Scala analysis: prodigy12
Prodigy[12] 225/224&441/440 hobbit, 72et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.667 cents 116.666670 2: 233.333 cents 233.333330 3: 266.667 cents 266.666670 4: 383.333 cents 383.333330 5: 500.000 cents 500.000000 6: 583.333 cents 583.333330 7: 700.000 cents 700.000000 8: 816.667 cents 816.666670 9: 933.333 cents 933.333330 10: 966.667 cents 966.666670 11: 1083.333 cents 1083.333330 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 116.6667 cents 116.6667 1: 116.6667 cents 116.6667 2: 116.6667 cents 116.6667 3: 33.3333 cents 33.3333 4: 116.6667 cents 116.6667 5: 116.6667 cents 116.6667 6: 83.3333 cents 83.3333 7: 116.6667 cents 116.6667 8: 116.6667 cents 116.6667 9: 116.6667 cents 116.6667 10: 33.3333 cents 33.3333 11: 116.6667 cents 116.6667 12: 116.6667 cents 116.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 33.33334 cents 1: 1 83.33333 cents 1: 9 116.66667 cents 2: 4 150.00000 cents 2: 2 200.00000 cents 2: 6 233.33333 cents 3: 6 266.66667 cents 3: 3 316.66666 cents 3: 3 350.00000 cents 4: 1 350.00000 cents 4: 7 383.33333 cents 4: 3 433.33333 cents 4: 1 466.66666 cents 5: 3 466.66666 cents 5: 7 500.00000 cents 5: 2 550.00000 cents 6: 1 533.33334 cents 6: 5 583.33333 cents 6: 5 616.66667 cents 6: 1 666.66666 cents 7: 2 650.00000 cents 7: 7 700.00000 cents 7: 3 733.33334 cents 8: 1 733.33334 cents 8: 3 766.66667 cents 8: 7 816.66667 cents 8: 1 850.00000 cents 9: 3 850.00000 cents 9: 3 883.33334 cents 9: 6 933.33333 cents 10: 6 966.66667 cents 10: 2 1000.00000 cents 10: 4 1050.00000 cents 11: 9 1083.33333 cents 11: 1 1116.66667 cents 11: 2 1166.66666 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 116.7 233.3 266.7 383.3 500.0 583.3 700.0 816.7 933.3 966.7 1083.3 1200.0 116.7 : 116.7 150.0 266.7 383.3 466.7 583.3 700.0 816.7 850.0 966.7 1083.3 1200.0 233.3 : 33.3 150.0 266.7 350.0 466.7 583.3 700.0 733.3 850.0 966.7 1083.3 1200.0 266.7 : 116.7 233.3 316.7 433.3 550.0 666.7 700.0 816.7 933.3 1050.0 1166.7 1200.0 383.3 : 116.7 200.0 316.7 433.3 550.0 583.3 700.0 816.7 933.3 1050.0 1083.3 1200.0 500.0 : 83.3 200.0 316.7 433.3 466.7 583.3 700.0 816.7 933.3 966.7 1083.3 1200.0 583.3 : 116.7 233.3 350.0 383.3 500.0 616.7 733.3 850.0 883.3 1000.0 1116.7 1200.0 700.0 : 116.7 233.3 266.7 383.3 500.0 616.7 733.3 766.7 883.3 1000.0 1083.3 1200.0 816.7 : 116.7 150.0 266.7 383.3 500.0 616.7 650.0 766.7 883.3 966.7 1083.3 1200.0 933.3 : 33.3 150.0 266.7 383.3 500.0 533.3 650.0 766.7 850.0 966.7 1083.3 1200.0 966.7 : 116.7 233.3 350.0 466.7 500.0 616.7 733.3 816.7 933.3 1050.0 1166.7 1200.0 1083.3: 116.7 233.3 350.0 383.3 500.0 616.7 700.0 816.7 933.3 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 33.33334 cents 2: 150.0000 .. 233.3333 cents 83.33333 cents 33.33333 cents 3: 266.6667 .. 350.0000 cents 83.33333 cents 33.33334 cents 4: 350.0000 .. 466.6667 cents 116.66666 cents 1/1, 0.0000 cents 5: 466.6667 .. 550.0000 cents 83.33334 cents 1/1, 0.0000 cents 6: 533.3333 .. 666.6667 cents 133.33332 cents -16.66666 cents 7: 650.0000 .. 733.3333 cents 83.33334 cents -16.66666 cents 8: 733.3333 .. 850.0000 cents 116.66666 cents 1/1, 0.0000 cents 9: 850.0000 .. 933.3333 cents 83.33333 cents 1/1, 0.0000 cents 10: 966.6667 .. 1050.0000 cents 83.33333 cents 33.33334 cents 11: 1083.3333 .. 1166.6667 cents 83.33333 cents 33.33333 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 33.33334 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 116.66667 cents Average / Smallest step : 2.999999 Largest / Average step : 1.166667 Largest / Smallest step : 3.499999 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 : 99.58974 cents, oct.: 1195.07692 cents Scale is not proper Scale is a mode of a 72-tone equal temperament with octave 1200.000 cents degrees: 7 14 16 23 30 35 42 49 56 58 65 72 Least number of segments generator : 37 of 616.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 65 of 1083.333 cents and inv. generated superset size: 17 = 5 more = 141.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAACAAABAA Step pattern size order : LLSLLMLLLSLL Interval vector is [ 0 2 0 0 1 0 9 0 4 0 0 2 0 6 0 6 0 0 3 0 4 0 7 0 0 3 0 4 0 7 0 1 2 0 5 0 ] Scale is not a Constant Structure Scale diversity : 1.384899 Lumma stability : 0.166667 Lumma impropriety factor : 0.027778 Rothenberg efficiency : 0.423605 redundancy: 0.576395 Efficiency x scale size : 5.083261 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 16.66666 cents Most common intervals : 116.66667 cents & inv., amount: 9 Most common triad is 0.0 116.667 1083.333 cents, amount: 6 Number of recognisable fifths : 7, average 700.0000 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 22.0479 c. M:-33.3333 c. Twelve-tone Chromatic (1/11-comma) 19: 2 2 0 2 2 1 2 2 2 0 2 2 N SD: 11.6950 c. M:-19.2982 c. 21: 2 2 1 2 2 1 2 2 2 1 2 2 P D3 SD: 12.5424 c. M:-19.0476 c. 22: 2 2 1 2 2 2 2 2 2 1 2 2 P D3 I SD: 9.5527 c. M:-16.6667 c. 31: 3 3 1 3 3 2 3 3 3 1 3 3 P SD: 2.8322 c. M:-4.3011 c. 41: 4 4 1 4 4 3 4 4 4 1 4 4 N SD: 2.1414 c. M:-3.2520 c. 72: 7 7 2 7 7 5 7 7 7 2 7 7 N SD: 0.0000 c. M:-0.0000 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: 0.9775 cents 3 x x x x 4 x x x 5 x x 6 S SD: 16.3379 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 1.0418 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 14.1448 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.9445 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.2545 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 6.2522 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 12.6606 cents 10:11 x 12 x 13:14:15:16:17 x 19:20 SD: 9.8364 cents 11:12 x 13:14:15 x 16:18:19 x 21:22 SD: 10.8812 cents 12:13 x 14:15:16:17:18:19 x 21:22:24 SD: 4.9874 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 7.0669 cents 14:15:16 x 17:19:20:21:22:24 x 26:28 SD: 7.4412 cents 15:16:17:18:19:20:21:22:24 x 26:28:30 S SD: 6.4060 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 6.0085 cents 17:18:19:20:21:23:24:25:27:29:30:32:34 SD: 5.9001 cents 18:19 x 21:22:24:25:27:29:31 x 34:36 SD: 4.9993 cents 19:20 x 22:24:25:27:28:30 x 33:36:38 SD: 6.9123 cents 20:21:23 x 25:27:28:30:32:34:35:37:40 SD: 4.1374 cents 22:24:25:26:27:29:31:33:35:38 x 41:44 SD: 5.4404 cents 23:25:26:27:29:31:32:34:37:39:40:43:46 SD: 4.6352 cents 24:26:27:28:30:32:34:36:38:41:42:45:48 SD: 3.9637 cents 25:27 x 29:31:33:35:37:40:43:44:47:50 SD: 3.6274 cents 26:28:30 x 32:35:36:39:42:45 x 49:52 SD: 4.6585 cents 27:29:31:32:34:36:38:40:43:46:47:50:54 SD: 3.8245 cents 28:30:32:33:35:37:39:42:45:48:49:52:56 SD: 2.5040 cents 32:34 x 37:40:43:45:48:51:55:56:60:64 SD: 2.4180 cents 33:35:38 x 41:44:46:49:53:57:58:62:66 SD: 2.9517 cents 35:37:40:41:44:47:49:52:56:60:61:65:70 SD: 2.8027 cents 36:39:41:42:45:48:50:54:58:62:63:67:72 SD: 2.6172 cents 39:42:45 x 49:52:55:58:63:67:68:73:78 SD: 2.8909 cents 40:43:46:47:50:53:56:60:64:69:70:75:80 SD: 2.0942 cents 42:45:48:49:52:56:59:63:67:72:73:79:84 SD: 1.8605 cents 48:51:55:56:60:64:67:72:77:82:84:90:96 SD: 1.3568 cents 60:64:69:70:75:80:84:90:96:103:105:112:120 SD: 0.9934 cents 84:90:96:98:105:112:118:126:135:144:147:157:168 SD: 0.7543 cents 113:121:129:132:141:151:158:169:181:194:198:211:226 SD: 0.7382 cents 125:134:143:146:156:167:175:187:200:214:218:234:250 SD: 0.6612 cents 126:135:144:147:157:168:176:189:202:216:220:236:252 SD: 0.6562 cents 132:141:151:154:165:176:185:198:212:226:231:247:264 SD: 0.5847 cents 144:154:165:168:180:192:202:216:231:247:252:269:288 SD: 0.5197 cents 158:169:181:184:197:211:221:237:253:271:276:295:316 SD: 0.4876 cents 173:185:198:202:216:231:242:259:277:297:302:323:346 SD: 0.4565 cents 174:186:199:203:217:232:244:261:279:298:304:325:348 SD: 0.3952 cents 214:229:245:250:267:286:300:321:343:367:374:400:428 SD: 0.3573 cents 215:230:246:251:268:287:301:322:345:369:376:402:430 SD: 0.3228 cents 227:243:260:265:283:303:318:340:364:389:397:424:454 SD: 0.3154 cents 229:245:262:267:286:306:321:343:367:393:400:428:458 SD: 0.2993 cents 242:259:277:282:302:323:339:363:388:415:423:452:484 SD: 0.2876 cents 257:275:294:300:321:343:360:385:412:441:449:481:514 SD: 0.2736 cents 269:288:308:314:336:359:377:403:431:461:470:503:538 SD: 0.2625 cents 277:296:317:323:346:370:388:415:444:475:484:518:554 SD: 0.2456 cents 299:320:342:349:373:399:419:448:479:513:523:559:598 SD: 0.2277 cents 319:341:365:372:398:426:447:478:511:547:558:596:638 SD: 0.2264 cents 347:371:397:405:433:463:486:520:556:595:606:649:694 SD: 0.1852 cents 415:444:475:484:518:554:581:622:665:712:725:776:830 SD: 0.1651 cents 444:475:508:518:554:593:622:665:712:761:776:830:888 SD: 0.1387 cents 504:539:577:588:629:673:706:755:808:864:881:942:1008 SD: 0.1214 cents 546:584:625:637:681:729:765:818:875:936:954:1021:1092 SD: 0.1210 cents 576:616:659:672:719:769:807:863:923:988:1007:1077:1152 SD: 0.1153 cents