Scala analysis: xen18-erlich-augmented-09
3L 6s MOS for Augmented, L=212.72, 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: 305.870 cents 305.870000 3: 399.020 cents 399.020000 4: 492.170 cents 492.170000 5: 704.890 cents 704.890000 6: 798.040 cents 798.040000 7: 891.190 cents 891.190000 8: 1103.910 cents 1103.910000 9: 1197.060 cents 1197.060000
SHOW/INTERVAL
0: 93.1500 cents 93.1500 1: 93.1500 cents 93.1500 2: 212.7200 cents 212.7200 3: 93.1500 cents 93.1500 4: 93.1500 cents 93.1500 5: 212.7200 cents 212.7200 6: 93.1500 cents 93.1500 7: 93.1500 cents 93.1500 8: 212.7200 cents 212.7200 9: 93.1500 cents 93.1500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 93.15000 cents 1: 3 212.72000 cents 2: 3 186.30000 cents 2: 6 305.87000 cents 3: 9 399.02000 cents 4: 6 492.17000 cents 4: 3 611.74000 cents 5: 3 585.32000 cents 5: 6 704.89000 cents 6: 9 798.04000 cents 7: 6 891.19000 cents 7: 3 1010.76000 cents 8: 3 984.34000 cents 8: 6 1103.91000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.75000 = 7/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 93.2 305.9 399.0 492.2 704.9 798.0 891.2 1103.9 1197.1 93.2 : 212.7 305.9 399.0 611.7 704.9 798.0 1010.8 1103.9 1197.1 305.9 : 93.2 186.3 399.0 492.2 585.3 798.0 891.2 984.3 1197.1 399.0 : 93.2 305.9 399.0 492.2 704.9 798.0 891.2 1103.9 1197.1 492.2 : 212.7 305.9 399.0 611.7 704.9 798.0 1010.8 1103.9 1197.1 704.9 : 93.2 186.3 399.0 492.2 585.3 798.0 891.2 984.3 1197.1 798.0 : 93.2 305.9 399.0 492.2 704.9 798.0 891.2 1103.9 1197.1 891.2 : 212.7 305.9 399.0 611.7 704.9 798.0 1010.8 1103.9 1197.1 1103.9: 93.1 186.3 399.0 492.2 585.3 798.0 891.2 984.3 1197.1 1197.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.1500 .. 212.7200 cents 119.57000 cents 93.15000 cents 2: 186.3000 .. 305.8700 cents 119.57000 cents -26.42000 cents 3: 399.0200 .. 399.0200 cents 1/1, 0.0000 cents 93.15000 cents 4: 492.1700 .. 611.7400 cents 119.57000 cents 93.15000 cents 5: 585.3200 .. 704.8900 cents 119.57000 cents -26.42000 cents 6: 798.0400 .. 798.0400 cents 1/1, 0.0000 cents 93.15000 cents 7: 891.1900 .. 1010.7600 cents 119.57000 cents 93.15000 cents 8: 984.3400 .. 1103.9100 cents 119.57000 cents -26.42000 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 93.15000 cents, class 1 Average step (divided formal octave): 133.0067 cents Largest one step interval : 212.72000 cents Average / Smallest step : 1.427876 Largest / Average step : 1.599318 Largest / Smallest step : 2.283629 Median interval of one step : 93.15000 cents, amount: 6 Most common interval of one step : 93.15000 cents, amount: 6 Least squares average step : 133.42621 cents, oct.: 1200.83589 cents Scale is not proper Scale has 3 repeating blocks of 3 notes Blocks have Myhill's property chromas: 119.57000 cents and 26.42000 cents, ratio: 4.525738 generators: 1 of 93.15000 cents and 2 of 305.87000 cents ET pair of linear temperament : 39&51 Scale is distributional even Scale is a mode of a 861-tone equal temperament with octave 1197.060 cents degrees: 67 220 287 354 507 574 641 794 861 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: 577 = 568 more = 6411.111% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAABA Step pattern size order : SLSSLSSLS Scale is a Constant Structure, by a margin of 26.42000 cents Scale diversity : 1.186535 Lumma stability : 0.466894 Lumma impropriety factor : 0.066212 Rothenberg efficiency (ambiguous key): 0.396825 redundancy: 0.603175 Efficiency x scale size : 3.571429 Number of different interval sizes : 14 = 1.75000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.75000 = 7/4 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 26.42000 cents Most common intervals : 399.02000 cents & inv., amount: 9 Most common triad is 0.0 399.020 798.040 cents, amount: 9 Number of recognisable fifths : 6, average 704.8900 cents Number of recognisable fourths : 6, average 492.1700 cents Formal octave complements present : 9 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 3 6 Limited inverse transpositions : 3 6 Inversional symmetry on degrees : 0 3 6 Inversional symmetry on intervals : 1-2 4-5 7-8 -- Rational properties --
FIT/MODE
9: 1 1 1 1 1 1 1 1 1 SP B ME I SD: 32.5428 c. M: 39.8567 c. Pelog Nawanada: Sunda 11: 1 2 1 1 1 1 1 2 1 N D3 I SD: 32.2646 c. M: 51.9482 c. 12: 1 2 1 1 2 1 1 2 1 P B ME I SD: 5.3930 c. M: 6.6050 c. Genus chromaticum, Tcherepnin Nonatonic mode 1, Augmented-9 27: 2 5 2 2 5 2 2 5 2 N B DE I SD: 3.6570 c. M: 4.4789 c. Augene-9 39: 3 7 3 3 7 3 3 7 3 N B DE I SD: 0.8724 c. M: 1.0685 c. Augmented-9 51: 4 9 4 4 9 4 4 9 4 N B DE I SD: 0.6018 c. M: 0.7371 c. Augmented-9 90: 7 16 7 7 16 7 7 16 7 N B DE I SD: 0.0370 c. M: 0.0453 c. Augmented-9 501: 39 89 39 39 89 39 39 89 39 N B DE I SD: 0.0280 c. M: 0.0343 c. 591: 46 105 46 46 105 46 46 105 46 N B DE I SD: 0.0181 c. M: 0.0222 c. 681: 53 121 53 53 121 53 53 121 53 N B DE I SD: 0.0108 c. M: 0.0133 c. 771: 60 137 60 60 137 60 60 137 60 N B DE I SD: 0.0052 c. M: 0.0064 c. 861: 67 153 67 67 153 67 67 153 67 N B DE I SD: 0.0008 c. M: 0.0010 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 2.9400 cents 2 x x x x 3 x x x 4 S SD: 2.0771 cents 3 x x x 4 x x 5 x 6 S SD: 3.1592 cents 4 x x 5 x 6 x 7 x 8 S SD: 19.6946 cents 5 x 6 x 7 x 8 x 9:10 S SD: 25.2671 cents 6 x 7 x 8:9 x 10:11:12 S SD: 11.2974 cents 7 x 8:9 x x 11:12:13:14 SD: 16.6055 cents 8 x x 10:11:12:13 x 15:16 SD: 12.6129 cents 9:10:11 x 12 x 14:15:17:18 SD: 14.9057 cents 10:11:12 x 13:15:16:17:19:20 SD: 11.0170 cents 11:12:13:14:15 x 17:18:21:22 SD: 12.2738 cents 12:13:14:15:16:18:19:20:23:24 SD: 7.3303 cents 13:14 x 16:17:20:21:22:25:26 SD: 10.8013 cents 14:15:17:18:19:21:22:23:26:28 SD: 8.9890 cents 15:16:18:19:20:23:24:25:28:30 SD: 5.7288 cents 16:17:19:20:21:24:25:27:30:32 SD: 4.9081 cents 19:20:23:24:25:29:30:32:36:38 SD: 4.8340 cents 22:23:26:28:29:33:35:37:42:44 SD: 4.2248 cents 30:32:36:38:40:45:48:50:57:60 SD: 3.4096 cents 31:33:37:39:41:47:49:52:59:62 SD: 2.9408 cents 34:36:41:43:45:51:54:57:64:68 SD: 2.6896 cents 36:38:43:45:48:54:57:60:68:72 SD: 1.8509 cents 55:58:66:69:73:83:87:92:104:110 SD: 1.6702 cents 58:61:69:73:77:87:92:97:110:116 SD: 1.1123 cents 73:77:87:92:97:110:116:122:138:146 SD: 0.8683 cents 92:97:110:116:122:138:146:154:174:184 SD: 0.8066 cents 104:110:124:131:138:156:165:174:197:208 SD: 0.7562 cents 128:135:153:161:170:192:203:214:242:256 SD: 0.6617 cents 159:168:190:200:211:239:252:266:301:317 SD: 0.5894 cents 165:174:197:208:219:248:262:276:312:329 SD: 0.5369 cents 177:187:211:223:235:266:281:296:335:353 SD: 0.4928 cents 197:208:235:248:262:296:312:330:373:393 SD: 0.4308 cents 201:212:240:253:267:302:319:336:380:401 SD: 0.3845 cents 232:245:277:292:308:349:368:388:439:463 SD: 0.3824 cents 239:252:285:301:318:359:379:400:452:477 SD: 0.3514 cents 258:272:308:325:343:388:409:432:488:515 SD: 0.3316 cents 270:285:322:340:359:406:428:452:511:539 SD: 0.2555 cents 289:305:345:364:384:434:458:484:547:577 SD: 0.2555 cents 325:343:388:409:432:488:515:544:615:649 SD: 0.2525 cents 340:359:406:428:452:511:539:569:643:679 SD: 0.2384 cents 343:362:409:432:456:515:544:574:649:685 SD: 0.2297 cents 362:382:432:456:481:544:574:606:685:723 SD: 0.1365 cents 398:420:475:501:529:598:631:666:753:795 SD: 0.1242 cents 563:594:672:709:748:846:893:942:1065:1124 SD: 0.1117 cents 575:607:686:724:764:864:912:962:1088:1148 SD: 0.1026 cents