Scala analysis: west12
Wilson Encompassing Spectrum Tuning (Metameantone-based)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 69.413 cents 69.413060 2: 191.261 cents 191.260870 3: 286.891 cents 286.891310 4: 382.522 cents 382.521750 5: 504.370 cents 504.369560 6: 573.783 cents 573.782620 7: 695.630 cents 695.630440 8: 778.152 cents 778.152190 9: 886.891 cents 886.891310 10: 995.630 cents 995.630440 11: 1078.152 cents 1078.152180 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 121.8478 cents 121.8478 1: 69.4131 cents 69.4131 2: 121.8478 cents 121.8478 3: 95.6304 cents 95.6304 4: 95.6304 cents 95.6304 5: 121.8478 cents 121.8478 6: 69.4131 cents 69.4131 7: 121.8478 cents 121.8478 8: 82.5218 cents 82.5218 9: 108.7391 cents 108.7391 10: 108.7391 cents 108.7391 11: 82.5217 cents 82.5217 12: 121.8478 cents 121.8478
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 69.41306 cents 1: 2 82.52175 cents 1: 2 95.63044 cents 1: 2 108.73912 cents 1: 4 121.84781 cents 2: 7 191.26087 cents 2: 2 204.36957 cents 2: 3 217.47825 cents 3: 2 273.78263 cents 3: 2 286.89131 cents 3: 2 300.00000 cents 3: 6 313.10869 cents 4: 5 382.52175 cents 4: 2 395.63044 cents 4: 2 408.73913 cents 4: 2 421.84782 cents 4: 1 434.95650 cents 5: 4 491.26088 cents 5: 8 504.36956 cents 6: 3 573.78262 cents 6: 2 586.89132 cents 6: 2 600.00000 cents 6: 2 613.10869 cents 6: 3 626.21738 cents 7: 8 695.63044 cents 7: 4 708.73913 cents 8: 1 765.04350 cents 8: 2 778.15219 cents 8: 2 791.26087 cents 8: 2 804.36957 cents 8: 5 817.47825 cents 9: 6 886.89131 cents 9: 2 900.00000 cents 9: 2 913.10869 cents 9: 2 926.21738 cents 10: 3 982.52175 cents 10: 2 995.63044 cents 10: 7 1008.73912 cents 11: 4 1078.15218 cents 11: 2 1091.26088 cents 11: 2 1104.36956 cents 11: 2 1117.47825 cents 11: 2 1130.58694 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.90909 = 43/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 69.4 191.3 286.9 382.5 504.4 573.8 695.6 778.2 886.9 995.6 1078.2 1200.0 69.4 : 121.8 217.5 313.1 435.0 504.4 626.2 708.7 817.5 926.2 1008.7 1130.6 1200.0 191.3 : 95.6 191.3 313.1 382.5 504.4 586.9 695.6 804.4 886.9 1008.7 1078.2 1200.0 286.9 : 95.6 217.5 286.9 408.7 491.3 600.0 708.7 791.3 913.1 982.5 1104.4 1200.0 382.5 : 121.8 191.3 313.1 395.6 504.4 613.1 695.6 817.5 886.9 1008.7 1104.4 1200.0 504.4 : 69.4 191.3 273.8 382.5 491.3 573.8 695.6 765.0 886.9 982.5 1078.2 1200.0 573.8 : 121.8 204.4 313.1 421.8 504.4 626.2 695.6 817.5 913.1 1008.7 1130.6 1200.0 695.6 : 82.5 191.3 300.0 382.5 504.4 573.8 695.6 791.3 886.9 1008.7 1078.2 1200.0 778.2 : 108.7 217.5 300.0 421.8 491.3 613.1 708.7 804.4 926.2 995.6 1117.5 1200.0 886.9 : 108.7 191.3 313.1 382.5 504.4 600.0 695.6 817.5 886.9 1008.7 1091.3 1200.0 995.6 : 82.5 204.4 273.8 395.6 491.3 586.9 708.7 778.2 900.0 982.5 1091.3 1200.0 1078.2: 121.8 191.3 313.1 408.7 504.4 626.2 695.6 817.5 900.0 1008.7 1117.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 69.4131 .. 121.8478 cents 52.43475 cents 69.41306 cents 2: 191.2609 .. 217.4782 cents 26.21738 cents 69.41306 cents 3: 273.7826 .. 313.1087 cents 39.32606 cents 56.30438 cents 4: 382.5217 .. 434.9565 cents 52.43475 cents 69.41306 cents 5: 491.2609 .. 504.3696 cents 13.10868 cents 56.30438 cents 6: 573.7826 .. 626.2174 cents 52.43476 cents 69.41306 cents 7: 695.6304 .. 708.7391 cents 13.10869 cents 69.41306 cents 8: 765.0435 .. 817.4782 cents 52.43475 cents 56.30437 cents 9: 886.8913 .. 926.2174 cents 39.32607 cents 69.41306 cents 10: 982.5217 .. 1008.7391 cents 26.21737 cents 56.30437 cents 11: 1078.1522 .. 1130.5869 cents 52.43476 cents 69.41306 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 69.41306 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 121.84781 cents Average / Smallest step : 1.440651 Largest / Average step : 1.218478 Largest / Smallest step : 1.755402 Median interval of one step : 102.18478 cents, amount: 0 Most common interval of one step : 121.84781 cents, amount: 4 Least squares average step : 98.61518 cents, oct.: 1183.38222 cents Scale is strictly proper Scale is a mode of a 1556-tone equal temperament with octave 2/1 degrees: 90 248 372 496 654 744 902 1009 1150 1291 1398 1556 Least number of segments generator : 779 of 600.771 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 981 of 756.555 cents and inv. generated superset size: 1043 = 1031 more = 8691.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCCBABDEEDB Step pattern size order : AECCEAEBDDBE Scale is a Constant Structure, by a margin of 56.30437 cents Scale diversity : 1.301532 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.650435 Rothenberg efficiency : 0.314478 redundancy: 0.685522 Efficiency x scale size : 3.773737 Number of different interval sizes : 43 = 3.90909 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 3.90909 = 43/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 13.10868 cents Most common intervals : 504.36956 cents & inv., amount: 8 Most common triad is 0.0 504.370 695.630 cents, amount: 7 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 52.4348 cents: 5 7 10 Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 9 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 16.7342 c. M:-30.5869 c. Twelve-tone Chromatic (1/11-comma) 17: 1 2 1 1 2 1 2 1 2 1 1 2 P M ME SD: 15.7771 c. M:-30.7557 c. 18: 1 2 1 2 2 1 1 2 1 2 1 2 P D3 SD: 18.7104 c. M: 28.9638 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 11.4744 c. M:-28.8982 c. Meantone Chromatic (1/3-comma) 20: 1 2 2 1 2 2 2 1 2 2 1 2 P D3 SD: 17.1807 c. M:-26.2174 c. 21: 1 2 2 2 2 1 2 2 2 1 2 2 P D3 SD: 15.6089 c. M:-27.3944 c. 23: 1 3 1 2 3 1 2 2 2 2 2 2 P D3 SD: 14.5086 c. M: 26.0217 c. 26: 1 3 2 2 3 1 3 2 2 2 2 3 P D3 S SD: 14.1268 c. M: 26.3997 c. 29: 2 3 2 2 3 2 3 2 2 3 2 3 SP M ME SD: 9.5001 c. M: 17.9258 c. Schismic-12 31: 2 3 2 3 3 2 3 2 3 3 2 3 SP M ME SD: 6.8968 c. M: 15.9236 c. 35: 2 4 2 3 4 2 3 3 3 3 2 4 SP SD: 9.3155 c. M: 15.2950 c. 37: 2 4 3 3 4 2 3 3 3 4 2 4 SP SD: 8.6995 c. M: 14.5494 c. 38: 2 4 3 3 4 2 4 3 3 3 3 4 SP D3 S SD: 6.6224 c. M: 16.6831 c. 40: 2 4 4 3 4 2 4 3 4 3 3 4 SP SD: 7.8063 c. M:-13.1087 c. 42: 2 5 3 3 5 2 4 3 4 4 3 4 SP S SD: 7.5080 c. M: 12.2702 c. 46: 3 4 4 4 4 3 5 3 4 4 3 5 SP D3 S SD: 6.4200 c. M:-8.8478 c. 50: 3 5 4 4 5 3 5 3 5 4 4 5 SP D3 SD: 4.6442 c. M: 11.6304 c. 57: 3 6 4 5 6 3 6 4 5 5 4 6 SP SD: 5.2086 c. M: 13.2071 c. 65: 4 6 6 5 6 4 7 4 6 6 4 7 SP SD: 4.9921 c. M:-8.4933 c. 66: 4 7 5 5 7 4 6 5 6 6 4 7 SP SD: 4.9266 c. M:-8.7391 c. 69: 4 7 5 6 7 4 7 5 6 6 5 7 SP SD: 3.0704 c. M: 8.6304 c. 71: 4 7 6 6 7 4 7 5 6 7 5 7 SP SD: 3.7117 c. M: 8.0181 c. 74: 4 8 6 6 7 4 8 5 7 6 5 8 SP SD: 4.7794 c. M: 7.8819 c. 76: 4 8 6 6 8 4 8 5 7 7 5 8 SP S SD: 3.4222 c. M: 6.2552 c. 86: 5 9 7 6 9 5 9 6 8 7 6 9 SP SD: 3.9309 c. M:-6.1319 c. 88: 5 9 7 7 9 5 9 6 8 8 6 9 SP S SD: 0.6736 c. M: 1.2312 c. 188: 11 19 15 15 19 11 19 13 17 17 13 19 SP S SD: 0.4375 c. M:-0.7997 c. 276: 16 28 22 22 28 16 28 19 25 25 19 28 SP S SD: 0.0832 c. M:-0.1522 c. 640: 37 65 51 51 65 37 65 44 58 58 44 65 SP S SD: 0.0208 c. M: 0.0381 c. 916: 53 93 73 73 93 53 93 63 83 83 63 93 SP S SD: 0.0105 c. M:-0.0193 c. 1556: 90 158 124 124 158 90 158 107 141 141 107 158 SP S SD: 0.0024 c. M: 0.0043 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 3.1623 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.2709 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.9501 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 10.2916 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.0462 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 13.1432 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 7.5926 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 8.2700 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.9404 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.5731 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 7.0310 cents 13:14 x 15:16:17:18:19:20:22:23:24:26 S SD: 9.3989 cents 14:15:16 x 17:19:20:21:22:23:25:26:28 SD: 8.9397 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 6.9287 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.5494 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 5.4952 cents 18:19:20:21:22:24:25:27:28:30:32:34:36 SD: 4.6465 cents 21:22:23:25:26:28:29:31:33:35:37:39:42 SD: 4.3030 cents 23:24:26:27:29:31:32:34:36:38:41:43:46 SD: 3.5212 cents 24:25:27:28:30:32:33:36:38:40:43:45:48 SD: 3.5032 cents 27:28:30:32:34:36:38:40:42:45:48:50:54 SD: 3.0599 cents 28:29:31:33:35:37:39:42:44:47:50:52:56 SD: 2.7163 cents 33:34:37:39:41:44:46:49:52:55:59:62:66 SD: 2.5813 cents 41:43:46:48:51:55:57:61:64:68:73:76:82 SD: 2.3832 cents 43:45:48:51:54:58:60:64:67:72:76:80:86 SD: 2.3396 cents 44:46:49:52:55:59:61:66:69:73:78:82:88 SD: 1.5586 cents 51:53:57:60:64:68:71:76:80:85:91:95:102 SD: 1.3797 cents 67:70:75:79:84:90:93:100:105:112:119:125:134 SD: 1.2807 cents 69:72:77:81:86:92:96:103:108:115:123:129:138 SD: 1.2410 cents 72:75:80:85:90:96:100:108:113:120:128:134:144 SD: 1.2336 cents 76:79:85:90:95:102:106:114:119:127:135:142:152 SD: 1.0380 cents 77:80:86:91:96:103:107:115:121:129:137:144:154 SD: 0.9536 cents 94:98:105:111:117:126:131:140:147:157:167:175:188 SD: 0.7869 cents 117:122:131:138:146:157:163:175:183:195:208:218:234 SD: 0.7277 cents 118:123:132:139:147:158:164:176:185:197:210:220:236 SD: 0.6633 cents 121:126:135:143:151:162:169:181:190:202:215:226:242 SD: 0.6208 cents 127:132:142:150:158:170:177:190:199:212:226:237:254 SD: 0.5569 cents 145:151:162:171:181:194:202:217:227:242:258:270:290 SD: 0.3961 cents 178:185:199:210:222:238:248:266:279:297:316:332:356 SD: 0.3564 cents 222:231:248:262:277:297:309:332:348:371:395:414:444 SD: 0.3018 cents 239:249:267:282:298:320:333:357:375:399:425:446:478 SD: 0.2949 cents 266:277:297:314:332:356:371:398:417:444:473:496:532 SD: 0.2904 cents 275:286:307:325:343:368:383:411:431:459:489:513:550 SD: 0.2720 cents 293:305:327:346:365:392:408:438:459:489:521:546:586 SD: 0.2588 cents 315:328:352:372:393:422:439:471:494:526:560:587:630 SD: 0.2572 cents 316:329:353:373:394:423:440:472:495:527:562:589:632 SD: 0.2231 cents 344:358:384:406:429:460:479:514:539:574:611:641:688 SD: 0.1963 cents 384:400:429:453:479:514:535:574:602:641:682:716:768 SD: 0.1830 cents 412:429:460:486:514:551:574:616:646:688:732:768:824 SD: 0.1798 cents 417:434:466:492:520:558:581:623:654:696:741:777:834 SD: 0.1604 cents 506:527:565:597:631:677:705:756:793:845:899:943:1012 SD: 0.1561 cents 514:535:574:607:641:688:716:768:806:858:914:958:1028 SD: 0.1388 cents 538:560:601:635:671:720:749:804:843:898:956:1003:1076 SD: 0.1095 cents 583:607:651:688:727:780:812:871:914:973:1036:1087:1166 SD: 0.0967 cents