Scala analysis: Miracle-12
A chain of 12 Miracle generators for mapping to standard keyboard
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.667 cents 116.666667 2: 233.333 cents 233.333333 3: 350.000 cents 350.000000 4: 466.667 cents 466.666667 5: 583.333 cents 583.333333 6: 700.000 cents 700.000000 7: 816.667 cents 816.666667 8: 850.000 cents 850.000000 9: 933.300 cents 933.300000 10: 966.667 cents 966.666667 11: 1083.333 cents 1083.333333 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.6667 cents 116.6667 1: 116.6667 cents 116.6667 2: 116.6667 cents 116.6667 3: 116.6667 cents 116.6667 4: 116.6667 cents 116.6667 5: 116.6667 cents 116.6667 6: 116.6667 cents 116.6667 7: 116.6667 cents 116.6667 8: 33.3333 cents 33.3333 9: 83.3000 cents 83.3000 10: 33.3667 cents 33.3667 11: 116.6667 cents 116.6667 12: 116.6667 cents 116.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.33333 cents 1: 1 33.36667 cents 1: 1 83.30000 cents 1: 9 116.66667 cents 2: 1 116.63333 cents 2: 1 116.66667 cents 2: 1 150.00000 cents 2: 1 150.03333 cents 2: 8 233.33333 cents 3: 1 150.00000 cents 3: 1 233.30000 cents 3: 1 233.33333 cents 3: 1 266.66667 cents 3: 1 266.70000 cents 3: 7 350.00000 cents 4: 2 266.66667 cents 4: 1 349.96667 cents 4: 1 350.00000 cents 4: 1 383.33333 cents 4: 1 383.36667 cents 4: 6 466.66667 cents 5: 3 383.33333 cents 5: 1 466.63333 cents 5: 1 466.66667 cents 5: 1 500.00000 cents 5: 1 500.03333 cents 5: 5 583.33333 cents 6: 4 500.00000 cents 6: 1 583.30000 cents 6: 1 583.33333 cents 6: 1 616.66667 cents 6: 1 616.70000 cents 6: 4 700.00000 cents 7: 5 616.66667 cents 7: 1 699.96667 cents 7: 1 700.00000 cents 7: 1 733.33333 cents 7: 1 733.36667 cents 7: 3 816.66667 cents 8: 6 733.33333 cents 8: 1 816.63333 cents 8: 1 816.66667 cents 8: 1 850.00000 cents 8: 1 850.03333 cents 8: 2 933.33333 cents 9: 7 850.00000 cents 9: 1 933.30000 cents 9: 1 933.33333 cents 9: 1 966.66667 cents 9: 1 966.70000 cents 9: 1 1050.00000 cents 10: 8 966.66667 cents 10: 1 1049.96667 cents 10: 1 1050.00000 cents 10: 1 1083.33333 cents 10: 1 1083.36667 cents 11: 9 1083.33333 cents 11: 1 1116.70000 cents 11: 1 1166.63333 cents 11: 1 1166.66667 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.45455 = 60/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 116.7 233.3 350.0 466.7 583.3 700.0 816.7 850.0 933.3 966.7 1083.3 1200.0 116.7 : 116.7 233.3 350.0 466.7 583.3 700.0 733.3 816.6 850.0 966.7 1083.3 1200.0 233.3 : 116.7 233.3 350.0 466.7 583.3 616.7 700.0 733.3 850.0 966.7 1083.3 1200.0 350.0 : 116.7 233.3 350.0 466.7 500.0 583.3 616.7 733.3 850.0 966.7 1083.3 1200.0 466.7 : 116.7 233.3 350.0 383.3 466.6 500.0 616.7 733.3 850.0 966.7 1083.3 1200.0 583.3 : 116.7 233.3 266.7 350.0 383.3 500.0 616.7 733.3 850.0 966.7 1083.3 1200.0 700.0 : 116.7 150.0 233.3 266.7 383.3 500.0 616.7 733.3 850.0 966.7 1083.3 1200.0 816.7 : 33.3 116.6 150.0 266.7 383.3 500.0 616.7 733.3 850.0 966.7 1083.3 1200.0 850.0 : 83.3 116.7 233.3 350.0 466.7 583.3 700.0 816.7 933.3 1050.0 1166.7 1200.0 933.3 : 33.4 150.0 266.7 383.4 500.0 616.7 733.4 850.0 966.7 1083.4 1116.7 1200.0 966.7 : 116.7 233.3 350.0 466.7 583.3 700.0 816.7 933.3 1050.0 1083.3 1166.6 1200.0 1083.3: 116.7 233.3 350.0 466.7 583.3 700.0 816.7 933.3 966.7 1050.0 1083.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 116.6667 cents 83.33333 cents 33.33333 cents 2: 116.6333 .. 233.3333 cents 116.70000 cents -0.03333 cents 3: 150.0000 .. 350.0000 cents 200.00000 cents -83.33333 cents 4: 266.6667 .. 466.6667 cents 200.00000 cents -83.33333 cents 5: 383.3333 .. 583.3333 cents 200.00000 cents -83.33333 cents 6: 500.0000 .. 700.0000 cents 200.00000 cents -83.33333 cents 7: 616.6667 .. 816.6667 cents 200.00000 cents -83.33333 cents 8: 733.3333 .. 933.3333 cents 200.00000 cents -83.33333 cents 9: 850.0000 .. 1050.0000 cents 200.00000 cents -83.33333 cents 10: 966.6667 .. 1083.3667 cents 116.70000 cents -83.33333 cents 11: 1083.3333 .. 1166.6667 cents 83.33333 cents -0.03333 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 33.33333 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 116.66667 cents Average / Smallest step : 3.000000 Largest / Average step : 1.166667 Largest / Smallest step : 3.500000 Median interval of one step : 116.66667 cents, amount: 9 Most common interval of one step : 116.66667 cents, amount: 9 Least squares average step : 103.87133 cents, oct.: 1246.45600 cents Scale is not proper Step pattern alph. order: AAAAAAABCDAA Step pattern size order : DDDDDDDACBDD Scale is not a Constant Structure Scale diversity : 1.189692 Lumma stability : 0.055556 Lumma impropriety factor : 0.555611 Rothenberg efficiency : 0.458333 redundancy: 0.541667 Efficiency x scale size : 5.500000 Number of different interval sizes : 42 = 3.81818 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 5.45455 = 60/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 0.03333 cents Most common intervals : 116.66667 cents & inv., amount: 10 Most common triad is 0.0 116.667 1083.333 cents, amount: 9 Number of recognisable fifths : 6, average 699.9944 cents Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 2 1 0 1 0 1 2 N SD: 50.4590 c. M: 83.3333 c. 13: 1 1 1 2 1 1 1 1 1 0 1 2 N SD: 45.8346 c. M: 78.2051 c. 14: 1 2 1 1 2 1 2 0 1 0 2 1 N SD: 23.8305 c. M:-40.4762 c. 16: 1 2 1 2 2 1 2 0 1 1 1 2 N SD: 26.5675 c. M: 50.0000 c. 17: 2 1 2 2 1 2 2 0 1 1 1 2 N SD: 19.2635 c. M:-30.3922 c. 19: 2 1 2 2 2 2 2 0 2 0 2 2 N SD: 21.5273 c. M: 43.8596 c. 20: 2 2 2 2 2 2 2 0 2 0 2 2 N D3 SD: 14.2127 c. M:-26.7000 c. 21: 2 2 2 2 2 2 2 1 1 1 2 2 N SD: 10.1430 c. M: 19.0143 c. 24: 2 3 2 2 3 2 2 1 2 0 3 2 N SD: 13.6117 c. M:-16.7000 c. 27: 3 2 3 3 2 3 2 1 2 1 2 3 N SD: 12.2138 c. M:-22.2222 c. 28: 3 2 3 3 3 2 3 1 2 1 2 3 N SD: 11.9466 c. M:-19.0476 c. 31: 3 3 3 3 3 3 3 1 2 1 3 3 N G SD: 2.2863 c. M: 4.2677 c. 41: 4 4 4 4 4 4 4 1 3 1 4 4 N G SD: 1.7378 c. M:-3.2854 c. 72: 7 7 7 7 7 7 7 2 5 2 7 7 N G SD: 0.0096 c. M:-0.0333 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 3 x x x x x 4 S SD: 0.9775 cents 3 x x x 4 x x x 5 x x x 6 S SD: 15.5103 cents 4 x x 5 x x 6 x x x 7 x 8 S SD: 9.1076 cents 5 x x 6 x 7 x 8 x x 9 x 10 S SD: 12.3027 cents 6 x 7 x 8 x 9 x 10 x x 11:12 S SD: 11.1152 cents 7 x 8 x 9:10 x 11 x 12 x 13:14 S SD: 8.4175 cents 8 x 9:10 x 11:12 x 13 x 14:15:16 S SD: 7.2154 cents 9 x 10:11:12:13 x 14:15 x 16:17:18 S SD: 11.8959 cents 10:11 x 12:13:14:15:16 x 17 x 19:20 SD: 7.5986 cents 11:12:13 x 14:15:16 x 18:19 x 21:22 SD: 12.6471 cents 12:13:14:15:16:17:18:19:20 x 21:22:24 S SD: 7.6511 cents 13:14:15:16:17:18:19:21 x 22:23:24:26 SD: 5.9623 cents 14:15:16:17:18:20:21:22:23:24 x 26:28 S SD: 5.5782 cents 15:16:17:18:20:21:22:24:25 x 26:28:30 S SD: 6.5790 cents 16:17:18:20:21:22:24 x 26:27:28:30:32 S SD: 5.9187 cents 17:18:19:21:22:24:25:27:28:29:30:32:34 SD: 5.7742 cents 18:19:21:22:24:25:27:29 x 31 x 34:36 SD: 5.7632 cents 19:20:22:23:25:27:28:30:31 x 33:36:38 SD: 6.0401 cents 20:21:23:24:26:28:30:32:33:34:35:37:40 SD: 4.7888 cents 21:22:24:26:28:29:31 x 34:36:37:39:42 SD: 6.1175 cents 22:24:25:27:29:31:33:35:36:38 x 41:44 SD: 3.9985 cents 25:27:29:31:33:35:37:40:41:43:44:47:50 SD: 3.9972 cents 26:28:30:32:34:36:39:42 x 45 x 49:52 SD: 3.8511 cents 27:29:31:33:35:38:40:43:44:46:47:50:54 SD: 3.1500 cents 28:30:32:34:37:39:42:45:46:48:49:52:56 SD: 2.3646 cents 40:43:46:49:52:56:60:64:65:69:70:75:80 SD: 1.9526 cents 48:51:55:59:63:67:72:77:78:82:84:90:96 SD: 1.6887 cents 55:59:63:67:72:77:82:88:90:94:96:103:110 SD: 1.2611 cents 68:73:78:83:89:95:102:109:111:117:119:127:136 SD: 1.0313 cents 84:90:96:103:110:118:126:135:137:144:147:157:168 SD: 0.7826 cents 90:96:103:110:118:126:135:144:147:154:157:168:180 SD: 0.7473 cents 98:105:112:120:128:137:147:157:160:168:171:183:196 SD: 0.6552 cents 126:135:144:154:165:176:189:202:206:216:220:236:252 SD: 0.6436 cents 130:139:149:159:170:182:195:208:212:223:227:243:260 SD: 0.5515 cents 139:149:159:170:182:195:208:223:227:238:243:260:278 SD: 0.5084 cents 159:170:182:195:208:223:238:255:260:273:278:297:318 SD: 0.4955 cents 174:186:199:213:228:244:261:279:284:298:304:325:348 SD: 0.3952 cents 187:200:214:229:245:262:280:300:306:321:327:350:374 SD: 0.3857 cents 200:214:229:245:262:280:300:321:327:343:350:374:400 SD: 0.3781 cents 214:229:245:262:280:300:321:343:350:367:374:400:428 SD: 0.2925 cents 229:245:262:280:300:321:343:367:374:393:400:428:458 SD: 0.2858 cents 255:273:292:312:334:357:382:409:417:437:446:477:510 SD: 0.2833 cents 259:277:296:317:339:363:388:415:423:444:453:484:518 SD: 0.2573 cents 277:296:317:339:363:388:415:444:453:475:484:518:554 SD: 0.2421 cents 285:305:326:349:373:399:427:457:466:489:498:533:570 SD: 0.2246 cents 317:339:363:388:415:444:475:508:518:543:554:593:634 SD: 0.1917 cents 375:401:429:459:491:525:562:601:613:643:655:701:750 SD: 0.1559 cents 456:488:522:558:597:639:683:731:745:782:797:853:912 SD: 0.1552 cents 459:491:525:562:601:643:688:736:750:787:802:858:918 SD: 0.1293 cents 514:550:588:629:673:720:770:824:840:881:898:961:1028 SD: 0.1125 cents 576:616:659:705:754:807:863:923:941:988:1007:1077:1152 SD: 0.1122 cents