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Wikispaces>JosephRuhf **Imported revision 565347717 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 598904070 - 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>2016-11-08 12:16:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>598904070</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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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. | 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 ||~ <span style="display: block; text-align: center;">**Generator size (cents)**</span> ||~ Pentachord steps ||~ Comments || | ||||||~ Generator ||~ <span style="display: block; text-align: center;">**Generator size (cents)**</span> ||~ '8:7:6:5:4' (cents) ||~ Pentachord steps ||~ Comments || | ||
||< 4\ | ||< 4\7 ||< ||< ||< 685.714 || 378.193+307.521+274.991+239.2945 ||< 1 1 1 0 ||< || | ||
||< 21\37 ||< ||< ||< 681.081 ||< 5 5 5 1 ||< || | ||< 21\37 ||< ||< ||< 681.081 || 375.877+305.204+277.308+241.611 ||< 5 5 5 1 ||< || | ||
||< 17\30 ||< ||< ||< 680 ||< 4 4 4 1 ||< L/s = 4 || | ||< 17\30 ||< ||< ||< 680 || 375.336+304.664+277.848+242;152 ||< 4 4 4 1 ||< L/s = 4 || | ||
||< ||< 30\53 ||< ||< 679.245 ||< 7 7 7 2 ||< || | ||< ||< 30\53 ||< ||< 679.245 || 374.959+304.286+278.226+242.529 ||< 7 7 7 2 ||< || | ||
|| || 43\76 || || 678.947 || 10 10 10 3 || || | || || 43\76 || || 678.947 || 374.81+304.1375+278.375+242.677 || [[tel/10 10 10 3|10 10 10 3]] || || | ||
|| || 56\99 || || 678.788 || 13 13 13 4 || || | || || 56\99 || || 678.788 || 374.73+304.058+278.4545+242.758 || [[tel/13 13 13 4|13 13 13 4]] || || | ||
|| || 69\122 || || 678.6885 || 16 16 16 5 || || | || || 69\122 || || [[tel/678.6885|678.6885]] || 374.6805+304.008+278.504+242.807 || [[tel/16 16 16 5|16 16 16 5]] || || | ||
|| || 82\145 || || 678.621 || 19 19 19 6 || || | || || 82\145 || || 678.621 || 374.647+303.974+278.538+242.841 || [[tel/19 19 19 6|19 19 19 6]] || || | ||
|| || 95\168 || || 678.571 || 22 22 22 7 || || | || || 95\168 || || 678.571 || 374.622+303.9495+278.563+242.866 || [[tel/22 22 22 7|22 22 22 7]] || || | ||
|| || || || 678.569 || π π π 1 || L/s = π || | || || || || 678.569 || 374.621+303.948+278.564+242.867 || π π π 1 || L/s = π || | ||
||< ||< 108\191 ||< ||< 678.534 ||< 25 25 25 8 ||< || | ||< ||< 108\191 ||< ||< 678.534 || 374.603+303.931+278.581+242.885 ||< [[tel/25 25 25 8|25 25 25 8]] ||< || | ||
||< ||< 121\214 ||< ||< 678.505 ||< 28 28 28 9 ||< 28;9 Superdiatonic 1/28-tone <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of | ||< ||< 121\214 ||< ||< 678.505 || 374.5885+303.916+278.596+242.899 ||< [[tel/28 28 28 9|28 28 28 9]] ||< 28;9 Superdiatonic 1/28-tone <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the Pythagorean wolf Fifth)</span> || | ||
|| || 134\237 || || 678.481 || 31 31 31 10 || HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span> || | || || 134\237 || || 678.481 || 374.577+303.904+278.608+242.911 || [[tel/31 31 31 10|31 31 31 10]] || HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span> || | ||
||< 13\23 ||< ||< ||< 678.261 ||< 3 3 3 1 ||< HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(Armodue 1/3-tone)</span> || | ||< 13\23 ||< ||< ||< 678.261 || 374.467+303.794+278.718+243.021 ||< 3 3 3 1 ||< HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(Armodue 1/3-tone)</span> || | ||
|| || 126\223 || || 678.027 || 29 29 29 10 || HORNBOSTEL TEMPERAMENT | || || 126\223 || || 678.027 || 374.35+303.677+278.835+243.138 || [[tel/29 29 29 10|29 29 29 10]] || HORNBOSTEL TEMPERAMENT | ||
<span style="font-size: 12.8000001907349px;">(Armodue 1/29-tone)</span> || | <span style="font-size: 12.8000001907349px;">(Armodue 1/29-tone)</span> || | ||
||< ||< 113\200 ||< ||< 678 ||< 26 26 26 9 ||< HORNBOSTEL (& [[Alexei Stepanovich Ogolevets|OGOLEVETS]]) TEMPERAMENT <span style="font-size: 12.8000001907349px;">(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')</span> || | ||< ||< 113\200 ||< ||< 678 || 374.336+303.664+278.848+243.152 ||< [[tel/26 26 26 9|26 26 26 9]] ||< HORNBOSTEL (& [[Alexei Stepanovich Ogolevets|OGOLEVETS]]) TEMPERAMENT <span style="font-size: 12.8000001907349px;">(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')</span> || | ||
||< ||< 100\177 ||< ||< 677.966 ||< 23 23 23 8 ||< || | ||< ||< 100\177 ||< ||< 677.966 || 374.319+303.647+278.865+243.1685 ||< [[tel/23 23 23 8|23 23 23 8]] ||< || | ||
||< ||< 87\154 ||< ||< 677.922 ||< 20 20 20 7 ||< || | ||< ||< 87\154 ||< ||< 677.922 || 374.297+303.625+278.887+243.191 ||< [[tel/20 20 20 7|20 20 20 7]] ||< || | ||
||< ||< 74\131 ||< ||< 677.863 ||< 17 17 17 6 ||< Armodue-Hornbostel 1/17-tone <span style="font-size: 12.8000001907349px;">(the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)</span> || | ||< ||< 74\131 ||< ||< 677.863 || 374.2675+303.595+278.917+243.22 ||< [[tel/17 17 17 6|17 17 17 6]] ||< Armodue-Hornbostel 1/17-tone <span style="font-size: 12.8000001907349px;">(the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)</span> || | ||
||< ||< 61\108 ||< ||< 677.778 ||< 14 14 14 5 ||< Armodue-Hornbostel 1/14-tone || | ||< ||< 61\108 ||< ||< 677.778 || 374.225+303.553+278.9595+243.263 ||< [[tel/14 14 14 5|14 14 14 5]] ||< Armodue-Hornbostel 1/14-tone || | ||
||< ||< 109\193 ||< ||< 677. | ||< ||< 109\193 ||< ||< 677.72 || 374.196+303.524+278.988+243.2915 ||< [[tel/25 25 25 9|25 25 25 9]] ||< Armodue-Hornbostel 1/25-tone || | ||
||< ||< 48\85 ||< ||< 677.647 || | ||< ||< 48\85 ||< ||< 677.647 || 374.15+303.487+279.025+243.328 ||< [[tel/11 11 11 4|11 11 11 4]] ||< Armodue-Hornbostel 1/11-tone <span style="font-size: 12.8000001907349px;">(Optimum accuracy of Phi interval, the note '7')</span> || | ||
||< ||< ||< ||< 677.562 ||< e e e 1 ||< L/s = e || | ||< ||< ||< ||< 677.562 || 374.117+303.445+279.0675+243.371 ||< e e e 1 ||< L/s = e || | ||
||< ||< 35\62 ||< ||< 677.419 ||< 8 8 8 3 ||< Armodue-Hornbostel 1/8-tone || | ||< ||< 35\62 ||< ||< 677.419 || 374.046+303.3735+279.139+243.442 ||< 8 8 8 3 ||< Armodue-Hornbostel 1/8-tone || | ||
||< ||< 92\163 ||< ||< 677.301 ||< 21 21 21 8 ||< 21;8 Superdiatonic 1/21-tone || | ||< ||< 92\163 ||< ||< 677.301 || 373.9865+303.314+279.198+243.501 ||< [[tel/21 21 21 8|21 21 21 8]] ||< 21;8 Superdiatonic 1/21-tone || | ||
||< ||< ||< ||< 677.28 ||< <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">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..) || | ||< ||< ||< ||< 677.28 || 373.976+303.304+279.208+243.511 ||< <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">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\101 ||< ||< 677.228 ||< 13 13 13 5 ||< 13;5 Superdiatonic 1/13-tone || | ||< ||< 57\101 ||< ||< 677.228 || 373.95+304.278+279.2345+243.538 ||< [[tel/13 13 13 5|13 13 13 5]] ||< 13;5 Superdiatonic 1/13-tone || | ||
||< 22\39 ||< ||< ||< 676.923 ||< 5 5 5 2 ||< Armodue-Hornbostel 1/5-tone <span style="font-size: 12.8000001907349px;">(Optimum low size of Hornbostel '6th')</span> || | ||< 22\39 ||< ||< ||< 676.923 || 373.798+303.125+279.387+243.69 ||< 5 5 5 2 ||< Armodue-Hornbostel 1/5-tone <span style="font-size: 12.8000001907349px;">(Optimum low size of Hornbostel '6th')</span> || | ||
||< ||< 75\133 ||< ||< 676.692 ||< 17 17 17 7 ||< 17;7 Superdiatonic 1/17-tone <span style="font-size: 12.8000001907349px;">(Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)</span> || | ||< ||< 75\133 ||< ||< 676.692 || 373.682+303.01+279.5025+243.805 ||< [[tel/17 17 17 7|17 17 17 7]] ||< 17;7 Superdiatonic 1/17-tone <span style="font-size: 12.8000001907349px;">(Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)</span> || | ||
||< ||< 53\94 ||< ||< 676.596 || | ||< ||< 53\94 ||< ||< 676.596 || 373.634+302.962+279.5505+243.854 ||< [[tel/12 12 12 5|12 12 12 5]] ||< || | ||
||< ||< 31\55 ||< ||< 676.364 ||< 7 7 7 3 ||< 7;3 Superdiatonic 1/7-tone || | ||< ||< 31\55 ||< ||< 676.364 || 373.518+302.846+279.667+243.97 ||< 7 7 7 3 ||< 7;3 Superdiatonic 1/7-tone || | ||
||< ||< 40\71 ||< ||< 676.056 || | ||< ||< 40\71 ||< ||< 676.056 || 373.364+302.692+279.82+244.123 ||< 9 9 9 4 ||< 9;4 Superdiatonic 1/9-tone || | ||
||< ||< 49\87 ||< ||< 675.862 ||< 11 11 11 5 ||< 11;5 Superdiatonic 1/11-tone || | ||< ||< 49\87 ||< ||< 675.862 || 373.267+302.595+279.917+244.221 ||< [[tel/11 11 11 5|11 11 11 5]] ||< 11;5 Superdiatonic 1/11-tone || | ||
||< ||< 58\103 ||< ||< 675.728 ||< 13 13 13 6 ||< 13;6 Superdiatonic 1/13-tone || | ||< ||< 58\103 ||< ||< 675.728 || 373.2+302.528+279.984+244.288 ||< [[tel/13 13 13 6|13 13 13 6]] ||< 13;6 Superdiatonic 1/13-tone || | ||
||< 9\16 ||< ||< ||< 675 ||< 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) || | ||< 9\16 ||< ||< ||< 675 || 372.836+302.164+280.348+244.652 ||< 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\105 ||< ||< 674.286 ||< 13 13 13 7 ||< Armodue-Mávila 1/13-tone || | ||< ||< 59\105 ||< ||< 674.286 || 372.48+301.807+280.7055+245.009 ||< [[tel/13 13 13 7|13 13 13 7]] ||< Armodue-Mávila 1/13-tone || | ||
||< ||< 50\89 ||< ||< 674.157 ||< 11 11 11 6 ||< Armodue-Mávila 1/11-tone || | ||< ||< 50\89 ||< ||< 674.157 || 372.415+301.742+280.77+245.073 ||< [[tel/11 11 11 6|11 11 11 6]] ||< Armodue-Mávila 1/11-tone || | ||
||< ||< 41\73 ||< ||< 673.973 ||< 9 9 9 5 ||< Armodue-Mávila 1/9-tone <span style="font-size: 12.8000001907349px;">(with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)</span> || | ||< ||< 41\73 ||< ||< 673.973 || 372.3225+301.65+280.862+245.165 ||< 9 9 9 5 ||< Armodue-Mávila 1/9-tone <span style="font-size: 12.8000001907349px;">(with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)</span> || | ||
||< ||< 32\57 ||< ||< 673.684 || | ||< ||< 32\57 ||< ||< 673.684 || 372.178+301.506+281.006+245.3095 ||< 7 7 7 4 ||< Armodue-Mávila 1/7-tone <span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Armodue, because its high accuracy of the [[xenharmonic/7_4|7/4]] interval, the note '8')</span> || | ||
|| || || || 673.577 || <span style="background-color: #ffffff;">√3 √3 √3 1</span> || || | || || || || 673.577 || 372.125+301.452+281.06+245.363 || <span style="background-color: #ffffff;">√3 √3 √3 1</span> || || | ||
||< ||< 55\98 ||< ||< 673.469 ||< 12 12 12 7 ||< || | ||< ||< 55\98 ||< ||< 673.469 || 372.071+301.3985+281.158+245.461 ||< [[tel/12 12 12 7|12 12 12 7]] ||< || | ||
||< ||< 78\139 ||< ||< 673.381 ||< 17 17 17 10 ||< Armodue-Mávila 1/17-tone || | ||< ||< 78\139 ||< ||< 673.381 || 372.027+301.354+281.158+245.461 ||< [[tel/17 17 17 10|17 17 17 10]] ||< Armodue-Mávila 1/17-tone || | ||
||< ||< 101\180 ||< ||< 673.333 ||< 22 22 22 13 ||< || | ||< ||< 101\180 ||< ||< 673.333 || 372.003+301.3305+281.182+245.485 ||< [[tel/22 22 22 13|22 22 22 13]] ||< || | ||
||< 23\41 ||< ||< ||< 673.171 ||< 5 5 5 3 ||< 5;3 Golden Armodue-Mávila 1/5-tone || | ||< 23\41 ||< ||< ||< 673.171 || 371.923+301.249+281.263+245.566 ||< 5 5 5 3 ||< 5;3 Golden Armodue-Mávila 1/5-tone || | ||
||< ||< 60\107 ||< ||< 672.897 ||< 13 13 13 8 ||< 13;8 Golden Mávila 1/13-tone || | ||< ||< 60\107 ||< ||< 672.897 || 371.785+301.112+281.4+245.703 ||< [[tel/13 13 13 8|13 13 13 8]] ||< 13;8 Golden Mávila 1/13-tone || | ||
||< ||< ||< ||< 672.85 || | ||< ||< ||< ||< 672.85 || 371.761+301.089+281.423+245.726 ||< <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">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\173 ||< 672.832 ||< 21 21 21 13 ||< 21;13 Golden Mávila 1/21-tone <span style="font-size: 12.8000001907349px;">(Phi is the step 120\173)</span> || | ||< ||< ||< 97\173 ||< 672.832 || 371.752+301.08+281.432+245.735 ||< [[tel/21 21 21 13|21 21 21 13]] ||< 21;13 Golden Mávila 1/21-tone <span style="font-size: 12.8000001907349px;">(Phi is the step 120\173)</span> || | ||
||< ||< 37\66 ||< ||< 672.727 || | ||< ||< 37\66 ||< ||< 672.727 || 371.7+301.027+281.485+245.788; ||< 8 8 8 5 ||< 8;5 Golden Mávila 1/8-tone || | ||
||< ||< 51\91 ||< ||< 672.527 ||< 11 11 11 7 ||< 11;7 Superdiatonic 1/11-tone || | ||< ||< 51\91 ||< ||< 672.527 || 371.6+300.9275+281.585+245.888 ||< [[tel/11 11 11 7|11 11 11 7]] ||< 11;7 Superdiatonic 1/11-tone || | ||
|| || || || 672.523 || | || || || || 672.523 || 371.598+300.925+281.587+245.89 || π π π 2 || || | ||
||< ||< ||< 116\207 ||< 672.464 ||< 25 25 25 16 ||< 25;16 Superdiatonic 1/25-tone || | ||< ||< ||< 116\207 ||< 672.464 || 371.568+300.896+281.6165+245.919 ||< [[tel/25 25 25 16|25 25 25 16]] ||< 25;16 Superdiatonic 1/25-tone || | ||
||< ||< 65\116 ||< ||< 672.414 ||< 14 14 | ||< ||< 65\116 ||< ||< 672.414 || 371.543+300.871+281.6415+245.945 ||< [[tel/14 14 14 9|14 14 14 9]] ||< 14;9 Superdiatonic 1/14-tone || | ||
||< ||< 79\141 ||< ||< 672. | ||< ||< 79\141 ||< ||< 672.34 || 371.506+300.834+281.671+245.981 ||< [[tel/17 17 17 11|17 17 17 11]] ||< 17;11 Superdiatonic 1/17-tone || | ||
||< ||< 93\166 ||< ||< 672.289 ||< 20 20 20 13 ||< || | ||< ||< 93\166 ||< ||< 672.289 || 371.481+300.808+281.704+246.007 ||< [[tel/20 20 20 13|20 20 20 13]] ||< || | ||
||< ||< 107\191 ||< ||< 672.251 ||< 23 23 23 15 ||< || | ||< ||< 107\191 ||< ||< 672.251 || 371.462+300.789+281.723+246.026 ||< [[tel/23 23 23 15|23 23 23 15]] ||< || | ||
||< ||< 121\216 ||< ||< 672.222 ||< 26 26 | ||< ||< 121\216 ||< ||< 672.222 || 371.447+300.775+281.737+246.0405 ||< [[tel/26 26 26 17|26 26 26 17]] ||< 26;17 Superdiatonic 1/26-tone || | ||
||< ||< 135\241 ||< ||< 672.199 ||< 29 29 29 19 ||< 29;19 Superdiatonic 1/29-tone || | ||< ||< 135\241 ||< ||< 672.199 || 371.436+300.763+281.749+246.052 ||< [[tel/29 29 29 19|29 29 29 19]] ||< 29;19 Superdiatonic 1/29-tone || | ||
||< 14\25 ||< ||< ||< 672 ||< 3 3 3 2 ||< 3;2 Golden Armodue-Mávila 1/3-tone || | ||< 14\25 ||< ||< ||< 672 || 371.336+300.664+281.848+246.152 ||< 3 3 3 2 ||< 3;2 Golden Armodue-Mávila 1/3-tone || | ||
||< ||< 145\259 ||< ||< 671.815 || | ||< ||< 145\259 ||< ||< 671.815 || 371.2435+300.571+281.941+246.244 ||< [[tel/31 31 31 21|31 31 31 21]] ||< 31;21 Superdiatonic 1/31-tone || | ||
||< ||< 131\234 ||< ||< 671.795 ||< 28 28 28 19 ||< 28;19 Superdiatonic 1/28-tone || | ||< ||< 131\234 ||< ||< 671.795 || 371.234+300.561+281.951+246.254 ||< [[tel/28 28 28 19|28 28 28 19]] ||< 28;19 Superdiatonic 1/28-tone || | ||
||< ||< 117\209 ||< ||< 671. | ||< ||< 117\209 ||< ||< 671.77 || 371.221+300.549+281.963+246.266 ||< [[tel/25 25 25 17|25 25 25 17]] ||< || | ||
||< ||< 103\184 ||< ||< 671.739 ||< 22 22 22 15 ||< || | ||< ||< 103\184 ||< ||< 671.739 || 371.206+300.533+281.979+246.282 ||< [[tel/22 22 22 15|22 22 22 15]] ||< || | ||
||< ||< 89\159 ||< ||< 671.698 || | ||< ||< 89\159 ||< ||< 671.698 || 371.185+300.513+281.999+246.3025 ||< [[tel/19 19 19 13|19 19 19 13]] ||< || | ||
||< ||< 75\134 ||< ||< 671.642 ||< 16 16 16 11 ||< || | ||< ||< 75\134 ||< ||< 671.642 || 371.157+300.485+282.0275+246.331 ||< [[tel/16 16 16 11|16 16 16 11]] ||< || | ||
||< ||< 61\109 ||< ||< 671.560 || | ||< ||< 61\109 ||< ||< 671.560 || 371.116+300.444+282.069+246.372 ||< [[tel/13 13 13 9|13 13 13 9]] ||< || | ||
||< | ||< ||< 47\84 ||< ||< 671.429 || 371.0505+300.378+282.134+246.437 ||< [[tel/10 10 10 7|10 10 10 7]] ||< || | ||
||< | ||< ||< 33\59 ||< ||< 671.186 || 370.929+300.257+282.255+246.558 ||< 7 7 7 5 ||< || | ||
||< 19\34 ||< ||< ||< 670.588 ||< 4 4 4 3 ||< || | ||< 19\34 ||< ||< ||< 670.588 || 370.63+299.958+282.554+246.8575 ||< 4 4 4 3 ||< || | ||
||< 24\43 ||< ||< ||< 669.767 ||< 5 5 5 4 ||< || | ||< 24\43 ||< ||< ||< 669.767 || 370.22+299.5475+282.965+247.268 ||< 5 5 5 4 ||< || | ||
||< 5\ | ||< 5\9 ||< ||< ||< 666.667 || 368.6695+297.997+284.515+248.818 ||< 1 1 1 1 ||< ||</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>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 /> | <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>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 /> | ||
| Line 98: | Line 98: | ||
</th> | </th> | ||
<th><span style="display: block; text-align: center;"><strong>Generator size (cents)</strong></span><br /> | <th><span style="display: block; text-align: center;"><strong>Generator size (cents)</strong></span><br /> | ||
</th> | |||
<th>'8:7:6:5:4' (cents)<br /> | |||
</th> | </th> | ||
<th>Pentachord steps<br /> | <th>Pentachord steps<br /> | ||
| Line 105: | Line 107: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;">4\ | <td style="text-align: left;">4\7<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 112: | Line 114: | ||
</td> | </td> | ||
<td style="text-align: left;">685.714<br /> | <td style="text-align: left;">685.714<br /> | ||
</td> | |||
<td>378.193+307.521+274.991+239.2945<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">1 1 1 0<br /> | <td style="text-align: left;">1 1 1 0<br /> | ||
| Line 126: | Line 130: | ||
</td> | </td> | ||
<td style="text-align: left;">681.081<br /> | <td style="text-align: left;">681.081<br /> | ||
</td> | |||
<td>375.877+305.204+277.308+241.611<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">5 5 5 1<br /> | <td style="text-align: left;">5 5 5 1<br /> | ||
| Line 140: | Line 146: | ||
</td> | </td> | ||
<td style="text-align: left;">680<br /> | <td style="text-align: left;">680<br /> | ||
</td> | |||
<td>375.336+304.664+277.848+242;152<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">4 4 4 1<br /> | <td style="text-align: left;">4 4 4 1<br /> | ||
| Line 154: | Line 162: | ||
</td> | </td> | ||
<td style="text-align: left;">679.245<br /> | <td style="text-align: left;">679.245<br /> | ||
</td> | |||
<td>374.959+304.286+278.226+242.529<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">7 7 7 2<br /> | <td style="text-align: left;">7 7 7 2<br /> | ||
| Line 169: | Line 179: | ||
<td>678.947<br /> | <td>678.947<br /> | ||
</td> | </td> | ||
<td>10 10 10 3<br /> | <td>374.81+304.1375+278.375+242.677<br /> | ||
</td> | |||
<td><a class="wiki_link" href="http://tel.wikispaces.com/10%2010%2010%203">10 10 10 3</a><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 183: | Line 195: | ||
<td>678.788<br /> | <td>678.788<br /> | ||
</td> | </td> | ||
<td>13 13 13 4<br /> | <td>374.73+304.058+278.4545+242.758<br /> | ||
</td> | |||
<td><a class="wiki_link" href="http://tel.wikispaces.com/13%2013%2013%204">13 13 13 4</a><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 195: | Line 209: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>678.6885<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/678.6885">678.6885</a><br /> | ||
</td> | </td> | ||
<td>16 16 16 5<br /> | <td>374.6805+304.008+278.504+242.807<br /> | ||
</td> | |||
<td><a class="wiki_link" href="http://tel.wikispaces.com/16%2016%2016%205">16 16 16 5</a><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 211: | Line 227: | ||
<td>678.621<br /> | <td>678.621<br /> | ||
</td> | </td> | ||
<td>19 19 19 6<br /> | <td>374.647+303.974+278.538+242.841<br /> | ||
</td> | |||
<td><a class="wiki_link" href="http://tel.wikispaces.com/19%2019%2019%206">19 19 19 6</a><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 225: | Line 243: | ||
<td>678.571<br /> | <td>678.571<br /> | ||
</td> | </td> | ||
<td>22 22 22 7<br /> | <td>374.622+303.9495+278.563+242.866<br /> | ||
</td> | |||
<td><a class="wiki_link" href="http://tel.wikispaces.com/22%2022%2022%207">22 22 22 7</a><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 238: | Line 258: | ||
</td> | </td> | ||
<td>678.569<br /> | <td>678.569<br /> | ||
</td> | |||
<td>374.621+303.948+278.564+242.867<br /> | |||
</td> | </td> | ||
<td>π π π 1<br /> | <td>π π π 1<br /> | ||
| Line 253: | Line 275: | ||
<td style="text-align: left;">678.534<br /> | <td style="text-align: left;">678.534<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">25 25 25 8<br /> | <td>374.603+303.931+278.581+242.885<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/25%2025%2025%208">25 25 25 8</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 267: | Line 291: | ||
<td style="text-align: left;">678.505<br /> | <td style="text-align: left;">678.505<br /> | ||
</td> | </td> | ||
<td | <td>374.5885+303.916+278.596+242.899<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">28;9 Superdiatonic 1/28-tone <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of | <td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/28%2028%2028%209">28 28 28 9</a><br /> | ||
</td> | |||
<td style="text-align: left;">28;9 Superdiatonic 1/28-tone <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the Pythagorean wolf Fifth)</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 281: | Line 307: | ||
<td>678.481<br /> | <td>678.481<br /> | ||
</td> | </td> | ||
<td>31 31 31 10<br /> | <td>374.577+303.904+278.608+242.911<br /> | ||
</td> | |||
<td><a class="wiki_link" href="http://tel.wikispaces.com/31%2031%2031%2010">31 31 31 10</a><br /> | |||
</td> | </td> | ||
<td>HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span><br /> | <td>HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span><br /> | ||
| Line 294: | Line 322: | ||
</td> | </td> | ||
<td style="text-align: left;">678.261<br /> | <td style="text-align: left;">678.261<br /> | ||
</td> | |||
<td>374.467+303.794+278.718+243.021<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">3 3 3 1<br /> | <td style="text-align: left;">3 3 3 1<br /> | ||
| Line 309: | Line 339: | ||
<td>678.027<br /> | <td>678.027<br /> | ||
</td> | </td> | ||
<td>29 29 29 10<br /> | <td>374.35+303.677+278.835+243.138<br /> | ||
</td> | |||
<td><a class="wiki_link" href="http://tel.wikispaces.com/29%2029%2029%2010">29 29 29 10</a><br /> | |||
</td> | </td> | ||
<td>HORNBOSTEL TEMPERAMENT<br /> | <td>HORNBOSTEL TEMPERAMENT<br /> | ||
| Line 324: | Line 356: | ||
<td style="text-align: left;">678<br /> | <td style="text-align: left;">678<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">26 26 26 9<br /> | <td>374.336+303.664+278.848+243.152<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/26%2026%2026%209">26 26 26 9</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">HORNBOSTEL (&amp; <a class="wiki_link" href="/Alexei%20Stepanovich%20Ogolevets">OGOLEVETS</a>) TEMPERAMENT <span style="font-size: 12.8000001907349px;">(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' &amp; '8')</span><br /> | <td style="text-align: left;">HORNBOSTEL (&amp; <a class="wiki_link" href="/Alexei%20Stepanovich%20Ogolevets">OGOLEVETS</a>) TEMPERAMENT <span style="font-size: 12.8000001907349px;">(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' &amp; '8')</span><br /> | ||
| Line 338: | Line 372: | ||
<td style="text-align: left;">677.966<br /> | <td style="text-align: left;">677.966<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">23 23 23 8<br /> | <td>374.319+303.647+278.865+243.1685<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/23%2023%2023%208">23 23 23 8</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 352: | Line 388: | ||
<td style="text-align: left;">677.922<br /> | <td style="text-align: left;">677.922<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">20 20 20 7<br /> | <td>374.297+303.625+278.887+243.191<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/20%2020%2020%207">20 20 20 7</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 366: | Line 404: | ||
<td style="text-align: left;">677.863<br /> | <td style="text-align: left;">677.863<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">17 17 17 6<br /> | <td>374.2675+303.595+278.917+243.22<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/17%2017%2017%206">17 17 17 6</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Hornbostel 1/17-tone <span style="font-size: 12.8000001907349px;">(the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)</span><br /> | <td style="text-align: left;">Armodue-Hornbostel 1/17-tone <span style="font-size: 12.8000001907349px;">(the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)</span><br /> | ||
| Line 380: | Line 420: | ||
<td style="text-align: left;">677.778<br /> | <td style="text-align: left;">677.778<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">14 14 14 5<br /> | <td>374.225+303.553+278.9595+243.263<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/14%2014%2014%205">14 14 14 5</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Hornbostel 1/14-tone<br /> | <td style="text-align: left;">Armodue-Hornbostel 1/14-tone<br /> | ||
| Line 392: | Line 434: | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">677. | <td style="text-align: left;">677.72<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">25 25 25 9<br /> | <td>374.196+303.524+278.988+243.2915<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/25%2025%2025%209">25 25 25 9</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Hornbostel 1/25-tone<br /> | <td style="text-align: left;">Armodue-Hornbostel 1/25-tone<br /> | ||
| Line 408: | Line 452: | ||
<td style="text-align: left;">677.647<br /> | <td style="text-align: left;">677.647<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">11 11 11 4<br /> | <td>374.15+303.487+279.025+243.328<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/11%2011%2011%204">11 11 11 4</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Hornbostel 1/11-tone <span style="font-size: 12.8000001907349px;">(Optimum accuracy of Phi interval, the note '7')</span><br /> | <td style="text-align: left;">Armodue-Hornbostel 1/11-tone <span style="font-size: 12.8000001907349px;">(Optimum accuracy of Phi interval, the note '7')</span><br /> | ||
| Line 421: | Line 467: | ||
</td> | </td> | ||
<td style="text-align: left;">677.562<br /> | <td style="text-align: left;">677.562<br /> | ||
</td> | |||
<td>374.117+303.445+279.0675+243.371<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">e e e 1<br /> | <td style="text-align: left;">e e e 1<br /> | ||
| Line 435: | Line 483: | ||
</td> | </td> | ||
<td style="text-align: left;">677.419<br /> | <td style="text-align: left;">677.419<br /> | ||
</td> | |||
<td>374.046+303.3735+279.139+243.442<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">8 8 8 3<br /> | <td style="text-align: left;">8 8 8 3<br /> | ||
| Line 450: | Line 500: | ||
<td style="text-align: left;">677.301<br /> | <td style="text-align: left;">677.301<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">21 21 21 8<br /> | <td>373.9865+303.314+279.198+243.501<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/21%2021%2021%208">21 21 21 8</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">21;8 Superdiatonic 1/21-tone<br /> | <td style="text-align: left;">21;8 Superdiatonic 1/21-tone<br /> | ||
| Line 463: | Line 515: | ||
</td> | </td> | ||
<td style="text-align: left;">677.28<br /> | <td style="text-align: left;">677.28<br /> | ||
</td> | |||
<td>373.976+303.304+279.208+243.511<br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ+1 φ+1 φ+1 1</span><br /> | <td style="text-align: left;"><span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ+1 φ+1 φ+1 1</span><br /> | ||
| Line 478: | Line 532: | ||
<td style="text-align: left;">677.228<br /> | <td style="text-align: left;">677.228<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">13 13 13 5<br /> | <td>373.95+304.278+279.2345+243.538<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/13%2013%2013%205">13 13 13 5</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">13;5 Superdiatonic 1/13-tone<br /> | <td style="text-align: left;">13;5 Superdiatonic 1/13-tone<br /> | ||
| Line 491: | Line 547: | ||
</td> | </td> | ||
<td style="text-align: left;">676.923<br /> | <td style="text-align: left;">676.923<br /> | ||
</td> | |||
<td>373.798+303.125+279.387+243.69<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">5 5 5 2<br /> | <td style="text-align: left;">5 5 5 2<br /> | ||
| Line 506: | Line 564: | ||
<td style="text-align: left;">676.692<br /> | <td style="text-align: left;">676.692<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">17 17 17 7<br /> | <td>373.682+303.01+279.5025+243.805<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/17%2017%2017%207">17 17 17 7</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">17;7 Superdiatonic 1/17-tone <span style="font-size: 12.8000001907349px;">(Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)</span><br /> | <td style="text-align: left;">17;7 Superdiatonic 1/17-tone <span style="font-size: 12.8000001907349px;">(Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)</span><br /> | ||
| Line 520: | Line 580: | ||
<td style="text-align: left;">676.596<br /> | <td style="text-align: left;">676.596<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">12 12 12 5<br /> | <td>373.634+302.962+279.5505+243.854<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/12%2012%2012%205">12 12 12 5</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 533: | Line 595: | ||
</td> | </td> | ||
<td style="text-align: left;">676.364<br /> | <td style="text-align: left;">676.364<br /> | ||
</td> | |||
<td>373.518+302.846+279.667+243.97<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">7 7 7 3<br /> | <td style="text-align: left;">7 7 7 3<br /> | ||
| Line 547: | Line 611: | ||
</td> | </td> | ||
<td style="text-align: left;">676.056<br /> | <td style="text-align: left;">676.056<br /> | ||
</td> | |||
<td>373.364+302.692+279.82+244.123<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">9 9 9 4<br /> | <td style="text-align: left;">9 9 9 4<br /> | ||
| Line 562: | Line 628: | ||
<td style="text-align: left;">675.862<br /> | <td style="text-align: left;">675.862<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">11 11 11 5<br /> | <td>373.267+302.595+279.917+244.221<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/11%2011%2011%205">11 11 11 5</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">11;5 Superdiatonic 1/11-tone<br /> | <td style="text-align: left;">11;5 Superdiatonic 1/11-tone<br /> | ||
| Line 576: | Line 644: | ||
<td style="text-align: left;">675.728<br /> | <td style="text-align: left;">675.728<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">13 13 13 6<br /> | <td>373.2+302.528+279.984+244.288<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/13%2013%2013%206">13 13 13 6</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">13;6 Superdiatonic 1/13-tone<br /> | <td style="text-align: left;">13;6 Superdiatonic 1/13-tone<br /> | ||
| Line 589: | Line 659: | ||
</td> | </td> | ||
<td style="text-align: left;">675<br /> | <td style="text-align: left;">675<br /> | ||
</td> | |||
<td>372.836+302.164+280.348+244.652<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">2 2 2 1<br /> | <td style="text-align: left;">2 2 2 1<br /> | ||
| Line 604: | Line 676: | ||
<td style="text-align: left;">674.286<br /> | <td style="text-align: left;">674.286<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">13 13 13 7<br /> | <td>372.48+301.807+280.7055+245.009<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/13%2013%2013%207">13 13 13 7</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Mávila 1/13-tone<br /> | <td style="text-align: left;">Armodue-Mávila 1/13-tone<br /> | ||
| Line 618: | Line 692: | ||
<td style="text-align: left;">674.157<br /> | <td style="text-align: left;">674.157<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">11 11 11 6<br /> | <td>372.415+301.742+280.77+245.073<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/11%2011%2011%206">11 11 11 6</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Mávila 1/11-tone<br /> | <td style="text-align: left;">Armodue-Mávila 1/11-tone<br /> | ||
| Line 631: | Line 707: | ||
</td> | </td> | ||
<td style="text-align: left;">673.973<br /> | <td style="text-align: left;">673.973<br /> | ||
</td> | |||
<td>372.3225+301.65+280.862+245.165<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">9 9 9 5<br /> | <td style="text-align: left;">9 9 9 5<br /> | ||
| Line 645: | Line 723: | ||
</td> | </td> | ||
<td style="text-align: left;">673.684<br /> | <td style="text-align: left;">673.684<br /> | ||
</td> | |||
<td>372.178+301.506+281.006+245.3095<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">7 7 7 4<br /> | <td style="text-align: left;">7 7 7 4<br /> | ||
| Line 659: | Line 739: | ||
</td> | </td> | ||
<td>673.577<br /> | <td>673.577<br /> | ||
</td> | |||
<td>372.125+301.452+281.06+245.363<br /> | |||
</td> | </td> | ||
<td><span style="background-color: #ffffff;">√3 √3 √3 1</span><br /> | <td><span style="background-color: #ffffff;">√3 √3 √3 1</span><br /> | ||
| Line 674: | Line 756: | ||
<td style="text-align: left;">673.469<br /> | <td style="text-align: left;">673.469<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">12 12 12 7<br /> | <td>372.071+301.3985+281.158+245.461<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/12%2012%2012%207">12 12 12 7</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 688: | Line 772: | ||
<td style="text-align: left;">673.381<br /> | <td style="text-align: left;">673.381<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">17 17 17 10<br /> | <td>372.027+301.354+281.158+245.461<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/17%2017%2017%2010">17 17 17 10</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Mávila 1/17-tone<br /> | <td style="text-align: left;">Armodue-Mávila 1/17-tone<br /> | ||
| Line 702: | Line 788: | ||
<td style="text-align: left;">673.333<br /> | <td style="text-align: left;">673.333<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">22 22 22 13<br /> | <td>372.003+301.3305+281.182+245.485<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/22%2022%2022%2013">22 22 22 13</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 715: | Line 803: | ||
</td> | </td> | ||
<td style="text-align: left;">673.171<br /> | <td style="text-align: left;">673.171<br /> | ||
</td> | |||
<td>371.923+301.249+281.263+245.566<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">5 5 5 3<br /> | <td style="text-align: left;">5 5 5 3<br /> | ||
| Line 730: | Line 820: | ||
<td style="text-align: left;">672.897<br /> | <td style="text-align: left;">672.897<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">13 13 13 8<br /> | <td>371.785+301.112+281.4+245.703<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/13%2013%2013%208">13 13 13 8</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">13;8 Golden Mávila 1/13-tone<br /> | <td style="text-align: left;">13;8 Golden Mávila 1/13-tone<br /> | ||
| Line 743: | Line 835: | ||
</td> | </td> | ||
<td style="text-align: left;">672.85<br /> | <td style="text-align: left;">672.85<br /> | ||
</td> | |||
<td>371.761+301.089+281.423+245.726<br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1</span><br /> | <td style="text-align: left;"><span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1</span><br /> | ||
| Line 758: | Line 852: | ||
<td style="text-align: left;">672.832<br /> | <td style="text-align: left;">672.832<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">21 21 21 13<br /> | <td>371.752+301.08+281.432+245.735<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/21%2021%2021%2013">21 21 21 13</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">21;13 Golden Mávila 1/21-tone <span style="font-size: 12.8000001907349px;">(Phi is the step 120\173)</span><br /> | <td style="text-align: left;">21;13 Golden Mávila 1/21-tone <span style="font-size: 12.8000001907349px;">(Phi is the step 120\173)</span><br /> | ||
| Line 771: | Line 867: | ||
</td> | </td> | ||
<td style="text-align: left;">672.727<br /> | <td style="text-align: left;">672.727<br /> | ||
</td> | |||
<td>371.7+301.027+281.485+245.788;<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">8 8 8 5<br /> | <td style="text-align: left;">8 8 8 5<br /> | ||
| Line 786: | Line 884: | ||
<td style="text-align: left;">672.527<br /> | <td style="text-align: left;">672.527<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">11 11 11 7<br /> | <td>371.6+300.9275+281.585+245.888<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/11%2011%2011%207">11 11 11 7</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">11;7 Superdiatonic 1/11-tone<br /> | <td style="text-align: left;">11;7 Superdiatonic 1/11-tone<br /> | ||
| Line 799: | Line 899: | ||
</td> | </td> | ||
<td>672.523<br /> | <td>672.523<br /> | ||
</td> | |||
<td>371.598+300.925+281.587+245.89<br /> | |||
</td> | </td> | ||
<td>π π π 2<br /> | <td>π π π 2<br /> | ||
| Line 814: | Line 916: | ||
<td style="text-align: left;">672.464<br /> | <td style="text-align: left;">672.464<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">25 25 25 16<br /> | <td>371.568+300.896+281.6165+245.919<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/25%2025%2025%2016">25 25 25 16</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">25;16 Superdiatonic 1/25-tone<br /> | <td style="text-align: left;">25;16 Superdiatonic 1/25-tone<br /> | ||
| Line 828: | Line 932: | ||
<td style="text-align: left;">672.414<br /> | <td style="text-align: left;">672.414<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">14 14 14 9<br /> | <td>371.543+300.871+281.6415+245.945<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/14%2014%2014%209">14 14 14 9</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">14;9 Superdiatonic 1/14-tone<br /> | <td style="text-align: left;">14;9 Superdiatonic 1/14-tone<br /> | ||
| Line 840: | Line 946: | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">672. | <td style="text-align: left;">672.34<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">17 17 17 11<br /> | <td>371.506+300.834+281.671+245.981<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/17%2017%2017%2011">17 17 17 11</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">17;11 Superdiatonic 1/17-tone<br /> | <td style="text-align: left;">17;11 Superdiatonic 1/17-tone<br /> | ||
| Line 856: | Line 964: | ||
<td style="text-align: left;">672.289<br /> | <td style="text-align: left;">672.289<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">20 20 20 13<br /> | <td>371.481+300.808+281.704+246.007<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/20%2020%2020%2013">20 20 20 13</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 870: | Line 980: | ||
<td style="text-align: left;">672.251<br /> | <td style="text-align: left;">672.251<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">23 23 23 15<br /> | <td>371.462+300.789+281.723+246.026<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/23%2023%2023%2015">23 23 23 15</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 884: | Line 996: | ||
<td style="text-align: left;">672.222<br /> | <td style="text-align: left;">672.222<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">26 26 26 17<br /> | <td>371.447+300.775+281.737+246.0405<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/26%2026%2026%2017">26 26 26 17</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">26;17 Superdiatonic 1/26-tone<br /> | <td style="text-align: left;">26;17 Superdiatonic 1/26-tone<br /> | ||
| Line 898: | Line 1,012: | ||
<td style="text-align: left;">672.199<br /> | <td style="text-align: left;">672.199<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">29 29 29 19<br /> | <td>371.436+300.763+281.749+246.052<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/29%2029%2029%2019">29 29 29 19</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">29;19 Superdiatonic 1/29-tone<br /> | <td style="text-align: left;">29;19 Superdiatonic 1/29-tone<br /> | ||
| Line 911: | Line 1,027: | ||
</td> | </td> | ||
<td style="text-align: left;">672<br /> | <td style="text-align: left;">672<br /> | ||
</td> | |||
<td>371.336+300.664+281.848+246.152<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">3 3 3 2<br /> | <td style="text-align: left;">3 3 3 2<br /> | ||
| Line 926: | Line 1,044: | ||
<td style="text-align: left;">671.815<br /> | <td style="text-align: left;">671.815<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">31 31 31 21<br /> | <td>371.2435+300.571+281.941+246.244<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/31%2031%2031%2021">31 31 31 21</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">31;21 Superdiatonic 1/31-tone<br /> | <td style="text-align: left;">31;21 Superdiatonic 1/31-tone<br /> | ||
| Line 940: | Line 1,060: | ||
<td style="text-align: left;">671.795<br /> | <td style="text-align: left;">671.795<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">28 28 28 19<br /> | <td>371.234+300.561+281.951+246.254<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/28%2028%2028%2019">28 28 28 19</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;">28;19 Superdiatonic 1/28-tone<br /> | <td style="text-align: left;">28;19 Superdiatonic 1/28-tone<br /> | ||
| Line 952: | Line 1,074: | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">671. | <td style="text-align: left;">671.77<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">25 25 25 17<br /> | <td>371.221+300.549+281.963+246.266<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/25%2025%2025%2017">25 25 25 17</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 968: | Line 1,092: | ||
<td style="text-align: left;">671.739<br /> | <td style="text-align: left;">671.739<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">22 22 22 15<br /> | <td>371.206+300.533+281.979+246.282<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/22%2022%2022%2015">22 22 22 15</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 982: | Line 1,108: | ||
<td style="text-align: left;">671.698<br /> | <td style="text-align: left;">671.698<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">19 19 19 13<br /> | <td>371.185+300.513+281.999+246.3025<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/19%2019%2019%2013">19 19 19 13</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 996: | Line 1,124: | ||
<td style="text-align: left;">671.642<br /> | <td style="text-align: left;">671.642<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">16 16 16 11<br /> | <td>371.157+300.485+282.0275+246.331<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/16%2016%2016%2011">16 16 16 11</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 1,010: | Line 1,140: | ||
<td style="text-align: left;">671.560<br /> | <td style="text-align: left;">671.560<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">13 13 13 9<br /> | <td>371.116+300.444+282.069+246.372<br /> | ||
</td> | |||
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/13%2013%2013%209">13 13 13 9</a><br /> | |||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 1,016: | Line 1,148: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | |||
</td> | |||
<td style="text-align: left;">47\84<br /> | <td style="text-align: left;">47\84<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;">671.429<br /> | ||
</td> | </td> | ||
<td | <td>371.0505+300.378+282.134+246.437<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">10 10 10 7<br /> | <td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/10%2010%2010%207">10 10 10 7</a><br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 1,030: | Line 1,164: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | |||
</td> | |||
<td style="text-align: left;">33\59<br /> | <td style="text-align: left;">33\59<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;">671.186<br /> | ||
</td> | </td> | ||
<td | <td>370.929+300.257+282.255+246.558<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">7 7 7 5<br /> | <td style="text-align: left;">7 7 7 5<br /> | ||
| Line 1,051: | Line 1,187: | ||
</td> | </td> | ||
<td style="text-align: left;">670.588<br /> | <td style="text-align: left;">670.588<br /> | ||
</td> | |||
<td>370.63+299.958+282.554+246.8575<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">4 4 4 3<br /> | <td style="text-align: left;">4 4 4 3<br /> | ||
| Line 1,065: | Line 1,203: | ||
</td> | </td> | ||
<td style="text-align: left;">669.767<br /> | <td style="text-align: left;">669.767<br /> | ||
</td> | |||
<td>370.22+299.5475+282.965+247.268<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">5 5 5 4<br /> | <td style="text-align: left;">5 5 5 4<br /> | ||
| Line 1,072: | Line 1,212: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;">5\ | <td style="text-align: left;">5\9<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
| Line 1,079: | Line 1,219: | ||
</td> | </td> | ||
<td style="text-align: left;">666.667<br /> | <td style="text-align: left;">666.667<br /> | ||
</td> | |||
<td>368.6695+297.997+284.515+248.818<br /> | |||
</td> | </td> | ||
<td style="text-align: left;">1 1 1 1<br /> | <td style="text-align: left;">1 1 1 1<br /> | ||
Revision as of 12:16, 8 November 2016
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 2016-11-08 12:16:51 UTC.
- The original revision id was 598904070.
- 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:
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 minimum 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 ||~ <span style="display: block; text-align: center;">**Generator size (cents)**</span> ||~ '8:7:6:5:4' (cents) ||~ Pentachord steps ||~ Comments || ||< 4\7 ||< ||< ||< 685.714 || 378.193+307.521+274.991+239.2945 ||< 1 1 1 0 ||< || ||< 21\37 ||< ||< ||< 681.081 || 375.877+305.204+277.308+241.611 ||< 5 5 5 1 ||< || ||< 17\30 ||< ||< ||< 680 || 375.336+304.664+277.848+242;152 ||< 4 4 4 1 ||< L/s = 4 || ||< ||< 30\53 ||< ||< 679.245 || 374.959+304.286+278.226+242.529 ||< 7 7 7 2 ||< || || || 43\76 || || 678.947 || 374.81+304.1375+278.375+242.677 || [[tel/10 10 10 3|10 10 10 3]] || || || || 56\99 || || 678.788 || 374.73+304.058+278.4545+242.758 || [[tel/13 13 13 4|13 13 13 4]] || || || || 69\122 || || [[tel/678.6885|678.6885]] || 374.6805+304.008+278.504+242.807 || [[tel/16 16 16 5|16 16 16 5]] || || || || 82\145 || || 678.621 || 374.647+303.974+278.538+242.841 || [[tel/19 19 19 6|19 19 19 6]] || || || || 95\168 || || 678.571 || 374.622+303.9495+278.563+242.866 || [[tel/22 22 22 7|22 22 22 7]] || || || || || || 678.569 || 374.621+303.948+278.564+242.867 || π π π 1 || L/s = π || ||< ||< 108\191 ||< ||< 678.534 || 374.603+303.931+278.581+242.885 ||< [[tel/25 25 25 8|25 25 25 8]] ||< || ||< ||< 121\214 ||< ||< 678.505 || 374.5885+303.916+278.596+242.899 ||< [[tel/28 28 28 9|28 28 28 9]] ||< 28;9 Superdiatonic 1/28-tone <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the Pythagorean wolf Fifth)</span> || || || 134\237 || || 678.481 || 374.577+303.904+278.608+242.911 || [[tel/31 31 31 10|31 31 31 10]] || HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span> || ||< 13\23 ||< ||< ||< 678.261 || 374.467+303.794+278.718+243.021 ||< 3 3 3 1 ||< HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(Armodue 1/3-tone)</span> || || || 126\223 || || 678.027 || 374.35+303.677+278.835+243.138 || [[tel/29 29 29 10|29 29 29 10]] || HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(Armodue 1/29-tone)</span> || ||< ||< 113\200 ||< ||< 678 || 374.336+303.664+278.848+243.152 ||< [[tel/26 26 26 9|26 26 26 9]] ||< HORNBOSTEL (& [[Alexei Stepanovich Ogolevets|OGOLEVETS]]) TEMPERAMENT <span style="font-size: 12.8000001907349px;">(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')</span> || ||< ||< 100\177 ||< ||< 677.966 || 374.319+303.647+278.865+243.1685 ||< [[tel/23 23 23 8|23 23 23 8]] ||< || ||< ||< 87\154 ||< ||< 677.922 || 374.297+303.625+278.887+243.191 ||< [[tel/20 20 20 7|20 20 20 7]] ||< || ||< ||< 74\131 ||< ||< 677.863 || 374.2675+303.595+278.917+243.22 ||< [[tel/17 17 17 6|17 17 17 6]] ||< Armodue-Hornbostel 1/17-tone <span style="font-size: 12.8000001907349px;">(the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)</span> || ||< ||< 61\108 ||< ||< 677.778 || 374.225+303.553+278.9595+243.263 ||< [[tel/14 14 14 5|14 14 14 5]] ||< Armodue-Hornbostel 1/14-tone || ||< ||< 109\193 ||< ||< 677.72 || 374.196+303.524+278.988+243.2915 ||< [[tel/25 25 25 9|25 25 25 9]] ||< Armodue-Hornbostel 1/25-tone || ||< ||< 48\85 ||< ||< 677.647 || 374.15+303.487+279.025+243.328 ||< [[tel/11 11 11 4|11 11 11 4]] ||< Armodue-Hornbostel 1/11-tone <span style="font-size: 12.8000001907349px;">(Optimum accuracy of Phi interval, the note '7')</span> || ||< ||< ||< ||< 677.562 || 374.117+303.445+279.0675+243.371 ||< e e e 1 ||< L/s = e || ||< ||< 35\62 ||< ||< 677.419 || 374.046+303.3735+279.139+243.442 ||< 8 8 8 3 ||< Armodue-Hornbostel 1/8-tone || ||< ||< 92\163 ||< ||< 677.301 || 373.9865+303.314+279.198+243.501 ||< [[tel/21 21 21 8|21 21 21 8]] ||< 21;8 Superdiatonic 1/21-tone || ||< ||< ||< ||< 677.28 || 373.976+303.304+279.208+243.511 ||< <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">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\101 ||< ||< 677.228 || 373.95+304.278+279.2345+243.538 ||< [[tel/13 13 13 5|13 13 13 5]] ||< 13;5 Superdiatonic 1/13-tone || ||< 22\39 ||< ||< ||< 676.923 || 373.798+303.125+279.387+243.69 ||< 5 5 5 2 ||< Armodue-Hornbostel 1/5-tone <span style="font-size: 12.8000001907349px;">(Optimum low size of Hornbostel '6th')</span> || ||< ||< 75\133 ||< ||< 676.692 || 373.682+303.01+279.5025+243.805 ||< [[tel/17 17 17 7|17 17 17 7]] ||< 17;7 Superdiatonic 1/17-tone <span style="font-size: 12.8000001907349px;">(Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)</span> || ||< ||< 53\94 ||< ||< 676.596 || 373.634+302.962+279.5505+243.854 ||< [[tel/12 12 12 5|12 12 12 5]] ||< || ||< ||< 31\55 ||< ||< 676.364 || 373.518+302.846+279.667+243.97 ||< 7 7 7 3 ||< 7;3 Superdiatonic 1/7-tone || ||< ||< 40\71 ||< ||< 676.056 || 373.364+302.692+279.82+244.123 ||< 9 9 9 4 ||< 9;4 Superdiatonic 1/9-tone || ||< ||< 49\87 ||< ||< 675.862 || 373.267+302.595+279.917+244.221 ||< [[tel/11 11 11 5|11 11 11 5]] ||< 11;5 Superdiatonic 1/11-tone || ||< ||< 58\103 ||< ||< 675.728 || 373.2+302.528+279.984+244.288 ||< [[tel/13 13 13 6|13 13 13 6]] ||< 13;6 Superdiatonic 1/13-tone || ||< 9\16 ||< ||< ||< 675 || 372.836+302.164+280.348+244.652 ||< 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\105 ||< ||< 674.286 || 372.48+301.807+280.7055+245.009 ||< [[tel/13 13 13 7|13 13 13 7]] ||< Armodue-Mávila 1/13-tone || ||< ||< 50\89 ||< ||< 674.157 || 372.415+301.742+280.77+245.073 ||< [[tel/11 11 11 6|11 11 11 6]] ||< Armodue-Mávila 1/11-tone || ||< ||< 41\73 ||< ||< 673.973 || 372.3225+301.65+280.862+245.165 ||< 9 9 9 5 ||< Armodue-Mávila 1/9-tone <span style="font-size: 12.8000001907349px;">(with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)</span> || ||< ||< 32\57 ||< ||< 673.684 || 372.178+301.506+281.006+245.3095 ||< 7 7 7 4 ||< Armodue-Mávila 1/7-tone <span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Armodue, because its high accuracy of the [[xenharmonic/7_4|7/4]] interval, the note '8')</span> || || || || || 673.577 || 372.125+301.452+281.06+245.363 || <span style="background-color: #ffffff;">√3 √3 √3 1</span> || || ||< ||< 55\98 ||< ||< 673.469 || 372.071+301.3985+281.158+245.461 ||< [[tel/12 12 12 7|12 12 12 7]] ||< || ||< ||< 78\139 ||< ||< 673.381 || 372.027+301.354+281.158+245.461 ||< [[tel/17 17 17 10|17 17 17 10]] ||< Armodue-Mávila 1/17-tone || ||< ||< 101\180 ||< ||< 673.333 || 372.003+301.3305+281.182+245.485 ||< [[tel/22 22 22 13|22 22 22 13]] ||< || ||< 23\41 ||< ||< ||< 673.171 || 371.923+301.249+281.263+245.566 ||< 5 5 5 3 ||< 5;3 Golden Armodue-Mávila 1/5-tone || ||< ||< 60\107 ||< ||< 672.897 || 371.785+301.112+281.4+245.703 ||< [[tel/13 13 13 8|13 13 13 8]] ||< 13;8 Golden Mávila 1/13-tone || ||< ||< ||< ||< 672.85 || 371.761+301.089+281.423+245.726 ||< <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">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\173 ||< 672.832 || 371.752+301.08+281.432+245.735 ||< [[tel/21 21 21 13|21 21 21 13]] ||< 21;13 Golden Mávila 1/21-tone <span style="font-size: 12.8000001907349px;">(Phi is the step 120\173)</span> || ||< ||< 37\66 ||< ||< 672.727 || 371.7+301.027+281.485+245.788; ||< 8 8 8 5 ||< 8;5 Golden Mávila 1/8-tone || ||< ||< 51\91 ||< ||< 672.527 || 371.6+300.9275+281.585+245.888 ||< [[tel/11 11 11 7|11 11 11 7]] ||< 11;7 Superdiatonic 1/11-tone || || || || || 672.523 || 371.598+300.925+281.587+245.89 || π π π 2 || || ||< ||< ||< 116\207 ||< 672.464 || 371.568+300.896+281.6165+245.919 ||< [[tel/25 25 25 16|25 25 25 16]] ||< 25;16 Superdiatonic 1/25-tone || ||< ||< 65\116 ||< ||< 672.414 || 371.543+300.871+281.6415+245.945 ||< [[tel/14 14 14 9|14 14 14 9]] ||< 14;9 Superdiatonic 1/14-tone || ||< ||< 79\141 ||< ||< 672.34 || 371.506+300.834+281.671+245.981 ||< [[tel/17 17 17 11|17 17 17 11]] ||< 17;11 Superdiatonic 1/17-tone || ||< ||< 93\166 ||< ||< 672.289 || 371.481+300.808+281.704+246.007 ||< [[tel/20 20 20 13|20 20 20 13]] ||< || ||< ||< 107\191 ||< ||< 672.251 || 371.462+300.789+281.723+246.026 ||< [[tel/23 23 23 15|23 23 23 15]] ||< || ||< ||< 121\216 ||< ||< 672.222 || 371.447+300.775+281.737+246.0405 ||< [[tel/26 26 26 17|26 26 26 17]] ||< 26;17 Superdiatonic 1/26-tone || ||< ||< 135\241 ||< ||< 672.199 || 371.436+300.763+281.749+246.052 ||< [[tel/29 29 29 19|29 29 29 19]] ||< 29;19 Superdiatonic 1/29-tone || ||< 14\25 ||< ||< ||< 672 || 371.336+300.664+281.848+246.152 ||< 3 3 3 2 ||< 3;2 Golden Armodue-Mávila 1/3-tone || ||< ||< 145\259 ||< ||< 671.815 || 371.2435+300.571+281.941+246.244 ||< [[tel/31 31 31 21|31 31 31 21]] ||< 31;21 Superdiatonic 1/31-tone || ||< ||< 131\234 ||< ||< 671.795 || 371.234+300.561+281.951+246.254 ||< [[tel/28 28 28 19|28 28 28 19]] ||< 28;19 Superdiatonic 1/28-tone || ||< ||< 117\209 ||< ||< 671.77 || 371.221+300.549+281.963+246.266 ||< [[tel/25 25 25 17|25 25 25 17]] ||< || ||< ||< 103\184 ||< ||< 671.739 || 371.206+300.533+281.979+246.282 ||< [[tel/22 22 22 15|22 22 22 15]] ||< || ||< ||< 89\159 ||< ||< 671.698 || 371.185+300.513+281.999+246.3025 ||< [[tel/19 19 19 13|19 19 19 13]] ||< || ||< ||< 75\134 ||< ||< 671.642 || 371.157+300.485+282.0275+246.331 ||< [[tel/16 16 16 11|16 16 16 11]] ||< || ||< ||< 61\109 ||< ||< 671.560 || 371.116+300.444+282.069+246.372 ||< [[tel/13 13 13 9|13 13 13 9]] ||< || ||< ||< 47\84 ||< ||< 671.429 || 371.0505+300.378+282.134+246.437 ||< [[tel/10 10 10 7|10 10 10 7]] ||< || ||< ||< 33\59 ||< ||< 671.186 || 370.929+300.257+282.255+246.558 ||< 7 7 7 5 ||< || ||< 19\34 ||< ||< ||< 670.588 || 370.63+299.958+282.554+246.8575 ||< 4 4 4 3 ||< || ||< 24\43 ||< ||< ||< 669.767 || 370.22+299.5475+282.965+247.268 ||< 5 5 5 4 ||< || ||< 5\9 ||< ||< ||< 666.667 || 368.6695+297.997+284.515+248.818 ||< 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 minimum 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 colspan="3">Generator<br />
</th>
<th><span style="display: block; text-align: center;"><strong>Generator size (cents)</strong></span><br />
</th>
<th>'8:7:6:5:4' (cents)<br />
</th>
<th>Pentachord steps<br />
</th>
<th>Comments<br />
</th>
</tr>
<tr>
<td style="text-align: left;">4\7<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">685.714<br />
</td>
<td>378.193+307.521+274.991+239.2945<br />
</td>
<td style="text-align: left;">1 1 1 0<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;">21\37<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">681.081<br />
</td>
<td>375.877+305.204+277.308+241.611<br />
</td>
<td style="text-align: left;">5 5 5 1<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;">17\30<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">680<br />
</td>
<td>375.336+304.664+277.848+242;152<br />
</td>
<td style="text-align: left;">4 4 4 1<br />
</td>
<td style="text-align: left;">L/s = 4<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">30\53<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">679.245<br />
</td>
<td>374.959+304.286+278.226+242.529<br />
</td>
<td style="text-align: left;">7 7 7 2<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>43\76<br />
</td>
<td><br />
</td>
<td>678.947<br />
</td>
<td>374.81+304.1375+278.375+242.677<br />
</td>
<td><a class="wiki_link" href="http://tel.wikispaces.com/10%2010%2010%203">10 10 10 3</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>56\99<br />
</td>
<td><br />
</td>
<td>678.788<br />
</td>
<td>374.73+304.058+278.4545+242.758<br />
</td>
<td><a class="wiki_link" href="http://tel.wikispaces.com/13%2013%2013%204">13 13 13 4</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>69\122<br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="http://tel.wikispaces.com/678.6885">678.6885</a><br />
</td>
<td>374.6805+304.008+278.504+242.807<br />
</td>
<td><a class="wiki_link" href="http://tel.wikispaces.com/16%2016%2016%205">16 16 16 5</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>82\145<br />
</td>
<td><br />
</td>
<td>678.621<br />
</td>
<td>374.647+303.974+278.538+242.841<br />
</td>
<td><a class="wiki_link" href="http://tel.wikispaces.com/19%2019%2019%206">19 19 19 6</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>95\168<br />
</td>
<td><br />
</td>
<td>678.571<br />
</td>
<td>374.622+303.9495+278.563+242.866<br />
</td>
<td><a class="wiki_link" href="http://tel.wikispaces.com/22%2022%2022%207">22 22 22 7</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>678.569<br />
</td>
<td>374.621+303.948+278.564+242.867<br />
</td>
<td>π π π 1<br />
</td>
<td>L/s = π<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">108\191<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">678.534<br />
</td>
<td>374.603+303.931+278.581+242.885<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/25%2025%2025%208">25 25 25 8</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">121\214<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">678.505<br />
</td>
<td>374.5885+303.916+278.596+242.899<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/28%2028%2028%209">28 28 28 9</a><br />
</td>
<td style="text-align: left;">28;9 Superdiatonic 1/28-tone <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the Pythagorean wolf Fifth)</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>134\237<br />
</td>
<td><br />
</td>
<td>678.481<br />
</td>
<td>374.577+303.904+278.608+242.911<br />
</td>
<td><a class="wiki_link" href="http://tel.wikispaces.com/31%2031%2031%2010">31 31 31 10</a><br />
</td>
<td>HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span><br />
</td>
</tr>
<tr>
<td style="text-align: left;">13\23<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">678.261<br />
</td>
<td>374.467+303.794+278.718+243.021<br />
</td>
<td style="text-align: left;">3 3 3 1<br />
</td>
<td style="text-align: left;">HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(Armodue 1/3-tone)</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>126\223<br />
</td>
<td><br />
</td>
<td>678.027<br />
</td>
<td>374.35+303.677+278.835+243.138<br />
</td>
<td><a class="wiki_link" href="http://tel.wikispaces.com/29%2029%2029%2010">29 29 29 10</a><br />
</td>
<td>HORNBOSTEL TEMPERAMENT<br />
<span style="font-size: 12.8000001907349px;">(Armodue 1/29-tone)</span><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">113\200<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">678<br />
</td>
<td>374.336+303.664+278.848+243.152<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/26%2026%2026%209">26 26 26 9</a><br />
</td>
<td style="text-align: left;">HORNBOSTEL (& <a class="wiki_link" href="/Alexei%20Stepanovich%20Ogolevets">OGOLEVETS</a>) TEMPERAMENT <span style="font-size: 12.8000001907349px;">(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')</span><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">100\177<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">677.966<br />
</td>
<td>374.319+303.647+278.865+243.1685<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/23%2023%2023%208">23 23 23 8</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">87\154<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">677.922<br />
</td>
<td>374.297+303.625+278.887+243.191<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/20%2020%2020%207">20 20 20 7</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">74\131<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">677.863<br />
</td>
<td>374.2675+303.595+278.917+243.22<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/17%2017%2017%206">17 17 17 6</a><br />
</td>
<td style="text-align: left;">Armodue-Hornbostel 1/17-tone <span style="font-size: 12.8000001907349px;">(the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)</span><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">61\108<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">677.778<br />
</td>
<td>374.225+303.553+278.9595+243.263<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/14%2014%2014%205">14 14 14 5</a><br />
</td>
<td style="text-align: left;">Armodue-Hornbostel 1/14-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">109\193<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">677.72<br />
</td>
<td>374.196+303.524+278.988+243.2915<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/25%2025%2025%209">25 25 25 9</a><br />
</td>
<td style="text-align: left;">Armodue-Hornbostel 1/25-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">48\85<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">677.647<br />
</td>
<td>374.15+303.487+279.025+243.328<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/11%2011%2011%204">11 11 11 4</a><br />
</td>
<td style="text-align: left;">Armodue-Hornbostel 1/11-tone <span style="font-size: 12.8000001907349px;">(Optimum accuracy of Phi interval, the note '7')</span><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;">677.562<br />
</td>
<td>374.117+303.445+279.0675+243.371<br />
</td>
<td style="text-align: left;">e e e 1<br />
</td>
<td style="text-align: left;">L/s = e<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">35\62<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">677.419<br />
</td>
<td>374.046+303.3735+279.139+243.442<br />
</td>
<td style="text-align: left;">8 8 8 3<br />
</td>
<td style="text-align: left;">Armodue-Hornbostel 1/8-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">92\163<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">677.301<br />
</td>
<td>373.9865+303.314+279.198+243.501<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/21%2021%2021%208">21 21 21 8</a><br />
</td>
<td style="text-align: left;">21;8 Superdiatonic 1/21-tone<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;">677.28<br />
</td>
<td>373.976+303.304+279.208+243.511<br />
</td>
<td style="text-align: left;"><span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ+1 φ+1 φ+1 1</span><br />
</td>
<td style="text-align: left;">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: left;"><br />
</td>
<td style="text-align: left;">57\101<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">677.228<br />
</td>
<td>373.95+304.278+279.2345+243.538<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/13%2013%2013%205">13 13 13 5</a><br />
</td>
<td style="text-align: left;">13;5 Superdiatonic 1/13-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;">22\39<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">676.923<br />
</td>
<td>373.798+303.125+279.387+243.69<br />
</td>
<td style="text-align: left;">5 5 5 2<br />
</td>
<td style="text-align: left;">Armodue-Hornbostel 1/5-tone <span style="font-size: 12.8000001907349px;">(Optimum low size of Hornbostel '6th')</span><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">75\133<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">676.692<br />
</td>
<td>373.682+303.01+279.5025+243.805<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/17%2017%2017%207">17 17 17 7</a><br />
</td>
<td style="text-align: left;">17;7 Superdiatonic 1/17-tone <span style="font-size: 12.8000001907349px;">(Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)</span><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">53\94<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">676.596<br />
</td>
<td>373.634+302.962+279.5505+243.854<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/12%2012%2012%205">12 12 12 5</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">31\55<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">676.364<br />
</td>
<td>373.518+302.846+279.667+243.97<br />
</td>
<td style="text-align: left;">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: left;"><br />
</td>
<td style="text-align: left;">40\71<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">676.056<br />
</td>
<td>373.364+302.692+279.82+244.123<br />
</td>
<td style="text-align: left;">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: left;"><br />
</td>
<td style="text-align: left;">49\87<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">675.862<br />
</td>
<td>373.267+302.595+279.917+244.221<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/11%2011%2011%205">11 11 11 5</a><br />
</td>
<td style="text-align: left;">11;5 Superdiatonic 1/11-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">58\103<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">675.728<br />
</td>
<td>373.2+302.528+279.984+244.288<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/13%2013%2013%206">13 13 13 6</a><br />
</td>
<td style="text-align: left;">13;6 Superdiatonic 1/13-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;">9\16<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">675<br />
</td>
<td>372.836+302.164+280.348+244.652<br />
</td>
<td style="text-align: left;">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 style="text-align: left;"><br />
</td>
<td style="text-align: left;">59\105<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">674.286<br />
</td>
<td>372.48+301.807+280.7055+245.009<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/13%2013%2013%207">13 13 13 7</a><br />
</td>
<td style="text-align: left;">Armodue-Mávila 1/13-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">50\89<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">674.157<br />
</td>
<td>372.415+301.742+280.77+245.073<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/11%2011%2011%206">11 11 11 6</a><br />
</td>
<td style="text-align: left;">Armodue-Mávila 1/11-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">41\73<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">673.973<br />
</td>
<td>372.3225+301.65+280.862+245.165<br />
</td>
<td style="text-align: left;">9 9 9 5<br />
</td>
<td style="text-align: left;">Armodue-Mávila 1/9-tone <span style="font-size: 12.8000001907349px;">(with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)</span><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">32\57<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">673.684<br />
</td>
<td>372.178+301.506+281.006+245.3095<br />
</td>
<td style="text-align: left;">7 7 7 4<br />
</td>
<td style="text-align: left;">Armodue-Mávila 1/7-tone <span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Armodue, because its high accuracy of the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7_4">7/4</a> interval, the note '8')</span><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>673.577<br />
</td>
<td>372.125+301.452+281.06+245.363<br />
</td>
<td><span style="background-color: #ffffff;">√3 √3 √3 1</span><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">55\98<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">673.469<br />
</td>
<td>372.071+301.3985+281.158+245.461<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/12%2012%2012%207">12 12 12 7</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">78\139<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">673.381<br />
</td>
<td>372.027+301.354+281.158+245.461<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/17%2017%2017%2010">17 17 17 10</a><br />
</td>
<td style="text-align: left;">Armodue-Mávila 1/17-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">101\180<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">673.333<br />
</td>
<td>372.003+301.3305+281.182+245.485<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/22%2022%2022%2013">22 22 22 13</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;">23\41<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">673.171<br />
</td>
<td>371.923+301.249+281.263+245.566<br />
</td>
<td style="text-align: left;">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: left;"><br />
</td>
<td style="text-align: left;">60\107<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">672.897<br />
</td>
<td>371.785+301.112+281.4+245.703<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/13%2013%2013%208">13 13 13 8</a><br />
</td>
<td style="text-align: left;">13;8 Golden Mávila 1/13-tone<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;">672.85<br />
</td>
<td>371.761+301.089+281.423+245.726<br />
</td>
<td style="text-align: left;"><span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1</span><br />
</td>
<td style="text-align: left;">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: left;"><br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">97\173<br />
</td>
<td style="text-align: left;">672.832<br />
</td>
<td>371.752+301.08+281.432+245.735<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/21%2021%2021%2013">21 21 21 13</a><br />
</td>
<td style="text-align: left;">21;13 Golden Mávila 1/21-tone <span style="font-size: 12.8000001907349px;">(Phi is the step 120\173)</span><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">37\66<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">672.727<br />
</td>
<td>371.7+301.027+281.485+245.788;<br />
</td>
<td style="text-align: left;">8 8 8 5<br />
</td>
<td style="text-align: left;">8;5 Golden Mávila 1/8-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">51\91<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">672.527<br />
</td>
<td>371.6+300.9275+281.585+245.888<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/11%2011%2011%207">11 11 11 7</a><br />
</td>
<td style="text-align: left;">11;7 Superdiatonic 1/11-tone<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>672.523<br />
</td>
<td>371.598+300.925+281.587+245.89<br />
</td>
<td>π π π 2<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;">116\207<br />
</td>
<td style="text-align: left;">672.464<br />
</td>
<td>371.568+300.896+281.6165+245.919<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/25%2025%2025%2016">25 25 25 16</a><br />
</td>
<td style="text-align: left;">25;16 Superdiatonic 1/25-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">65\116<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">672.414<br />
</td>
<td>371.543+300.871+281.6415+245.945<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/14%2014%2014%209">14 14 14 9</a><br />
</td>
<td style="text-align: left;">14;9 Superdiatonic 1/14-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">79\141<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">672.34<br />
</td>
<td>371.506+300.834+281.671+245.981<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/17%2017%2017%2011">17 17 17 11</a><br />
</td>
<td style="text-align: left;">17;11 Superdiatonic 1/17-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">93\166<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">672.289<br />
</td>
<td>371.481+300.808+281.704+246.007<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/20%2020%2020%2013">20 20 20 13</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">107\191<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">672.251<br />
</td>
<td>371.462+300.789+281.723+246.026<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/23%2023%2023%2015">23 23 23 15</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">121\216<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">672.222<br />
</td>
<td>371.447+300.775+281.737+246.0405<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/26%2026%2026%2017">26 26 26 17</a><br />
</td>
<td style="text-align: left;">26;17 Superdiatonic 1/26-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">135\241<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">672.199<br />
</td>
<td>371.436+300.763+281.749+246.052<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/29%2029%2029%2019">29 29 29 19</a><br />
</td>
<td style="text-align: left;">29;19 Superdiatonic 1/29-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;">14\25<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">672<br />
</td>
<td>371.336+300.664+281.848+246.152<br />
</td>
<td style="text-align: left;">3 3 3 2<br />
</td>
<td style="text-align: left;">3;2 Golden Armodue-Mávila 1/3-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">145\259<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">671.815<br />
</td>
<td>371.2435+300.571+281.941+246.244<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/31%2031%2031%2021">31 31 31 21</a><br />
</td>
<td style="text-align: left;">31;21 Superdiatonic 1/31-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">131\234<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">671.795<br />
</td>
<td>371.234+300.561+281.951+246.254<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/28%2028%2028%2019">28 28 28 19</a><br />
</td>
<td style="text-align: left;">28;19 Superdiatonic 1/28-tone<br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">117\209<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">671.77<br />
</td>
<td>371.221+300.549+281.963+246.266<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/25%2025%2025%2017">25 25 25 17</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">103\184<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">671.739<br />
</td>
<td>371.206+300.533+281.979+246.282<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/22%2022%2022%2015">22 22 22 15</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">89\159<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">671.698<br />
</td>
<td>371.185+300.513+281.999+246.3025<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/19%2019%2019%2013">19 19 19 13</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">75\134<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">671.642<br />
</td>
<td>371.157+300.485+282.0275+246.331<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/16%2016%2016%2011">16 16 16 11</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">61\109<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">671.560<br />
</td>
<td>371.116+300.444+282.069+246.372<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/13%2013%2013%209">13 13 13 9</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">47\84<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">671.429<br />
</td>
<td>371.0505+300.378+282.134+246.437<br />
</td>
<td style="text-align: left;"><a class="wiki_link" href="http://tel.wikispaces.com/10%2010%2010%207">10 10 10 7</a><br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">33\59<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">671.186<br />
</td>
<td>370.929+300.257+282.255+246.558<br />
</td>
<td style="text-align: left;">7 7 7 5<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;">19\34<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">670.588<br />
</td>
<td>370.63+299.958+282.554+246.8575<br />
</td>
<td style="text-align: left;">4 4 4 3<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;">24\43<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">669.767<br />
</td>
<td>370.22+299.5475+282.965+247.268<br />
</td>
<td style="text-align: left;">5 5 5 4<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
<tr>
<td style="text-align: left;">5\9<br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;"><br />
</td>
<td style="text-align: left;">666.667<br />
</td>
<td>368.6695+297.997+284.515+248.818<br />
</td>
<td style="text-align: left;">1 1 1 1<br />
</td>
<td style="text-align: left;"><br />
</td>
</tr>
</table>
</body></html>