Scala analysis: 37-EDO_generator11_8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 162.162 cents 162.162150 2: 259.459 cents 259.459450 3: 356.757 cents 356.756750 4: 454.054 cents 454.054050 5: 551.351 cents 551.351350 6: 713.513 cents 713.513500 7: 810.811 cents 810.810800 8: 908.108 cents 908.108100 9: 1005.405 cents 1005.405400 10: 1102.703 cents 1102.702700 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 97.2973 cents 97.2973 1: 162.1621 cents 162.1621 2: 97.2973 cents 97.2973 3: 97.2973 cents 97.2973 4: 97.2973 cents 97.2973 5: 97.2973 cents 97.2973 6: 162.1621 cents 162.1621 7: 97.2973 cents 97.2973 8: 97.2973 cents 97.2973 9: 97.2973 cents 97.2973 10: 97.2973 cents 97.2973 11: 97.2973 cents 97.2973
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 97.29730 cents 1: 2 162.16215 cents 2: 7 194.59460 cents 2: 4 259.45945 cents 3: 5 291.89190 cents 3: 6 356.75675 cents 4: 3 389.18920 cents 4: 8 454.05405 cents 5: 1 486.48650 cents 5: 10 551.35135 cents 6: 10 648.64865 cents 6: 1 713.51350 cents 7: 8 745.94595 cents 7: 3 810.81080 cents 8: 6 843.24325 cents 8: 5 908.10810 cents 9: 4 940.54055 cents 9: 7 1005.40540 cents 10: 2 1037.83785 cents 10: 9 1102.70270 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 162.2 259.5 356.8 454.1 551.4 713.5 810.8 908.1 1005.4 1102.7 1200.0 162.2 : 97.3 194.6 291.9 389.2 551.4 648.6 745.9 843.2 940.5 1037.8 1200.0 259.5 : 97.3 194.6 291.9 454.1 551.4 648.6 745.9 843.2 940.5 1102.7 1200.0 356.8 : 97.3 194.6 356.8 454.1 551.4 648.6 745.9 843.2 1005.4 1102.7 1200.0 454.1 : 97.3 259.5 356.8 454.1 551.4 648.6 745.9 908.1 1005.4 1102.7 1200.0 551.4 : 162.2 259.5 356.8 454.1 551.4 648.6 810.8 908.1 1005.4 1102.7 1200.0 713.5 : 97.3 194.6 291.9 389.2 486.5 648.6 745.9 843.2 940.5 1037.8 1200.0 810.8 : 97.3 194.6 291.9 389.2 551.4 648.6 745.9 843.2 940.5 1102.7 1200.0 908.1 : 97.3 194.6 291.9 454.1 551.4 648.6 745.9 843.2 1005.4 1102.7 1200.0 1005.4: 97.3 194.6 356.8 454.1 551.4 648.6 745.9 908.1 1005.4 1102.7 1200.0 1102.7: 97.3 259.5 356.8 454.1 551.4 648.6 810.8 908.1 1005.4 1102.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.2973 .. 162.1621 cents 64.86485 cents 97.29730 cents 2: 194.5946 .. 259.4595 cents 64.86485 cents 32.43245 cents 3: 291.8919 .. 356.7567 cents 64.86485 cents 32.43245 cents 4: 389.1892 .. 454.0540 cents 64.86485 cents 32.43245 cents 5: 486.4865 .. 551.3513 cents 64.86485 cents 32.43245 cents 6: 648.6486 .. 713.5135 cents 64.86485 cents 97.29730 cents 7: 745.9459 .. 810.8108 cents 64.86485 cents 32.43245 cents 8: 843.2432 .. 908.1081 cents 64.86485 cents 32.43245 cents 9: 940.5405 .. 1005.4054 cents 64.86485 cents 32.43245 cents 10: 1037.8378 .. 1102.7027 cents 64.86485 cents 32.43245 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 97.29730 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 162.16215 cents Average / Smallest step : 1.121212 Largest / Average step : 1.486486 Largest / Smallest step : 1.666666 Median interval of one step : 97.29730 cents, amount: 9 Most common interval of one step : 97.29730 cents, amount: 9 Least squares average step : 112.29569 cents, oct.: 1235.25264 cents Scale is strictly proper Scale has Myhill's property chromas: 64.86485 cents and 32.43245 cents, ratio: 1.999998 generators: 5 of 551.35135 cents and 648.64865 cents ET pair of linear temperament : 11&13 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 37-tone equal temperament with octave 2/1 degrees: 5 8 11 14 17 22 25 28 31 34 37 generators: 17 and 20 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBBBABBBBB Step pattern size order : LSSSSLSSSSS Interval vector is [ 0 0 9 0 2 7 0 4 5 0 6 3 0 8 1 0 10 0 ] Scale is a Constant Structure, by a margin of 32.43245 cents Scale diversity : 1.211207 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.459460 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 32.43245 cents Most common intervals : 551.35135 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 551.351 1102.703 cents Most common triad is 0.0 551.351 648.649 cents, amount: 9 Number of recognisable fifths : 1, average 713.5135 cents Scale contains two identical disjunct pentachords Best minor thirds form a closed circle Formal octave complements present : 1 = 9.0909% Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 Inversional symmetry on intervals : 8-9 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 34.8860 c. M: 58.9680 c. 13: 2 1 1 1 1 2 1 1 1 1 1 P M ME S SD: 14.7595 c. M:-24.9480 c. 22: 3 2 2 1 2 3 2 2 1 2 2 P T3 SD: 14.4305 c. M:-25.0614 c. 23: 3 2 2 2 2 3 2 1 2 2 2 P T3 SD: 14.8076 c. M:-23.9718 c. 24: 3 2 2 2 2 3 2 2 2 2 2 SP M ME S SD: 7.9947 c. M: 13.5135 c. Freivald-11 37: 5 3 3 3 3 5 3 3 3 3 3 SP M DE S SD: 0.0000 c. M:-0.0000 c. Freivald-11
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x x 4 S SD: 5.7792 cents 3 x x x 4 x x x 5 x x 6 S SD: 16.6641 cents 4 x x 5 x x 6 x x 7 x 8 S SD: 12.1070 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 10.6177 cents 6 x 7 x 8 x 9 x 10:11 x 12 S SD: 11.3285 cents 7 x 8 x 9:10 x 11:12 x 13:14 S SD: 12.7159 cents 8:9 x 10 x 11:12:13 x 14:15:16 S SD: 8.9962 cents 9:10 x 11:12 x x 14:15:16:17:18 S SD: 9.0071 cents 10:11 x 12:13:14:15:16:17:18:19:20 S SD: 5.6064 cents 11:12:13 x 14:15:17:18:19:20:21:22 SD: 9.2323 cents 12:13:14:15:16:17:18:19:20:21:23:24 SD: 8.5831 cents 13:14:15:16:17:18:20:21:22:23:25:26 SD: 5.8540 cents 17:19:20:21:22:23:26:27:29:30:32:34 SD: 5.5556 cents 18:20:21:22:23:25:27:29:30:32:34:36 SD: 4.7612 cents 19:21:22:23:25:26:29:30:32:34:36:38 SD: 4.2053 cents 23:25:27:28:30:32:35:37:39:41:43:46 SD: 4.1904 cents 26:29:30:32:34:36:39:42:44:46:49:52 SD: 4.0470 cents 27:30:31:33:35:37:41:43:46:48:51:54 SD: 3.3778 cents 29:32:34:36:38:40:44:46:49:52:55:58 SD: 3.0507 cents 30:33:35:37:39:41:45:48:51:54:57:60 SD: 2.3846 cents 39:43:45:48:51:54:59:62:66:70:74:78 SD: 2.2641 cents 43:47:50:53:56:59:65:69:73:77:81:86 SD: 1.5872 cents 57:63:66:70:74:78:86:91:96:102:108:114 SD: 1.5297 cents 61:67:71:75:79:84:92:97:103:109:115:122 SD: 1.1195 cents 70:77:81:86:91:96:106:112:118:125:132:140 SD: 1.1009 cents 74:81:86:91:96:102:112:118:125:132:140:148 SD: 0.9191 cents 80:88:93:98:104:110:121:128:135:143:151:160 SD: 0.7537 cents 104:114:121:128:135:143:157:166:176:186:197:208 SD: 0.6506 cents 123:135:143:151:160:169:186:196:208:220:233:246 SD: 0.6221 cents 131:144:152:161:170:180:198:209:221:234:248:262 SD: 0.5558 cents 141:155:164:173:183:194:213:225:238:252:267:282 SD: 0.5516 cents 149:164:173:183:194:205:225:238:252:266:282:298 SD: 0.5453 cents 154:169:179:189:200:212:233:246:260:275:291:308 SD: 0.5045 cents 161:177:187:198:209:221:243:257:272:288:304:322 SD: 0.4894 cents 173:190:201:213:225:238:261:276:292:309:327:346 SD: 0.4555 cents 174:191:202:214:226:239:263:278:294:311:329:348 SD: 0.3182 cents 184:202:214:226:239:253:278:294:311:329:348:368 SD: 0.2721 cents 253:278:294:311:329:348:382:404:427:452:478:506 SD: 0.2711 cents 283:311:329:348:368:389:427:452:478:506:535:566 SD: 0.2569 cents 296:325:344:364:385:407:447:473:500:529:560:592 SD: 0.2092 cents 357:392:415:439:464:491:539:570:603:638:675:714 SD: 0.1861 cents 376:413:437:462:489:517:568:601:635:672:711:752 SD: 0.1860 cents 390:428:453:479:507:536:589:623:659:697:737:780 SD: 0.1791 cents 427:469:496:525:555:587:645:682:721:763:807:854 SD: 0.1734 cents 437:480:508:537:568:601:660:698:738:781:826:874 SD: 0.1529 cents 477:524:554:586:620:656:720:762:806:853:902:954 SD: 0.1311 cents 551:605:640:677:716:758:832:880:931:985:1042:1102 SD: 0.1112 cents