Scala analysis: xen18-erlich-augmented-12
3L 9s MOS for Augmented, L=119.57, s=93.15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93.150 cents 93.150000 2: 212.720 cents 212.720000 3: 305.870 cents 305.870000 4: 399.020 cents 399.020000 5: 492.170 cents 492.170000 6: 611.740 cents 611.740000 7: 704.890 cents 704.890000 8: 798.040 cents 798.040000 9: 891.190 cents 891.190000 10: 1010.760 cents 1010.760000 11: 1103.910 cents 1103.910000 12: 1197.060 cents 1197.060000
SHOW/INTERVAL
0: 93.1500 cents 93.1500 1: 93.1500 cents 93.1500 2: 119.5700 cents 119.5700 3: 93.1500 cents 93.1500 4: 93.1500 cents 93.1500 5: 93.1500 cents 93.1500 6: 119.5700 cents 119.5700 7: 93.1500 cents 93.1500 8: 93.1500 cents 93.1500 9: 93.1500 cents 93.1500 10: 119.5700 cents 119.5700 11: 93.1500 cents 93.1500 12: 93.1500 cents 93.1500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 93.15000 cents 1: 3 119.57000 cents 2: 6 186.30000 cents 2: 6 212.72000 cents 3: 3 279.45000 cents 3: 9 305.87000 cents 4: 12 399.02000 cents 5: 9 492.17000 cents 5: 3 518.59000 cents 6: 6 585.32000 cents 6: 6 611.74000 cents 7: 3 678.47000 cents 7: 9 704.89000 cents 8: 12 798.04000 cents 9: 9 891.19000 cents 9: 3 917.61000 cents 10: 6 984.34000 cents 10: 6 1010.76000 cents 11: 3 1077.49000 cents 11: 9 1103.91000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.81818 = 20/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 93.2 212.7 305.9 399.0 492.2 611.7 704.9 798.0 891.2 1010.8 1103.9 1197.1 93.2 : 119.6 212.7 305.9 399.0 518.6 611.7 704.9 798.0 917.6 1010.8 1103.9 1197.1 212.7 : 93.2 186.3 279.4 399.0 492.2 585.3 678.5 798.0 891.2 984.3 1077.5 1197.1 305.9 : 93.2 186.3 305.9 399.0 492.2 585.3 704.9 798.0 891.2 984.3 1103.9 1197.1 399.0 : 93.2 212.7 305.9 399.0 492.2 611.7 704.9 798.0 891.2 1010.8 1103.9 1197.1 492.2 : 119.6 212.7 305.9 399.0 518.6 611.7 704.9 798.0 917.6 1010.8 1103.9 1197.1 611.7 : 93.2 186.3 279.5 399.0 492.2 585.3 678.5 798.0 891.2 984.3 1077.5 1197.1 704.9 : 93.2 186.3 305.9 399.0 492.2 585.3 704.9 798.0 891.2 984.3 1103.9 1197.1 798.0 : 93.2 212.7 305.9 399.0 492.2 611.7 704.9 798.0 891.2 1010.8 1103.9 1197.1 891.2 : 119.6 212.7 305.9 399.0 518.6 611.7 704.9 798.0 917.6 1010.8 1103.9 1197.1 1010.8: 93.2 186.3 279.5 399.0 492.2 585.3 678.5 798.0 891.2 984.3 1077.5 1197.1 1103.9: 93.1 186.3 305.9 399.0 492.2 585.3 704.9 798.0 891.2 984.3 1103.9 1197.1 1197.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.1500 .. 119.5700 cents 26.42000 cents 93.15000 cents 2: 186.3000 .. 212.7200 cents 26.42000 cents 66.73000 cents 3: 279.4500 .. 305.8700 cents 26.42000 cents 66.73000 cents 4: 399.0200 .. 399.0200 cents 1/1, 0.0000 cents 93.15000 cents 5: 492.1700 .. 518.5900 cents 26.42000 cents 93.15000 cents 6: 585.3200 .. 611.7400 cents 26.42000 cents 66.73000 cents 7: 678.4700 .. 704.8900 cents 26.42000 cents 66.73000 cents 8: 798.0400 .. 798.0400 cents 1/1, 0.0000 cents 93.15000 cents 9: 891.1900 .. 917.6100 cents 26.42000 cents 93.15000 cents 10: 984.3400 .. 1010.7600 cents 26.42000 cents 66.73000 cents 11: 1077.4900 .. 1103.9100 cents 26.42000 cents 66.73000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 93.15000 cents, class 1 Average step (divided formal octave): 99.7550 cents Largest one step interval : 119.57000 cents Average / Smallest step : 1.070907 Largest / Average step : 1.198637 Largest / Smallest step : 1.283629 Median interval of one step : 93.15000 cents, amount: 9 Most common interval of one step : 93.15000 cents, amount: 9 Least squares average step : 100.18178 cents, oct.: 1202.18142 cents Scale is strictly proper Scale has 3 repeating blocks of 4 notes Blocks have Myhill's property chromas: 26.42000 cents and 66.73000 cents, ratio: 2.525738 generators: 1 of 93.15000 cents and 3 of 305.87000 cents ET pair of linear temperament : 39&51 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 861-tone equal temperament with octave 1197.060 cents degrees: 67 153 220 287 354 440 507 574 641 727 794 861 Least number of segments generator : 431 of 599.225 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 641 of 891.191 cents and inv. generated superset size: 578 = 566 more = 4816.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAAABAA Step pattern size order : SLSSSLSSSLSS Scale is a Constant Structure, by a margin of 66.73000 cents Scale diversity : 1.139063 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.801363 Rothenberg efficiency (ambiguous key): 0.386905 redundancy: 0.613095 Efficiency x scale size : 4.642857 Number of different interval sizes : 20 = 1.81818 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.81818 = 20/11 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 26.42000 cents Most common intervals : 399.02000 cents & inv., amount: 12 Most common triad is 0.0 399.020 798.040 cents, amount: 12 Number of recognisable fifths : 9, average 704.8900 cents Number of recognisable fourths : 9, average 492.1700 cents Best fifths form a closed circle Formal octave complements present : 9 = 75.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 4 8 Limited inverse transpositions : 3 7 11 Inversional symmetry on intervals : 1-2 3-4 5-6 7-8 9-10 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.0894 c. M: 13.2100 c. Twelve-tone Chromatic (1/11-comma) 27: 2 3 2 2 2 3 2 2 2 3 2 2 SP B ME SD: 5.4855 c. M:-8.9578 c. Starling-12 39: 3 4 3 3 3 4 3 3 3 4 3 3 SP B ME SD: 1.3086 c. M:-2.1369 c. 51: 4 5 4 4 4 5 4 4 4 5 4 4 SP B ME SD: 0.9027 c. M: 1.4741 c. 90: 7 9 7 7 7 9 7 7 7 9 7 7 SP B DE SD: 0.0555 c. M:-0.0907 c. 501: 39 50 39 39 39 50 39 39 39 50 39 39 SP B DE SD: 0.0420 c. M: 0.0686 c. 591: 46 59 46 46 46 59 46 46 46 59 46 46 SP B DE SD: 0.0272 c. M: 0.0444 c. 681: 53 68 53 53 53 68 53 53 53 68 53 53 SP B DE SD: 0.0162 c. M: 0.0265 c. 771: 60 77 60 60 60 77 60 60 60 77 60 60 SP B DE SD: 0.0079 c. M: 0.0128 c. 861: 67 86 67 67 67 86 67 67 67 86 67 67 SP B DE SD: 0.0012 c. M: 0.0020 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 2.9400 cents 2 x x x x x x 3 x x x x 4 S SD: 2.0771 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.1592 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 11.0033 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.0709 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.2939 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.8155 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 10.8708 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.5962 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.6044 cents 11:12 x 13:14:15:16 x 17:18:20:21:22 S SD: 10.7673 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 6.9941 cents 13:14:15 x 16:17:19:20:21:22:23:25:26 SD: 9.6509 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 6.9557 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 4.9827 cents 16:17:18:19:20:21:23:24:25:27:29:30:32 SD: 4.2949 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.9338 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.3794 cents 30:32:34:36:38:40:43:45:48:50:54:57:60 SD: 2.8094 cents 31:33:35:37:39:41:44:47:49:52:56:59:62 SD: 2.5096 cents 36:38:41:43:45:48:51:54:57:60:65:68:72 SD: 2.1353 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 2.0188 cents 51:54:58:61:64:68:73:77:81:85:91:96:102 SD: 2.0132 cents 52:55:59:62:65:69:74:78:82:87:93:98:104 SD: 1.6523 cents 54:57:61:64:68:72:77:81:86:90:97:102:108 SD: 1.4966 cents 58:61:66:69:73:77:83:87:92:97:104:110:116 SD: 1.4360 cents 67:71:76:80:84:89:95:101:106:112:120:127:134 SD: 1.3564 cents 68:72:77:81:86:90:97:102:108:114:122:129:136 SD: 1.2436 cents 73:77:83:87:92:97:104:110:116:122:131:138:146 SD: 1.0390 cents 77:81:87:92:97:102:110:116:122:129:138:146:154 SD: 1.0192 cents 89:94:101:106:112:118:127:134:141:149:160:168:178 SD: 1.0019 cents 92:97:104:110:116:122:131:138:146:154:165:174:184 SD: 0.6080 cents 146:154:165:174:184:194:208:219:231:244:262:276:292 SD: 0.5852 cents 159:168:180:190:200:211:226:239:252:266:285:301:317 SD: 0.5363 cents 161:170:182:192:203:214:229:242:255:269:289:305:321 SD: 0.5031 cents 177:187:200:211:223:235:252:266:281:296:317:335:353 SD: 0.4143 cents 201:212:227:240:253:267:286:302:319:336:360:380:401 SD: 0.3824 cents 213:225:241:254:268:283:303:320:338:356:382:403:425 SD: 0.3449 cents 253:267:286:302:319:336:360:380:401:423:454:479:505 SD: 0.3186 cents 259:273:293:309:326:344:369:389:411:433:464:490:517 SD: 0.3092 cents 270:285:305:322:340:359:384:406:428:452:484:511:539 SD: 0.2902 cents 285:301:322:340:359:379:406:428:452:477:511:539:569 SD: 0.2457 cents 290:306:328:346:365:385:413:436:460:485:520:549:579 SD: 0.2195 cents 328:346:371:391:413:436:467:493:520:549:588:621:655 SD: 0.2073 cents 362:382:409:432:456:481:515:544:574:606:649:685:723 SD: 0.1957 cents 382:403:432:456:481:508:544:574:606:639:685:723:763 SD: 0.1773 cents 398:420:450:475:501:529:567:598:631:666:714:753:795 SD: 0.1499 cents 420:443:475:501:529:558:598:631:666:703:753:795:839 SD: 0.1486 cents 521:550:589:622:656:692:742:783:826:872:934:986:1040 SD: 0.1421 cents 529:558:598:631:666:703:753:795:839:885:948:1001:1056 SD: 0.1381 cents 545:575:616:650:686:724:776:819:864:912:977:1031:1088 SD: 0.1297 cents 559:590:632:667:704:743:796:840:886:935:1002:1058:1116 SD: 0.1147 cents 575:607:650:686:724:764:819:864:912:962:1031:1088:1148 SD: 0.1012 cents