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Wikispaces>JosephRuhf **Imported revision 529070012 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 540670544 - 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:JosephRuhf|JosephRuhf]] and made on <tt> | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-11 17:31:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>540670544</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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-- | -- | ||
||||||||||||~ Generator ||~ Cents ||~ L ||~ s ||~ Comments || | |||
|| 3\10 | || 3\10 || || || || || || 360 || 120 || 120 ||= || | ||
|| 28\93 | || 28\93 || || || || || || 361.290 || 129.032 || 116.129 ||= || | ||
|| 25\83 | || 25\83 || || || || || || 361.446 || 130.1205 || 115.663 ||= || | ||
|| 22\73 | || 22\73 || || || || || || 361.644 || 131.507 || 115.0685 ||= || | ||
|| 19\63 | || 19\63 || || || || || || 361.905 || 133.333 || 114.286 ||= || | ||
|| 16\53 | || 16\53 || || || || || || 362.264 || 135.849 || 113.2075 ||= || | ||
|| 13\43 | || 13\43 || || || || || || 362.791 || 139.535 || 111.628 ||= || | ||
|| 10\33 | || 10\33 || || || || || || 363.636 || 145.455 || 109.091 ||= || | ||
|| 7\23 | || 7\23 || || || || || || 365.217 || 156.522 || 104.348 ||= || | ||
|| || 18\59 || || || || || 366.102 || 162.712 || 104.29 ||= || | |||
|| || || 47\154 || || || || 366.234 || 163.636 || 101.299 ||= || | |||
|| || || || 123\403 || || || 366.253 || 163.771 || 101.241 ||= || | |||
|| || || || || 322\1055 || || 366.256 || 163.791 || 101.232 || || | |||
|| || || || || || 521\1707 || 366.257 || 163.796 || 101.230 ||= Golden Sephiroth || | |||
|| || || || || 199\652 || || 366.258 || 163.804 || 101.227 || | |||
|| || || || 76\249 || || || 366.265 || 163.855 || 101.205 ||= || | |||
|| || || 29\95 || || || || 366.316 || 164.2105 || 101.053 ||= || | |||
|| || 11\36 | || || 11\36 || || || || || 366.667 || 166.667 || 100 ||= || | ||
|| || 15\49 || || || || || 367.347 || 171.429 || 97.959 ||= || | |||
|| 4\13 | || 4\13 || || || || || || 369.231 || 184.615 || 92.308 ||= Boundary of propriety | ||
(smaller generators are proper) || | (smaller generators are proper) || | ||
|| || 13\42 | || || 13\42 || || || || || 371.429 || 200 || 85.714 ||= || | ||
|| 9\29 | || || 9\29 || || || || || 372.414 || 206.897 || 82.759 ||= || | ||
|| || || 23/74 | || || || 23/74 || || || || 372.973 || 210.811 || 81.081 || || | ||
|| || || || 60/193 || || || 373.057 || 211.399 || 80.829 || || | |||
|| || || || || 157/505 || || 373.069 || 211.485 || 80.792 || || | |||
|| || || || 97/312 || || || 373.077 || 211.5385 || 80.769 || || | |||
|| || || 37/119 || || || || 373.109 || 211.765 || 80.672 || || | |||
|| || 14/45 || || || || || || || || || | || || 14/45 || || || || || 373.333 || 213.333 || 80 ||= || | ||
|| 5\16 || || || || || || || | || || || || || || || 374.870 || 224.090 || 75.390 || || | ||
|| | || 5\16 || || || || || || 375 || 225 || 75 ||= || | ||
|| 6\19 | || || || || || || || 375.130 || 225.910 || 74.610 || || | ||
|| || 11\35 || || || || || 377.143 || 240 || 68.571 ||= || | |||
|| || 13\41 | || 6\19 || || || || || || 378.947 || 252.632 || 63.158 ||= || | ||
|| || 19\60 || || || || || 380 || 260 || 60 ||= Magic is around here || | |||
|| 7\22 | || || 13\41 || || || || || 380.488 || 263.415 || 58.537 ||= || | ||
|| 8\25 | || || 20\63 || || || || || 380.952 || 266.667 || 57.143 ||= || | ||
|| 9\28 | || 7\22 || || || || || || 381.818 || 272.72 || 54.545 ||= || | ||
|| 10\31 | || 8\25 || || || || || || 384 || 288 || 48 ||= || | ||
|| || 21\65 | || 9\28 || || || || || || 385.714 || 300 || 42.857 ||= || | ||
|| 11\34 | || 10\31 || || || || || || 387.097 || 309.677 || 38.710 ||= || | ||
|| 12\37 | || || 21\65 || || || || || 387.692 || 313.846 || 36.923 ||= Würschmidt is around here || | ||
|| 13\40 | || 11\34 || || || || || || 388.235 || 317.647 || 35.294 ||= || | ||
|| 14\43 | || 12\37 || || || || || || 389.189 || 324.324 || 32.432 ||= || | ||
|| || 29\89 | || 13\40 || || || || || || 390 || 330 || 30 || || | ||
|| 15\46 | || 14\43 || || || || || || 390.698 || 334.884 || 27,907 || || | ||
|| 1\3 | || || 29\89 || || || || || 391.011 || 337.079 || 26.966 ||= Amigo is around here || | ||
|| 15\46 || || || || || || 391.304 || 339.130 || 26.087 || || | |||
|| 1\3 || || || || || || 400 || 400 || 0 ||= || | |||
L=1 s=1 [[10edo]] | L=1 s=1 [[10edo]] | ||
| Line 133: | Line 135: | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<th colspan=" | <th colspan="6">Generator<br /> | ||
</th> | </th> | ||
<th>Cents<br /> | <th>Cents<br /> | ||
| Line 146: | Line 148: | ||
<tr> | <tr> | ||
<td>3\10<br /> | <td>3\10<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 176: | Line 170: | ||
<tr> | <tr> | ||
<td>28\93<br /> | <td>28\93<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 206: | Line 192: | ||
<tr> | <tr> | ||
<td>25\83<br /> | <td>25\83<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 236: | Line 214: | ||
<tr> | <tr> | ||
<td>22\73<br /> | <td>22\73<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 266: | Line 236: | ||
<tr> | <tr> | ||
<td>19\63<br /> | <td>19\63<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 296: | Line 258: | ||
<tr> | <tr> | ||
<td>16\53<br /> | <td>16\53<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 326: | Line 280: | ||
<tr> | <tr> | ||
<td>13\43<br /> | <td>13\43<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 356: | Line 302: | ||
<tr> | <tr> | ||
<td>10\33<br /> | <td>10\33<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 386: | Line 324: | ||
<tr> | <tr> | ||
<td>7\23<br /> | <td>7\23<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 415: | Line 345: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>18\59<br /> | <td>18\59<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 445: | Line 367: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 454: | Line 372: | ||
</td> | </td> | ||
<td>47\154<br /> | <td>47\154<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 475: | Line 389: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 488: | Line 396: | ||
</td> | </td> | ||
<td>123\403<br /> | <td>123\403<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 505: | Line 411: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 535: | Line 433: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 565: | Line 455: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 580: | Line 464: | ||
</td> | </td> | ||
<td>199\652<br /> | <td>199\652<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 593: | Line 475: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 604: | Line 482: | ||
</td> | </td> | ||
<td>76\249<br /> | <td>76\249<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 623: | Line 497: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 630: | Line 502: | ||
</td> | </td> | ||
<td>29\95<br /> | <td>29\95<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 656: | Line 522: | ||
</td> | </td> | ||
<td>11\36<br /> | <td>11\36<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 683: | Line 541: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>15\49<br /> | <td>15\49<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 714: | Line 564: | ||
<tr> | <tr> | ||
<td>4\13<br /> | <td>4\13<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 747: | Line 589: | ||
</td> | </td> | ||
<td>13\42<br /> | <td>13\42<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 774: | Line 608: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>9\29<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 809: | Line 635: | ||
</td> | </td> | ||
<td>23/74<br /> | <td>23/74<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 834: | Line 652: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 843: | Line 659: | ||
</td> | </td> | ||
<td>60/193<br /> | <td>60/193<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 864: | Line 674: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 877: | Line 683: | ||
</td> | </td> | ||
<td>157/505<br /> | <td>157/505<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 894: | Line 696: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 905: | Line 703: | ||
</td> | </td> | ||
<td>97/312<br /> | <td>97/312<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 924: | Line 718: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 931: | Line 723: | ||
</td> | </td> | ||
<td>37/119<br /> | <td>37/119<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 957: | Line 743: | ||
</td> | </td> | ||
<td>14/45<br /> | <td>14/45<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 984: | Line 762: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 993: | Line 773: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>374.870<br /> | |||
</td> | |||
<td>224.090<br /> | |||
</td> | |||
<td>75.390<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5\16<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,016: | Line 808: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td><br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>375.130<br /> | |||
</td> | |||
<td>225.910<br /> | |||
</td> | |||
<td>74.610<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<td><br /> | <td><br /> | ||
</td> | |||
<td>11\35<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,045: | Line 851: | ||
<tr> | <tr> | ||
<td>6\19<br /> | <td>6\19<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,074: | Line 872: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>19\60<br /> | <td>19\60<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,107: | Line 897: | ||
</td> | </td> | ||
<td>13\41<br /> | <td>13\41<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,134: | Line 916: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>20\63<br /> | <td>20\63<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,165: | Line 939: | ||
<tr> | <tr> | ||
<td>7\22<br /> | <td>7\22<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,195: | Line 961: | ||
<tr> | <tr> | ||
<td>8\25<br /> | <td>8\25<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,225: | Line 983: | ||
<tr> | <tr> | ||
<td>9\28<br /> | <td>9\28<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,255: | Line 1,005: | ||
<tr> | <tr> | ||
<td>10\31<br /> | <td>10\31<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,287: | Line 1,029: | ||
</td> | </td> | ||
<td>21\65<br /> | <td>21\65<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,315: | Line 1,049: | ||
<tr> | <tr> | ||
<td>11\34<br /> | <td>11\34<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,345: | Line 1,071: | ||
<tr> | <tr> | ||
<td>12\37<br /> | <td>12\37<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,375: | Line 1,093: | ||
<tr> | <tr> | ||
<td>13\40<br /> | <td>13\40<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,405: | Line 1,115: | ||
<tr> | <tr> | ||
<td>14\43<br /> | <td>14\43<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,437: | Line 1,139: | ||
</td> | </td> | ||
<td>29\89<br /> | <td>29\89<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,465: | Line 1,159: | ||
<tr> | <tr> | ||
<td>15\46<br /> | <td>15\46<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,495: | Line 1,181: | ||
<tr> | <tr> | ||
<td>1\3<br /> | <td>1\3<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Revision as of 17:31, 11 February 2015
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author JosephRuhf and made on 2015-02-11 17:31:52 UTC.
- The original revision id was 540670544.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=3L+7s "Fair Mosh" (Modi Sephirotorum)= = = Fair Mosh is found in [[Magic|magic]] (chains of the 5th harmonic). It occupies the spectrum from 10edo (L=s) to 3edo (s=0). This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). In the region of the spectrum around 23 edo (L=3 s=2) , the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephirotorum. Temperament using phi directly approximates the higher Fibonacci harmonics best. If L=s, ie. multiples of 10edo, the 13th harmonic becomes nearly perfect. 121 edo seems to be the first to 'accurately' represent the comma (which might as well be represented accurately as it's quite small). Towards the other end, where the large and small steps are more contrasted, the comma 65/64 is liable to be tempered out, equating 5/4 and 13/8. In this category fall [[13edo]], [[16edo]], [[19edo]], [[22edo]], [[29edo]], and so on. This ends at s=0 which gives multiples of [[3edo]]. Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10) is symmetrical - not ascending but rather descending, and so reminiscent of ancient Greek practice. These scales, and their truncated heptatonic forms referenced below, are strikingly linear in several ways and so seem suited to a similar outlook as traditional western music (modality, baroque tonality, classical tonality, etc. progressing to today) but with higher harmonics. For more details [[http://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf]] (I know it should be "tractatus", changing it is just a bother) There are MODMOS as well, but I haven't explored them yet. There's enough undiscovered harmonic resource already in these to last me a while! Taking this approach to the 13th harmonic also yields heptatonic MOS with similar properties: [[3L 4s|4s+3L "mish"]] in the form of modes of ssLsLsL "led". (ascending) s s s L s s L s s L - Mode Keter s s L s s L s s L s - Chesed s L s s L s s L s s - Netzach L s s L s s L s s s - Malkuth s s L s s L s s s L - Binah s L s s L s s s L s - Tiferet L s s L s s s L s s - Yesod s s L s s s L s s L - Chokmah s L s s s L s s L s - Gevurah L s s s L s s L s s - Hod -- ||||||||||||~ Generator ||~ Cents ||~ L ||~ s ||~ Comments || || 3\10 || || || || || || 360 || 120 || 120 ||= || || 28\93 || || || || || || 361.290 || 129.032 || 116.129 ||= || || 25\83 || || || || || || 361.446 || 130.1205 || 115.663 ||= || || 22\73 || || || || || || 361.644 || 131.507 || 115.0685 ||= || || 19\63 || || || || || || 361.905 || 133.333 || 114.286 ||= || || 16\53 || || || || || || 362.264 || 135.849 || 113.2075 ||= || || 13\43 || || || || || || 362.791 || 139.535 || 111.628 ||= || || 10\33 || || || || || || 363.636 || 145.455 || 109.091 ||= || || 7\23 || || || || || || 365.217 || 156.522 || 104.348 ||= || || || 18\59 || || || || || 366.102 || 162.712 || 104.29 ||= || || || || 47\154 || || || || 366.234 || 163.636 || 101.299 ||= || || || || || 123\403 || || || 366.253 || 163.771 || 101.241 ||= || || || || || || 322\1055 || || 366.256 || 163.791 || 101.232 || || || || || || || || 521\1707 || 366.257 || 163.796 || 101.230 ||= Golden Sephiroth || || || || || || 199\652 || || 366.258 || 163.804 || 101.227 || || || || || 76\249 || || || 366.265 || 163.855 || 101.205 ||= || || || || 29\95 || || || || 366.316 || 164.2105 || 101.053 ||= || || || 11\36 || || || || || 366.667 || 166.667 || 100 ||= || || || 15\49 || || || || || 367.347 || 171.429 || 97.959 ||= || || 4\13 || || || || || || 369.231 || 184.615 || 92.308 ||= Boundary of propriety (smaller generators are proper) || || || 13\42 || || || || || 371.429 || 200 || 85.714 ||= || || || 9\29 || || || || || 372.414 || 206.897 || 82.759 ||= || || || || 23/74 || || || || 372.973 || 210.811 || 81.081 || || || || || || 60/193 || || || 373.057 || 211.399 || 80.829 || || || || || || || 157/505 || || 373.069 || 211.485 || 80.792 || || || || || || 97/312 || || || 373.077 || 211.5385 || 80.769 || || || || || 37/119 || || || || 373.109 || 211.765 || 80.672 || || || || 14/45 || || || || || 373.333 || 213.333 || 80 ||= || || || || || || || || 374.870 || 224.090 || 75.390 || || || 5\16 || || || || || || 375 || 225 || 75 ||= || || || || || || || || 375.130 || 225.910 || 74.610 || || || || 11\35 || || || || || 377.143 || 240 || 68.571 ||= || || 6\19 || || || || || || 378.947 || 252.632 || 63.158 ||= || || || 19\60 || || || || || 380 || 260 || 60 ||= Magic is around here || || || 13\41 || || || || || 380.488 || 263.415 || 58.537 ||= || || || 20\63 || || || || || 380.952 || 266.667 || 57.143 ||= || || 7\22 || || || || || || 381.818 || 272.72 || 54.545 ||= || || 8\25 || || || || || || 384 || 288 || 48 ||= || || 9\28 || || || || || || 385.714 || 300 || 42.857 ||= || || 10\31 || || || || || || 387.097 || 309.677 || 38.710 ||= || || || 21\65 || || || || || 387.692 || 313.846 || 36.923 ||= Würschmidt is around here || || 11\34 || || || || || || 388.235 || 317.647 || 35.294 ||= || || 12\37 || || || || || || 389.189 || 324.324 || 32.432 ||= || || 13\40 || || || || || || 390 || 330 || 30 || || || 14\43 || || || || || || 390.698 || 334.884 || 27,907 || || || || 29\89 || || || || || 391.011 || 337.079 || 26.966 ||= Amigo is around here || || 15\46 || || || || || || 391.304 || 339.130 || 26.087 || || || 1\3 || || || || || || 400 || 400 || 0 ||= || L=1 s=1 [[10edo]] L=2 s=1 [[13edo]] (L=3 s=1 [[16edo]]) L=3 s=2 [[23edo]] (L=4 s=1 [[19edo]]) L=4 s=3 [[33edo]] (L=5 s=1 [[22edo]]) (L=5 s=2 [[29edo]]) L=5 s=3 [[36edo]] L=5 s=4 [[43edo]] (L=6 s=1 [[25edo|25edo)]] L=6 s=5 [[53edo]] L=7 s=6 [[63edo]] L=7 s=5 [[56edo]] L=7 s=4 [[49edo]] etc.
Original HTML content:
<html><head><title>3L 7s</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x3L+7s "Fair Mosh" (Modi Sephirotorum)"></a><!-- ws:end:WikiTextHeadingRule:0 -->3L+7s "Fair Mosh" (Modi Sephirotorum)</h1>
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h1>
Fair Mosh is found in <a class="wiki_link" href="/Magic">magic</a> (chains of the 5th harmonic). It occupies the spectrum from 10edo (L=s) to 3edo (s=0).<br />
<br />
This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). In the region of the spectrum around 23 edo (L=3 s=2) , the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephirotorum. Temperament using phi directly approximates the higher Fibonacci harmonics best.<br />
<br />
If L=s, ie. multiples of 10edo, the 13th harmonic becomes nearly perfect. 121 edo seems to be the first to 'accurately' represent the comma (which might as well be represented accurately as it's quite small). Towards the other end, where the large and small steps are more contrasted, the comma 65/64 is liable to be tempered out, equating 5/4 and 13/8. In this category fall <a class="wiki_link" href="/13edo">13edo</a>, <a class="wiki_link" href="/16edo">16edo</a>, <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/29edo">29edo</a>, and so on. This ends at s=0 which gives multiples of <a class="wiki_link" href="/3edo">3edo</a>.<br />
<br />
Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10) is symmetrical - not ascending but rather descending, and so reminiscent of ancient Greek practice. These scales, and their truncated heptatonic forms referenced below, are strikingly linear in several ways and so seem suited to a similar outlook as traditional western music (modality, baroque tonality, classical tonality, etc. progressing to today) but with higher harmonics. For more details <a class="wiki_link_ext" href="http://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf" rel="nofollow">http://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf</a><br />
(I know it should be "tractatus", changing it is just a bother)<br />
<br />
There are MODMOS as well, but I haven't explored them yet. There's enough undiscovered harmonic resource already in these to last me a while! Taking this approach to the 13th harmonic also yields heptatonic MOS with similar properties: <a class="wiki_link" href="/3L%204s">4s+3L "mish"</a> in the form of modes of ssLsLsL "led".<br />
<br />
(ascending)<br />
s s s L s s L s s L - Mode Keter<br />
s s L s s L s s L s - Chesed<br />
s L s s L s s L s s - Netzach<br />
L s s L s s L s s s - Malkuth<br />
s s L s s L s s s L - Binah<br />
s L s s L s s s L s - Tiferet<br />
L s s L s s s L s s - Yesod<br />
s s L s s s L s s L - Chokmah<br />
s L s s s L s s L s - Gevurah<br />
L s s s L s s L s s - Hod<br />
<br />
--<br />
<table class="wiki_table">
<tr>
<th colspan="6">Generator<br />
</th>
<th>Cents<br />
</th>
<th>L<br />
</th>
<th>s<br />
</th>
<th>Comments<br />
</th>
</tr>
<tr>
<td>3\10<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>360<br />
</td>
<td>120<br />
</td>
<td>120<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>28\93<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>361.290<br />
</td>
<td>129.032<br />
</td>
<td>116.129<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>25\83<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>361.446<br />
</td>
<td>130.1205<br />
</td>
<td>115.663<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>22\73<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>361.644<br />
</td>
<td>131.507<br />
</td>
<td>115.0685<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>19\63<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>361.905<br />
</td>
<td>133.333<br />
</td>
<td>114.286<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>16\53<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>362.264<br />
</td>
<td>135.849<br />
</td>
<td>113.2075<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>13\43<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>362.791<br />
</td>
<td>139.535<br />
</td>
<td>111.628<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>10\33<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>363.636<br />
</td>
<td>145.455<br />
</td>
<td>109.091<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>7\23<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>365.217<br />
</td>
<td>156.522<br />
</td>
<td>104.348<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>18\59<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>366.102<br />
</td>
<td>162.712<br />
</td>
<td>104.29<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>47\154<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>366.234<br />
</td>
<td>163.636<br />
</td>
<td>101.299<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>123\403<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>366.253<br />
</td>
<td>163.771<br />
</td>
<td>101.241<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>322\1055<br />
</td>
<td><br />
</td>
<td>366.256<br />
</td>
<td>163.791<br />
</td>
<td>101.232<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>521\1707<br />
</td>
<td>366.257<br />
</td>
<td>163.796<br />
</td>
<td>101.230<br />
</td>
<td style="text-align: center;">Golden Sephiroth<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>199\652<br />
</td>
<td><br />
</td>
<td>366.258<br />
</td>
<td>163.804<br />
</td>
<td>101.227<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>76\249<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>366.265<br />
</td>
<td>163.855<br />
</td>
<td>101.205<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>29\95<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>366.316<br />
</td>
<td>164.2105<br />
</td>
<td>101.053<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>11\36<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>366.667<br />
</td>
<td>166.667<br />
</td>
<td>100<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>15\49<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>367.347<br />
</td>
<td>171.429<br />
</td>
<td>97.959<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>4\13<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>369.231<br />
</td>
<td>184.615<br />
</td>
<td>92.308<br />
</td>
<td style="text-align: center;">Boundary of propriety<br />
(smaller generators are proper)<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>13\42<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>371.429<br />
</td>
<td>200<br />
</td>
<td>85.714<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>9\29<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>372.414<br />
</td>
<td>206.897<br />
</td>
<td>82.759<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>23/74<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>372.973<br />
</td>
<td>210.811<br />
</td>
<td>81.081<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>60/193<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>373.057<br />
</td>
<td>211.399<br />
</td>
<td>80.829<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>157/505<br />
</td>
<td><br />
</td>
<td>373.069<br />
</td>
<td>211.485<br />
</td>
<td>80.792<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>97/312<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>373.077<br />
</td>
<td>211.5385<br />
</td>
<td>80.769<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>37/119<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>373.109<br />
</td>
<td>211.765<br />
</td>
<td>80.672<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>14/45<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>373.333<br />
</td>
<td>213.333<br />
</td>
<td>80<br />
</td>
<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><br />
</td>
<td>374.870<br />
</td>
<td>224.090<br />
</td>
<td>75.390<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>5\16<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>375<br />
</td>
<td>225<br />
</td>
<td>75<br />
</td>
<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><br />
</td>
<td>375.130<br />
</td>
<td>225.910<br />
</td>
<td>74.610<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>11\35<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>377.143<br />
</td>
<td>240<br />
</td>
<td>68.571<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>6\19<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>378.947<br />
</td>
<td>252.632<br />
</td>
<td>63.158<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>19\60<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>380<br />
</td>
<td>260<br />
</td>
<td>60<br />
</td>
<td style="text-align: center;">Magic is around here<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>13\41<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>380.488<br />
</td>
<td>263.415<br />
</td>
<td>58.537<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>20\63<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>380.952<br />
</td>
<td>266.667<br />
</td>
<td>57.143<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>7\22<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>381.818<br />
</td>
<td>272.72<br />
</td>
<td>54.545<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>8\25<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>384<br />
</td>
<td>288<br />
</td>
<td>48<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>9\28<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>385.714<br />
</td>
<td>300<br />
</td>
<td>42.857<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>10\31<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>387.097<br />
</td>
<td>309.677<br />
</td>
<td>38.710<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>21\65<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>387.692<br />
</td>
<td>313.846<br />
</td>
<td>36.923<br />
</td>
<td style="text-align: center;">Würschmidt is around here<br />
</td>
</tr>
<tr>
<td>11\34<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>388.235<br />
</td>
<td>317.647<br />
</td>
<td>35.294<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>12\37<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>389.189<br />
</td>
<td>324.324<br />
</td>
<td>32.432<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>13\40<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>390<br />
</td>
<td>330<br />
</td>
<td>30<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>14\43<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>390.698<br />
</td>
<td>334.884<br />
</td>
<td>27,907<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>29\89<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>391.011<br />
</td>
<td>337.079<br />
</td>
<td>26.966<br />
</td>
<td style="text-align: center;">Amigo is around here<br />
</td>
</tr>
<tr>
<td>15\46<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>391.304<br />
</td>
<td>339.130<br />
</td>
<td>26.087<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1\3<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>400<br />
</td>
<td>400<br />
</td>
<td>0<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
</table>
<br />
L=1 s=1 <a class="wiki_link" href="/10edo">10edo</a><br />
L=2 s=1 <a class="wiki_link" href="/13edo">13edo</a><br />
<br />
(L=3 s=1 <a class="wiki_link" href="/16edo">16edo</a>)<br />
L=3 s=2 <a class="wiki_link" href="/23edo">23edo</a><br />
<br />
(L=4 s=1 <a class="wiki_link" href="/19edo">19edo</a>)<br />
L=4 s=3 <a class="wiki_link" href="/33edo">33edo</a><br />
<br />
(L=5 s=1 <a class="wiki_link" href="/22edo">22edo</a>)<br />
(L=5 s=2 <a class="wiki_link" href="/29edo">29edo</a>)<br />
L=5 s=3 <a class="wiki_link" href="/36edo">36edo</a><br />
L=5 s=4 <a class="wiki_link" href="/43edo">43edo</a><br />
<br />
(L=6 s=1 <a class="wiki_link" href="/25edo">25edo)</a><br />
L=6 s=5 <a class="wiki_link" href="/53edo">53edo</a><br />
<br />
L=7 s=6 <a class="wiki_link" href="/63edo">63edo</a><br />
L=7 s=5 <a class="wiki_link" href="/56edo">56edo</a><br />
L=7 s=4 <a class="wiki_link" href="/49edo">49edo</a><br />
etc.</body></html>