Scala analysis: smalldimos11
Small diesic 11-note MOS, 31/120 version
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40.000 cents 40.000000 2: 270.000 cents 270.000000 3: 310.000 cents 310.000000 4: 350.000 cents 350.000000 5: 580.000 cents 580.000000 6: 620.000 cents 620.000000 7: 850.000 cents 850.000000 8: 890.000 cents 890.000000 9: 930.000 cents 930.000000 10: 1160.000 cents 1160.000000 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 40.0000 cents 40.0000 1: 40.0000 cents 40.0000 2: 230.0000 cents 230.0000 3: 40.0000 cents 40.0000 4: 40.0000 cents 40.0000 5: 230.0000 cents 230.0000 6: 40.0000 cents 40.0000 7: 230.0000 cents 230.0000 8: 40.0000 cents 40.0000 9: 40.0000 cents 40.0000 10: 230.0000 cents 230.0000 11: 40.0000 cents 40.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 40.00000 cents 1: 4 230.00000 cents 2: 3 80.00000 cents 2: 8 270.00000 cents 3: 10 310.00000 cents 3: 1 500.00000 cents 4: 6 350.00000 cents 4: 5 540.00000 cents 5: 2 390.00000 cents 5: 9 580.00000 cents 6: 9 620.00000 cents 6: 2 810.00000 cents 7: 5 660.00000 cents 7: 6 850.00000 cents 8: 1 700.00000 cents 8: 10 890.00000 cents 9: 8 930.00000 cents 9: 3 1120.00000 cents 10: 4 970.00000 cents 10: 7 1160.00000 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 : 40.0 270.0 310.0 350.0 580.0 620.0 850.0 890.0 930.0 1160.0 1200.0 40.0 : 230.0 270.0 310.0 540.0 580.0 810.0 850.0 890.0 1120.0 1160.0 1200.0 270.0 : 40.0 80.0 310.0 350.0 580.0 620.0 660.0 890.0 930.0 970.0 1200.0 310.0 : 40.0 270.0 310.0 540.0 580.0 620.0 850.0 890.0 930.0 1160.0 1200.0 350.0 : 230.0 270.0 500.0 540.0 580.0 810.0 850.0 890.0 1120.0 1160.0 1200.0 580.0 : 40.0 270.0 310.0 350.0 580.0 620.0 660.0 890.0 930.0 970.0 1200.0 620.0 : 230.0 270.0 310.0 540.0 580.0 620.0 850.0 890.0 930.0 1160.0 1200.0 850.0 : 40.0 80.0 310.0 350.0 390.0 620.0 660.0 700.0 930.0 970.0 1200.0 890.0 : 40.0 270.0 310.0 350.0 580.0 620.0 660.0 890.0 930.0 1160.0 1200.0 930.0 : 230.0 270.0 310.0 540.0 580.0 620.0 850.0 890.0 1120.0 1160.0 1200.0 1160.0: 40.0 80.0 310.0 350.0 390.0 620.0 660.0 890.0 930.0 970.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.0000 .. 230.0000 cents 190.00000 cents 40.00000 cents 2: 80.0000 .. 270.0000 cents 190.00000 cents -150.00000 cents 3: 310.0000 .. 500.0000 cents 190.00000 cents 40.00000 cents 4: 350.0000 .. 540.0000 cents 190.00000 cents -150.00000 cents 5: 390.0000 .. 580.0000 cents 190.00000 cents -150.00000 cents 6: 620.0000 .. 810.0000 cents 190.00000 cents 40.00000 cents 7: 660.0000 .. 850.0000 cents 190.00000 cents -150.00000 cents 8: 700.0000 .. 890.0000 cents 190.00000 cents -150.00000 cents 9: 930.0000 .. 1120.0000 cents 190.00000 cents 40.00000 cents 10: 970.0000 .. 1160.0000 cents 190.00000 cents -150.00000 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 40.00000 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 230.00000 cents Average / Smallest step : 2.727273 Largest / Average step : 2.108333 Largest / Smallest step : 5.750000 Median interval of one step : 40.00000 cents, amount: 7 Most common interval of one step : 40.00000 cents, amount: 7 Least squares average step : 110.21739 cents, oct.: 1212.39130 cents Scale is not proper Scale has Myhill's property chromas: 190.00000 cents and 150.00000 cents, ratio: 1.266667 generators: 3 of 310.00000 cents and 8 of 890.00000 cents ET pair of linear temperament : 27&31 Scale is distributional even Scale is a mode of a 120-tone equal temperament with octave 2/1 degrees: 4 27 31 35 58 62 85 89 93 116 120 generators: 31 and 89 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABABAABA Step pattern size order : SLSSLSLSSLS Interval vector is [ 0 0 0 7 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 8 0 0 0 10 0 0 0 6 0 0 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 5 0 0 0 9 0 0 ] Scale is a Constant Structure, by a margin of 40.00000 cents Scale diversity : 1.127611 Lumma stability : 0.166667 Lumma impropriety factor : 0.566667 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 : 40.00000 cents Most common intervals : 310.00000 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 350.000 890.000 cents Most common triad is 0.0 310.000 890.000 cents, amount: 9 Number of recognisable fifths : 1, average 700.0000 cents Scale contains two identical conjunct hexachords Formal octave complements present : 11 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
11: 0 2 0 1 2 0 2 1 0 2 1 N T3 SD: 57.0434 c. M: 91.8182 c. 12: 0 2 1 0 2 1 2 0 1 2 1 N T3 SD: 53.0866 c. M: 90.0000 c. 13: 0 3 0 1 2 1 2 1 0 3 0 N I SD: 26.2708 c. M:-40.0000 c. 14: 0 3 1 0 3 0 3 0 1 3 0 N I SD: 24.4797 c. M:-40.0000 c. 17: 1 3 0 1 3 1 3 1 0 3 1 N I SD: 19.5176 c. M:-30.5882 c. 18: 1 3 1 0 4 0 4 0 1 3 1 N I SD: 18.8025 c. M: 26.6667 c. 21: 1 4 0 1 4 1 4 1 0 4 1 N I SD: 15.1063 c. M: 24.2857 c. 23: 1 4 1 1 4 1 4 1 1 4 1 N M DE I SD: 9.6243 c. M:-15.2174 c. 27: 1 5 1 1 5 1 5 1 1 5 1 N M DE I SD: 3.5136 c. M:-5.5556 c. Myna-11 31: 1 6 1 1 6 1 6 1 1 6 1 N M DE I SD: 1.0201 c. M: 1.6129 c. Myna-11 89: 3 17 3 3 17 3 17 3 3 17 3 N M DE I SD: 0.3553 c. M: 0.5618 c. Myna-11 120: 4 23 4 4 23 4 23 4 4 23 4 N M DE I SD: 0.0000 c. M:-0.0000 c. Myna-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: 40.9775 cents 3 x x x x 4 x x 5 x x 6 S SD: 27.3830 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 24.4218 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 19.0052 cents 6 x 7 x x 8:9 x 10 x x 12 S SD: 23.2163 cents 7 x 8 x 9 x 10:11 x 12 x 14 S SD: 19.2355 cents 8 x 9 x 10:11 x 13 x 14 x 16 SD: 15.0059 cents 9 x x x 11 x 13 x 15 x x 18 SD: 4.4349 cents 10 x x 12 x 14 x 16 x 17 x 20 SD: 7.7093 cents 11:12:13 x x 15:16:18 x 19 x 22 SD: 17.8168 cents 12:13:14 x 15 x 17 x 20:21:23:24 SD: 14.7943 cents 13:14:15 x 16:18:19:21 x 22:25:26 SD: 11.9480 cents 14:15:16 x 17 x 20:23 x 24:27:28 SD: 11.6214 cents 15:16 x 18 x 21 x x 25:26:29:30 SD: 11.1210 cents 16:17 x 19:20:22:23:26:27 x 31:32 SD: 9.3955 cents 17:18:20 x 21:24 x 28 x 29:33:34 SD: 8.3870 cents 18:19:21 x 22:25:26:29:30:31:35:36 SD: 6.4170 cents 19:20:22 x 23 x 27:31:32:33:37:38 SD: 7.0389 cents 20:21:23:24 x 28:29:33 x 34:39:40 SD: 6.8260 cents 21:22 x 25:26:29:30:34:35:36:41:42 SD: 5.3391 cents 22:23:26 x 27:31 x 36:37:38:43:44 SD: 5.3440 cents 23:24:27 x 28:32:33:38 x 39:45:46 SD: 4.9666 cents 24:25:28:29 x x 34:39:40:41:47:48 SD: 4.5713 cents 25:26:29:30:31:35:36:41:42:43:49:50 SD: 3.8873 cents 27:28 x 32:33:38:39:44:45:46:53:54 SD: 3.6958 cents 28:29:33 x 34:39:40:46:47:48:55:56 SD: 3.3159 cents 29:30:34:35:36:41 x 47:48:50:57:58 SD: 4.8671 cents 30:31:35:36:37:42:43:49:50:51:59:60 SD: 2.5562 cents 33:34:39 x 40:46:47:54:55:56:64:66 SD: 3.6081 cents 34:35:40:41:42:48:49:56:57:58:66:68 SD: 3.5332 cents 35:36:41:42:43:49:50:57:59:60:68:70 SD: 2.0731 cents 40:41:47:48:49:56:57:65:67:68:78:80 SD: 1.8658 cents 41:42:48:49:50:57:59:67:69:70:80:82 SD: 1.8106 cents 46:47:54:55:56:64:66:75:77:79:90:92 SD: 1.5969 cents 58:59:68:69:71:81:83:95:97:99:113:116 SD: 1.5581 cents 66:68:77:79:81:92:94:108:110:113:129:132 SD: 1.5570 cents 70:72:82:84:86:98:100:114:117:120:137:140 SD: 1.3671 cents 71:73:83:85:87:99:102:116:119:121:139:142 SD: 1.3460 cents 72:74:84:86:88:101:103:118:120:123:141:144 SD: 1.2640 cents 76:78:89:91:93:106:109:124:127:130:149:152 SD: 0.9631 cents 88:90:103:105:108:123:126:144:147:151:172:176 SD: 0.8151 cents 118:121:138:141:144:165:169:193:197:202:231:236 SD: 0.7440 cents 125:128:146:150:153:175:179:204:209:214:244:250 SD: 0.6575 cents 128:131:150:153:157:179:183:209:214:219:250:256 SD: 0.5689 cents 153:157:179:183:187:214:219:250:256:262:299:306 SD: 0.5452 cents 170:174:199:203:208:238:243:278:284:291:332:340 SD: 0.5061 cents 173:177:202:207:212:242:248:283:289:296:338:346 SD: 0.4785 cents 174:178:203:208:213:243:249:284:291:298:340:348 SD: 0.4091 cents 183:187:214:219:224:256:262:299:306:313:358:366 SD: 0.3509 cents 214:219:250:256:262:299:306:350:358:366:418:428 SD: 0.2542 cents 219:224:256:262:268:306:313:358:366:375:428:438 SD: 0.2541 cents 290:297:339:347:355:405:415:474:485:496:567:580 SD: 0.2451 cents 336:344:393:402:411:470:481:549:562:575:657:672 SD: 0.2446 cents 342:350:400:409:419:478:489:559:572:585:668:684 SD: 0.2409 cents 344:352:402:411:421:481:492:562:575:589:672:688 SD: 0.2283 cents 357:365:417:427:437:499:511:583:597:611:698:714 SD: 0.2255 cents 374:383:437:447:458:523:535:611:625:640:731:748 SD: 0.2109 cents 397:406:464:475:486:555:568:649:664:679:776:794 SD: 0.1730 cents 432:442:505:517:529:604:618:706:722:739:844:864 SD: 0.1606 cents 464:475:542:555:568:649:664:758:776:794:907:928 SD: 0.1500 cents 509:521:595:609:623:712:728:832:851:871:995:1018 SD: 0.1451 cents 546:559:638:653:668:763:781:892:913:934:1067:1092 SD: 0.1411 cents 550:563:643:658:673:769:787:899:920:941:1075:1100 SD: 0.1305 cents 592:606:692:708:725:828:847:967:990:1013:1157:1184 SD: 0.1305 cents 598:612:699:715:732:836:856:977:1000:1023:1169:1196 SD: 0.1244 cents