Scala analysis: 12highschool2-miracle
12highschool2 tempered in 11-limit POTE-tuned miracle
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.633 cents 116.632740 2: 199.593 cents 199.592910 3: 316.226 cents 316.225660 4: 383.571 cents 383.570800 5: 500.204 cents 500.203540 6: 616.836 cents 616.836290 7: 699.796 cents 699.796460 8: 816.429 cents 816.429200 9: 883.774 cents 883.774340 10: 966.735 cents 966.734510 11: 1083.367 cents 1083.367260 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 116.6327 cents 116.6327 1: 116.6327 cents 116.6327 2: 82.9602 cents 82.9602 3: 116.6328 cents 116.6328 4: 67.3451 cents 67.3451 5: 116.6327 cents 116.6327 6: 116.6327 cents 116.6327 7: 82.9602 cents 82.9602 8: 116.6327 cents 116.6327 9: 67.3451 cents 67.3451 10: 82.9602 cents 82.9602 11: 116.6328 cents 116.6328 12: 116.6327 cents 116.6327
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 67.34514 cents 1: 3 82.96017 cents 1: 7 116.63274 cents 2: 1 150.30531 cents 2: 3 183.97789 cents 2: 5 199.59291 cents 2: 3 233.26549 cents 3: 4 266.93806 cents 3: 2 300.61063 cents 3: 5 316.22566 cents 3: 1 349.89823 cents 4: 1 349.89822 cents 4: 6 383.57080 cents 4: 1 417.24338 cents 4: 4 432.85840 cents 5: 2 466.53097 cents 5: 8 500.20354 cents 5: 1 515.81857 cents 5: 1 549.49115 cents 6: 1 567.54868 cents 6: 5 583.16372 cents 6: 5 616.83629 cents 6: 1 632.45132 cents 7: 1 650.50885 cents 7: 1 684.18143 cents 7: 8 699.79646 cents 7: 2 733.46903 cents 8: 4 767.14160 cents 8: 1 782.75662 cents 8: 6 816.42920 cents 8: 1 850.10178 cents 9: 1 850.10177 cents 9: 5 883.77434 cents 9: 2 899.38937 cents 9: 4 933.06194 cents 10: 3 966.73451 cents 10: 5 1000.40709 cents 10: 3 1016.02211 cents 10: 1 1049.69469 cents 11: 7 1083.36726 cents 11: 3 1117.03983 cents 11: 2 1132.65486 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.81818 = 42/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 116.6 199.6 316.2 383.6 500.2 616.8 699.8 816.4 883.8 966.7 1083.4 1200.0 116.6 : 83.0 199.6 266.9 383.6 500.2 583.2 699.8 767.1 850.1 966.7 1083.4 1200.0 199.6 : 116.6 184.0 300.6 417.2 500.2 616.8 684.2 767.1 883.8 1000.4 1117.0 1200.0 316.2 : 67.3 184.0 300.6 383.6 500.2 567.5 650.5 767.1 883.8 1000.4 1083.4 1200.0 383.6 : 116.6 233.3 316.2 432.9 500.2 583.2 699.8 816.4 933.1 1016.0 1132.7 1200.0 500.2 : 116.6 199.6 316.2 383.6 466.5 583.2 699.8 816.4 899.4 1016.0 1083.4 1200.0 616.8 : 83.0 199.6 266.9 349.9 466.5 583.2 699.8 782.8 899.4 966.7 1083.4 1200.0 699.8 : 116.6 184.0 266.9 383.6 500.2 616.8 699.8 816.4 883.8 1000.4 1117.0 1200.0 816.4 : 67.3 150.3 266.9 383.6 500.2 583.2 699.8 767.1 883.8 1000.4 1083.4 1200.0 883.8 : 83.0 199.6 316.2 432.9 515.8 632.5 699.8 816.4 933.1 1016.0 1132.7 1200.0 966.7 : 116.6 233.3 349.9 432.9 549.5 616.8 733.5 850.1 933.1 1049.7 1117.0 1200.0 1083.4: 116.6 233.3 316.2 432.9 500.2 616.8 733.5 816.4 933.1 1000.4 1083.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.3451 .. 116.6327 cents 49.28760 cents 67.34514 cents 2: 150.3053 .. 233.2655 cents 82.96018 cents 33.67257 cents 3: 266.9381 .. 349.8982 cents 82.96017 cents 33.67257 cents 4: 349.8982 .. 432.8584 cents 82.96018 cents -0.00001 cents 5: 466.5310 .. 549.4912 cents 82.96018 cents 33.67257 cents 6: 567.5487 .. 632.4513 cents 64.90264 cents 18.05753 cents 7: 650.5089 .. 733.4690 cents 82.96018 cents 18.05753 cents 8: 767.1416 .. 850.1018 cents 82.96018 cents 33.67257 cents 9: 850.1018 .. 933.0619 cents 82.96017 cents -0.00001 cents 10: 966.7345 .. 1049.6947 cents 82.96018 cents 33.67257 cents 11: 1083.3673 .. 1132.6549 cents 49.28760 cents 33.67257 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 67.34514 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 116.63274 cents Average / Smallest step : 1.484888 Largest / Average step : 1.166327 Largest / Smallest step : 1.731866 Median interval of one step : 116.63274 cents, amount: 7 Most common interval of one step : 116.63274 cents, amount: 7 Least squares average step : 99.33720 cents, oct.: 1192.04634 cents Scale is proper Scale is a mode of a 1461-tone equal temperament with octave 1200.000 cents degrees: 142 243 385 467 609 751 852 994 1076 1177 1319 1461 Least number of segments generator : 731 of 600.411 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1319 of 1083.368 cents and inv. generated superset size: 27 = 15 more = 225.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACAABACBAA Step pattern size order : LMLSLLMLSMLL Scale is not a Constant Structure Scale diversity : 1.432227 Rothenberg stability : 0.969697 = 32/33 Lumma stability : 0.310701 Rothenberg efficiency : 0.357735 redundancy: 0.642265 Efficiency x scale size : 4.292821 Number of different interval sizes : 40 = 3.63636 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.81818 = 42/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 15.61502 cents Most common intervals : 500.20354 cents & inv., amount: 8 Most common triad is 0.0 500.204 699.796 cents, amount: 5 Number of recognisable fifths : 8, average 699.7965 cents Best fifths form a closed circle Formal octave complements present : 9 = 75.0000% -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 15.8377 c. M:-33.2655 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 2 1 2 2 1 2 1 1 2 2 N D3 SD: 9.0215 c. M: 19.3661 c. 22: 2 2 2 1 2 2 2 2 1 2 2 2 P D3 I SD: 10.7753 c. M:-18.5889 c. 29: 3 2 3 1 3 3 2 3 1 2 3 3 N SD: 9.6626 c. M: 15.0104 c. 31: 3 2 3 2 3 3 2 3 2 2 3 3 P D3 SD: 3.8002 c. M:-6.5482 c. 41: 4 3 4 2 4 4 3 4 2 3 4 4 P SD: 3.3227 c. M:-5.7256 c. 53: 5 4 5 3 5 5 4 5 3 4 5 5 SP SD: 3.3133 c. M:-6.8504 c. 72: 7 5 7 4 7 7 5 7 4 5 7 7 P SD: 0.2559 c. M:-0.4410 c. 247: 24 17 24 14 24 24 17 24 14 17 24 24 P SD: 0.2531 c. M:-0.4362 c. 319: 31 22 31 18 31 31 22 31 18 22 31 31 P SD: 0.1382 c. M:-0.2382 c. 391: 38 27 38 22 38 38 27 38 22 27 38 38 P SD: 0.0657 c. M:-0.1131 c. 463: 45 32 45 26 45 45 32 45 26 32 45 45 P SD: 0.0156 c. M:-0.0270 c. 998: 97 69 97 56 97 97 69 97 56 69 97 97 P SD: 0.0040 c. M:-0.0068 c. 1461: 142 101 142 82 142 142 101 142 82 101 142 142 P SD: 0.0023 c. M:-0.0039 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: 1.0793 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.7454 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 1.0173 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 12.2848 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 10.0026 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 11.1287 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 7.1290 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.2342 cents 10 x 11:12 x 13:14:15:16:17 x 19:20 SD: 8.9529 cents 11:12 x 13:14:15:16 x x 18:19:21:22 SD: 9.9997 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.2471 cents 13:14:15 x 16:17:19 x 21:22:23:24:26 SD: 8.8152 cents 14:15:16:17 x 19:20:21:22:23:24:26:28 SD: 6.5724 cents 15:16:17:18:19:20:21:22:24:25:26:28:30 S SD: 5.0923 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 4.2582 cents 18:19:20:22 x 24:26:27:29:30:31:34:36 SD: 5.1849 cents 23:25:26:28:29:31:33:34:37:38:40:43:46 SD: 4.5954 cents 24:26:27:29:30:32:34:36:38:40:42:45:48 SD: 3.0075 cents 30:32:34:36:37:40:43:45:48:50:52:56:60 SD: 2.6515 cents 32:34:36:38:40:43:46:48:51:53:56:60:64 SD: 2.6361 cents 39:42:44:47:49:52:56:58:63:65:68:73:78 SD: 2.4608 cents 40:43:45:48:50:53:57:60:64:67:70:75:80 SD: 1.6841 cents 56:60:63:67:70:75:80:84:90:93:98:105:112 SD: 1.1412 cents 60:64:67:72:75:80:86:90:96:100:105:112:120 SD: 1.1044 cents 75:80:84:90:94:100:107:112:120:125:131:140:150 SD: 1.0050 cents 84:90:94:101:105:112:120:126:135:140:147:157:168 SD: 0.7761 cents 105:112:118:126:131:140:150:157:168:175:184:196:210 SD: 0.7576 cents 114:122:128:137:142:152:163:171:183:190:199:213:228 SD: 0.5649 cents 129:138:145:155:161:172:184:193:207:215:225:241:258 SD: 0.5641 cents 140:150:157:168:175:187:200:210:224:233:245:262:280 SD: 0.5346 cents 156:167:175:187:195:208:223:234:250:260:273:292:312 SD: 0.5035 cents 161:172:181:193:201:215:230:241:258:268:281:301:322 SD: 0.4732 cents 170:182:191:204:212:227:243:255:272:283:297:318:340 SD: 0.4332 cents 173:185:194:208:216:231:247:259:277:288:302:323:346 SD: 0.4305 cents 189:202:212:227:236:252:270:283:303:315:330:353:378 SD: 0.3527 cents 215:230:241:258:268:287:307:322:345:358:376:402:430 SD: 0.3339 cents 229:245:257:275:286:306:327:343:367:382:400:428:458 SD: 0.2761 cents 245:262:275:294:306:327:350:367:393:408:428:458:490 SD: 0.2290 cents 269:288:302:323:336:359:384:403:431:448:470:503:538 SD: 0.2206 cents 329:352:369:395:411:439:470:493:527:548:575:615:658 SD: 0.2083 cents 359:384:403:431:448:479:513:538:575:598:627:671:718 SD: 0.2055 cents 360:385:404:432:449:481:514:539:577:600:629:673:720 SD: 0.2027 cents 400:428:449:480:499:534:571:599:641:666:699:748:800 SD: 0.1630 cents 444:475:498:533:554:593:634:665:712:740:776:830:888 SD: 0.1572 cents 460:492:516:552:574:614:657:689:737:766:804:860:920 SD: 0.1252 cents 516:552:579:619:644:689:737:773:827:860:902:965:1032 SD: 0.1228 cents 588:629:660:706:734:785:840:881:942:980:1028:1099:1176 SD: 0.1203 cents