Scala analysis: xen18-erlich-augene-09
3L 6s MOS for Augene, L=214.10, s=92.46
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92.460 cents 92.460000 2: 306.560 cents 306.560000 3: 399.020 cents 399.020000 4: 491.480 cents 491.480000 5: 705.580 cents 705.580000 6: 798.040 cents 798.040000 7: 890.500 cents 890.500000 8: 1104.600 cents 1104.600000 9: 1197.060 cents 1197.060000
SHOW/INTERVAL
0: 92.4600 cents 92.4600 1: 92.4600 cents 92.4600 2: 214.1000 cents 214.1000 3: 92.4600 cents 92.4600 4: 92.4600 cents 92.4600 5: 214.1000 cents 214.1000 6: 92.4600 cents 92.4600 7: 92.4600 cents 92.4600 8: 214.1000 cents 214.1000 9: 92.4600 cents 92.4600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 92.46000 cents 1: 3 214.10000 cents 2: 3 184.92000 cents 2: 6 306.56000 cents 3: 9 399.02000 cents 4: 6 491.48000 cents 4: 3 613.12000 cents 5: 3 583.94000 cents 5: 6 705.58000 cents 6: 9 798.04000 cents 7: 6 890.50000 cents 7: 3 1012.14000 cents 8: 3 982.96000 cents 8: 6 1104.60000 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 : 92.5 306.6 399.0 491.5 705.6 798.0 890.5 1104.6 1197.1 92.5 : 214.1 306.6 399.0 613.1 705.6 798.0 1012.1 1104.6 1197.1 306.6 : 92.5 184.9 399.0 491.5 583.9 798.0 890.5 983.0 1197.1 399.0 : 92.5 306.6 399.0 491.5 705.6 798.0 890.5 1104.6 1197.1 491.5 : 214.1 306.6 399.0 613.1 705.6 798.0 1012.1 1104.6 1197.1 705.6 : 92.5 184.9 399.0 491.5 583.9 798.0 890.5 983.0 1197.1 798.0 : 92.5 306.6 399.0 491.5 705.6 798.0 890.5 1104.6 1197.1 890.5 : 214.1 306.6 399.0 613.1 705.6 798.0 1012.1 1104.6 1197.1 1104.6: 92.5 184.9 399.0 491.5 583.9 798.0 890.5 983.0 1197.1 1197.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.4600 .. 214.1000 cents 121.64000 cents 92.46000 cents 2: 184.9200 .. 306.5600 cents 121.64000 cents -29.18000 cents 3: 399.0200 .. 399.0200 cents 1/1, 0.0000 cents 92.46000 cents 4: 491.4800 .. 613.1200 cents 121.64000 cents 92.46000 cents 5: 583.9400 .. 705.5800 cents 121.64000 cents -29.18000 cents 6: 798.0400 .. 798.0400 cents 1/1, 0.0000 cents 92.46000 cents 7: 890.5000 .. 1012.1400 cents 121.64000 cents 92.46000 cents 8: 982.9600 .. 1104.6000 cents 121.64000 cents -29.18000 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 92.46000 cents, class 1 Average step (divided formal octave): 133.0067 cents Largest one step interval : 214.10000 cents Average / Smallest step : 1.438532 Largest / Average step : 1.609694 Largest / Smallest step : 2.315596 Median interval of one step : 92.46000 cents, amount: 6 Most common interval of one step : 92.46000 cents, amount: 6 Least squares average step : 133.43347 cents, oct.: 1200.90126 cents Scale is not proper Scale has 3 repeating blocks of 3 notes Blocks have Myhill's property chromas: 121.64000 cents and 29.18000 cents, ratio: 4.168609 generators: 1 of 92.46000 cents and 2 of 306.56000 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: 19 63 82 101 145 164 183 227 246 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: 167 = 158 more = 1855.556% 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 29.18000 cents Scale diversity : 1.191177 Lumma stability : 0.463435 Lumma impropriety factor : 0.073129 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 : 29.18000 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 705.5800 cents Number of recognisable fourths : 6, average 491.4800 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: 33.1062 c. M: 40.5467 c. Pelog Nawanada: Sunda 11: 1 2 1 1 1 1 1 2 1 N D3 I SD: 32.4922 c. M: 52.6382 c. 12: 1 2 1 1 2 1 1 2 1 P B ME I SD: 5.9563 c. M: 7.2950 c. Genus chromaticum, Tcherepnin Nonatonic mode 1, Augmented-9 27: 2 5 2 2 5 2 2 5 2 N B DE I SD: 3.0936 c. M: 3.7889 c. Augene-9 39: 3 7 3 3 7 3 3 7 3 N B DE I SD: 0.3090 c. M:-0.3785 c. Augmented-9 129: 10 23 10 10 23 10 10 23 10 N B DE I SD: 0.2738 c. M: 0.3353 c. 168: 13 30 13 13 30 13 13 30 13 N B DE I SD: 0.1385 c. M: 0.1696 c. 207: 16 37 16 16 37 16 16 37 16 N B DE I SD: 0.0542 c. M: 0.0664 c. 246: 19 44 19 19 44 19 19 44 19 N B DE I SD: 0.0034 c. M: 0.0041 c. 1929: 149 345 149 149 345 149 149 345 149 N B DE I SD: 0.0028 c. M: 0.0034 c. 2175: 168 389 168 168 389 168 168 389 168 N B DE I SD: 0.0021 c. M: 0.0026 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: 2.3337 cents 3 x x x 4 x x 5 x 6 S SD: 3.1527 cents 4 x x 5 x 6 x 7 x 8 S SD: 19.8717 cents 5 x 6 x 7 x 8 x 9:10 S SD: 25.4499 cents 6 x 7 x 8:9 x 10:11:12 S SD: 11.4612 cents 7 x 8:9 x x 11:12:13:14 SD: 16.7776 cents 8 x x 10:11:12:13 x 15:16 SD: 12.7320 cents 9:10:11 x 12 x 14:15:17:18 SD: 14.9542 cents 10:11:12 x 13:15:16:17:19:20 SD: 11.0651 cents 11:12:13:14:15 x 17:18:21:22 SD: 12.3321 cents 12:13:14:15:16:18:19:20:23:24 SD: 7.4067 cents 13:14 x 16:17:20:21:22:25:26 SD: 10.7609 cents 14:15:17:18:19:21:22:23:27:28 SD: 9.0044 cents 15:16:18:19:20:23:24:25:28:30 SD: 5.7261 cents 16:17:19:20:21:24:25:27:30:32 SD: 4.9669 cents 19:20:23:24:25:29:30:32:36:38 SD: 4.7224 cents 22:23:26:28:29:33:35:37:42:44 SD: 4.1941 cents 30:32:36:38:40:45:48:50:57:60 SD: 3.4235 cents 31:33:37:39:41:47:49:52:59:62 SD: 2.9031 cents 34:36:41:43:45:51:54:57:64:68 SD: 2.6828 cents 36:38:43:45:48:54:57:60:68:72 SD: 1.8766 cents 55:58:66:69:73:83:87:92:104:110 SD: 1.5759 cents 58:61:69:73:77:87:92:97:110:116 SD: 1.0950 cents 73:77:87:92:97:110:116:122:138:146 SD: 0.8461 cents 92:97:110:116:122:138:146:154:174:184 SD: 0.7826 cents 109:115:130:137:145:164:173:182:206:218 SD: 0.7807 cents 113:119:135:142:150:170:179:189:214:226 SD: 0.6905 cents 128:135:153:161:170:192:203:214:242:256 SD: 0.6615 cents 143:151:171:180:190:215:227:239:271:286 SD: 0.6275 cents 159:168:190:200:211:239:252:266:301:317 SD: 0.5514 cents 165:174:197:208:219:248:262:276:312:329 SD: 0.5001 cents 186:196:222:234:247:280:295:311:352:371 SD: 0.4461 cents 201:212:240:253:267:302:319:336:380:401 SD: 0.3656 cents 217:229:259:273:288:326:344:363:411:433 SD: 0.3265 cents 232:245:277:292:308:349:368:388:439:463 SD: 0.3233 cents 274:289:327:345:364:412:434:458:519:547 SD: 0.2894 cents 278:293:332:350:369:418:441:465:526:555 SD: 0.2656 cents 290:306:346:365:385:436:460:485:549:579 SD: 0.1999 cents 366:386:437:461:486:550:580:612:693:731 SD: 0.1906 cents 439:463:524:553:583:660:696:734:831:877 SD: 0.1631 cents 475:501:567:598:631:714:753:794:899:948 SD: 0.1553 cents 548:578:654:690:728:824:869:917:1037:1094 SD: 0.1357 cents 567:598:677:714:753:852:899:948:1073:1132 SD: 0.1241 cents 598:631:714:753:794:899:948:1000:1132:1194 SD: 0.1238 cents