |||
</td> | |||
<td>480<br /> | |||
</td> | |||
<td>400<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||