Scala analysis: cupid
Decatonic MOS from 13-tET.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 184.615 cents 184.615000 2: 276.923 cents 276.923000 3: 369.231 cents 369.231000 4: 553.846 cents 553.846000 5: 646.154 cents 646.154000 6: 738.462 cents 738.462000 7: 923.077 cents 923.077000 8: 1015.385 cents 1015.385000 9: 1107.692 cents 1107.692000 10: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 92.3080 cents 92.3080 1: 184.6150 cents 184.6150 2: 92.3080 cents 92.3080 3: 92.3080 cents 92.3080 4: 184.6150 cents 184.6150 5: 92.3080 cents 92.3080 6: 92.3080 cents 92.3080 7: 184.6150 cents 184.6150 8: 92.3080 cents 92.3080 9: 92.3070 cents 92.3070 10: 92.3080 cents 92.3080
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 92.30700 cents 1: 6 92.30800 cents 1: 3 184.61500 cents 2: 2 184.61500 cents 2: 2 184.61600 cents 2: 6 276.92300 cents 3: 1 276.92300 cents 3: 2 369.23000 cents 3: 7 369.23100 cents 4: 4 461.53800 cents 4: 4 461.53900 cents 4: 2 553.84600 cents 5: 4 553.84600 cents 5: 1 553.84700 cents 5: 1 646.15300 cents 5: 4 646.15400 cents 6: 2 646.15400 cents 6: 4 738.46100 cents 6: 4 738.46200 cents 7: 7 830.76900 cents 7: 2 830.77000 cents 7: 1 923.07700 cents 8: 6 923.07700 cents 8: 2 1015.38400 cents 8: 2 1015.38500 cents 9: 3 1015.38500 cents 9: 6 1107.69200 cents 9: 1 1107.69300 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.11111 = 28/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 184.6 276.9 369.2 553.8 646.2 738.5 923.1 1015.4 1107.7 1200.0 184.6 : 92.3 184.6 369.2 461.5 553.8 738.5 830.8 923.1 1015.4 1200.0 276.9 : 92.3 276.9 369.2 461.5 646.2 738.5 830.8 923.1 1107.7 1200.0 369.2 : 184.6 276.9 369.2 553.8 646.2 738.5 830.8 1015.4 1107.7 1200.0 553.8 : 92.3 184.6 369.2 461.5 553.8 646.2 830.8 923.1 1015.4 1200.0 646.2 : 92.3 276.9 369.2 461.5 553.8 738.5 830.8 923.1 1107.7 1200.0 738.5 : 184.6 276.9 369.2 461.5 646.2 738.5 830.8 1015.4 1107.7 1200.0 923.1 : 92.3 184.6 276.9 461.5 553.8 646.2 830.8 923.1 1015.4 1200.0 1015.4: 92.3 184.6 369.2 461.5 553.8 738.5 830.8 923.1 1107.7 1200.0 1107.7: 92.3 276.9 369.2 461.5 646.2 738.5 830.8 1015.4 1107.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.3070 .. 184.6150 cents 92.30800 cents 92.30700 cents 2: 184.6150 .. 276.9230 cents 92.30800 cents 1/1, 0.0000 cents 3: 276.9230 .. 369.2310 cents 92.30800 cents 1/1, 0.0000 cents 4: 461.5380 .. 553.8460 cents 92.30800 cents 92.30700 cents 5: 553.8460 .. 646.1540 cents 92.30800 cents 1/1, 0.0000 cents 6: 646.1540 .. 738.4620 cents 92.30800 cents 1/1, 0.0000 cents 7: 830.7690 .. 923.0770 cents 92.30800 cents 92.30700 cents 8: 923.0770 .. 1015.3850 cents 92.30800 cents 1/1, 0.0000 cents 9: 1015.3850 .. 1107.6930 cents 92.30800 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 92.30700 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 184.61500 cents Average / Smallest step : 1.300010 Largest / Average step : 1.538458 Largest / Smallest step : 2.000011 Median interval of one step : 92.30800 cents, amount: 6 Most common interval of one step : 92.30800 cents, amount: 6 Least squares average step : 125.39462 cents, oct.: 1253.94616 cents Scale is proper Scale is a mode of a 13-tone equal temperament with octave 1200.000 cents degrees: 2 3 4 6 7 8 10 11 12 13 Least number of segments generator : 9 of 830.769 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 9 of 830.769 cents and inv. generated superset size: 10 = 0 more = 100.000% Number of contiguous 1-step segments: 3 Step pattern alph. order: ABBABBABCB Step pattern size order : LMMLMMLMSM Interval vector is [ 6 2 7 7 4 1 ] Scale is not a Constant Structure Scale diversity : 1.113951 Rothenberg stability : 0.600000 = 3/5 Lumma stability : 0.307690 Rothenberg efficiency : 0.500635 redundancy: 0.499365 Efficiency x scale size : 5.006349 Number of different interval sizes : 22 = 2.44444 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.11111 = 28/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 0.00100 cents Number of recognisable fifths : 0 Formal octave complements present : 7 = 70.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 8-9 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 49.2788 c. M: 83.0770 c. 11: 1 1 1 2 1 1 1 1 1 1 P M ME SD: 39.5386 c. M: 75.5241 c. 12: 2 1 0 2 1 1 2 1 1 1 N D3 SD: 35.9159 c. M: 69.2310 c. 13: 2 1 1 2 1 1 2 1 1 1 P M ME SD: 0.0003 c. M: 0.0005 c.
FIT/HARMONIC
1 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 4 S SD: 18.2535 cents 3 x x x 4 x x 5 x x 6 S SD: 22.6393 cents 4 x x 5 x x 6:7 x x 8 S SD: 15.2429 cents 5 x 6 x 7 x 8 x 9 x 10 S SD: 17.8711 cents 6 x 7 x 8 x 9:10:11 x 12 S SD: 14.1433 cents 7 x 8:9 x 10:11:12 x 13:14 S SD: 14.6986 cents 8:9 x 10:11 x 12:14 x 15:16 S SD: 9.5549 cents 9:10 x 11:12:13:14:15:16:17:18 S SD: 8.8200 cents 10:11:12 x 14 x 15:17:18:19:20 SD: 7.9795 cents 11:12:13:14:15:16:17:19:20:21:22 SD: 7.2221 cents 12:13:14:15 x 17:18:20:22:23:24 SD: 10.3687 cents 13:14:15:16:18:19:20:22:23:25:26 SD: 7.6752 cents 14 x 16:17:19:20:21:24:25:27:28 SD: 9.3443 cents 15:17:18:19:21:22:23:26:27:28:30 SD: 8.2651 cents 16:18:19:20:22:23:25:27:29:30:32 SD: 5.8791 cents 17:19:20:21:23:25:26:29:31:32:34 SD: 4.7643 cents 24:27:28:30:33:35:37:41:43:46:48 SD: 3.6572 cents 28:31:33:35:39:41:43:48:50:53:56 SD: 3.5666 cents 29:32:34:36:40:42:44:49:52:55:58 SD: 2.8056 cents 34:38:40:42:47:49:52:58:61:64:68 SD: 2.2429 cents 45:50:53:56:62:65:69:77:81:85:90 SD: 1.7980 cents 51:57:60:63:70:74:78:87:92:97:102 SD: 1.4261 cents 64:71:75:79:88:93:98:109:115:121:128 SD: 0.9340 cents 88:98:103:109:121:128:135:150:158:167:176 SD: 0.7044 cents 98:109:115:121:135:142:150:167:176:186:196 SD: 0.6609 cents 109:121:128:135:150:158:167:186:196:207:218 SD: 0.6483 cents 115:128:135:142:158:167:176:196:207:218:230 SD: 0.6438 cents 122:136:143:151:168:177:187:208:219:231:244 SD: 0.5757 cents 143:159:168:177:197:208:219:244:257:271:286 SD: 0.4166 cents 186:207:218:230:256:270:285:317:334:353:372 SD: 0.3904 cents 212:236:249:262:292:308:325:361:381:402:424 SD: 0.3876 cents 214:238:251:265:295:311:328:365:385:406:428 SD: 0.3349 cents 223:248:262:276:307:324:342:380:401:423:446 SD: 0.3112 cents 241:268:283:298:332:350:369:411:433:457:482 SD: 0.2912 cents 265:295:311:328:365:385:406:452:476:502:530 SD: 0.2845 cents 278:309:326:344:383:404:426:474:500:527:556 SD: 0.2711 cents 310:345:364:384:427:450:475:528:557:588:620 SD: 0.2674 cents 311:346:365:385:428:452:476:530:559:590:622 SD: 0.2430 cents 329:366:386:407:453:478:504:561:591:624:658 SD: 0.1954 cents 374:416:439:463:515:543:573:637:672:709:748 SD: 0.1799 cents 416:463:488:515:573:604:637:709:748:789:832 SD: 0.1586 cents 480:534:563:594:661:697:735:818:863:910:960 SD: 0.1320 cents 559:622:656:692:770:812:856:953:1005:1060:1118 SD: 0.1154 cents 588:654:690:728:810:854:901:1002:1057:1115:1176 SD: 0.1086 cents