7L 2s
IMPORTED REVISION FROM WIKISPACES
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Original Wikitext content:
This page is about of a [[MOSScales|MOSScale]] with 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL). If you're looking for highly accurate scales (that is, ones that approximate JI closely), there are much better scale patterns to look at. However, if your harmonic entropy is coarse enough (that is, if 678 cents is an acceptable '3/2' to you), then [[Pelogic family|mávila]] is an important harmonic entropy here. So a general name for this MOS pattern could be "Mávila Superdiatonic" or simply 'Superdiatonic'. These scales are strongly associated with the [[Armodue]] project/system applied too on Septimal-mávila and Hornbostel temperaments. Optional types of 'JI [[Blown Fifth]]' Generators: 31/21, 34/23, 65/44, 71/48, 99/67, 105/71, 108/73, 133/90, 145/98, 176/119 & 250/169. ||~ ||~ ||||||||||||||~ Generator ||~ Generator size (cents) ||~ Scale steps ||~ Comments || ||= 4\[[7edo|7]] ||= ||= ||= ||= ||= ||= ||= ||= || 685.714 ||< 1 1 1 0 1 1 1 1 0 ||< || ||= ||= 21\[[37edo|37]] ||= ||= ||= ||= ||= ||= ||= || 681.081 ||< 5 5 5 1 5 5 5 5 1 ||< || ||= ||= ||= 17\[[30edo|30]] ||= ||= ||= ||= ||= ||= || 680 ||< 4 4 4 1 4 4 4 4 1 ||< generators larger than this are "impractical" || ||= ||= ||= ||= 30\[[53edo|53]] ||= ||= ||= ||= ||= || 679.245 ||< 7 7 7 2 7 7 7 7 2 ||< || ||= ||= ||= ||= ||= 121\[[214edo|214]] ||= ||= ||= ||= || 678.505 ||< 28 28 28 9 28 28 28 28 9 ||< 28;9 Superdiatonic 1/28-tone (a slight exceeded representation of the ratio 262144/177147, the Pythagorean wolf Fifth) || ||= ||= ||= ||= 134\[[237edo|237]] ||= ||= ||= ||= ||= || 678.481 ||< 31 31 31 10 31 31 31 31 10 ||< HORNBOSTEL TEMPERAMENT (1/31-tone; Optimum high size of Hornbostel '6th') || ||= ||= ||= 13\[[23edo|23]] ||= ||= ||= ||= ||= ||= || 678.261 ||< 3 3 3 1 3 3 3 3 1 ||< HORNBOSTEL TEMPERAMENT (Armodue 1/3-tone) generators largerer than this may be considered "impractical" || || || || || 126\[[223edo|223]] || || || || || || 678.027 || 29 29 29 10 29 29 29 29 10 || HORNBOSTEL TEMPERAMENT (Armodue 1/29-tone) || ||= ||= ||= ||= ||= 113\[[200edo|200]] ||= ||= ||= ||= || 678 ||< 26 26 26 9 26 26 26 26 9 ||< HORNBOSTEL (& [[Alexei Stepanovich Ogolevets|OGOLEVETS]]) TEMPERAMENT (Armodue 1/26-tone; Best equillibrium between 6/5, Phi (833.1 Cent) and Square root of Pi (990.9 Cent), the notes '3', '7' & '8') || ||= ||= ||= ||= ||= ||= 74\[[131edo|131]] ||= ||= ||= || 677.863 ||< 17 17 17 6 17 17 17 17 6 ||< Armodue-Hornbostel 1/17-tone (the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments) || || || || || || || || 61\[[108edo|108]] || || || 677.778 || 14 14 14 5 14 14 14 14 5 || Armodue-Hornbostel 1/14-tone || || || || || || || || || || 109\[[193edo|193]] || 677.720 || 25 25 25 9 25 25 25 25 9 || Armodue-Hornbostel 1/25-tone || ||= ||= ||= ||= ||= ||= ||= ||= 48\[[85edo|85]] ||= || 677.647 ||< 11 11 11 4 11 11 11 11 4 ||< Armodue-Hornbostel 1/11-tone (Optimum accuracy of Phi interval, the note '7') || ||= ||= ||= ||= ||= ||= ||= 35\[[62edo|62]] ||= ||= || 677.419 ||< 8 8 8 3 8 8 8 8 3 ||< Armodue-Hornbostel 1/8-tone || || || || || || || 92\[[163edo|163]] || || || || 677.301 || 21 21 21 8 21 21 21 21 8 || 21;8 Superdiatonic 1/21-tone || || || || || || || || || || || 677.2804 || <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ+1 φ+1 φ+1 1 φ+1 φ+1 φ+1 φ+1 1</span> || Split φ superdiatonic relation (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..) || ||= ||= ||= ||= ||= 57\[[101edo|101]] ||= ||= ||= ||= || 677.228 ||< 13 13 13 5 13 13 13 13 5 ||< 13;5 Superdiatonic 1/13-tone || ||= ||= ||= ||= 22\[[39edo|39]] ||= ||= ||= ||= ||= || 676.923 ||< 5 5 5 2 5 5 5 5 2 ||< Armodue-Hornbostel 1/5-tone (Optimum low size of Hornbostel '6th') || ||= ||= ||= ||= ||= 75\[[133edo|133]] ||= ||= ||= ||= || 676.692 ||< 17 17 17 7 17 17 17 17 7 ||< 17;7 Superdiatonic 1/17-tone (Note the very accuracy of the step 75 with the ratio 34/23 with a error of +0.011 Cents) || ||= ||= ||= ||= ||= ||= 31\[[55edo|55]] ||= ||= ||= || 676.364 ||< 7 7 7 3 7 7 7 7 3 ||< 7;3 Superdiatonic 1/7-tone || ||= ||= ||= ||= ||= ||= ||= 40\[[71edo|71]] ||= ||= || 676.056 ||< 9 9 9 4 9 9 9 9 4 ||< 9;4 Superdiatonic 1/9-tone || ||= ||= ||= ||= ||= ||= ||= ||= 49\[[87edo|87]] ||= || 675.862 ||< 11 11 11 5 11 11 11 11 5 ||< 11;5 Superdiatonic 1/11-tone || || || || || || || || || || 58\[[103edo|103]] || 675.728 || 13 13 13 6 13 13 13 13 6 || 13;6 Superdiatonic 1/13-tone || ||= ||= 9\[[16edo|16]] ||= ||= ||= ||= ||= ||= ||= || 675 ||< 2 2 2 1 2 2 2 2 1 ||< <span style="display: block; text-align: left;">**[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]**</span>ARMODUE ESADECAFONIA (or Goldsmith Temperament) || || || || || || || || || || 59\[[105edo|105]] || 674.286 || 13 13 13 7 13 13 13 13 7 || Armodue-Mávila 1/13-tone || ||= ||= ||= ||= ||= ||= ||= ||= 50\[[89edo|89]] ||= || 674.157 ||< 11 11 11 6 11 11 11 11 6 ||< Armodue-Mávila 1/11-tone || ||= ||= ||= ||= ||= ||= ||= 41\[[73edo|73]] ||= ||= || 673.973 ||< 9 9 9 5 9 9 9 9 5 ||< Armodue-Mávila 1/9-tone (with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents) || ||= ||= ||= ||= ||= ||= 32\[[57edo|57]] ||= ||= ||= || 673.684 ||< 7 7 7 4 7 7 7 7 4 ||< Armodue-Mávila 1/7-tone (the 'Commatic' version of Armodue, because its highly accuracy of the [[7_4|7/4]] interval, the note '8') || || || || || || 78\[[139edo|139]] || || || || || 673.381 || 17 17 17 10 17 17 17 17 10 || Armodue-Mávila 1/17-tone || ||= ||= ||= ||= 23\[[41edo|41]] ||= ||= ||= ||= ||= || 673.171 ||< 5 5 5 3 5 5 5 5 3 ||< 5;3 Golden Armodue-Mávila 1/5-tone || ||= ||= ||= ||= ||= 60\[[107edo|107]] ||= ||= ||= ||= || 672.897 ||< 13 13 13 8 13 13 13 13 8 ||< 13;8 Golden Mávila 1/13-tone || || || || || || || || || || || 672.8503 || <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1 φ φ φ φ 1</span> || GOLDEN MÁVILA (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span> || ||= ||= ||= ||= ||= ||= 97\[[173edo|173]] ||= ||= ||= || 672.832 ||< 21 21 21 13 21 21 21 21 13 ||< 21;13 Golden Mávila 1/21-tone (ratio between large and small steps is Phi, and Phi in the step 120\173) || ||= ||= ||= ||= ||= ||= ||= 37\[[66edo|66]] ||= ||= || 672.727 ||< 8 8 8 5 8 8 8 8 5 ||< 8;5 Golden Mávila 1/8-tone || || || || || || || || || 51\[[91edo|91]] || || 672.527 || 11 11 11 7 11 11 11 11 7 || 11;7 Superdiatonic 1/11-tone || || || || || || || || || || 116\[[207]] || 672.464 || 25 25 25 16 25 25 25 25 16 || 25;16 Superdiatonic 1/25-tone || || || || || || || || 65\[[116edo|116]] || || || 672.414 || 14 14 14 9 14 14 14 14 9 || 14;9 Superdiatonic 1/14-tone || || || || || || || 79\[[141edo|141]] || || || || 672.340 || 17 17 17 11 17 17 17 17 11 || 17;11 Superdiatonic 1/17-tone || || || || || || 121\[[216edo|216]] || || || || || 672.222 || 26 26 26 17 26 26 26 26 17 || 26;17 Superdiatonic 1/26-tone || || || || || 135\[[241edo|241]] || || || || || || 672.199 || 29 29 29 19 29 29 29 29 19 || 29;19 Superdiatonic 1/29-tone || ||= ||= ||= 14\[[25edo|25]] ||= ||= ||= ||= ||= ||= || 672 ||< 3 3 3 2 3 3 3 3 2 ||< 3;2 Golden Armodue-Mávila 1/3-tone || || || || || 145\[[259edo|259]] || || || || || || 671.815 || 31 31 31 21 31 31 31 31 21 || 31;21 Superdiatonic 1/31-tone || || || || || || 131\[[234edo|234]] || || || || || 671.795 || 28 28 28 19 28 28 28 28 19 || 28;19 Superdiatonic 1/28-tone || ||= ||= ||= ||= 33\[[59edo|59]] ||= ||= ||= ||= ||= || 671.186 ||< 7 7 7 5 7 7 7 7 5 ||< || ||= ||= ||= 19\[[34edo|34]] ||= ||= ||= ||= ||= ||= || 670.588 ||< 4 4 4 3 4 4 4 4 3 ||< || ||= ||= 24\[[43edo|43]] ||= ||= ||= ||= ||= ||= ||= || 669.767 ||< 5 5 5 4 5 5 5 5 4 ||< || ||= 5\[[9edo|9]] ||= ||= ||= ||= ||= ||= ||= ||= || 666.667 ||< 1 1 1 1 1 1 1 1 1 ||< ||
Original HTML content:
<html><head><title>7L 2s</title></head><body>This page is about of a <a class="wiki_link" href="/MOSScales">MOSScale</a> with 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).<br />
<br />
If you're looking for highly accurate scales (that is, ones that approximate JI closely), there are much better scale patterns to look at. However, if your harmonic entropy is coarse enough (that is, if 678 cents is an acceptable '3/2' to you), then <a class="wiki_link" href="/Pelogic%20family">mávila</a> is an important harmonic entropy here. So a general name for this MOS pattern could be "Mávila Superdiatonic" or simply 'Superdiatonic'.<br />
These scales are strongly associated with the <a class="wiki_link" href="/Armodue">Armodue</a> project/system applied too on Septimal-mávila and Hornbostel temperaments.<br />
<br />
Optional types of 'JI <a class="wiki_link" href="/Blown%20Fifth">Blown Fifth</a>' Generators: 31/21, 34/23, 65/44, 71/48, 99/67, 105/71, 108/73, 133/90, 145/98, 176/119 & 250/169.<br />
<table class="wiki_table">
<tr>
<th><br />
</th>
<th><br />
</th>
<th colspan="7">Generator<br />
</th>
<th>Generator size (cents)<br />
</th>
<th>Scale steps<br />
</th>
<th>Comments<br />
</th>
</tr>
<tr>
<td style="text-align: center;">4\<a class="wiki_link" href="/7edo">7</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>685.714<br />
</td>
<td style="text-align: left;">1 1 1 0 1 1 1 1 0<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">21\<a class="wiki_link" href="/37edo">37</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>681.081<br />
</td>
<td style="text-align: left;">5 5 5 1 5 5 5 5 1<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">17\<a class="wiki_link" href="/30edo">30</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>680<br />
</td>
<td style="text-align: left;">4 4 4 1 4 4 4 4 1<br />
</td>
<td style="text-align: left;">generators larger than this are "impractical"<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">30\<a class="wiki_link" href="/53edo">53</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>679.245<br />
</td>
<td style="text-align: left;">7 7 7 2 7 7 7 7 2<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">121\<a class="wiki_link" href="/214edo">214</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>678.505<br />
</td>
<td style="text-align: left;">28 28 28 9 28 28 28 28 9<br />
</td>
<td style="text-align: left;">28;9 Superdiatonic 1/28-tone (a slight exceeded representation of the ratio 262144/177147, the Pythagorean wolf Fifth)<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">134\<a class="wiki_link" href="/237edo">237</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>678.481<br />
</td>
<td style="text-align: left;">31 31 31 10 31 31 31 31 10<br />
</td>
<td style="text-align: left;">HORNBOSTEL TEMPERAMENT (1/31-tone; Optimum high size<br />
of Hornbostel '6th')<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">13\<a class="wiki_link" href="/23edo">23</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>678.261<br />
</td>
<td style="text-align: left;">3 3 3 1 3 3 3 3 1<br />
</td>
<td style="text-align: left;">HORNBOSTEL TEMPERAMENT (Armodue 1/3-tone)<br />
generators largerer than this may be considered "impractical"<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>126\<a class="wiki_link" href="/223edo">223</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>678.027<br />
</td>
<td>29 29 29 10 29 29 29 29 10<br />
</td>
<td>HORNBOSTEL TEMPERAMENT (Armodue 1/29-tone)<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">113\<a class="wiki_link" href="/200edo">200</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>678<br />
</td>
<td style="text-align: left;">26 26 26 9 26 26 26 26 9<br />
</td>
<td style="text-align: left;">HORNBOSTEL (& <a class="wiki_link" href="/Alexei%20Stepanovich%20Ogolevets">OGOLEVETS</a>) TEMPERAMENT<br />
(Armodue 1/26-tone; Best equillibrium between 6/5, Phi (833.1 Cent) and Square root of Pi (990.9 Cent), the notes '3', '7' & '8')<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">74\<a class="wiki_link" href="/131edo">131</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>677.863<br />
</td>
<td style="text-align: left;">17 17 17 6 17 17 17 17 6<br />
</td>
<td style="text-align: left;">Armodue-Hornbostel 1/17-tone (the Golden Tone System of<br />
Thorvald Kornerup and a temperament of the Alexei<br />
Ogolevets's list of temperaments)<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>61\<a class="wiki_link" href="/108edo">108</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>677.778<br />
</td>
<td>14 14 14 5 14<br />
14 14 14 5<br />
</td>
<td>Armodue-Hornbostel 1/14-tone<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>109\<a class="wiki_link" href="/193edo">193</a><br />
</td>
<td>677.720<br />
</td>
<td>25 25 25 9 25<br />
25 25 25 9<br />
</td>
<td>Armodue-Hornbostel 1/25-tone<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">48\<a class="wiki_link" href="/85edo">85</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>677.647<br />
</td>
<td style="text-align: left;">11 11 11 4 11<br />
11 11 11 4<br />
</td>
<td style="text-align: left;">Armodue-Hornbostel 1/11-tone (Optimum accuracy of Phi<br />
interval, the note '7')<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">35\<a class="wiki_link" href="/62edo">62</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>677.419<br />
</td>
<td style="text-align: left;">8 8 8 3 8 8 8 8 3<br />
</td>
<td style="text-align: left;">Armodue-Hornbostel 1/8-tone<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>92\<a class="wiki_link" href="/163edo">163</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>677.301<br />
</td>
<td>21 21 21 8 21 21 21 21 8<br />
</td>
<td>21;8 Superdiatonic 1/21-tone<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>677.2804<br />
</td>
<td><span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ+1 φ+1 φ+1 1 φ+1 φ+1 φ+1 φ+1 1</span><br />
</td>
<td>Split φ superdiatonic relation (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..)<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">57\<a class="wiki_link" href="/101edo">101</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>677.228<br />
</td>
<td style="text-align: left;">13 13 13 5 13 13 13 13 5<br />
</td>
<td style="text-align: left;">13;5 Superdiatonic 1/13-tone<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">22\<a class="wiki_link" href="/39edo">39</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>676.923<br />
</td>
<td style="text-align: left;">5 5 5 2 5 5 5 5 2<br />
</td>
<td style="text-align: left;">Armodue-Hornbostel 1/5-tone (Optimum low size of Hornbostel '6th')<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">75\<a class="wiki_link" href="/133edo">133</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>676.692<br />
</td>
<td style="text-align: left;">17 17 17 7 17 17 17 17 7<br />
</td>
<td style="text-align: left;">17;7 Superdiatonic 1/17-tone (Note the very accuracy of the step 75 with the ratio 34/23 with a error of +0.011 Cents)<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">31\<a class="wiki_link" href="/55edo">55</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>676.364<br />
</td>
<td style="text-align: left;">7 7 7 3 7 7 7 7 3<br />
</td>
<td style="text-align: left;">7;3 Superdiatonic 1/7-tone<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">40\<a class="wiki_link" href="/71edo">71</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>676.056<br />
</td>
<td style="text-align: left;">9 9 9 4 9 9 9 9 4<br />
</td>
<td style="text-align: left;">9;4 Superdiatonic 1/9-tone<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">49\<a class="wiki_link" href="/87edo">87</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>675.862<br />
</td>
<td style="text-align: left;">11 11 11 5 11 11 11 11 5<br />
</td>
<td style="text-align: left;">11;5 Superdiatonic 1/11-tone<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>58\<a class="wiki_link" href="/103edo">103</a><br />
</td>
<td>675.728<br />
</td>
<td>13 13 13 6 13<br />
13 13 13 6<br />
</td>
<td>13;6 Superdiatonic 1/13-tone<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">9\<a class="wiki_link" href="/16edo">16</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>675<br />
</td>
<td style="text-align: left;">2 2 2 1 2 2 2 2 1<br />
</td>
<td style="text-align: left;"><span style="display: block; text-align: left;"><strong>[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]</strong></span>ARMODUE ESADECAFONIA (or Goldsmith Temperament)<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>59\<a class="wiki_link" href="/105edo">105</a><br />
</td>
<td>674.286<br />
</td>
<td>13 13 13 7 13<br />
13 13 13 7<br />
</td>
<td>Armodue-Mávila 1/13-tone<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">50\<a class="wiki_link" href="/89edo">89</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>674.157<br />
</td>
<td style="text-align: left;">11 11 11 6 11 11 11 11 6<br />
</td>
<td style="text-align: left;">Armodue-Mávila 1/11-tone<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">41\<a class="wiki_link" href="/73edo">73</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>673.973<br />
</td>
<td style="text-align: left;">9 9 9 5 9 9 9 9 5<br />
</td>
<td style="text-align: left;">Armodue-Mávila 1/9-tone (with an approximation<br />
of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">32\<a class="wiki_link" href="/57edo">57</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>673.684<br />
</td>
<td style="text-align: left;">7 7 7 4 7 7 7 7 4<br />
</td>
<td style="text-align: left;">Armodue-Mávila 1/7-tone (the 'Commatic' version of<br />
Armodue, because its highly accuracy of the <a class="wiki_link" href="/7_4">7/4</a><br />
interval, the note '8')<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>78\<a class="wiki_link" href="/139edo">139</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>673.381<br />
</td>
<td>17 17 17 10 17 17 17 17 10<br />
</td>
<td>Armodue-Mávila 1/17-tone<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">23\<a class="wiki_link" href="/41edo">41</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>673.171<br />
</td>
<td style="text-align: left;">5 5 5 3 5 5 5 5 3<br />
</td>
<td style="text-align: left;">5;3 Golden Armodue-Mávila 1/5-tone<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">60\<a class="wiki_link" href="/107edo">107</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>672.897<br />
</td>
<td style="text-align: left;">13 13 13 8 13 13 13 13 8<br />
</td>
<td style="text-align: left;">13;8 Golden Mávila 1/13-tone<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>672.8503<br />
</td>
<td><span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1 φ φ φ φ 1</span><br />
</td>
<td>GOLDEN MÁVILA (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">97\<a class="wiki_link" href="/173edo">173</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>672.832<br />
</td>
<td style="text-align: left;">21 21 21 13 21 21 21 21 13<br />
</td>
<td style="text-align: left;">21;13 Golden Mávila 1/21-tone (ratio between large and small steps is Phi, and Phi in the step 120\173)<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">37\<a class="wiki_link" href="/66edo">66</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>672.727<br />
</td>
<td style="text-align: left;">8 8 8 5 8 8 8 8 5<br />
</td>
<td style="text-align: left;">8;5 Golden Mávila 1/8-tone<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>51\<a class="wiki_link" href="/91edo">91</a><br />
</td>
<td><br />
</td>
<td>672.527<br />
</td>
<td>11 11 11 7 11<br />
11 11 11 7<br />
</td>
<td>11;7 Superdiatonic 1/11-tone<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>116\<a class="wiki_link" href="/207">207</a><br />
</td>
<td>672.464<br />
</td>
<td>25 25 25 16 25 25 25 25 16<br />
</td>
<td>25;16 Superdiatonic 1/25-tone<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>65\<a class="wiki_link" href="/116edo">116</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>672.414<br />
</td>
<td>14 14 14 9 14<br />
14 14 14 9<br />
</td>
<td>14;9 Superdiatonic 1/14-tone<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>79\<a class="wiki_link" href="/141edo">141</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>672.340<br />
</td>
<td>17 17 17 11 17 17 17 17 11<br />
</td>
<td>17;11 Superdiatonic 1/17-tone<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>121\<a class="wiki_link" href="/216edo">216</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>672.222<br />
</td>
<td>26 26 26 17 26 26 26 26 17<br />
</td>
<td>26;17 Superdiatonic 1/26-tone<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>135\<a class="wiki_link" href="/241edo">241</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>672.199<br />
</td>
<td>29 29 29 19 29 29 29 29 19<br />
</td>
<td>29;19 Superdiatonic 1/29-tone<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">14\<a class="wiki_link" href="/25edo">25</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>672<br />
</td>
<td style="text-align: left;">3 3 3 2 3 3 3 3 2<br />
</td>
<td style="text-align: left;">3;2 Golden Armodue-Mávila 1/3-tone<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>145\<a class="wiki_link" href="/259edo">259</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>671.815<br />
</td>
<td>31 31 31 21 31 31 31 31 21<br />
</td>
<td>31;21 Superdiatonic 1/31-tone<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>131\<a class="wiki_link" href="/234edo">234</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>671.795<br />
</td>
<td>28 28 28 19 28 28 28 28 19<br />
</td>
<td>28;19 Superdiatonic 1/28-tone<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">33\<a class="wiki_link" href="/59edo">59</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>671.186<br />
</td>
<td style="text-align: left;">7 7 7 5 7 7 7 7 5<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">19\<a class="wiki_link" href="/34edo">34</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>670.588<br />
</td>
<td style="text-align: left;">4 4 4 3 4 4 4 4 3<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">24\<a class="wiki_link" href="/43edo">43</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>669.767<br />
</td>
<td style="text-align: left;">5 5 5 4 5 5 5 5 4<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">5\<a class="wiki_link" href="/9edo">9</a><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td>666.667<br />
</td>
<td style="text-align: left;">1 1 1 1 1 1 1 1 1<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
</table>
</body></html>