|
|
| (229 intermediate revisions by 19 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | |en=4L 3s |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-10 23:47:54 UTC</tt>.<br>
| | |es= |
| : The original revision id was <tt>540552366</tt>.<br>
| | |de= |
| : The revision comment was: <tt></tt><br>
| | |ja=4L 3s |
| 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>
| | {{Infobox MOS}} |
| <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">4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of [[4edo]], 300¢) to 2\7edo (two degrees of [[7edo]], or approx. 342.857¢). The spectrum looks like this:
| |
| ||||||||||||||~ Generator ||~ Tetrachord ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments || | |
| || 1\4 || || || || || || || 1 0 1 || 300.000 || 600.000 || 900.000 || 0.000 ||= ||
| |
| || || || || || || || 8\31 || 7 1 7 || 309.677 || 619.355 || 929.023 || 38.71 ||= Myna is around here || | |
| || || || || || || 7\27 || || 6 1 6 || 311.111 || 622.222 || 933.333 || 44.444 ||= || | |
| || || || || || 6\23 || || || 5 1 5 || 313.043 || 626.087 || 939.13 || 52.174 ||= ||
| |
| || || || || 5\19 || || || || 4 1 4 || 315.789 || 631.579 || 947.368 || 63.158 ||= L/s = 4 ||
| |
| || || || || || 9\34 || || || 7 2 7 || 317.647 || 634.294 || 951.941 || 70.588 ||= Hanson/Keemun is around here ||
| |
| || || || || || || || || 3.03 1 3,03 || 319.8525 || 639.705 || 959.558 || 79.410 ||= <span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span> ||
| |
| || || || 4\15 || || || || || 3 1 3 || 320.000 || 640.000 || 960.000 || 80.000 ||= L/s = 3 ||
| |
| || || || || || || || || 2.97 1 2.97 || 320.148 || 640.297 || 960.445 || 80.593 || <span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span> ||
| |
| || || || || 7\26 || || || || 5 2 5 || 323.077 || 646.154 || 969.231 || 92.308 ||= Orgone is around here ||
| |
| || || 3\11 || || || || || || 2 1 2 || 327.273 || 654.545 || 981.818 || 109.091 ||= Boundary of propriety (generators
| |
| larger than this are proper) ||
| |
| || || || || 8\29 || || || || 5 3 5 || 331.034 || 662.069 || 993.013 || 124.138 ||= ||
| |
| || || || || || || 21\76 || || 13 8 13 || 331.579 || 663.158 || 994.739 || 126.316 ||= ||
| |
| || || || || || || || 34\123 || 21 13 21 || 331.707 || 663.415 || 995.122 || 126.829 ||= Unnamed golden temperament ||
| |
| || || || || || 13\47 || || || 8 5 8 || 331.915 || 663.83 || 995.745 || 127.66 ||= ||
| |
| || || || 5\18 || || || || || 3 2 3 || 333.333 || 666.667 || 1000.000 || 133.333 ||= Optimum rank range (L/s=3/2) ||
| |
| || || || || 7\25 || || || || 4 3 4 || 336.000 || 672.000 || 1008.000 || 144.000 ||= ||
| |
| || || || || || 9\32 || || || 5 4 5 || 337.5 || 675.000 || 1012.500 || 150.000 ||= Sixix ||
| |
| || || || || || || 11\39 || || 6 5 6 || 338.462 || 676.923 || 1015.385 || 153.846 ||= Sixix ||
| |
| || || || || || || || 13\46 || 7 6 7 || 339.130 || 678.261 || 1017.391 || 156.522 ||= (17/14)^3=9/5 ||
| |
| || 2\7 || || || || || || || 1 1 1 || 342.857 || 685.714 || 1028.571 || 171.429 ||= ||
| |
| There are two notable harmonic entropy minima: [[Kleismic family|hanson/keemun]], in which the generator is 6/5 and 6 of them make a 3/1, and [[Starling temperaments|myna]], in which the generator is also 6/5 but now **10** of them make a 6/1 (so no 4/3's or 3/2's appear in this scale).</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>4L 3s</title></head><body>4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of <a class="wiki_link" href="/4edo">4edo</a>, 300¢) to 2\7edo (two degrees of <a class="wiki_link" href="/7edo">7edo</a>, or approx. 342.857¢). The spectrum looks like this:<br />
| |
|
| |
|
| | {{MOS intro}} |
| | 4L 3s can be seen as a [[Warped diatonic|warped diatonic scale]], where one large step of diatonic ([[5L 2s]]) is replaced with a small step. |
|
| |
|
| <table class="wiki_table">
| | == Name == |
| <tr>
| | {{TAMNAMS name}} |
| <th colspan="7">Generator<br />
| |
| </th>
| |
| <th>Tetrachord<br />
| |
| </th>
| |
| <th>g in cents<br />
| |
| </th>
| |
| <th>2g<br />
| |
| </th>
| |
| <th>3g<br />
| |
| </th>
| |
| <th>4g<br />
| |
| </th>
| |
| <th>Comments<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1\4<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1 0 1<br />
| |
| </td>
| |
| <td>300.000<br />
| |
| </td>
| |
| <td>600.000<br />
| |
| </td>
| |
| <td>900.000<br />
| |
| </td>
| |
| <td>0.000<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>8\31<br />
| |
| </td>
| |
| <td>7 1 7<br />
| |
| </td>
| |
| <td>309.677<br />
| |
| </td>
| |
| <td>619.355<br />
| |
| </td>
| |
| <td>929.023<br />
| |
| </td>
| |
| <td>38.71<br />
| |
| </td>
| |
| <td style="text-align: center;">Myna is around here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7\27<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>6 1 6<br />
| |
| </td>
| |
| <td>311.111<br />
| |
| </td>
| |
| <td>622.222<br />
| |
| </td>
| |
| <td>933.333<br />
| |
| </td>
| |
| <td>44.444<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>6\23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5 1 5<br />
| |
| </td>
| |
| <td>313.043<br />
| |
| </td>
| |
| <td>626.087<br />
| |
| </td>
| |
| <td>939.13<br />
| |
| </td>
| |
| <td>52.174<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5\19<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4 1 4<br />
| |
| </td>
| |
| <td>315.789<br />
| |
| </td>
| |
| <td>631.579<br />
| |
| </td>
| |
| <td>947.368<br />
| |
| </td>
| |
| <td>63.158<br />
| |
| </td>
| |
| <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>9\34<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7 2 7<br />
| |
| </td>
| |
| <td>317.647<br />
| |
| </td>
| |
| <td>634.294<br />
| |
| </td>
| |
| <td>951.941<br />
| |
| </td>
| |
| <td>70.588<br />
| |
| </td>
| |
| <td style="text-align: center;">Hanson/Keemun is around here<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>3.03 1 3,03<br />
| |
| </td>
| |
| <td>319.8525<br />
| |
| </td>
| |
| <td>639.705<br />
| |
| </td>
| |
| <td>959.558<br />
| |
| </td>
| |
| <td>79.410<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4\15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3 1 3<br />
| |
| </td>
| |
| <td>320.000<br />
| |
| </td>
| |
| <td>640.000<br />
| |
| </td>
| |
| <td>960.000<br />
| |
| </td>
| |
| <td>80.000<br />
| |
| </td>
| |
| <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><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>2.97 1 2.97<br />
| |
| </td>
| |
| <td>320.148<br />
| |
| </td>
| |
| <td>640.297<br />
| |
| </td>
| |
| <td>960.445<br />
| |
| </td>
| |
| <td>80.593<br />
| |
| </td>
| |
| <td><span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7\26<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5 2 5<br />
| |
| </td>
| |
| <td>323.077<br />
| |
| </td>
| |
| <td>646.154<br />
| |
| </td>
| |
| <td>969.231<br />
| |
| </td>
| |
| <td>92.308<br />
| |
| </td>
| |
| <td style="text-align: center;">Orgone is around here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>3\11<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>2 1 2<br />
| |
| </td>
| |
| <td>327.273<br />
| |
| </td>
| |
| <td>654.545<br />
| |
| </td>
| |
| <td>981.818<br />
| |
| </td>
| |
| <td>109.091<br />
| |
| </td>
| |
| <td style="text-align: center;">Boundary of propriety (generators<br />
| |
| larger than this are proper)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>8\29<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5 3 5<br />
| |
| </td>
| |
| <td>331.034<br />
| |
| </td>
| |
| <td>662.069<br />
| |
| </td>
| |
| <td>993.013<br />
| |
| </td>
| |
| <td>124.138<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>21\76<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>13 8 13<br />
| |
| </td>
| |
| <td>331.579<br />
| |
| </td>
| |
| <td>663.158<br />
| |
| </td>
| |
| <td>994.739<br />
| |
| </td>
| |
| <td>126.316<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>34\123<br />
| |
| </td>
| |
| <td>21 13 21<br />
| |
| </td>
| |
| <td>331.707<br />
| |
| </td>
| |
| <td>663.415<br />
| |
| </td>
| |
| <td>995.122<br />
| |
| </td>
| |
| <td>126.829<br />
| |
| </td>
| |
| <td style="text-align: center;">Unnamed golden temperament<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>13\47<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>8 5 8<br />
| |
| </td>
| |
| <td>331.915<br />
| |
| </td>
| |
| <td>663.83<br />
| |
| </td>
| |
| <td>995.745<br />
| |
| </td>
| |
| <td>127.66<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5\18<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3 2 3<br />
| |
| </td>
| |
| <td>333.333<br />
| |
| </td>
| |
| <td>666.667<br />
| |
| </td>
| |
| <td>1000.000<br />
| |
| </td>
| |
| <td>133.333<br />
| |
| </td>
| |
| <td style="text-align: center;">Optimum rank range (L/s=3/2)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7\25<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4 3 4<br />
| |
| </td>
| |
| <td>336.000<br />
| |
| </td>
| |
| <td>672.000<br />
| |
| </td>
| |
| <td>1008.000<br />
| |
| </td>
| |
| <td>144.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>9\32<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5 4 5<br />
| |
| </td>
| |
| <td>337.5<br />
| |
| </td>
| |
| <td>675.000<br />
| |
| </td>
| |
| <td>1012.500<br />
| |
| </td>
| |
| <td>150.000<br />
| |
| </td>
| |
| <td style="text-align: center;">Sixix<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>11\39<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>6 5 6<br />
| |
| </td>
| |
| <td>338.462<br />
| |
| </td>
| |
| <td>676.923<br />
| |
| </td>
| |
| <td>1015.385<br />
| |
| </td>
| |
| <td>153.846<br />
| |
| </td>
| |
| <td style="text-align: center;">Sixix<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>13\46<br />
| |
| </td>
| |
| <td>7 6 7<br />
| |
| </td>
| |
| <td>339.130<br />
| |
| </td>
| |
| <td>678.261<br />
| |
| </td>
| |
| <td>1017.391<br />
| |
| </td>
| |
| <td>156.522<br />
| |
| </td>
| |
| <td style="text-align: center;">(17/14)^3=9/5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2\7<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1 1 1<br />
| |
| </td>
| |
| <td>342.857<br />
| |
| </td>
| |
| <td>685.714<br />
| |
| </td>
| |
| <td>1028.571<br />
| |
| </td>
| |
| <td>171.429<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| There are two notable harmonic entropy minima: <a class="wiki_link" href="/Kleismic%20family">hanson/keemun</a>, in which the generator is 6/5 and 6 of them make a 3/1, and <a class="wiki_link" href="/Starling%20temperaments">myna</a>, in which the generator is also 6/5 but now <strong>10</strong> of them make a 6/1 (so no 4/3's or 3/2's appear in this scale).</body></html></pre></div> | | == Scale properties == |
| | {{TAMNAMS use}} |
| | |
| | === Intervals === |
| | {{MOS intervals}} |
| | |
| | === Generator chain === |
| | {{MOS genchain}} |
| | |
| | === Modes === |
| | {{MOS mode degrees}} |
| | |
| | ==== Proposed names ==== |
| | Alexandru Ianu ([[User:Ayceman|Ayceman]])<ref>Description of ''Sylvian Moon Dance'' mentioning the naming proposal https://musescore.com/user/36772625/scores/6700443 – The theme relates to the mystical nature of the Tribunal and TES lore, which fits smitonic.</ref> has proposed the following mode names relating to the Almsivi in Morrowind (TES): |
| | {{MOS modes |
| | | Mode Names=Nerevarine $ |
| | Vivecan $ |
| | Lorkhanic $ |
| | Sothic $ |
| | Kagrenacan $ |
| | Almalexian $ |
| | Dagothic $ |
| | }} |
| | |
| | == Theory == |
| | === Low harmonic entropy scales === |
| | There are two notable harmonic entropy minima: |
| | * [[Kleismic family|Kleismic temperament]], in which the generator is 6/5 and 6 of them make a 3/1. |
| | * [[myna|Myna temperament]], in which the generator is also 6/5 but it takes 10 of them to make a 6/1, meaning that a larger MOS than 4L 3s is required to reach 3/2 or 4/3. |
| | |
| | === Temperament interpretations === |
| | {{main|4L 3s/Temperaments}} |
| | 4L 3s has the following temperament interpretations: |
| | * [[Sixix]], with generators around 338.6{{c}}. |
| | * [[Orgone]], with generators around 323.4{{c}}. |
| | * [[Kleismic]], with generators around 317{{c}}. |
| | |
| | Other temperaments, such as [[amity]] and [[myna]], require more than 7 pitches to contain the concordant chords optimized by these temperaments. If restricted to a rank-2 approach, a [[MODMOS]] or a larger MOS gamut is necessary to access these pitches. |
| | |
| | == Tuning ranges == |
| | {{Todo|Populate|comment=Populate with JI ratios from prior edits of this page.|inline=1}} |
| | |
| | === Simple tunings === |
| | The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing 11edo, 15edo, and 18edo, respectively. |
| | {{MOS tunings}} |
| | |
| | === Parasoft tunings === |
| | Parasoft smitonic tunings can be considered "meantone smitonic" since it has the following features of [[meantone]] diatonic tunings: |
| | |
| | * The major 1-mosstep, or large step, is around [[10/9]] to [[9/8]], thus making it a "meantone". |
| | * The augmented 2-mosstep is around the size of a meantone-sized major 3rd and can be used as a stand-in for such. |
| | |
| | These tunings have a major 4-mosstep and minor 4-mosstep that are about equally off a just 3/2 (702{{c}}), and they have otherwise fairly convincing versions of both diatonic structure and tertian harmony, provided you frequently modify using the comma-like chromas. For this reason, parasoft might be the most accessible smitonic tuning range. |
| | |
| | Edos include [[18edo]], [[25edo]], and [[43edo]]. Some key considerations include: |
| | |
| | * 18edo can be used to make the large and small steps more distinct, or can be considered a distorted 19edo diatonic. |
| | ** 18edo has a major 1-mosstep that is close to 9/8 (203{{c}}). |
| | ** 18edo's major and minor 4-mossteps are both equally off from 12edo's diatonic perfect 5th (700{{c}}) by 33.3{{c}}. |
| | ** 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry. |
| | * The augmented 2-mosstep of 25edo is very close to 5/4 (386{{c}}). |
| | {{MOS tunings|Step Ratios=3/2; 7/5; 4/3}} |
| | |
| | === Hyposoft tunings === |
| | Hyposoft smitonic tunings (3:2 to 2:1) are characterized by generators that are a supraminor 3rd, between 327{{c}} and 333{{c}}. By analogy of parasoft tunings being called "meantone smitonic", these tunings can be considered "[[Gentle region|neogothic]] smitonic" or "[[archy]] smitonic". |
| | |
| | Edos include [[11edo]] (not shown), [[18edo]], and [[29edo]]. |
| | |
| | {{MOS tunings|Step Ratios=3/2; 5/3; 7/4}} |
| | |
| | === Hypohard tunings=== |
| | Hypohard smitonic tunings (2:1 to 3:1) have generators between 320{{c}} and 327{{c}}. The major 1-mosstep, or large step, tends to approximate [[8/7]] (231{{c}}) and the major 3-mosstep tends to approximate [[11/8]] (551{{c}}). [[26edo]] approximates these two intervals very well. These JI approximations are associated with [[orgone]] temperament. |
| | |
| | Other hypohard edos include [[11edo]] (not shown), [[15edo]] and [[37edo]]. |
| | |
| | {{MOS tunings|Step Ratios=3/1; 5/2; 7/3}} |
| | |
| | === Parahard tunings === |
| | Parahard smitonic tunings (3:1 to 4:1) have generators between 315.9{{c}} and 320{{c}}, putting it close to a pure 6/5 (316{{c}}). Stacking six generators and octave-reducing approximates 3/2 (702{{c}}), a diatonic perfect 5th, represented by the diminished 5-mosstep. |
| | |
| | This range contains very accurate edos such as [[53edo]] and [[72edo]], and has very accurate approximations to many [[low-overtone JI]] intervals, namely basic [[5-limit]] ratios and some ratios involving 13. However, 4L 3s only has one interval of 3/2, so it's suggested to use a larger MOS, such as [[4L 7s]], to achieve 5-limit harmony. |
| | |
| | These JI approximations are associated with [[kleismic]] temperament, through the 2.3.5.13 extension known as [[Kleismic family#Cata|cata]]. |
| | |
| | Parahard edos smaller than 53edo include [[15edo]] (not shown), [[19edo]], and [[34edo]]. |
| | |
| | {{MOS tunings|Step Ratios=4/1; 11/3; 7/2}} |
| | |
| | == Scales == |
| | * [[Orgone7]] |
| | * [[Cata7]] |
| | * [[Myna7]] |
| | |
| | == Scale tree== |
| | {{MOS tuning spectrum |
| | | 6/5 = [[Amity]]/[[hitchcock]] ↑ |
| | | 5/4 = [[Sixix]] |
| | | 4/3 = [[Supramin]] |
| | | 13/8 = Golden 4L 3s (868.3282{{c}}) |
| | | 12/5 = [[Hyperkleismic]] |
| | | 5/2 = [[Orgone]] |
| | | 13/5 = Golden superkleismic |
| | | 8/3 = [[Superkleismic]] |
| | | 11/3 = [[Hanson]]/[[keemun]] |
| | | 6/1 = [[Oolong]]/[[myna]] ↓ |
| | }} |
| | |
| | == Music == |
| | * [[City of the Asleep]], [https://cityoftheasleep.bandcamp.com/album/an-amputated-elliptic-knob-of-the-cryptocurve-regenerates "An Amputated Elliptic Knob of the Cryptocurve Regenerates"] (Various orgone edos) |
| | * [[User:Ks26|ks26]], [https://www.youtube.com/watch?v=AEnEYk3X1as Ghost Bridge] (11edo) |
| | * [[User:Ayceman|Alexandru Ianu]], [https://youtu.be/81uZbsmbet8 Sylvian Moon Dance] (11edo) ([[:File:Sylvian_Moon_Dance.pdf|sheet music]]) |
| | |
| | == References == |
| | <references /> |
| | |
| | [[Category:Smitonic|*]] <!--Main article--> |
| | [[Category:7-tone scales]] |