Scala analysis: malcolmm
Malcolm's monochord in 1/4-kleisma marvel
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 115.587 cents 115.587047 2: 200.054 cents 200.054240 3: 315.641 cents 315.641288 4: 384.386 cents 384.385833 5: 499.973 cents 499.972880 6: 584.440 cents 584.440075 7: 700.027 cents 700.027121 8: 815.614 cents 815.614167 9: 884.359 cents 884.358713 10: 999.946 cents 999.945760 11: 1084.413 cents 1084.412954 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 115.5870 cents 115.5870 1: 115.5870 cents 115.5870 2: 84.4672 cents 84.4672 3: 115.5870 cents 115.5870 4: 68.7445 cents 68.7445 5: 115.5870 cents 115.5870 6: 84.4672 cents 84.4672 7: 115.5870 cents 115.5870 8: 115.5870 cents 115.5870 9: 68.7445 cents 68.7445 10: 115.5870 cents 115.5870 11: 84.4672 cents 84.4672 12: 115.5870 cents 115.5870
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 68.74454 cents 1: 3 84.46719 cents 1: 7 115.58705 cents 2: 4 184.33159 cents 2: 6 200.05424 cents 2: 2 231.17409 cents 3: 3 268.79879 cents 3: 3 299.91864 cents 3: 6 315.64129 cents 4: 7 384.38583 cents 4: 1 400.10848 cents 4: 1 415.50568 cents 4: 3 431.22833 cents 5: 1 468.85303 cents 5: 9 499.97288 cents 5: 2 515.69553 cents 6: 1 568.71742 cents 6: 5 584.44007 cents 6: 5 615.55993 cents 6: 1 631.28258 cents 7: 2 684.30447 cents 7: 9 700.02712 cents 7: 1 731.14697 cents 8: 3 768.77167 cents 8: 1 784.49432 cents 8: 1 799.89152 cents 8: 7 815.61417 cents 9: 6 884.35871 cents 9: 3 900.08136 cents 9: 3 931.20121 cents 10: 2 968.82591 cents 10: 6 999.94576 cents 10: 4 1015.66841 cents 11: 7 1084.41295 cents 11: 3 1115.53281 cents 11: 2 1131.25546 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 : 115.6 200.1 315.6 384.4 500.0 584.4 700.0 815.6 884.4 999.9 1084.4 1200.0 115.6 : 84.5 200.1 268.8 384.4 468.9 584.4 700.0 768.8 884.4 968.8 1084.4 1200.0 200.1 : 115.6 184.3 299.9 384.4 500.0 615.6 684.3 799.9 884.4 999.9 1115.5 1200.0 315.6 : 68.7 184.3 268.8 384.4 500.0 568.7 684.3 768.8 884.4 999.9 1084.4 1200.0 384.4 : 115.6 200.1 315.6 431.2 500.0 615.6 700.0 815.6 931.2 1015.7 1131.3 1200.0 500.0 : 84.5 200.1 315.6 384.4 500.0 584.4 700.0 815.6 900.1 1015.7 1084.4 1200.0 584.4 : 115.6 231.2 299.9 415.5 500.0 615.6 731.1 815.6 931.2 999.9 1115.5 1200.0 700.0 : 115.6 184.3 299.9 384.4 500.0 615.6 700.0 815.6 884.4 999.9 1084.4 1200.0 815.6 : 68.7 184.3 268.8 384.4 500.0 584.4 700.0 768.8 884.4 968.8 1084.4 1200.0 884.4 : 115.6 200.1 315.6 431.2 515.7 631.3 700.0 815.6 900.1 1015.7 1131.3 1200.0 999.9 : 84.5 200.1 315.6 400.1 515.7 584.4 700.0 784.5 900.1 1015.7 1084.4 1200.0 1084.4: 115.6 231.2 315.6 431.2 500.0 615.6 700.0 815.6 931.2 999.9 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 68.7445 .. 115.5870 cents 46.84250 cents 68.74454 cents 2: 184.3316 .. 231.1741 cents 46.84250 cents 68.74455 cents 3: 268.7988 .. 315.6413 cents 46.84250 cents 37.62469 cents 4: 384.3858 .. 431.2283 cents 46.84250 cents 68.74454 cents 5: 468.8530 .. 515.6955 cents 46.84250 cents 37.62469 cents 6: 568.7174 .. 631.2826 cents 62.56515 cents 53.02190 cents 7: 684.3045 .. 731.1470 cents 46.84250 cents 53.02190 cents 8: 768.7717 .. 815.6142 cents 46.84250 cents 37.62469 cents 9: 884.3587 .. 931.2012 cents 46.84250 cents 68.74455 cents 10: 968.8259 .. 1015.6684 cents 46.84250 cents 37.62469 cents 11: 1084.4130 .. 1131.2555 cents 46.84250 cents 68.74455 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 68.74454 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 115.58705 cents Average / Smallest step : 1.454661 Largest / Average step : 1.155870 Largest / Smallest step : 1.681400 Median interval of one step : 115.58705 cents, amount: 7 Most common interval of one step : 115.58705 cents, amount: 7 Least squares average step : 99.56769 cents, oct.: 1194.81229 cents Scale is strictly proper Step pattern alph. order: ABACABAACABA Step pattern size order : LMLSLMLLSLML Scale is a Constant Structure, by a margin of 37.62469 cents Scale diversity : 1.334285 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.557508 Rothenberg efficiency : 0.416997 redundancy: 0.583003 Efficiency x scale size : 5.003968 Number of different interval sizes : 36 = 3.27273 / 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 : 15.39720 cents Most common intervals : 499.97288 cents & inv., amount: 9 Most common triad is 0.0 499.973 700.027 cents, amount: 6 Number of recognisable fifths : 9, average 700.0271 cents Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% Limited inverse transpositions with margin 46.8425 cents: 7 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.9196 c. M: 15.6413 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 2 1 2 1 2 2 1 2 1 2 P M ME SD: 8.2960 c. M: 16.0190 c. Genus diatonico-chromaticum, Yasser's Supradiatonic inverse 29: 3 2 3 1 3 2 3 3 1 3 2 3 P SD: 9.3548 c. M: 15.3932 c. 31: 3 2 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 4.1497 c. M: 6.5059 c. Genus diatonico-chromaticum 41: 4 3 4 2 4 3 4 4 2 4 3 4 SP SD: 3.8020 c. M: 6.3099 c. "Just" Chromatic 53: 5 4 5 3 5 4 5 5 3 5 4 5 SP SD: 2.3806 c. M:-4.2392 c. "Just" Chromatic 72: 7 5 7 4 7 5 7 7 4 7 5 7 SP SD: 0.8104 c. M: 1.1067 c. "Just" Chromatic 156: 15 11 15 9 15 11 15 15 9 15 11 15 SP SD: 0.1725 c. M: 0.2567 c. 228: 22 16 22 13 22 16 22 22 13 22 16 22 SP SD: 0.1436 c. M: 0.2295 c. 384: 37 27 37 22 37 27 37 37 22 37 27 37 SP SD: 0.0356 c. M: 0.0651 c. 924: 89 65 89 53 89 65 89 89 53 89 65 89 SP SD: 0.0368 c. M: 0.0569 c. 1308: 126 92 126 75 126 92 126 126 75 126 92 126 SP SD: 0.0336 c. M:-0.0542 c. 1692: 163 119 163 97 163 119 163 163 97 163 119 163 SP SD: 0.0328 c. M: 0.0542 c. 1973: 190 139 190 113 190 139 190 190 113 190 139 190 SP SD: 0.0294 c. M:-0.0505 c. 2201: 212 155 212 126 212 155 212 212 126 212 155 212 SP SD: 0.0233 c. M:-0.0366 c. 2357: 227 166 227 135 227 166 227 227 135 227 166 227 SP SD: 0.0189 c. M:-0.0317 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: 0.9639 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.6426 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.8098 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 3.5720 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 10.0201 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.9899 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 6.5232 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.2354 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.4417 cents 11:12 x 13:14:15 x 16 x 18:20:21:22 S SD: 11.3823 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.9602 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.2351 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 6.5666 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.2609 cents 18:19:20:22 x 24:25:27:29:30:32:34:36 SD: 4.5008 cents 24:26:27:29:30:32:34:36:38:40:43:45:48 SD: 3.2829 cents 30:32:34:36:37:40:42:45:48:50:53:56:60 SD: 2.6244 cents 32:34:36:38:40:43:45:48:51:53:57:60:64 SD: 2.4143 cents 40:43:45:48:50:53:56:60:64:67:71:75:80 SD: 1.7039 cents 55:59:62:66:69:73:77:82:88:92:98:103:110 SD: 1.6183 cents 56:60:63:67:70:75:78:84:90:93:100:105:112 SD: 1.4792 cents 60:64:67:72:75:80:84:90:96:100:107:112:120 SD: 0.9574 cents 90:96:101:108:112:120:126:135:144:150:160:168:180 SD: 0.8041 cents 100:107:112:120:125:133:140:150:160:167:178:187:200 SD: 0.7762 cents 105:112:118:126:131:140:147:157:168:175:187:196:210 SD: 0.6468 cents 129:138:145:155:161:172:181:193:207:215:230:241:258 SD: 0.5476 cents 146:156:164:175:182:195:205:219:234:243:260:273:292 SD: 0.5079 cents 156:167:175:187:195:208:219:234:250:260:278:292:312 SD: 0.4637 cents 161:172:181:193:201:215:226:241:258:268:287:301:322 SD: 0.4525 cents 170:182:191:204:212:227:238:255:272:283:303:318:340 SD: 0.4525 cents 185:198:208:222:231:247:259:277:296:308:330:346:370 SD: 0.4456 cents 186:199:209:223:232:248:261:279:298:310:331:348:372 SD: 0.4331 cents 189:202:212:227:236:252:265:283:303:315:337:354:378 SD: 0.3489 cents 221:236:248:265:276:295:310:331:354:368:394:413:442 SD: 0.3262 cents 229:245:257:275:286:306:321:343:367:382:408:428:458 SD: 0.3059 cents 261:279:293:313:326:348:366:391:418:435:465:488:522 SD: 0.2264 cents 301:322:338:361:376:402:422:451:482:502:536:563:602 SD: 0.2231 cents 319:341:358:383:398:426:447:478:511:532:568:597:638 SD: 0.2103 cents 334:357:375:401:417:446:468:500:535:557:595:625:668 SD: 0.1921 cents 349:373:392:419:436:466:489:523:559:582:622:653:698 SD: 0.1839 cents 394:421:442:473:492:526:552:590:631:657:702:737:788 SD: 0.1822 cents 434:464:487:521:542:579:608:650:695:723:773:812:868 SD: 0.1699 cents 435:465:488:522:543:581:610:652:697:725:775:814:870 SD: 0.1678 cents 450:481:505:540:562:601:631:674:721:750:802:842:900 SD: 0.1418 cents 490:524:550:588:612:654:687:734:785:817:873:917:980 SD: 0.1189 cents 540:577:606:648:674:721:757:809:865:900:962:1010:1080 SD: 0.1168 cents 580:620:651:696:724:774:813:869:929:967:1033:1085:1160 SD: 0.0961 cents