Scala analysis: smith-exotic1
Exotic temperament featuring four pure 14/11 thirds and two pure fifths
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 86.062 cents 86.061694 2: 198.385 cents 198.385340 3: 310.709 cents 310.708979 4: 391.246 cents 391.246017 5: 503.570 cents 503.569655 6: 589.631 cents 589.631356 7: 701.955 cents 701.955001 8: 782.492 cents 782.492032 9: 894.816 cents 894.815678 10: 1007.139 cents 1007.139316 11: 1093.201 cents 1093.201017 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 106.7990 cents 106.7990 1: 86.0617 cents 86.0617 2: 112.3236 cents 112.3236 3: 112.3236 cents 112.3236 4: 80.5370 cents 80.5370 5: 112.3236 cents 112.3236 6: 86.0617 cents 86.0617 7: 112.3236 cents 112.3236 8: 80.5370 cents 80.5370 9: 112.3236 cents 112.3236 10: 112.3236 cents 112.3236 11: 86.0617 cents 86.0617 12: 106.7990 cents 106.7990
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 80.53704 cents 1: 3 86.06169 cents 1: 1 106.79898 cents 1: 6 112.32365 cents 2: 6 192.86068 cents 2: 4 198.38534 cents 2: 2 224.64729 cents 3: 3 278.92238 cents 3: 6 305.18432 cents 3: 3 310.70898 cents 4: 8 391.24602 cents 4: 4 417.50796 cents 5: 1 471.78305 cents 5: 2 498.04500 cents 5: 9 503.56966 cents 6: 4 584.10669 cents 6: 2 589.63136 cents 6: 2 610.36864 cents 6: 4 615.89331 cents 7: 9 696.43034 cents 7: 2 701.95500 cents 7: 1 728.21695 cents 8: 4 782.49203 cents 8: 8 808.75398 cents 9: 3 889.29102 cents 9: 6 894.81568 cents 9: 3 921.07762 cents 10: 2 975.35272 cents 10: 4 1001.61466 cents 10: 6 1007.13932 cents 11: 6 1087.67635 cents 11: 1 1093.20102 cents 11: 3 1113.93831 cents 11: 2 1119.46296 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 86.1 198.4 310.7 391.2 503.6 589.6 702.0 782.5 894.8 1007.1 1093.2 1200.0 86.1 : 112.3 224.6 305.2 417.5 503.6 615.9 696.4 808.8 921.1 1007.1 1113.9 1200.0 198.4 : 112.3 192.9 305.2 391.2 503.6 584.1 696.4 808.8 894.8 1001.6 1087.7 1200.0 310.7 : 80.5 192.9 278.9 391.2 471.8 584.1 696.4 782.5 889.3 975.4 1087.7 1200.0 391.2 : 112.3 198.4 310.7 391.2 503.6 615.9 702.0 808.8 894.8 1007.1 1119.5 1200.0 503.6 : 86.1 198.4 278.9 391.2 503.6 589.6 696.4 782.5 894.8 1007.1 1087.7 1200.0 589.6 : 112.3 192.9 305.2 417.5 503.6 610.4 696.4 808.8 921.1 1001.6 1113.9 1200.0 702.0 : 80.5 192.9 305.2 391.2 498.0 584.1 696.4 808.8 889.3 1001.6 1087.7 1200.0 782.5 : 112.3 224.6 310.7 417.5 503.6 615.9 728.2 808.8 921.1 1007.1 1119.5 1200.0 894.8 : 112.3 198.4 305.2 391.2 503.6 615.9 696.4 808.8 894.8 1007.1 1087.7 1200.0 1007.1: 86.1 192.9 278.9 391.2 503.6 584.1 696.4 782.5 894.8 975.4 1087.7 1200.0 1093.2: 106.8 192.9 305.2 417.5 498.0 610.4 696.4 808.8 889.3 1001.6 1113.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 112.3236 cents 31.78661 cents 80.53704 cents 2: 192.8607 .. 224.6473 cents 31.78661 cents 80.53703 cents 3: 278.9224 .. 310.7090 cents 31.78660 cents 54.27509 cents 4: 391.2460 .. 417.5080 cents 26.26194 cents 80.53704 cents 5: 471.7831 .. 503.5697 cents 31.78660 cents 54.27509 cents 6: 584.1067 .. 615.8933 cents 31.78662 cents 80.53704 cents 7: 696.4303 .. 728.2169 cents 31.78661 cents 80.53703 cents 8: 782.4920 .. 808.7540 cents 26.26195 cents 54.27508 cents 9: 889.2910 .. 921.0776 cents 31.78660 cents 80.53704 cents 10: 975.3527 .. 1007.1393 cents 31.78660 cents 54.27509 cents 11: 1087.6764 .. 1119.4630 cents 31.78661 cents 80.53704 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 80.53703 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 112.32365 cents Average / Smallest step : 1.241665 Largest / Average step : 1.123236 Largest / Smallest step : 1.394683 Median interval of one step : 109.56131 cents, amount: 0 Most common interval of one step : 112.32365 cents, amount: 6 Least squares average step : 99.62946 cents, oct.: 1195.55347 cents Scale is strictly proper Step pattern alph. order: ABBCBABCBBAD Step pattern size order : BDDADBDADDBC Scale is a Constant Structure, by a margin of 54.27508 cents Scale diversity : 1.212069 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.717831 Rothenberg efficiency : 0.439743 redundancy: 0.560257 Efficiency x scale size : 5.276912 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 5.52466 cents Most common intervals : 503.56966 cents & inv., amount: 9 Most common triad is 0.0 503.570 696.430 cents, amount: 6 Number of recognisable fifths : 11, average 697.4348 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- 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: 8.8641 c. M:-17.5080 c. Twelve-tone Chromatic (1/11-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 5.7782 c. M: 9.3300 c. Meantone Chromatic (53/220-comma) 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 2.8222 c. M: 4.8289 c. Meantone Chromatic (1/5-comma) 55: 4 5 5 4 5 4 5 4 5 5 4 5 SP M ME SD: 2.5711 c. M: 5.2544 c. Meantone Chromatic (3/17-comma) 98: 7 9 9 7 9 7 9 7 9 9 7 9 SP M DE SD: 2.4603 c. M: 4.5865 c. Meantone Chromatic (5/27-comma) 101: 7 10 9 7 9 8 9 7 9 10 7 9 SP SD: 2.7517 c. M: 4.5598 c. 114: 8 11 11 7 11 8 11 7 11 11 8 10 SP SD: 2.5037 c. M:-5.0805 c. 121: 9 11 11 8 12 8 12 8 11 12 8 11 SP SD: 2.9122 c. M: 4.5074 c. 122: 9 11 12 8 11 9 11 9 11 11 9 11 SP SD: 2.6328 c. M:-4.3932 c. 123: 9 11 12 8 12 8 12 8 12 11 9 11 SP SD: 2.3507 c. M: 4.2655 c. 126: 9 12 12 8 12 9 12 8 12 12 9 11 SP SD: 1.7915 c. M:-3.5767 c. 135: 10 12 13 9 13 9 13 9 13 12 10 12 SP SD: 2.0567 c. M:-3.0970 c. 138: 10 13 13 9 13 10 13 9 13 13 10 12 SP SD: 1.5037 c. M:-2.4512 c. 150: 11 14 14 10 14 11 14 10 14 14 11 13 SP SD: 1.6028 c. M:-2.7990 c. 157: 11 15 15 10 15 11 15 10 15 15 11 14 SP SD: 1.5412 c. M: 2.8742 c. 169: 12 16 16 11 16 12 16 11 16 16 12 15 SP SD: 0.8774 c. M:-1.7171 c. 181: 13 17 17 12 17 13 17 12 17 17 13 16 SP SD: 0.4959 c. M:-0.8932 c. 224: 16 21 21 15 21 16 21 15 21 21 16 20 SP SD: 0.2234 c. M: 0.3492 c. 405: 29 38 38 27 38 29 38 27 38 38 29 36 SP SD: 0.1974 c. M:-0.4021 c. 417: 30 39 39 28 39 30 39 28 39 39 30 37 SP SD: 0.1922 c. M:-0.3242 c. 460: 33 43 43 31 43 33 43 31 43 43 33 41 SP SD: 0.1375 c. M: 0.2742 c. 641: 46 60 60 43 60 46 60 43 60 60 46 57 SP SD: 0.0519 c. M:-0.0907 c. 865: 62 81 81 58 81 62 81 58 81 81 62 77 SP SD: 0.0325 c. M: 0.0643 c. 1506: 108 141 141 101 141 108 141 101 141 141 108 134 SP SD: 0.0239 c. M:-0.0480 c. 1966: 141 184 184 132 184 141 184 132 184 184 141 175 SP SD: 0.0139 c. M: 0.0274 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: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.9422 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.6574 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.8042 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.3340 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.7883 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 9.6519 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.4057 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.4829 cents 11 x 12:13:14:15 x x 17:18:20:21:22 SD: 10.3203 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 8.0070 cents 13:14:15 x 16:17:18 x 20:22:23:24:26 S SD: 10.2170 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.4014 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.4153 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.1882 cents 18:19:20:22:23:24:25:27:28:30:32:34:36 SD: 5.1544 cents 19:20:21:23:24:25:27:29:30:32:34:36:38 SD: 4.9880 cents 20:21:22:24:25:27:28:30:31:34:36:38:40 SD: 4.5929 cents 23:24:26:28:29:31:32:35:36:39:41:43:46 SD: 4.5758 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 2.7604 cents 32:34:36:38:40:43:45:48:50:54:57:60:64 SD: 2.5713 cents 35:37:39:42:44:47:49:53:55:59:63:66:70 SD: 2.4413 cents 39:41:44:47:49:52:55:59:61:65:70:73:78 SD: 2.3894 cents 40:42:45:48:50:54:56:60:63:67:72:75:80 SD: 1.9370 cents 42:44:47:50:53:56:59:63:66:70:75:79:84 SD: 1.6813 cents 56:59:63:67:70:75:79:84:88:94:100:105:112 SD: 1.0340 cents 82:86:92:98:103:110:115:123:129:137:147:154:164 SD: 0.9535 cents 96:101:108:115:120:128:135:144:151:161:172:181:192 SD: 0.9249 cents 98:103:110:117:123:131:138:147:154:164:175:184:196 SD: 0.6548 cents 118:124:132:141:148:158:166:177:185:198:211:222:236 SD: 0.5851 cents 133:140:149:159:167:178:187:200:209:223:238:250:266 SD: 0.5365 cents 142:149:159:170:178:190:200:213:223:238:254:267:284 SD: 0.4438 cents 158:166:177:189:198:211:222:237:248:265:283:297:316 SD: 0.3803 cents 198:208:222:237:248:265:278:297:311:332:354:372:396 SD: 0.2990 cents 214:225:240:256:268:286:301:321:336:359:383:402:428 SD: 0.2979 cents 276:290:310:330:346:369:388:414:434:463:494:519:552 SD: 0.2952 cents 294:309:330:352:369:393:413:441:462:493:526:553:588 SD: 0.2782 cents 296:311:332:354:371:396:416:444:465:496:530:557:592 SD: 0.2135 cents 352:370:395:421:441:471:495:528:553:590:630:662:704 SD: 0.1836 cents 394:414:442:471:494:527:554:591:619:661:705:741:788 SD: 0.1816 cents 418:439:469:500:524:559:588:627:657:701:748:786:836 SD: 0.1746 cents 436:458:489:522:547:583:613:654:685:731:780:820:872 SD: 0.1737 cents 454:477:509:543:569:607:638:681:713:761:812:854:908 SD: 0.1732 cents 468:492:525:560:587:626:658:702:735:785:837:880:936 SD: 0.1554 cents 488:513:547:584:612:653:686:732:767:818:873:918:976 SD: 0.1405 cents 528:555:592:632:662:706:742:792:830:885:945:993:1056 SD: 0.1318 cents 544:572:610:651:682:728:765:816:855:912:973:1023:1088 SD: 0.1258 cents 560:589:628:670:702:749:787:840:880:939:1002:1053:1120 SD: 0.1223 cents 569:598:638:681:713:761:800:854:894:954:1018:1070:1138 SD: 0.1148 cents 584:614:655:699:732:781:821:876:918:979:1045:1098:1168 SD: 0.0997 cents