Scala analysis: xen18-erlich-augmented-06
3L 3s MOS for Augmented, L=305.87, s=93.15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 305.870 cents 305.870000 2: 399.020 cents 399.020000 3: 704.890 cents 704.890000 4: 798.040 cents 798.040000 5: 1103.910 cents 1103.910000 6: 1197.060 cents 1197.060000
SHOW/INTERVAL
0: 93.1500 cents 93.1500 1: 305.8700 cents 305.8700 2: 93.1500 cents 93.1500 3: 305.8700 cents 305.8700 4: 93.1500 cents 93.1500 5: 305.8700 cents 305.8700 6: 93.1500 cents 93.1500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 93.15000 cents 1: 3 305.87000 cents 2: 6 399.02000 cents 3: 3 492.17000 cents 3: 3 704.89000 cents 4: 6 798.04000 cents 5: 3 891.19000 cents 5: 3 1103.91000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.60000 = 8/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 305.9 399.0 704.9 798.0 1103.9 1197.1 305.9 : 93.2 399.0 492.2 798.0 891.2 1197.1 399.0 : 305.9 399.0 704.9 798.0 1103.9 1197.1 704.9 : 93.2 399.0 492.2 798.0 891.2 1197.1 798.0 : 305.9 399.0 704.9 798.0 1103.9 1197.1 1103.9: 93.1 399.0 492.2 798.0 891.2 1197.1 1197.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.1500 .. 305.8700 cents 212.72000 cents 93.15000 cents 2: 399.0200 .. 399.0200 cents 1/1, 0.0000 cents 93.15000 cents 3: 492.1700 .. 704.8900 cents 212.72000 cents 93.15000 cents 4: 798.0400 .. 798.0400 cents 1/1, 0.0000 cents 93.15000 cents 5: 891.1900 .. 1103.9100 cents 212.72000 cents 93.15000 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 93.15000 cents, class 1 Average step (divided formal octave): 199.5100 cents Largest one step interval : 305.87000 cents Average / Smallest step : 2.141814 Largest / Average step : 1.533106 Largest / Smallest step : 3.283629 Median interval of one step : 199.51000 cents, amount: 0 Least squares average step : 210.02912 cents, oct.: 1260.17473 cents Scale is strictly proper Scale has 3 repeating blocks of 2 notes Blocks have Myhill's property chromas: 212.72000 cents and 119.57000 cents, ratio: 1.779042 generator: 93.15000 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: 220 287 507 574 794 861 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: 576 = 570 more = 9600.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAB Step pattern size order : LSLSLS Scale is a Constant Structure, by a margin of 93.15000 cents Scale diversity : 1.135713 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.466894 Rothenberg efficiency (ambiguous key): 1.000000 redundancy: 0.000000 Efficiency x scale size : 6.000000 Number of different interval sizes : 8 = 1.60000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.60000 = 8/5 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 93.15000 cents Most common intervals : 399.02000 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 704.890 798.040 cents Most common triad is 0.0 399.020 798.040 cents, amount: 6 Number of recognisable fifths : 3, average 704.8900 cents Number of recognisable fourths : 3, average 492.1700 cents Formal octave complements present : 3 = 50.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 2 4 Limited inverse transpositions : 1 3 5 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 75.2079 c. M: 106.3600 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 2 0 2 1 1 1 P D3 SD: 48.8231 c. M: 77.8586 c. 9: 2 1 2 1 2 1 SP B ME SD: 28.1829 c. M: 39.8567 c. August-6 12: 3 1 3 1 3 1 SP B DE SD: 4.6704 c. M: 6.6050 c. Messiaen truncated mode 3 inverse, Major Augmented, Genus tertium, Raga Devamani 27: 7 2 7 2 7 2 SP B DE SD: 3.1671 c. M:-4.4789 c. Augene-6 39: 10 3 10 3 10 3 SP B DE SD: 0.7555 c. M:-1.0685 c. Augmented-6 51: 13 4 13 4 13 4 SP B DE SD: 0.5212 c. M: 0.7371 c. Augmented-6 90: 23 7 23 7 23 7 SP B DE SD: 0.0321 c. M:-0.0453 c. Augmented-6 501: 128 39 128 39 128 39 SP B DE SD: 0.0243 c. M: 0.0343 c. 591: 151 46 151 46 151 46 SP B DE SD: 0.0157 c. M: 0.0222 c. 681: 174 53 174 53 174 53 SP B DE SD: 0.0094 c. M: 0.0133 c. 771: 197 60 197 60 197 60 SP B DE SD: 0.0045 c. M: 0.0064 c. 861: 220 67 220 67 220 67 SP B DE SD: 0.0007 c. M: 0.0010 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 2.9400 cents 2 x x 3 x x 4 S SD: 2.0771 cents 3 x 4 x 5 x 6 S SD: 43.7994 cents 4 x 5:6 x x 8 S SD: 4.4561 cents 5:6 x x 8:9:10 S SD: 22.0780 cents 7:8:9 x 11:13:14 SD: 18.0752 cents 8 x 10:12:13:15:16 SD: 9.4415 cents 9:11 x x 14:17:18 SD: 13.3216 cents 10:12:13:15:16:19:20 SD: 9.7994 cents 11:13:14 x 17:21:22 SD: 10.6611 cents 12:14:15:18:19:23:24 SD: 7.8315 cents 13 x 16:20:21:25:26 SD: 14.2513 cents 14:17:18:21:22:26:28 SD: 9.8779 cents 15:18:19:23:24:28:30 SD: 7.8739 cents 16:19:20:24:25:30:32 SD: 5.6248 cents 20:24:25:30:32:38:40 SD: 3.9865 cents 26:31:33:39:41:49:52 SD: 3.0907 cents 36:43:45:54:57:68:72 SD: 2.3339 cents 46:55:58:69:73:87:92 SD: 1.0170 cents 104:124:131:156:165:197:208 SD: 0.8260 cents 135:161:170:203:214:255:270 SD: 0.7406 cents 155:185:195:233:246:293:309 SD: 0.6536 cents 177:211:223:266:281:335:353 SD: 0.5907 cents 181:216:228:272:287:342:361 SD: 0.5059 cents 193:230:243:290:306:365:385 SD: 0.4716 cents 201:240:253:302:319:380:401 SD: 0.4715 cents 213:254:268:320:338:403:425 SD: 0.4169 cents 239:285:301:359:379:452:477 SD: 0.2724 cents 285:340:359:428:452:539:569 SD: 0.2375 cents 316:377:398:475:501:598:631 SD: 0.1626 cents 362:432:456:544:574:685:723 SD: 0.1535 cents 517:617:651:777:820:978:1032 SD: 0.1453 cents 555:662:699:834:880:1050:1108 SD: 0.1325 cents 575:686:724:864:912:1088:1148 SD: 0.1062 cents