7L 2s: Difference between revisions

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Line 26: Line 26:
! colspan="3" | Generator
! colspan="3" | Generator
! | <span style="display: block; text-align: center;">'''Generator size (cents)'''</span>
! | <span style="display: block; text-align: center;">'''Generator size (cents)'''</span>
!<span style="display: block; text-align: center;">'''Generator size (sats)'''</span>
! | Pentachord steps
! | Pentachord steps
! | Comments
! | Comments
Line 32: Line 33:
| |  
| |  
| |  
| |  
| | 685.714
| | 685.714…
| | 1 1 1 0
|914.286…
| | <nowiki>1 1|1 0</nowiki>
| |  
| |  
|-
|-
Line 40: Line 42:
|
|
|684
|684
|14 14 14 1
|912
|<nowiki>14 14|14 1</nowiki>
|
|
|-
|-
Line 46: Line 49:
|
|
|
|
|683.871
|683.870…
|[[Tel:13 13 13 1|13 13 13 1]]
|911.827…
|<nowiki>13 13|13 1</nowiki>
|
|
|-
|-
Line 53: Line 57:
| | 102\[[179edo|179]]
| | 102\[[179edo|179]]
| |  
| |  
| | 683.798
| | 683.798…
| | [[Tel:25 25 25 2|25 25 25 2]]
|911.731…
| | <nowiki>25 25|25 2</nowiki>
| | Approximately 0.03 cents away from [[95/64]]
| | Approximately 0.03 cents away from [[95/64]]
|-
|-
Line 60: Line 65:
|
|
|
|
|683.721
|683.720…
|[[Tel:12 12 12 1|12 12 12 1]]
|911.527…
|<nowiki>12 12|12 1</nowiki>
|
|
|-
|-
Line 67: Line 73:
|94\165
|94\165
|
|
|683.636
|683.6̄3̄
|[[Tel:23 23 23 2|23 23 23 2]]
|911.5̄1̄
|<nowiki>23 23|23 2</nowiki>
|
|
|-
|-
Line 74: Line 81:
|
|
|
|
|683.544
|683.544…
|[[Tel:11 11 11 1|11 11 11 1]]
|911.392…
|<nowiki>11 11|11 1</nowiki>
|
|
|-
|-
Line 81: Line 89:
|86\151
|86\151
|
|
|683.444
|683.443…
|[[Tel:21 21 21 2|21 21 21 2]]
|911.258…
|<nowiki>21 21|21 2</nowiki>
|
|
|-
|-
Line 88: Line 97:
|
|
|
|
|683.333
|683.3̄
|[[Tel:10 10 10 1|10 10 10 1]]
|911.1̄
|<nowiki>10 10|10 1</nowiki>
|
|
|-
|-
Line 95: Line 105:
|78\137
|78\137
|
|
|683.212
|683.211…
|[[Tel:19 19 19 2|19 19 19 2]]
|910.948…
|<nowiki>19 19|19 2</nowiki>
|
|
|-
|-
Line 102: Line 113:
|
|
|
|
|683.077
|683.076…
|9 9 9 1
|910.769…
|<nowiki>9 9|9 1</nowiki>
|
|
|-
|-
Line 109: Line 121:
|70\123
|70\123
|
|
|682.927
|682.926…
|[[Tel:17 17 17 2|17 17 17 2]]
|910.569…
|<nowiki>17 17|17 2</nowiki>
|
|
|-
|-
Line 116: Line 129:
| |  
| |  
| |  
| |  
| | 682.758
| | 682.758…
| | 8 8 8 1
|910.344…
| | <nowiki>8 8|8 1</nowiki>
| | 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.
|-
|-
Line 123: Line 137:
|62\109
|62\109
|
|
|682.569
|682.568…
|[[Tel:15 15 15 2|15 15 15 2]]
|910.091…
|<nowiki>15 15|15 2</nowiki>
|
|
|-
|-
Line 130: Line 145:
|
|
|
|
|682.353
|682.352…
|7 7 7 1
|909.803…
|<nowiki>7 7|7 1</nowiki>
|
|
|-
|-
Line 137: Line 153:
|54\95
|54\95
|
|
|682.105
|682.105…
|[[Tel:13 13 13 2|13 13 13 2]]
|909.473…
|<nowiki>13 13|13 2</nowiki>
|
|
|-
|-
Line 144: Line 161:
|
|
|
|
|681.818
|681.8̄1̄
|6 6 6 1
|909.0̄9̄
|<nowiki>6 6|6 1</nowiki>
|
|
|-
|-
Line 151: Line 169:
|46\81
|46\81
|
|
|[[Tel:681.4815|681.4815]]
|681.4̄8̄1̄
|[[Tel:11 11 11 2|11 11 11 2]]
|908.641…
|<nowiki>11 11|11 2</nowiki>
|
|
|-
|-
Line 158: Line 177:
| |  
| |  
| |  
| |  
| | 681.081
| | 681.0̄8̄1̄
| | 5 5 5 1
|908.1̄0̄8̄
| | <nowiki>5 5|5 1</nowiki>
| |  
| |  
|-
|-
Line 165: Line 185:
|59\104
|59\104
|
|
|680.769
|680.769…
|[[Tel:14 14 14 3|14 14 14 3]]
|907.692…
|<nowiki>14 14|14 3</nowiki>
|
|
|-
|-
Line 172: Line 193:
|38\67
|38\67
|
|
|680.597
|680.597…
|9 9 9 2
|907.462…
|<nowiki>9 9|9 2</nowiki>
|
|
|-
|-
Line 179: Line 201:
|55\97
|55\97
|
|
|680.412
|680.412…
|[[Tel:13 13 13 3|13 13 13 3]]
|907.216…
|<nowiki>13 13|13 3</nowiki>
|
|
|-
|-
Line 187: Line 210:
| |  
| |  
| | 680
| | 680
| | 4 4 4 1
|906.6̄
| | <nowiki>4 4|4 1</nowiki>
| | L/s = 4
| | L/s = 4
|-
|-
Line 193: Line 217:
|47\83
|47\83
|
|
|679.518
|679.518…
|[[Tel:11 11 11 3|11 11 11 3]]
|906.024…
|<nowiki>11 11|11 3</nowiki>
|
|
|-
|-
Line 200: Line 225:
| | 30\53
| | 30\53
| |  
| |  
| | 679.245
| | 679.245…
| | 7 7 7 2
|905.660…
| | <nowiki>7 7|7 2</nowiki>
| |  
| |  
|-
|-
Line 207: Line 233:
| | 43\76
| | 43\76
| |  
| |  
| | 678.947
| | 678.947…
| | [[Tel:10 10 10 3|10 10 10 3]]
|905.263…
| | <nowiki>10 10|10 3</nowiki>
| |  
| |  
|-
|-
Line 214: Line 241:
| | 56\99
| | 56\99
| |  
| |  
| | 678.788
| | 678.7̄8̄
| | [[Tel:13 13 13 4|13 13 13 4]]
|905.0̄5̄
| | <nowiki>13 13|13 4</nowiki>
| |  
| |  
|-
|-
Line 221: Line 249:
| | 69\122
| | 69\122
| |  
| |  
| | [[Tel:678.6885|678.6885]]
| | 678.688…
| | [[Tel:16 16 16 5|16 16 16 5]]
|904.918…
| | <nowiki>16 16|16 5</nowiki>
| |  
| |  
|-
|-
Line 228: Line 257:
| | 82\145
| | 82\145
| |  
| |  
| | 678.621
| | 678.620…
| | [[Tel:19 19 19 6|19 19 19 6]]
|904.827…
| | <nowiki>19 19|19 6</nowiki>
| |  
| |  
|-
|-
Line 235: Line 265:
| | 95\168
| | 95\168
| |  
| |  
| | 678.571
| | 678.571…
| | [[Tel:22 22 22 7|22 22 22 7]]
|904.761…
| | <nowiki>22 22|22 7</nowiki>
| |  
| |  
|-
|-
Line 242: Line 273:
| |  
| |  
| |  
| |  
| | 678.569
| | 678.568…
| | π π π 1
|904.758…
| | <nowiki>π π|π 1</nowiki>
| | L/s = π
| | L/s = π
|-
|-
Line 249: Line 281:
| | 108\191
| | 108\191
| |  
| |  
| | 678.534
| | 678.534…
| | [[Tel:25 25 25 8|25 25 25 8]]
|904.712…
| | <nowiki>25 25|25 8</nowiki>
| |  
| |  
|-
|-
Line 256: Line 289:
| | 121\214
| | 121\214
| |  
| |  
| | 678.505
| | 678.504…
| | [[Tel:28 28 28 9|28 28 28 9]]
|904.672…
| | 28;9 Superdiatonic 1/28-tone <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the ratio [[Tel:262144/177147|262144/177147]], the Pythagorean wolf Fifth)</span>
| | <nowiki>28 28|28 9</nowiki>
| | 28;9 Superdiatonic 1/28-tone <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the Pythagorean wolf Fifth)</span>
|-
|-
| |  
| |  
| | 134\237
| | 134\237
| |  
| |  
| | 678.481
| | 678.481…
| | [[Tel:31 31 31 10|31 31 31 10]]
|904.642…
| | <nowiki>31 31|31 10</nowiki>
| | 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>
|-
|-
Line 270: Line 305:
| |  
| |  
| |  
| |  
| | 678.261
| | 678.260…
| | 3 3 3 1
|904.347…
| | <nowiki>3 3|3 1</nowiki>
| | 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>
|-
|-
Line 277: Line 313:
| | 126\223
| | 126\223
| |  
| |  
| | 678.027
| | 678.026…
| | [[Tel:29 29 29 10|29 29 29 10]]
|904.035…
| | <nowiki>29 29|29 10</nowiki>
| | HORNBOSTEL TEMPERAMENT
| | HORNBOSTEL TEMPERAMENT


Line 287: Line 324:
| |  
| |  
| | 678
| | 678
| | [[Tel:26 26 26 9|26 26 26 9]]
|904
| | <nowiki>26 26|26 9</nowiki>
| | HORNBOSTEL (&amp; [[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' &amp; '8')</span>
| | HORNBOSTEL (&amp; [[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' &amp; '8')</span>
|-
|-
Line 293: Line 331:
| | 100\177
| | 100\177
| |  
| |  
| | 677.966
| | 677.966…
| | [[Tel:23 23 23 8|23 23 23 8]]
|903.954…
| | <nowiki>23 23|23 8</nowiki>
| |  
| |  
|-
|-
Line 300: Line 339:
| | 87\154
| | 87\154
| |  
| |  
| | 677.922
| | 677.922…
| | [[Tel:20 20 20 7|20 20 20 7]]
|903.896…
| | <nowiki>20 20|20 7</nowiki>
| |  
| |  
|-
|-
Line 307: Line 347:
| | 74\131
| | 74\131
| |  
| |  
| | 677.863
| | 677.862…
| | [[Tel:17 17 17 6|17 17 17 6]]
|903.816…
| | <nowiki>17 17|17 6</nowiki>
| | 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>
|-
|-
Line 314: Line 355:
| | 61\108
| | 61\108
| |  
| |  
| | 677.778
| | 677.7̄
| | [[Tel:14 14 14 5|14 14 14 5]]
|903.7̄0̄3̄
| | <nowiki>14 14|14 5</nowiki>
| | Armodue-Hornbostel 1/14-tone
| | Armodue-Hornbostel 1/14-tone
|-
|-
Line 321: Line 363:
| |  
| |  
| | 109\193
| | 109\193
| | 677.720
| | 677.720…
| | [[Tel:25 25 25 9|25 25 25 9]]
|903.626…
| | <nowiki>25 25|25 9</nowiki>
| | Armodue-Hornbostel 1/25-tone
| | Armodue-Hornbostel 1/25-tone
|-
|-
Line 328: Line 371:
| | 48\85
| | 48\85
| |  
| |  
| | 677.647
| | 677.647…
| | [[Tel:11 11 11 4|11 11 11 4]]
|903.529…
| | <nowiki>11 11|11 4</nowiki>
| | 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>
|-
|-
Line 335: Line 379:
| |  
| |  
| |  
| |  
| | 677.562
| | 677.561…
| | e e e 1
|903.415…
| | <nowiki>e e|e 1</nowiki>
| | L/s = e
| | L/s = e
|-
|-
Line 342: Line 387:
| | 35\62
| | 35\62
| |  
| |  
| | 677.419
| | 677.419…
| | 8 8 8 3
|903.225…
| | <nowiki>8 8|8 3</nowiki>
| | Armodue-Hornbostel 1/8-tone
| | Armodue-Hornbostel 1/8-tone
|-
|-
Line 349: Line 395:
| |  
| |  
| | 92\163
| | 92\163
| | 677.301
| | 677.300…
| | [[Tel:21 21 21 8|21 21 21 8]]
|903.067…
| | <nowiki>21 21|21 8</nowiki>
| | 21;8 Superdiatonic 1/21-tone
| | 21;8 Superdiatonic 1/21-tone
|-
|-
Line 356: Line 403:
| |  
| |  
| |  
| |  
| | 677.28
| | 677.280…
| | <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ+1 φ+1 φ+1 1</span>
|903.040…
| |<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"><nowiki>φ+1 φ+1|φ+1 1</nowiki></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..)
|-
|-
Line 363: Line 411:
| | 57\101
| | 57\101
| |  
| |  
| | 677.228
| | 677.227…
| | [[Tel:13 13 13 5|13 13 13 5]]
|902.970"
| | <nowiki>13 13|13 5</nowiki>
| | 13;5 Superdiatonic 1/13-tone
| | 13;5 Superdiatonic 1/13-tone
|-
|-
Line 370: Line 419:
| |  
| |  
| |  
| |  
| | 676.923
| | 676.923…
| | 5 5 5 2
|902.564…
| | <nowiki>5 5|5 2</nowiki>
| | 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>
|-
|-
Line 377: Line 427:
| | 75\133
| | 75\133
| |  
| |  
| | 676.692
| | 676.691…
| | [[Tel:17 17 17 7|17 17 17 7]]
|902.255…
| | <nowiki>17 17|17 7</nowiki>
| | 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>
|-
|-
Line 384: Line 435:
| | 53\94
| | 53\94
| |  
| |  
| | 676.596
| | 676.5̄9̄6̄
| | [[Tel:12 12 12 5|12 12 12 5]]
|902.127…
| | <nowiki>12 12|12 5</nowiki>
| |  
| |  
|-
|-
Line 391: Line 443:
| | 31\55
| | 31\55
| |  
| |  
| | 676.364
| | 676.3̄6̄
| | 7 7 7 3
|901.8̄1̄
| | <nowiki>7 7|7 3</nowiki>
| | 7;3 Superdiatonic 1/7-tone
| | 7;3 Superdiatonic 1/7-tone
|-
|-
Line 398: Line 451:
| | 40\71
| | 40\71
| |  
| |  
| | 676.056
| | 676.056…
| | 9 9 9 4
|901.408…
| | <nowiki>9 9|9 4</nowiki>
| | 9;4 Superdiatonic 1/9-tone
| | 9;4 Superdiatonic 1/9-tone
|-
|-
Line 405: Line 459:
| | 49\87
| | 49\87
| |  
| |  
| | 675.862
| | 675.862…
| | [[Tel:11 11 11 5|11 11 11 5]]
|901.149…
| | <nowiki>11 11|11 5</nowiki>
| | 11;5 Superdiatonic 1/11-tone
| | 11;5 Superdiatonic 1/11-tone
|-
|-
Line 412: Line 467:
| | 58\103
| | 58\103
| |  
| |  
| | 675.728
| | 675.728…
| | [[Tel:13 13 13 6|13 13 13 6]]
|900.970…
| | <nowiki>13 13|13 6</nowiki>
| | 13;6 Superdiatonic 1/13-tone
| | 13;6 Superdiatonic 1/13-tone
|-
|-
Line 420: Line 476:
| |  
| |  
| | 675
| | 675
| | 2 2 2 1
|900
| | <nowiki>2 2|2 1</nowiki>
| | <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)
|-
|-
Line 426: Line 483:
| | 59\105
| | 59\105
| |  
| |  
| | 674.286
| | 674.285…
| | [[Tel:13 13 13 7|13 13 13 7]]
|899.047…
| | <nowiki>13 13|13 7</nowiki>
| | Armodue-Mavila 1/13-tone
| | Armodue-Mavila 1/13-tone
|-
|-
Line 433: Line 491:
| | 50\89
| | 50\89
| |  
| |  
| | 674.157
| | 674.157…
| | [[Tel:11 11 11 6|11 11 11 6]]
|898.876…
| | <nowiki>11 11|11 6</nowiki>
| | Armodue-Mavila 1/11-tone
| | Armodue-Mavila 1/11-tone
|-
|-
Line 440: Line 499:
| | 41\73
| | 41\73
| |  
| |  
| | 673.973
| | 673.9̄7̄3̄
| | 9 9 9 5
|898.630…
| | <nowiki>9 9|9 5</nowiki>
| | 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>
|-
|-
Line 447: Line 507:
| | 32\57
| | 32\57
| |  
| |  
| | 673.684
| | 673.684…
| | 7 7 7 4
|898.245…
| | <nowiki>7 7|7 4</nowiki>
| | 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>
|-
|-
Line 454: Line 515:
| |  
| |  
| |  
| |  
| | 673.577
| | 673.577…
| | <span style="background-color: #ffffff;">√3 √3 √3 1</span>
|898.102…
| |<span style="background-color: #ffffff;"><nowiki>√3 √3|√3 1</nowiki></span>
| |  
| |  
|-
|-
| |
| |  
| |  
| | 55\98
| | 55\98
| | 673.469…
|897.959…
| | <nowiki>12 12|12 7</nowiki>
| |  
| |  
| | 673.469
|-
| | [[Tel:12 12 12 7|12 12 12 7]]
| |  
| |  
|-
| |  
| |  
| | 78\139
| | 78\139
| |  
| | 673.381…
| | 673.381
|897.841…
| | [[Tel:17 17 17 10|17 17 17 10]]
| | <nowiki>17 17|17 10</nowiki>
| | Armodue-Mavila 1/17-tone
| | Armodue-Mavila 1/17-tone
|-
|-
| |
| |  
| |  
| | 101\180
| | 101\180
| | 673.3̄
|897.7̄
| | <nowiki>22 22|22 13</nowiki>
| |  
| |  
| | 673.333
|-
| | [[Tel:22 22 22 13|22 22 22 13]]
| |  
| |  
|-
| | 23\41
| | 23\41
| |  
| |  
| |  
| | 673.170…
| | 673.171
|897.560…
| | 5 5 5 3
| | <nowiki>5 5|5 3</nowiki>
| | 5;3 Golden Armodue-Mavila 1/5-tone
| | 5;3 Golden Armodue-Mavila 1/5-tone
|-
|-
| |
| |  
| |  
| | 60\107
| | 60\107
| |  
| | 672.897…
| | 672.897
|897.196…
| | [[Tel:13 13 13 8|13 13 13 8]]
| | <nowiki>13 13|13 8</nowiki>
| | 13;8 Golden Mavila 1/13-tone
| | 13;8 Golden Mavila 1/13-tone
|-
|-
Line 496: Line 563:
| |  
| |  
| |  
| |  
| | 672.85
| | 672.850…
| | <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1</span>
|897.133…
| |<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"><nowiki>φ φ|φ 1</nowiki></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>
|-
|-
Line 503: Line 571:
| |  
| |  
| | 97\173
| | 97\173
| | 672.832
| | 672.832…
| | [[Tel:21 21 21 13|21 21 21 13]]
|897.109…
| | <nowiki>21 21|21 13</nowiki>
| | 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>
|-
|-
Line 510: Line 579:
| | 37\66
| | 37\66
| |  
| |  
| | 672.727
| | 672.7̄2̄
|896.9̄6̄
| | 8 8 8 5
| | 8 8 8 5
| | 8;5 Golden Mavila 1/8-tone
| | 8;5 Golden Mavila 1/8-tone
Line 517: Line 587:
| | 51\91
| | 51\91
| |  
| |  
| | 672.527
| | 672.527…
| | [[Tel:11 11 11 7|11 11 11 7]]
|896.703…
| | <nowiki>11 11|11 7</nowiki>
| | 11;7 Superdiatonic 1/11-tone
| | 11;7 Superdiatonic 1/11-tone
|-
|-
Line 524: Line 595:
| |  
| |  
| |  
| |  
| | 672.523
| | 672.522…
| | π π π 2
|869.697…
| | <nowiki>π π|π 2</nowiki>
| |  
| |  
|-
|-
Line 531: Line 603:
| |  
| |  
| | 116\207
| | 116\207
| | 672.464
| | 672.464…
| | [[Tel:25 25 25 16|25 25 25 16]]
|896.618…
| | <nowiki>25 25|25 16</nowiki>
| | 25;16 Superdiatonic 1/25-tone
| | 25;16 Superdiatonic 1/25-tone
|-
|-
Line 538: Line 611:
| | 65\116
| | 65\116
| |  
| |  
| | 672.414
| | 672.413…
| | [[Tel:14 14 14 9|14 14 14 9]]
|896.551…
| | <nowiki>14 14|14 9</nowiki>
| | 14;9 Superdiatonic 1/14-tone
| | 14;9 Superdiatonic 1/14-tone
|-
|-
Line 545: Line 619:
| | 79\141
| | 79\141
| |  
| |  
| | 672.340
| | 672.340…
| | [[Tel:17 17 17 11|17 17 17 11]]
|896.453…
| | <nowiki>17 17|17 11</nowiki>
| | 17;11 Superdiatonic 1/17-tone
| | 17;11 Superdiatonic 1/17-tone
|-
|-
Line 552: Line 627:
| | 93\166
| | 93\166
| |  
| |  
| | 672.289
| | 672.289…
| | [[Tel:20 20 20 13|20 20 20 13]]
|896.385…
| | <nowiki>20 20|20 13</nowiki>
| |  
| |  
|-
|-
Line 559: Line 635:
| | 107\191
| | 107\191
| |  
| |  
| | 672.251
| | 672.251…
| | [[Tel:23 23 23 15|23 23 23 15]]
|896.335…
| | <nowiki>23 23|23 15</nowiki>
| |  
| |  
|-
|-
Line 566: Line 643:
| | 121\216
| | 121\216
| |  
| |  
| | 672.222
| | 672.2̄
| | [[Tel:26 26 26 17|26 26 26 17]]
|896.2̄9̄6̄
| | <nowiki>26 26|26 17</nowiki>
| | 26;17 Superdiatonic 1/26-tone
| | 26;17 Superdiatonic 1/26-tone
|-
|-
Line 573: Line 651:
| | 135\241
| | 135\241
| |  
| |  
| | 672.199
| | 672.199…
| | [[Tel:29 29 29 19|29 29 29 19]]
|896.265…
| | <nowiki>29 29|29 19</nowiki>
| | 29;19 Superdiatonic 1/29-tone
| | 29;19 Superdiatonic 1/29-tone
|-
|-
Line 581: Line 660:
| |  
| |  
| | 672
| | 672
| | 3 3 3 2
|896
| | <nowiki>3 3|3 2</nowiki>
| | 3;2 Golden Armodue-Mavila 1/3-tone
| | 3;2 Golden Armodue-Mavila 1/3-tone
|-
|-
Line 587: Line 667:
| | 145\259
| | 145\259
| |  
| |  
| | 671.815
| | 671.814…
| | [[Tel:31 31 31 21|31 31 31 21]]
|895.752…
| | <nowiki>31 31|31 21</nowiki>
| | 31;21 Superdiatonic 1/31-tone
| | 31;21 Superdiatonic 1/31-tone
|-
|-
Line 594: Line 675:
| | 131\234
| | 131\234
| |  
| |  
| | 671.795
| | 671.794…
| | [[Tel:28 28 28 19|28 28 28 19]]
|895.726…
| | <nowiki>28 28|28 19</nowiki>
| | 28;19 Superdiatonic 1/28-tone
| | 28;19 Superdiatonic 1/28-tone
|-
|-
Line 601: Line 683:
| | 117\209
| | 117\209
| |  
| |  
| | 671.770
| | 671.770…
| | [[Tel:25 25 25 17|25 25 25 17]]
|895.693…
| | <nowiki>25 25|25 17</nowiki>
| |  
| |  
|-
|-
Line 608: Line 691:
| | 103\184
| | 103\184
| |  
| |  
| | 671.739
| | 671.739…
| | [[Tel:22 22 22 15|22 22 22 15]]
|895.652…
| | <nowiki>22 22|22 15</nowiki>
| |  
| |  
|-
|-
Line 615: Line 699:
| | 89\159
| | 89\159
| |  
| |  
| | 671.698
| | 671.698…
| | [[Tel:19 19 19 13|19 19 19 13]]
|895.579…
| | <nowiki>19 19|19 13</nowiki>
| |  
| |  
|-
|-
Line 622: Line 707:
| | 75\134
| | 75\134
| |  
| |  
| | 671.642
| | 671.641…
| | [[Tel:16 16 16 11|16 16 16 11]]
|895.522…
| | <nowiki>16 16|16 11</nowiki>
| |  
| |  
|-
|-
Line 629: Line 715:
| | 61\109
| | 61\109
| |  
| |  
| | 671.560
| | 671.559…
| | [[Tel:13 13 13 9|13 13 13 9]]
|895.412…
| | <nowiki>13 13|13 9</nowiki>
| |  
| |  
|-
|-
Line 636: Line 723:
| | 47\84
| | 47\84
| |  
| |  
| | 671.429
| | 671.428…
| | [[Tel:10 10 10 7|10 10 10 7]]
|895.238…
| | <nowiki>10 10|10 7</nowiki>
| |  
| |  
|-
|-
Line 643: Line 731:
|
|
|80\143
|80\143
|671.329
|671.328…
|[[Tel:17 17 17 12|17 17 17 12]]
|895.104…
|<nowiki>17 17|17 12</nowiki>
|
|
|-
|-
Line 650: Line 739:
| | 33\59
| | 33\59
| |  
| |  
| | 671.186
| | 671.186…
| | 7 7 7 5
|894.915…
| | <nowiki>7 7|7 5</nowiki>
| |  
| |  
|-
|-
Line 657: Line 747:
|52\93
|52\93
|
|
|670.968
|670.967…
|[[Tel:11 11 11 8|11 11 11 8]]
|894.623…
|<nowiki>11 11|11 8</nowiki>
|
|
|-
|-
Line 664: Line 755:
| |  
| |  
| |  
| |  
| | 670.588
| | 670.588…
| | 4 4 4 3
|894.117…
| | <nowiki>4 4|4 3</nowiki>
| |  
| |  
|-
|-
Line 671: Line 763:
|43\77
|43\77
|
|
|670.13
|670.129…
|9 9 9 7
|893.506…
|<nowiki>9 9|9 7</nowiki>
|
|
|-
|-
Line 678: Line 771:
| |  
| |  
| |  
| |  
| | 669.767
| | 669.767…
| | 5 5 5 4
|893.023…
| | <nowiki>5 5|5 4</nowiki>
| |  
| |  
|-
|-
Line 685: Line 779:
|53\95
|53\95
|
|
|669.474
|669.473…
|[[Tel:11 11 11 9|11 11 11 9]]
|892.631…
|<nowiki>11 11|11 9</nowiki>
|
|
|-
|-
Line 692: Line 787:
|
|
|
|
|669.231
|669.230…
|6 6 6 5
|892.308…
|<nowiki>6 6|6 5</nowiki>
|
|
|-
|-
Line 699: Line 795:
|63\113
|63\113
|
|
|[[Tel:669.0265|669.0265]]
|669.026…
|[[Tel:13 13 13 11|13 13 13 11]]
|892.035…
|<nowiki>13 13|13 11</nowiki>
|
|
|-
|-
Line 706: Line 803:
|
|
|
|
|[[Tel:668.8525|668.8525]]
|668.852…
|7 7 7 6
|891.803…
|<nowiki>7 7|7 6</nowiki>
|
|
|-
|-
Line 713: Line 811:
|73\131
|73\131
|
|
|668.702
|668.702…
|[[Tel:15 15 15 13|15 15 15 13]]
|891.603…
|<nowiki>15 15|15 13</nowiki>
|
|
|-
|-
Line 720: Line 819:
|
|
|
|
|668.571
|668.571…
|8 8 8 7
|891.428…
|<nowiki>8 8|8 7</nowiki>
|
|
|-
|-
Line 727: Line 827:
|83\149
|83\149
|
|
|668.456
|668.456…
|[[Tel:17 17 17 15|17 17 17 15]]
|891.275…
|<nowiki>17 17|17 15</nowiki>
|
|
|-
|-
Line 734: Line 835:
|
|
|
|
|668.354
|668.354…
|9 9 9 8
|891.139…
|<nowiki>9 9|9 8</nowiki>
|
|
|-
|-
Line 741: Line 843:
|93\167
|93\167
|
|
|[[Tel:668.2365|668.2365]]
|668.236…
|[[Tel:19 19 19 17|19 19 19 17]]
|891.017…
|<nowiki>19 19|19 17</nowiki>
|
|
|-
|-
Line 748: Line 851:
|
|
|
|
|668.182
|668.1̄8̄
|[[Tel:10 10 10 9|10 10 10 9]]
|890.9̄0̄
|<nowiki>10 10|10 9</nowiki>
|
|
|-
|-
Line 755: Line 859:
|103\185
|103\185
|
|
|668.108
|668.1̄0̄8̄
|[[Tel:21 21 21 9|21 21 21 9]]
|890.8̄1̄0̄
|<nowiki>21 21|21 9</nowiki>
|
|
|-
|-
Line 762: Line 867:
|
|
|
|
|668.041
|668.041…
|[[Tel:11 11 11 10|11 11 11 10]]
|890.721…
|<nowiki>11 11|11 10</nowiki>
|
|
|-
|-
Line 769: Line 875:
|113\203
|113\203
|
|
|667.98
|667.980…
|[[Tel:23 23 23 21|23 23 23 21]]
|890.640…
|<nowiki>23 23|23 21</nowiki>
|
|
|-
|-
Line 776: Line 883:
|
|
|
|
|667.925
|667.924…
|[[Tel:12 12 12 11|12 12 12 11]]
|890.566…
|<nowiki>12 12|12 11</nowiki>
|
|
|-
|-
Line 783: Line 891:
|123\221
|123\221
|
|
|667.873
|667.873…
|[[Tel:25 25 25 23|25 25 25 23]]
|890.497…
|<nowiki>25 25|25 23</nowiki>
|
|
|-
|-
Line 790: Line 899:
|
|
|
|
|667.826
|667.826…
|[[Tel:13 13 13 12|13 13 13 12]]
|890.434…
|<nowiki>13 13|13 12</nowiki>
|
|
|-
|-
Line 797: Line 907:
|
|
|
|
|667.742
|667.741…
|14 14 14 13
|890.325…
|<nowiki>14 14|14 13</nowiki>
|
|-
|74\133
|
|
|667.669…
|890.225…
|<nowiki>15 15|15 14</nowiki>
|
|-
|79\142
|
|
|667.605…
|890.140…
|<nowiki>16 16|16 15</nowiki>
|
|-
|84\151
|
|
|667.549…
|890.662…
|<nowiki>17 17|17 16</nowiki>
|
|-
|89\160
|
|
|667.5
|890
|<nowiki>18 18|18 17</nowiki>
|
|-
|94\169
|
|
|667.455…
|889.940…
|<nowiki>19 19|19 18</nowiki>
|
|
|-
|-
Line 804: Line 955:
| |  
| |  
| |  
| |  
| | 666.667
| | 666.6̄
|888.8̄
| | 1 1 1 1
| | 1 1 1 1
| |  
| |  

Revision as of 03:07, 21 August 2021

↖ 6L 1s ↑ 7L 1s 8L 1s ↗
← 6L 2s 7L 2s 8L 2s →
↙ 6L 3s ↓ 7L 3s 8L 3s ↘ 
┌╥╥╥╥┬╥╥╥┬┐
│║║║║│║║║││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLs
sLLLsLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\9 to 4\7 (666.7 ¢ to 685.7 ¢)
Dark 3\7 to 4\9 (514.3 ¢ to 533.3 ¢)
TAMNAMS information
Name armotonic
Prefix arm-
Abbrev. arm
Related MOS scales
Parent 2L 5s
Sister 2L 7s
Daughters 9L 7s, 7L 9s
Neutralized 5L 4s
2-Flought 16L 2s, 7L 11s
Equal tunings
Equalized (L:s = 1:1) 5\9 (666.7 ¢)
Supersoft (L:s = 4:3) 19\34 (670.6 ¢)
Soft (L:s = 3:2) 14\25 (672.0 ¢)
Semisoft (L:s = 5:3) 23\41 (673.2 ¢)
Basic (L:s = 2:1) 9\16 (675.0 ¢)
Semihard (L:s = 5:2) 22\39 (676.9 ¢)
Hard (L:s = 3:1) 13\23 (678.3 ¢)
Superhard (L:s = 4:1) 17\30 (680.0 ¢)
Collapsed (L:s = 1:0) 4\7 (685.7 ¢)

This page is about of a MOSScale with 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).

Name

The name superdiatonic has been established by Armodue theorists, and so TAMNAMS adopts it as well.

Temperaments

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 mavila is an important harmonic entropy minimum here. So a general name for this MOS pattern could be "Mavila Superdiatonic" or simply 'Superdiatonic'.

These scales are strongly associated with the Armodue project/system applied to septimal mavila and Hornbostel temperaments.

Intervals

Note: In TAMNAMS, a k-step interval class in superdiatonic may be called a "k-step", "k-mosstep", or "k-armstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.

Scale tree

Optional types of 'JI Blown Fifth' Generators: 31/21, 34/23, 65/44, 71/48, 99/67, 105/71, 108/73, 133/90, 145/98, 176/119 & 250/169.

Generator Generator size (cents) Generator size (sats) Pentachord steps Comments
4\7 685.714… 914.286… 1 1|1 0
57\100 684 912 14 14|14 1
53\93 683.870… 911.827… 13 13|13 1
102\179 683.798… 911.731… 25 25|25 2 Approximately 0.03 cents away from 95/64
49\86 683.720… 911.527… 12 12|12 1
94\165 683.6̄3̄ 911.5̄1̄ 23 23|23 2
45\79 683.544… 911.392… 11 11|11 1
86\151 683.443… 911.258… 21 21|21 2
41\72 683.3̄ 911.1̄ 10 10|10 1
78\137 683.211… 910.948… 19 19|19 2
37\65 683.076… 910.769… 9 9|9 1
70\123 682.926… 910.569… 17 17|17 2
33\58 682.758… 910.344… 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.
62\109 682.568… 910.091… 15 15|15 2
29\51 682.352… 909.803… 7 7|7 1
54\95 682.105… 909.473… 13 13|13 2
25\44 681.8̄1̄ 909.0̄9̄ 6 6|6 1
46\81 681.4̄8̄1̄ 908.641… 11 11|11 2
21\37 681.0̄8̄1̄ 908.1̄0̄8̄ 5 5|5 1
59\104 680.769… 907.692… 14 14|14 3
38\67 680.597… 907.462… 9 9|9 2
55\97 680.412… 907.216… 13 13|13 3
17\30 680 906.6̄ 4 4|4 1 L/s = 4
47\83 679.518… 906.024… 11 11|11 3
30\53 679.245… 905.660… 7 7|7 2
43\76 678.947… 905.263… 10 10|10 3
56\99 678.7̄8̄ 905.0̄5̄ 13 13|13 4
69\122 678.688… 904.918… 16 16|16 5
82\145 678.620… 904.827… 19 19|19 6
95\168 678.571… 904.761… 22 22|22 7
678.568… 904.758… π π|π 1 L/s = π
108\191 678.534… 904.712… 25 25|25 8
121\214 678.504… 904.672… 28 28|28 9 28;9 Superdiatonic 1/28-tone (a slight exceeded representation of the Pythagorean wolf Fifth)
134\237 678.481… 904.642… 31 31|31 10 HORNBOSTEL TEMPERAMENT (1/31-tone; Optimum high size of Hornbostel '6th')
13\23 678.260… 904.347… 3 3|3 1 HORNBOSTEL TEMPERAMENT (Armodue 1/3-tone)
126\223 678.026… 904.035… 29 29|29 10 HORNBOSTEL TEMPERAMENT

(Armodue 1/29-tone)

113\200 678 904 26 26|26 9 HORNBOSTEL (& OGOLEVETS) TEMPERAMENT (Armodue 1/26-tone; Best equillibrium between 6/5, Phi (833.1 Cent) and Square root of Pi (990.9 Cent), the notes '3', '7' & '8')
100\177 677.966… 903.954… 23 23|23 8
87\154 677.922… 903.896… 20 20|20 7
74\131 677.862… 903.816… 17 17|17 6 Armodue-Hornbostel 1/17-tone (the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)
61\108 677.7̄ 903.7̄0̄3̄ 14 14|14 5 Armodue-Hornbostel 1/14-tone
109\193 677.720… 903.626… 25 25|25 9 Armodue-Hornbostel 1/25-tone
48\85 677.647… 903.529… 11 11|11 4 Armodue-Hornbostel 1/11-tone (Optimum accuracy of Phi interval, the note '7')
677.561… 903.415… e e|e 1 L/s = e
35\62 677.419… 903.225… 8 8|8 3 Armodue-Hornbostel 1/8-tone
92\163 677.300… 903.067… 21 21|21 8 21;8 Superdiatonic 1/21-tone
677.280… 903.040… φ+1 φ+1|φ+1 1 Split φ superdiatonic relation (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..)
57\101 677.227… 902.970" 13 13|13 5 13;5 Superdiatonic 1/13-tone
22\39 676.923… 902.564… 5 5|5 2 Armodue-Hornbostel 1/5-tone (Optimum low size of Hornbostel '6th')
75\133 676.691… 902.255… 17 17|17 7 17;7 Superdiatonic 1/17-tone (Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)
53\94 676.5̄9̄6̄ 902.127… 12 12|12 5
31\55 676.3̄6̄ 901.8̄1̄ 7 7|7 3 7;3 Superdiatonic 1/7-tone
40\71 676.056… 901.408… 9 9|9 4 9;4 Superdiatonic 1/9-tone
49\87 675.862… 901.149… 11 11|11 5 11;5 Superdiatonic 1/11-tone
58\103 675.728… 900.970… 13 13|13 6 13;6 Superdiatonic 1/13-tone
9\16 675 900 2 2|2 1 [BOUNDARY OF PROPRIETY: smaller generators are strictly proper]ARMODUE ESADECAFONIA (or Goldsmith Temperament)
59\105 674.285… 899.047… 13 13|13 7 Armodue-Mavila 1/13-tone
50\89 674.157… 898.876… 11 11|11 6 Armodue-Mavila 1/11-tone
41\73 673.9̄7̄3̄ 898.630… 9 9|9 5 Armodue-Mavila 1/9-tone (with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)
32\57 673.684… 898.245… 7 7|7 4 Armodue-Mavila 1/7-tone (the 'Commatic' version of Armodue, because its high accuracy of the 7/4 interval, the note '8')
673.577… 898.102… √3 √3|√3 1
55\98 673.469… 897.959… 12 12|12 7
78\139 673.381… 897.841… 17 17|17 10 Armodue-Mavila 1/17-tone
101\180 673.3̄ 897.7̄ 22 22|22 13
23\41 673.170… 897.560… 5 5|5 3 5;3 Golden Armodue-Mavila 1/5-tone
60\107 672.897… 897.196… 13 13|13 8 13;8 Golden Mavila 1/13-tone
672.850… 897.133… φ φ|φ 1 GOLDEN MAVILA (L/s = φ)
97\173 672.832… 897.109… 21 21|21 13 21;13 Golden Mavila 1/21-tone (Phi is the step 120\173)
37\66 672.7̄2̄ 896.9̄6̄ 8 8 8 5 8;5 Golden Mavila 1/8-tone
51\91 672.527… 896.703… 11 11|11 7 11;7 Superdiatonic 1/11-tone
672.522… 869.697… π π|π 2
116\207 672.464… 896.618… 25 25|25 16 25;16 Superdiatonic 1/25-tone
65\116 672.413… 896.551… 14 14|14 9 14;9 Superdiatonic 1/14-tone
79\141 672.340… 896.453… 17 17|17 11 17;11 Superdiatonic 1/17-tone
93\166 672.289… 896.385… 20 20|20 13
107\191 672.251… 896.335… 23 23|23 15
121\216 672.2̄ 896.2̄9̄6̄ 26 26|26 17 26;17 Superdiatonic 1/26-tone
135\241 672.199… 896.265… 29 29|29 19 29;19 Superdiatonic 1/29-tone
14\25 672 896 3 3|3 2 3;2 Golden Armodue-Mavila 1/3-tone
145\259 671.814… 895.752… 31 31|31 21 31;21 Superdiatonic 1/31-tone
131\234 671.794… 895.726… 28 28|28 19 28;19 Superdiatonic 1/28-tone
117\209 671.770… 895.693… 25 25|25 17
103\184 671.739… 895.652… 22 22|22 15
89\159 671.698… 895.579… 19 19|19 13
75\134 671.641… 895.522… 16 16|16 11
61\109 671.559… 895.412… 13 13|13 9
47\84 671.428… 895.238… 10 10|10 7
80\143 671.328… 895.104… 17 17|17 12
33\59 671.186… 894.915… 7 7|7 5
52\93 670.967… 894.623… 11 11|11 8
19\34 670.588… 894.117… 4 4|4 3
43\77 670.129… 893.506… 9 9|9 7
24\43 669.767… 893.023… 5 5|5 4
53\95 669.473… 892.631… 11 11|11 9
29\52 669.230… 892.308… 6 6|6 5
63\113 669.026… 892.035… 13 13|13 11
34\61 668.852… 891.803… 7 7|7 6
73\131 668.702… 891.603… 15 15|15 13
39\70 668.571… 891.428… 8 8|8 7
83\149 668.456… 891.275… 17 17|17 15
44\79 668.354… 891.139… 9 9|9 8
93\167 668.236… 891.017… 19 19|19 17
49\88 668.1̄8̄ 890.9̄0̄ 10 10|10 9
103\185 668.1̄0̄8̄ 890.8̄1̄0̄ 21 21|21 9
54\97 668.041… 890.721… 11 11|11 10
113\203 667.980… 890.640… 23 23|23 21
59\106 667.924… 890.566… 12 12|12 11
123\221 667.873… 890.497… 25 25|25 23
64\115 667.826… 890.434… 13 13|13 12
69\124 667.741… 890.325… 14 14|14 13
74\133 667.669… 890.225… 15 15|15 14
79\142 667.605… 890.140… 16 16|16 15
84\151 667.549… 890.662… 17 17|17 16
89\160 667.5 890 18 18|18 17
94\169 667.455… 889.940… 19 19|19 18
5\9 666.6̄ 888.8̄ 1 1 1 1
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