Scala analysis: xen18-erlich-augene-06
3L 3s MOS for Augene, L=306.56, s=92.46
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 306.560 cents 306.560000 2: 399.020 cents 399.020000 3: 705.580 cents 705.580000 4: 798.040 cents 798.040000 5: 1104.600 cents 1104.600000 6: 1197.060 cents 1197.060000
SHOW/INTERVAL
0: 92.4600 cents 92.4600 1: 306.5600 cents 306.5600 2: 92.4600 cents 92.4600 3: 306.5600 cents 306.5600 4: 92.4600 cents 92.4600 5: 306.5600 cents 306.5600 6: 92.4600 cents 92.4600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 92.46000 cents 1: 3 306.56000 cents 2: 6 399.02000 cents 3: 3 491.48000 cents 3: 3 705.58000 cents 4: 6 798.04000 cents 5: 3 890.50000 cents 5: 3 1104.60000 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 : 306.6 399.0 705.6 798.0 1104.6 1197.1 306.6 : 92.5 399.0 491.5 798.0 890.5 1197.1 399.0 : 306.6 399.0 705.6 798.0 1104.6 1197.1 705.6 : 92.5 399.0 491.5 798.0 890.5 1197.1 798.0 : 306.6 399.0 705.6 798.0 1104.6 1197.1 1104.6: 92.5 399.0 491.5 798.0 890.5 1197.1 1197.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.4600 .. 306.5600 cents 214.10000 cents 92.46000 cents 2: 399.0200 .. 399.0200 cents 1/1, 0.0000 cents 92.46000 cents 3: 491.4800 .. 705.5800 cents 214.10000 cents 92.46000 cents 4: 798.0400 .. 798.0400 cents 1/1, 0.0000 cents 92.46000 cents 5: 890.5000 .. 1104.6000 cents 214.10000 cents 92.46000 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 92.46000 cents, class 1 Average step (divided formal octave): 199.5100 cents Largest one step interval : 306.56000 cents Average / Smallest step : 2.157798 Largest / Average step : 1.536565 Largest / Smallest step : 3.315596 Median interval of one step : 199.51000 cents, amount: 0 Least squares average step : 210.09736 cents, oct.: 1260.58418 cents Scale is strictly proper Scale has 3 repeating blocks of 2 notes Blocks have Myhill's property chromas: 214.10000 cents and 121.64000 cents, ratio: 1.760112 generator: 92.46000 cents ET pair of linear temperament : 39&207 Scale is distributional even Scale is a mode of a 246-tone equal temperament with octave 1197.060 cents degrees: 63 82 145 164 227 246 Least number of segments generator : 125 of 608.262 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 145 of 705.584 cents and inv. generated superset size: 166 = 160 more = 2766.667% 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 92.46000 cents Scale diversity : 1.132733 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.463435 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 : 92.46000 cents Most common intervals : 399.02000 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 705.580 798.040 cents Most common triad is 0.0 399.020 798.040 cents, amount: 6 Number of recognisable fifths : 3, average 705.5800 cents Number of recognisable fourths : 3, average 491.4800 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: 75.6958 c. M: 107.0500 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 2 0 2 1 1 1 P D3 SD: 48.9727 c. M: 78.5486 c. 9: 2 1 2 1 2 1 SP B ME SD: 28.6708 c. M: 40.5467 c. August-6 12: 3 1 3 1 3 1 SP B DE SD: 5.1583 c. M: 7.2950 c. Messiaen truncated mode 3 inverse, Major Augmented, Genus tertium, Raga Devamani 27: 7 2 7 2 7 2 SP B DE SD: 2.6791 c. M:-3.7889 c. Augene-6 39: 10 3 10 3 10 3 SP B DE SD: 0.2676 c. M:-0.3785 c. Augmented-6 129: 33 10 33 10 33 10 SP B DE SD: 0.2371 c. M: 0.3353 c. 168: 43 13 43 13 43 13 SP B DE SD: 0.1200 c. M: 0.1696 c. 207: 53 16 53 16 53 16 SP B DE SD: 0.0469 c. M: 0.0664 c. 246: 63 19 63 19 63 19 SP B DE SD: 0.0029 c. M:-0.0041 c. 1929: 494 149 494 149 494 149 SP B DE SD: 0.0024 c. M: 0.0034 c. 2175: 557 168 557 168 557 168 SP B DE SD: 0.0018 c. M: 0.0026 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 2.9400 cents 2 x x 3 x x 4 S SD: 2.3337 cents 3 x 4 x 5 x 6 S SD: 43.7994 cents 4 x 5:6 x x 8 S SD: 4.5121 cents 5:6 x x 8:9:10 S SD: 22.2283 cents 7:8:9 x 11:13:14 SD: 18.2388 cents 8 x 10:12:13:15:16 SD: 9.4977 cents 9:11 x x 14:17:18 SD: 13.1981 cents 10:12:13:15:16:19:20 SD: 9.7738 cents 11:13:14 x 17:21:22 SD: 10.6658 cents 12:14:15:18:19:23:24 SD: 7.8817 cents 13 x 16:20:21:25:26 SD: 14.1182 cents 14:17:18:21:22:27:28 SD: 9.8472 cents 15:18:19:23:24:28:30 SD: 7.8238 cents 16:19:20:24:25:30:32 SD: 5.7193 cents 20:24:25:30:32:38:40 SD: 3.9231 cents 26:31:33:39:41:49:52 SD: 3.1650 cents 31:37:39:47:49:59:62 SD: 3.1326 cents 36:43:45:54:57:68:72 SD: 2.3754 cents 46:55:58:69:73:87:92 SD: 1.0381 cents 77:92:97:116:122:146:154 SD: 1.0200 cents 104:124:131:156:165:197:208 SD: 0.8995 cents 113:135:142:170:179:214:226 SD: 0.8977 cents 119:142:150:179:189:225:238 SD: 0.8391 cents 123:147:155:185:195:233:246 SD: 0.7002 cents 155:185:195:233:246:293:309 SD: 0.6924 cents 159:190:200:239:252:301:317 SD: 0.6163 cents 169:202:213:254:268:320:337 SD: 0.5966 cents 181:216:228:272:287:343:361 SD: 0.4867 cents 205:245:258:308:325:388:409 SD: 0.4523 cents 212:253:267:319:336:401:423 SD: 0.4356 cents 217:259:273:326:344:411:433 SD: 0.4087 cents 227:271:286:341:360:430:453 SD: 0.3689 cents 232:277:292:349:368:439:463 SD: 0.3283 cents 258:308:325:388:409:488:515 SD: 0.2828 cents 278:332:350:418:441:526:555 SD: 0.2349 cents 316:377:398:475:501:598:631 SD: 0.1916 cents 336:401:423:505:533:636:671 SD: 0.1721 cents 475:567:598:714:753:899:948 SD: 0.1481 cents 521:622:656:783:826:986:1040 SD: 0.1049 cents 598:714:753:899:948:1132:1194 SD: 0.0991 cents