7L 2s: Difference between revisions
mNo edit summary |
Undo revision 78205 by Moremajorthanmajor (talk) unnecessary Tag: Undo |
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| | 685.714 | | | 685.714 | ||
| | | | | 1 1 1 0 | ||
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|683.871 | |683.871 | ||
| | |13 13 13 1 | ||
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| | 683.798 | | | 683.798 | ||
| | | | | 25 25 25 2 | ||
| | Approximately 0.03 cents away from [[95/64]] | | | Approximately 0.03 cents away from [[95/64]] | ||
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|683.721 | |683.721 | ||
| | |12 12 12 1 | ||
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|683.636 | |683.636 | ||
| | |23 23 23 2 | ||
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|683.544 | |683.544 | ||
| | |11 11 11 1 | ||
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|683.444 | |683.444 | ||
| | |21 21 21 2 | ||
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|683.333 | |683.333 | ||
| | |10 10 10 1 | ||
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|683.212 | |683.212 | ||
| | |19 19 19 2 | ||
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|683.077 | |683.077 | ||
| | |9 9 9 1 | ||
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|682.927 | |682.927 | ||
| | |17 17 17 2 | ||
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| | 682.758 | | | 682.758 | ||
| | | | | 8 8 8 1 | ||
| | 2 generators equal 11/10, 6 equal 4/3, creating a hybrid Mavila/Porcupine scale with three perfect 5ths as well as the flat ones. | | | 2 generators equal 11/10, 6 equal 4/3, creating a hybrid Mavila/Porcupine scale with three perfect 5ths as well as the flat ones. | ||
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|682.569 | |682.569 | ||
| | |15 15 15 2 | ||
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|682.353 | |682.353 | ||
| | |7 7 7 1 | ||
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|682.105 | |682.105 | ||
| | |13 13 13 2 | ||
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|681.818 | |681.818 | ||
| | |6 6 6 1 | ||
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|681.4815 | |681.4815 | ||
| | |11 11 11 2 | ||
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| | 681.081 | | | 681.081 | ||
| | | | | 5 5 5 1 | ||
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|680.769 | |680.769 | ||
| | |14 14 14 3 | ||
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|680.597 | |680.597 | ||
| | |9 9 9 2 | ||
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|680.412 | |680.412 | ||
| | |13 13 13 3 | ||
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|679.518 | |679.518 | ||
| | |11 11 11 3 | ||
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| | 679.245 | | | 679.245 | ||
| | | | | 7 7 7 2 | ||
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| | 678.947 | | | 678.947 | ||
| | | | | 10 10 10 3 | ||
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| | 678.788 | | | 678.788 | ||
| | | | | 13 13 13 4 | ||
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| | 678.6885 | | | 678.6885 | ||
| | | | | 16 16 16 5 | ||
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| | 678.621 | | | 678.621 | ||
| | | | | 19 19 19 6 | ||
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| | 678.571 | | | 678.571 | ||
| | | | | 22 22 22 7 | ||
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| | 678.569 | | | 678.569 | ||
| | | | | π π π 1 | ||
| | L/s = π | | | L/s = π | ||
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| | 678.534 | | | 678.534 | ||
| | | | | 25 25 25 8 | ||
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| | 678.505 | | | 678.505 | ||
| | | | | 28 28 28 9 | ||
| | 28;9 Superdiatonic 1/28-tone <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the ratio | | | 28;9 Superdiatonic 1/28-tone <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the ratio 262144/177147, the Pythagorean wolf Fifth)</span> | ||
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Line 257: | Line 257: | ||
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| | 678.481 | | | 678.481 | ||
| | | | | 31 31 31 10 | ||
| | HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span> | | | HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span> | ||
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Line 264: | Line 264: | ||
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| | 678.261 | | | 678.261 | ||
| | | | | 3 3 3 1 | ||
| | HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(Armodue 1/3-tone)</span> | | | HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(Armodue 1/3-tone)</span> | ||
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| | 678.027 | | | 678.027 | ||
| | | | | 29 29 29 10 | ||
| | HORNBOSTEL TEMPERAMENT | | | HORNBOSTEL TEMPERAMENT | ||
Line 280: | Line 280: | ||
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| | 678 | | | 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> | | | 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> | ||
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Line 287: | Line 287: | ||
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| | 677.966 | | | 677.966 | ||
| | | | | 23 23 23 8 | ||
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Line 294: | Line 294: | ||
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| | 677.922 | | | 677.922 | ||
| | | | | 20 20 20 7 | ||
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Line 301: | Line 301: | ||
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| | 677.863 | | | 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> | | | 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> | ||
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Line 308: | Line 308: | ||
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| | 677.778 | | | 677.778 | ||
| | | | | 14 14 14 5 | ||
| | Armodue-Hornbostel 1/14-tone | | | Armodue-Hornbostel 1/14-tone | ||
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Line 315: | Line 315: | ||
| | 109\193 | | | 109\193 | ||
| | 677.720 | | | 677.720 | ||
| | | | | 25 25 25 9 | ||
| | Armodue-Hornbostel 1/25-tone | | | Armodue-Hornbostel 1/25-tone | ||
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Line 322: | Line 322: | ||
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| | 677.647 | | | 677.647 | ||
| | | | | 11 11 11 4 | ||
| | Armodue-Hornbostel 1/11-tone <span style="font-size: 12.8000001907349px;">(Optimum accuracy of Phi interval, the note '7')</span> | | | Armodue-Hornbostel 1/11-tone <span style="font-size: 12.8000001907349px;">(Optimum accuracy of Phi interval, the note '7')</span> | ||
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Line 329: | Line 329: | ||
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| | 677.562 | | | 677.562 | ||
| | | | | e e e 1 | ||
| | L/s = e | | | L/s = e | ||
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Line 336: | Line 336: | ||
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| | 677.419 | | | 677.419 | ||
| | | | | 8 8 8 3 | ||
| | Armodue-Hornbostel 1/8-tone | | | Armodue-Hornbostel 1/8-tone | ||
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| | 92\163 | | | 92\163 | ||
| | 677.301 | | | 677.301 | ||
| | | | | 21 21 21 8 | ||
| | 21;8 Superdiatonic 1/21-tone | | | 21;8 Superdiatonic 1/21-tone | ||
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Line 350: | Line 350: | ||
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| | 677.28 | | | 677.28 | ||
| |<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;" | | | <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..) | | | Split φ superdiatonic relation (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..) | ||
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Line 357: | Line 357: | ||
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| | 677.228 | | | 677.228 | ||
| | | | | 13 13 13 5 | ||
| | 13;5 Superdiatonic 1/13-tone | | | 13;5 Superdiatonic 1/13-tone | ||
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Line 364: | Line 364: | ||
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| | 676.923 | | | 676.923 | ||
| | | | | 5 5 5 2 | ||
| | Armodue-Hornbostel 1/5-tone <span style="font-size: 12.8000001907349px;">(Optimum low size of Hornbostel '6th')</span> | | | Armodue-Hornbostel 1/5-tone <span style="font-size: 12.8000001907349px;">(Optimum low size of Hornbostel '6th')</span> | ||
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| | 676.692 | | | 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> | | | 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> | ||
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Line 378: | Line 378: | ||
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| | 676.596 | | | 676.596 | ||
| | | | | 12 12 12 5 | ||
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Line 385: | Line 385: | ||
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| | 676.364 | | | 676.364 | ||
| | | | | 7 7 7 3 | ||
| | 7;3 Superdiatonic 1/7-tone | | | 7;3 Superdiatonic 1/7-tone | ||
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Line 392: | Line 392: | ||
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| | 676.056 | | | 676.056 | ||
| | | | | 9 9 9 4 | ||
| | 9;4 Superdiatonic 1/9-tone | | | 9;4 Superdiatonic 1/9-tone | ||
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Line 399: | Line 399: | ||
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| | 675.862 | | | 675.862 | ||
| | | | | 11 11 11 5 | ||
| | 11;5 Superdiatonic 1/11-tone | | | 11;5 Superdiatonic 1/11-tone | ||
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Line 406: | Line 406: | ||
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| | 675.728 | | | 675.728 | ||
| | | | | 13 13 13 6 | ||
| | 13;6 Superdiatonic 1/13-tone | | | 13;6 Superdiatonic 1/13-tone | ||
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Line 413: | Line 413: | ||
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| | 675 | | | 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) | | | <span style="display: block; text-align: left;">'''[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]'''</span>ARMODUE ESADECAFONIA (or Goldsmith Temperament) | ||
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Line 420: | Line 420: | ||
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| | 674.286 | | | 674.286 | ||
| | | | | 13 13 13 7 | ||
| | Armodue-Mavila 1/13-tone | | | Armodue-Mavila 1/13-tone | ||
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Line 427: | Line 427: | ||
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| | 674.157 | | | 674.157 | ||
| | | | | 11 11 11 6 | ||
| | Armodue-Mavila 1/11-tone | | | Armodue-Mavila 1/11-tone | ||
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| | 673.973 | | | 673.973 | ||
| | | | | 9 9 9 5 | ||
| | Armodue-Mavila 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> | | | Armodue-Mavila 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> | ||
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Line 441: | Line 441: | ||
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| | 673.684 | | | 673.684 | ||
| | | | | 7 7 7 4 | ||
| | Armodue-Mavila 1/7-tone <span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Armodue, because its high accuracy of the [[7/4|7/4]] interval, the note '8')</span> | | | Armodue-Mavila 1/7-tone <span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Armodue, because its high accuracy of the [[7/4|7/4]] interval, the note '8')</span> | ||
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Line 448: | Line 448: | ||
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| | 673.577 | | | 673.577 | ||
| |<span style="background-color: #ffffff;" | | | <span style="background-color: #ffffff;">√3 √3 √3 1</span> | ||
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Line 455: | Line 455: | ||
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| | 673.469 | | | 673.469 | ||
| | | | | 12 12 12 7 | ||
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Line 462: | Line 462: | ||
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| | 673.381 | | | 673.381 | ||
| | | | | 17 17 17 10 | ||
| | Armodue-Mavila 1/17-tone | | | Armodue-Mavila 1/17-tone | ||
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Line 469: | Line 469: | ||
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| | 673.333 | | | 673.333 | ||
| | | | | 22 22 22 13 | ||
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Line 476: | Line 476: | ||
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| | 673.171 | | | 673.171 | ||
| | | | | 5 5 5 3 | ||
| | 5;3 Golden Armodue-Mavila 1/5-tone | | | 5;3 Golden Armodue-Mavila 1/5-tone | ||
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Line 483: | Line 483: | ||
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| | 672.897 | | | 672.897 | ||
| | | | | 13 13 13 8 | ||
| | 13;8 Golden Mavila 1/13-tone | | | 13;8 Golden Mavila 1/13-tone | ||
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Line 490: | Line 490: | ||
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| | 672.85 | | | 672.85 | ||
| |<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;" | | | <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1</span> | ||
| | GOLDEN MAVILA (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span> | | | GOLDEN MAVILA (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span> | ||
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Line 497: | Line 497: | ||
| | 97\173 | | | 97\173 | ||
| | 672.832 | | | 672.832 | ||
| | | | | 21 21 21 13 | ||
| | 21;13 Golden Mavila 1/21-tone <span style="font-size: 12.8000001907349px;">(Phi is the step 120\173)</span> | | | 21;13 Golden Mavila 1/21-tone <span style="font-size: 12.8000001907349px;">(Phi is the step 120\173)</span> | ||
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Line 504: | Line 504: | ||
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| | 672.727 | | | 672.727 | ||
| | | | | 8 8 8 5 | ||
| | 8;5 Golden Mavila 1/8-tone | | | 8;5 Golden Mavila 1/8-tone | ||
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Line 511: | Line 511: | ||
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| | 672.527 | | | 672.527 | ||
| | | | | 11 11 11 7 | ||
| | 11;7 Superdiatonic 1/11-tone | | | 11;7 Superdiatonic 1/11-tone | ||
|- | |- | ||
Line 518: | Line 518: | ||
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| | 672.523 | | | 672.523 | ||
| | | | | π π π 2 | ||
| | | | | | ||
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Line 525: | Line 525: | ||
| | 116\207 | | | 116\207 | ||
| | 672.464 | | | 672.464 | ||
| | | | | 25 25 25 16 | ||
| | 25;16 Superdiatonic 1/25-tone | | | 25;16 Superdiatonic 1/25-tone | ||
|- | |- | ||
Line 532: | Line 532: | ||
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| | 672.414 | | | 672.414 | ||
| | | | | 14 14 14 9 | ||
| | 14;9 Superdiatonic 1/14-tone | | | 14;9 Superdiatonic 1/14-tone | ||
|- | |- | ||
Line 539: | Line 539: | ||
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| | 672.340 | | | 672.340 | ||
| | | | | 17 17 17 11 | ||
| | 17;11 Superdiatonic 1/17-tone | | | 17;11 Superdiatonic 1/17-tone | ||
|- | |- | ||
Line 546: | Line 546: | ||
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| | 672.289 | | | 672.289 | ||
| | | | | 20 20 20 13 | ||
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Line 553: | Line 553: | ||
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| | 672.251 | | | 672.251 | ||
| | | | | 23 23 23 15 | ||
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Line 560: | Line 560: | ||
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| | 672.222 | | | 672.222 | ||
| | | | | 26 26 26 17 | ||
| | 26;17 Superdiatonic 1/26-tone | | | 26;17 Superdiatonic 1/26-tone | ||
|- | |- | ||
Line 567: | Line 567: | ||
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| | 672.199 | | | 672.199 | ||
| | | | | 29 29 29 19 | ||
| | 29;19 Superdiatonic 1/29-tone | | | 29;19 Superdiatonic 1/29-tone | ||
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Line 574: | Line 574: | ||
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| | 672 | | | 672 | ||
| | | | | 3 3 3 2 | ||
| | 3;2 Golden Armodue-Mavila 1/3-tone | | | 3;2 Golden Armodue-Mavila 1/3-tone | ||
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Line 581: | Line 581: | ||
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| | 671.815 | | | 671.815 | ||
| | | | | 31 31 31 21 | ||
| | 31;21 Superdiatonic 1/31-tone | | | 31;21 Superdiatonic 1/31-tone | ||
|- | |- | ||
Line 588: | Line 588: | ||
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| | 671.795 | | | 671.795 | ||
| | | | | 28 28 28 19 | ||
| | 28;19 Superdiatonic 1/28-tone | | | 28;19 Superdiatonic 1/28-tone | ||
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Line 595: | Line 595: | ||
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| | 671.770 | | | 671.770 | ||
| | | | | 25 25 25 17 | ||
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Line 602: | Line 602: | ||
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| | 671.739 | | | 671.739 | ||
| | | | | 22 22 22 15 | ||
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Line 609: | Line 609: | ||
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| | 671.698 | | | 671.698 | ||
| | | | | 19 19 19 13 | ||
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Line 616: | Line 616: | ||
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| | 671.642 | | | 671.642 | ||
| | | | | 16 16 16 11 | ||
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Line 623: | Line 623: | ||
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| | 671.560 | | | 671.560 | ||
| | | | | 13 13 13 9 | ||
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Line 630: | Line 630: | ||
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| | 671.429 | | | 671.429 | ||
| | | | | 10 10 10 7 | ||
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Line 637: | Line 637: | ||
|80\143 | |80\143 | ||
|671.329 | |671.329 | ||
| | |17 17 17 12 | ||
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Line 644: | Line 644: | ||
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| | 671.186 | | | 671.186 | ||
| | | | | 7 7 7 5 | ||
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Line 651: | Line 651: | ||
| | | | ||
|670.968 | |670.968 | ||
| | |11 11 11 8 | ||
| | | | ||
|- | |- | ||
Line 658: | Line 658: | ||
| | | | | | ||
| | 670.588 | | | 670.588 | ||
| | | | | 4 4 4 3 | ||
| | | | | | ||
|- | |- | ||
Line 665: | Line 665: | ||
| | | | ||
|670.13 | |670.13 | ||
| | |9 9 9 7 | ||
| | | | ||
|- | |- | ||
Line 672: | Line 672: | ||
| | | | | | ||
| | 669.767 | | | 669.767 | ||
| | | | | 5 5 5 4 | ||
| | | | | | ||
|- | |- | ||
Line 679: | Line 679: | ||
| | | | ||
|669.474 | |669.474 | ||
| | |11 11 11 9 | ||
| | | | ||
|- | |- | ||
Line 686: | Line 686: | ||
| | | | ||
|669.231 | |669.231 | ||
| | |6 6 6 5 | ||
| | | | ||
|- | |- | ||
Line 693: | Line 693: | ||
| | | | ||
|669.0265 | |669.0265 | ||
| | |13 13 13 11 | ||
| | | | ||
|- | |- | ||
Line 700: | Line 700: | ||
| | | | ||
|668.8525 | |668.8525 | ||
| | |7 7 7 6 | ||
| | | | ||
|- | |- | ||
Line 707: | Line 707: | ||
| | | | ||
|668.702 | |668.702 | ||
| | |15 15 15 13 | ||
| | | | ||
|- | |- | ||
Line 714: | Line 714: | ||
| | | | ||
|668.571 | |668.571 | ||
| | |8 8 8 7 | ||
| | | | ||
|- | |- | ||
Line 721: | Line 721: | ||
| | | | ||
|668.456 | |668.456 | ||
| | |17 17 17 15 | ||
| | | | ||
|- | |- | ||
Line 728: | Line 728: | ||
| | | | ||
|668.354 | |668.354 | ||
| | |9 9 9 8 | ||
| | | | ||
|- | |- | ||
Line 735: | Line 735: | ||
| | | | ||
|668.2365 | |668.2365 | ||
| | |19 19 19 17 | ||
| | | | ||
|- | |- | ||
Line 742: | Line 742: | ||
| | | | ||
|668.182 | |668.182 | ||
| | |10 10 10 9 | ||
| | | | ||
|- | |- | ||
Line 749: | Line 749: | ||
| | | | ||
|668.108 | |668.108 | ||
| | |21 21 21 9 | ||
| | | | ||
|- | |- | ||
Line 756: | Line 756: | ||
| | | | ||
|668.041 | |668.041 | ||
| | |11 11 11 10 | ||
| | | | ||
|- | |- | ||
Line 763: | Line 763: | ||
| | | | ||
|667.98 | |667.98 | ||
| | |23 23 23 21 | ||
| | | | ||
|- | |- | ||
Line 770: | Line 770: | ||
| | | | ||
|667.925 | |667.925 | ||
| | |12 12 12 11 | ||
| | | | ||
|- | |- | ||
Line 777: | Line 777: | ||
| | | | ||
|667.873 | |667.873 | ||
| | |25 25 25 23 | ||
| | | | ||
|- | |- | ||
Line 784: | Line 784: | ||
| | | | ||
|667.826 | |667.826 | ||
| | |13 13 13 12 | ||
| | | | ||
|- | |- | ||
Line 791: | Line 791: | ||
| | | | | | ||
| | 666.667 | | | 666.667 | ||
| | | | | 1 1 1 1 | ||
| | | | | | ||
|} | |} |