Scala analysis: tenred5_12m
Tenney reduced 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: 568.717 cents 568.717426 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: 68.7445 cents 68.7445 7: 131.3097 cents 131.3097 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: 3 68.74454 cents 1: 2 84.46719 cents 1: 6 115.58705 cents 1: 1 131.30969 cents 2: 5 184.33159 cents 2: 5 200.05424 cents 2: 1 231.17409 cents 2: 1 246.89674 cents 3: 1 253.07614 cents 3: 2 268.79879 cents 3: 2 299.91864 cents 3: 7 315.64129 cents 4: 1 368.66319 cents 4: 6 384.38583 cents 4: 1 400.10848 cents 4: 4 431.22833 cents 5: 1 453.13038 cents 5: 8 499.97288 cents 5: 3 515.69553 cents 6: 2 568.71743 cents 6: 4 584.44007 cents 6: 4 615.55993 cents 6: 2 631.28257 cents 7: 3 684.30447 cents 7: 8 700.02712 cents 7: 1 746.86962 cents 8: 4 768.77167 cents 8: 1 799.89152 cents 8: 6 815.61417 cents 8: 1 831.33681 cents 9: 7 884.35871 cents 9: 2 900.08136 cents 9: 2 931.20121 cents 9: 1 946.92386 cents 10: 1 953.10326 cents 10: 1 968.82591 cents 10: 5 999.94576 cents 10: 5 1015.66841 cents 11: 1 1068.69031 cents 11: 6 1084.41295 cents 11: 2 1115.53281 cents 11: 3 1131.25546 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 : 115.6 200.1 315.6 384.4 500.0 568.7 700.0 815.6 884.4 999.9 1084.4 1200.0 115.6 : 84.5 200.1 268.8 384.4 453.1 584.4 700.0 768.8 884.4 968.8 1084.4 1200.0 200.1 : 115.6 184.3 299.9 368.7 500.0 615.6 684.3 799.9 884.4 999.9 1115.5 1200.0 315.6 : 68.7 184.3 253.1 384.4 500.0 568.7 684.3 768.8 884.4 999.9 1084.4 1200.0 384.4 : 115.6 184.3 315.6 431.2 500.0 615.6 700.0 815.6 931.2 1015.7 1131.3 1200.0 500.0 : 68.7 200.1 315.6 384.4 500.0 584.4 700.0 815.6 900.1 1015.7 1084.4 1200.0 568.7 : 131.3 246.9 315.6 431.2 515.7 631.3 746.9 831.3 946.9 1015.7 1131.3 1200.0 700.0 : 115.6 184.3 299.9 384.4 500.0 615.6 700.0 815.6 884.4 999.9 1068.7 1200.0 815.6 : 68.7 184.3 268.8 384.4 500.0 584.4 700.0 768.8 884.4 953.1 1084.4 1200.0 884.4 : 115.6 200.1 315.6 431.2 515.7 631.3 700.0 815.6 884.4 1015.7 1131.3 1200.0 999.9 : 84.5 200.1 315.6 400.1 515.7 584.4 700.0 768.8 900.1 1015.7 1084.4 1200.0 1084.4: 115.6 231.2 315.6 431.2 500.0 615.6 684.3 815.6 931.2 999.9 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 68.7445 .. 131.3097 cents 62.56515 cents 68.74454 cents 2: 184.3316 .. 246.8967 cents 62.56515 cents 53.02190 cents 3: 253.0761 .. 315.6413 cents 62.56515 cents 6.17940 cents 4: 368.6632 .. 431.2283 cents 62.56515 cents 53.02190 cents 5: 453.1304 .. 515.6955 cents 62.56515 cents 21.90205 cents 6: 568.7174 .. 631.2826 cents 62.56515 cents 53.02190 cents 7: 684.3045 .. 746.8696 cents 62.56515 cents 53.02190 cents 8: 768.7717 .. 831.3368 cents 62.56515 cents 21.90205 cents 9: 884.3587 .. 946.9239 cents 62.56515 cents 53.02190 cents 10: 953.1033 .. 1015.6684 cents 62.56515 cents 6.17940 cents 11: 1068.6903 .. 1131.2555 cents 62.56515 cents 53.02190 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 : 131.30969 cents Average / Smallest step : 1.454661 Largest / Average step : 1.313097 Largest / Smallest step : 1.910111 Median interval of one step : 115.58705 cents, amount: 6 Most common interval of one step : 115.58705 cents, amount: 6 Least squares average step : 99.42256 cents, oct.: 1193.07071 cents Scale is strictly proper Step pattern alph. order: ABACACDACABA Step pattern size order : CBCACADCACBC Scale is a Constant Structure, by a margin of 6.17940 cents Scale diversity : 1.391120 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.426486 Rothenberg efficiency : 0.358063 redundancy: 0.641937 Efficiency x scale size : 4.296753 Number of different interval sizes : 42 = 3.81818 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.81818 = 42/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 6.17940 cents Most common intervals : 499.97288 cents & inv., amount: 8 Most common triad is 0.0 499.973 700.027 cents, amount: 5 Number of recognisable fifths : 8, average 700.0271 cents Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% Limited inverse transpositions with margin 62.5651 cents: 7 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 14.2637 c. M:-31.2826 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 2 1 2 1 2 2 1 2 1 2 P M ME SD: 6.8882 c. M: 10.7287 c. Genus diatonico-chromaticum, Yasser's Supradiatonic inverse 31: 3 2 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 5.2797 c. M:-11.9277 c. Genus diatonico-chromaticum 41: 4 3 4 2 4 2 5 4 2 4 3 4 N SD: 5.2589 c. M: 12.6199 c. 43: 4 3 4 3 4 2 5 4 3 4 3 4 P SD: 5.9751 c. M: 10.5779 c. 48: 5 3 5 2 5 3 5 5 2 5 3 5 P SD: 6.8802 c. M: 9.4130 c. 49: 5 3 5 3 4 3 6 4 3 5 3 5 P SD: 6.3976 c. M: 10.1770 c. 50: 5 3 5 3 5 3 5 5 3 5 3 5 SP M DE SD: 4.8389 c. M:-8.0542 c. 53: 5 4 5 3 5 3 6 5 3 5 4 5 P SD: 2.1836 c. M:-3.7193 c. 72: 7 5 7 4 7 4 8 7 4 7 5 7 P SD: 0.9514 c. M: 2.0508 c. 137: 13 10 13 8 13 8 15 13 8 13 10 13 SP SD: 1.0605 c. M: 1.7184 c. 156: 15 11 15 9 15 9 17 15 9 15 11 15 SP SD: 0.2217 c. M:-0.5133 c. 228: 22 16 22 13 22 13 25 22 13 22 16 22 SP SD: 0.1534 c. M: 0.2964 c. 384: 37 27 37 22 37 22 42 37 22 37 27 37 SP SD: 0.0317 c. M: 0.0542 c. 1973: 190 139 190 113 190 113 216 190 113 190 139 190 SP SD: 0.0281 c. M:-0.0471 c. 2129: 205 150 205 122 205 122 233 205 122 205 150 205 SP SD: 0.0257 c. M: 0.0398 c. 2357: 227 166 227 135 227 135 258 227 135 227 166 227 SP SD: 0.0185 c. M:-0.0306 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: 4.4969 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: 13.9639 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 5.4901 cents 9 x 10:11 x 12 x 13:14:15:16:17:18 S SD: 10.0658 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.5660 cents 11:12 x 13:14 x 15:16 x 18:20:21:22 S SD: 11.1863 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 7.4371 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.0242 cents 14:15:16:17 x 19 x 21:22:23:25:26:28 SD: 6.4229 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.4103 cents 18:19:20:22 x 24:25:27:29:30:32:34:36 SD: 4.2679 cents 24:26:27:29:30:32:33:36:38:40:43:45:48 SD: 3.2385 cents 30:32:34:36:37:40:42:45:48:50:53:56:60 SD: 2.8606 cents 32:34:36:38:40:43:44:48:51:53:57:60:64 SD: 2.7747 cents 33:35:37:40:41:44:46:49:53:55:59:62:66 SD: 2.5923 cents 39:42:44:47:49:52:54:58:62:65:69:73:78 SD: 2.5401 cents 40:43:45:48:50:53:56:60:64:67:71:75:80 SD: 2.0492 cents 41:44:46:49:51:55:57:61:66:68:73:77:82 SD: 1.9630 cents 48:51:54:58:60:64:67:72:77:80:86:90:96 SD: 1.8088 cents 54:58:61:65:67:72:75:81:86:90:96:101:108 SD: 1.7799 cents 55:59:62:66:69:73:76:82:88:92:98:103:110 SD: 1.7707 cents 56:60:63:67:70:75:78:84:90:93:100:105:112 SD: 1.2450 cents 60:64:67:72:75:80:83:90:96:100:107:112:120 SD: 1.1069 cents 72:77:81:86:90:96:100:108:115:120:128:135:144 SD: 1.0037 cents 84:90:94:101:105:112:117:126:135:140:150:157:168 SD: 0.9917 cents 90:96:101:108:112:120:125:135:144:150:160:168:180 SD: 0.7878 cents 100:107:112:120:125:133:139:150:160:167:178:187:200 SD: 0.7681 cents 105:112:118:126:131:140:146:157:168:175:187:196:210 SD: 0.6478 cents 116:124:130:139:145:155:161:174:186:193:207:217:232 SD: 0.5612 cents 129:138:145:155:161:172:179:193:207:215:230:241:258 SD: 0.5411 cents 141:151:158:169:176:188:196:211:226:235:251:264:282 SD: 0.5193 cents 146:156:164:175:182:195:203:219:234:243:260:273:292 SD: 0.4628 cents 156:167:175:187:195:208:217:234:250:260:278:292:312 SD: 0.4570 cents 170:182:191:204:212:227:236:255:272:283:303:318:340 SD: 0.4284 cents 185:198:208:222:231:247:257:277:296:308:330:346:370 SD: 0.4168 cents 188:201:211:226:235:251:261:282:301:313:335:352:376 SD: 0.4048 cents 201:215:226:241:251:268:279:301:322:335:358:376:402 SD: 0.3498 cents 221:236:248:265:276:295:307:331:354:368:394:413:442 SD: 0.3049 cents 261:279:293:313:326:348:363:391:418:435:465:488:522 SD: 0.2916 cents 293:313:329:352:366:391:407:439:469:488:522:548:586 SD: 0.2597 cents 301:322:338:361:376:402:418:451:482:502:536:563:602 SD: 0.2194 cents 319:341:358:383:398:426:443:478:511:532:568:597:638 SD: 0.2087 cents 334:357:375:401:417:446:464:500:535:557:595:625:668 SD: 0.1916 cents 391:418:439:469:488:522:543:586:626:652:697:731:782 SD: 0.1882 cents 394:421:442:473:492:526:547:590:631:657:702:737:788 SD: 0.1830 cents 409:437:459:491:511:546:568:613:655:682:729:765:818 SD: 0.1753 cents 434:464:487:521:542:579:603:650:695:723:773:812:868 SD: 0.1654 cents 435:465:488:522:543:581:604:652:697:725:775:814:870 SD: 0.1548 cents 450:481:505:540:562:601:625:674:721:750:802:842:900 SD: 0.1244 cents 540:577:606:648:674:721:750:809:865:900:962:1010:1080 SD: 0.1129 cents