Scala analysis: xen18-erlich-tetracot-13
7L 6s MOS for Tetracot, L=142.37, s=33.74
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 142.370 cents 142.370000 2: 176.110 cents 176.110000 3: 318.480 cents 318.480000 4: 352.220 cents 352.220000 5: 494.590 cents 494.590000 6: 528.330 cents 528.330000 7: 670.700 cents 670.700000 8: 704.440 cents 704.440000 9: 846.810 cents 846.810000 10: 880.550 cents 880.550000 11: 1022.920 cents 1022.920000 12: 1056.660 cents 1056.660000 13: 1199.030 cents 1199.030000
SHOW/INTERVAL
0: 142.3700 cents 142.3700 1: 142.3700 cents 142.3700 2: 33.7400 cents 33.7400 3: 142.3700 cents 142.3700 4: 33.7400 cents 33.7400 5: 142.3700 cents 142.3700 6: 33.7400 cents 33.7400 7: 142.3700 cents 142.3700 8: 33.7400 cents 33.7400 9: 142.3700 cents 142.3700 10: 33.7400 cents 33.7400 11: 142.3700 cents 142.3700 12: 33.7400 cents 33.7400 13: 142.3700 cents 142.3700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 33.74000 cents 1: 7 142.37000 cents 2: 12 176.11000 cents 2: 1 284.74000 cents 3: 5 209.85000 cents 3: 8 318.48000 cents 4: 11 352.22000 cents 4: 2 460.85000 cents 5: 4 385.96000 cents 5: 9 494.59000 cents 6: 10 528.33000 cents 6: 3 636.96000 cents 7: 3 562.07000 cents 7: 10 670.70000 cents 8: 9 704.44000 cents 8: 4 813.07000 cents 9: 2 738.18000 cents 9: 11 846.81000 cents 10: 8 880.55000 cents 10: 5 989.18000 cents 11: 1 914.29000 cents 11: 12 1022.92000 cents 12: 7 1056.66000 cents 12: 6 1165.29000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 0.0 : 142.4 176.1 318.5 352.2 494.6 528.3 670.7 704.4 846.8 880.5 1022.9 1056.7 1199.0 142.4 : 33.7 176.1 209.9 352.2 386.0 528.3 562.1 704.4 738.2 880.5 914.3 1056.7 1199.0 176.1 : 142.4 176.1 318.5 352.2 494.6 528.3 670.7 704.4 846.8 880.6 1022.9 1165.3 1199.0 318.5 : 33.7 176.1 209.9 352.2 386.0 528.3 562.1 704.4 738.2 880.5 1022.9 1056.7 1199.0 352.2 : 142.4 176.1 318.5 352.2 494.6 528.3 670.7 704.4 846.8 989.2 1022.9 1165.3 1199.0 494.6 : 33.7 176.1 209.9 352.2 386.0 528.3 562.1 704.4 846.8 880.5 1022.9 1056.7 1199.0 528.3 : 142.4 176.1 318.5 352.2 494.6 528.3 670.7 813.1 846.8 989.2 1022.9 1165.3 1199.0 670.7 : 33.7 176.1 209.8 352.2 386.0 528.3 670.7 704.4 846.8 880.5 1022.9 1056.7 1199.0 704.4 : 142.4 176.1 318.5 352.2 494.6 637.0 670.7 813.1 846.8 989.2 1022.9 1165.3 1199.0 846.8 : 33.7 176.1 209.9 352.2 494.6 528.3 670.7 704.4 846.8 880.5 1022.9 1056.7 1199.0 880.5 : 142.4 176.1 318.5 460.9 494.6 637.0 670.7 813.1 846.8 989.2 1022.9 1165.3 1199.0 1022.9: 33.7 176.1 318.5 352.2 494.6 528.3 670.7 704.4 846.8 880.6 1022.9 1056.7 1199.0 1056.7: 142.4 284.7 318.5 460.8 494.6 637.0 670.7 813.1 846.8 989.2 1022.9 1165.3 1199.0 1199.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.7400 .. 142.3700 cents 108.63000 cents 33.74000 cents 2: 176.1100 .. 284.7400 cents 108.63000 cents 33.74000 cents 3: 209.8500 .. 318.4800 cents 108.63000 cents -74.89000 cents 4: 352.2200 .. 460.8500 cents 108.63000 cents 33.74000 cents 5: 385.9600 .. 494.5900 cents 108.63000 cents -74.89000 cents 6: 528.3300 .. 636.9600 cents 108.63000 cents 33.74000 cents 7: 562.0700 .. 670.7000 cents 108.63000 cents -74.89000 cents 8: 704.4400 .. 813.0700 cents 108.63000 cents 33.74000 cents 9: 738.1800 .. 846.8100 cents 108.63000 cents -74.89000 cents 10: 880.5500 .. 989.1800 cents 108.63000 cents 33.74000 cents 11: 914.2900 .. 1022.9200 cents 108.63000 cents -74.89000 cents 12: 1056.6600 .. 1165.2900 cents 108.63000 cents 33.74000 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 33.74000 cents, class 1 Average step (divided formal octave): 92.2331 cents Largest one step interval : 142.37000 cents Average / Smallest step : 2.733642 Largest / Average step : 1.543589 Largest / Smallest step : 4.219621 Median interval of one step : 142.37000 cents, amount: 7 Most common interval of one step : 142.37000 cents, amount: 7 Least squares average step : 91.30462 cents, oct.: 1186.96000 cents Scale is not proper Scale has Myhill's property chromas: 108.63000 cents and 74.89000 cents, ratio: 1.450527 generators: 2 of 176.11000 cents and 11 of 1022.92000 cents ET pair of linear temperament : 34&143 Scale is distributional even Scale is a mode of a 1137-tone equal temperament with octave 1199.030 cents degrees: 135 167 302 334 469 501 636 668 803 835 970 1002 1137 generators: 167 and 970 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABABA Step pattern size order : LSLSLSLSLSLSL Scale is a Constant Structure, by a margin of 33.74000 cents Scale diversity : 1.166940 Lumma stability : 0.225115 Lumma impropriety factor : 0.312294 Rothenberg efficiency : 0.717949 redundancy: 0.282051 Efficiency x scale size : 9.333333 Number of different interval sizes : 24 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 33.74000 cents Most common intervals : 176.11000 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 176.110 352.220 cents Most common triad is 0.0 176.110 1022.920 cents, amount: 11 Number of recognisable fifths : 9, average 704.4400 cents Number of recognisable fourths : 9, average 494.5900 cents Scale contains two identical disjunct hexachords Formal octave complements present : 13 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 6-7 -- Rational properties --
FIT/MODE
13: 2 0 1 1 1 1 1 1 1 1 1 0 2 N T3 I SD: 29.3847 c. M: 42.0962 c. 14: 2 0 2 0 2 0 2 0 2 0 2 0 2 N M DE I SD: 18.0348 c. M:-28.9200 c. 18: 2 1 2 0 2 1 2 1 2 0 2 1 2 N T3 I SD: 17.7510 c. M: 28.3006 c. 19: 2 1 2 1 2 0 3 0 2 1 2 1 2 N I SD: 16.6352 c. M:-26.4211 c. 20: 2 1 2 1 2 1 2 1 2 1 2 1 2 P M ME I SD: 14.0106 c. M:-22.4670 c. 25: 3 1 3 0 3 1 3 1 3 0 3 1 3 N I SD: 12.6750 c. M:-17.2484 c. 26: 3 1 3 1 3 0 4 0 3 1 3 1 3 N I SD: 12.3300 c. M: 21.0481 c. 27: 3 1 3 1 3 1 3 1 3 1 3 1 3 N M DE I SD: 5.7026 c. M:-9.1444 c. 34: 4 1 4 1 4 1 4 1 4 1 4 1 4 N M DE I SD: 0.8155 c. M:-1.3076 c. 109: 13 3 13 3 13 3 13 3 13 3 13 3 13 N M DE I SD: 0.3951 c. M: 0.6336 c. 143: 17 4 17 4 17 4 17 4 17 4 17 4 17 N M DE I SD: 0.1073 c. M:-0.1720 c. 177: 21 5 21 5 21 5 21 5 21 5 21 5 21 N M DE I SD: 0.0700 c. M: 0.1122 c. 320: 38 9 38 9 38 9 38 9 38 9 38 9 38 N M DE I SD: 0.0092 c. M:-0.0148 c. 817: 97 23 97 23 97 23 97 23 97 23 97 23 97 N M DE I SD: 0.0079 c. M: 0.0127 c. 1137: 135 32 135 32 135 32 135 32 135 32 135 32 135 N M DE I SD: 0.0031 c. M:-0.0050 c. 1457: 173 41 173 41 173 41 173 41 173 41 173 41 173 N M DE I SD: 0.0004 c. M:-0.0006 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.9700 cents 2 x x x x x x x 3 x x x x 4 S SD: 1.3338 cents 3 x x x x 4 x x x x 5 x x 6 S SD: 1.7443 cents 4 x x x 5 x x x 6 x x 7 x 8 S SD: 15.9994 cents 5 x x 6 x x 7 x x 8 x 9 x 10 S SD: 12.7597 cents 6 x x 7 x 8 x x 9 x 10 x 11:12 S SD: 8.7406 cents 7 x 8 x x 9 x 10 x 11:12 x 13:14 S SD: 18.3687 cents 8 x 9 x 10 x 11 x 12:13 x 14:15:16 S SD: 10.0277 cents 9 x 10 x 11:12 x 13:14 x 15:16:17:18 S SD: 9.6858 cents 10 x 11:12 x 13:14 x 15:16:17:18 x 20 S SD: 9.4809 cents 11:12 x 13 x x 15:16:17:18 x 20 x 22 SD: 7.9890 cents 12:13 x 14:15:16 x x 18 x 20 x 22:24 S SD: 7.8333 cents 13:14 x x 16:17:18:19:20:21:22:23:24:26 S SD: 7.4612 cents 14:15:16 x 17 x 19 x 21:23 x 25:26:28 SD: 7.5157 cents 15:16:17:18 x 20 x 22:23:24:25:27:28:30 SD: 6.8277 cents 16:17:18:19:20:21:22 x 24:26:27:29 x 32 SD: 6.8041 cents 17:18:19:20:21 x 23:25:26 x 28 x 31:34 SD: 7.2637 cents 18 x 20 x 22:24 x x 27:29:30 x 33:36 SD: 3.0532 cents 19 x 21:23 x 25:26:28:29:31:32:34:35:38 SD: 4.3031 cents 20 x 22:24:25 x 27:29:30 x 33:36:37:40 SD: 4.9131 cents 21:23 x 25:26:28 x 31:32:34:35:38:39:42 SD: 3.9281 cents 22:24 x 26:27:29:30:32:33:36:37:40:41:44 SD: 4.3832 cents 23:25 x x 28 x 31:34:35 x 38 x 42:46 SD: 4.2238 cents 24:26:27:29 x 32:33:35:36:39:40:43:44:48 SD: 3.7368 cents 25:27:28:30:31:33:34:37:38:41:42:45:46:50 SD: 3.4642 cents 26:28:29:31:32 x 35:38:39:42:43:47:48:52 SD: 3.1059 cents 28:30:31 x 34:37:38:41:42:46:47:51:52:56 SD: 3.6545 cents 29:31:32:35:36 x 39:43:44:47:48:52:53:58 SD: 4.1255 cents 30 x 33:36:37:40:41:44:45:49:50:54:55:60 SD: 2.0154 cents 31 x 34:37:38:41:42:46:47:51:52:56:57:62 SD: 3.1177 cents 32:35 x 38:39 x 43:47:48:52:53:58:59:64 SD: 3.0882 cents 33:36:37:40 x 44:45:49:50:54:55:60:61:66 SD: 3.2291 cents 34:37:38:41:42:45:46:50:51:55:57:61:63:68 SD: 2.7423 cents 35:38:39:42:43:47 x 52:53:57:58:63:64:70 SD: 2.6642 cents 36:39:40:43:44:48:49:53:54:59:60:65:66:72 SD: 1.5077 cents 41 x 45:49:50:55:56:60:62:67:68:74:75:82 SD: 2.8215 cents 43:47:48:52:53:57:58:63:65:70:72:78:79:86 SD: 2.5901 cents 44:48:49:53:54:59:60:65:66:72:73:79:81:88 SD: 1.9105 cents 45:49:50:54:55:60:61:66:68:73:75:81:83:90 SD: 1.5667 cents 48:52:53:58:59:64:65:71:72:78:80:87:88:96 SD: 1.4912 cents 57:62:63:69:70:76:77:84:86:93:95:103:105:114 SD: 1.3947 cents 67:73:74:81:82:89:91:99:101:109:111:121:123:134 SD: 1.3854 cents 68:74:75:82:83:90:92:100:102:111:113:123:125:136 SD: 1.3099 cents 70:76:77:84:86:93:95:103:105:114:116:126:129:140 SD: 1.1973 cents 76:83:84:91:93:101:103:112:114:124:126:137:140:152 SD: 1.1340 cents 81:88:90:97:99:108:110:119:122:132:135:146:149:162 SD: 1.0637 cents 84:91:93:101:103:112:114:124:126:137:140:152:155:168 SD: 0.7360 cents 93:101:103:112:114:124:126:137:140:152:155:168:171:186 SD: 0.6854 cents 103:112:114:124:126:137:140:152:155:168:171:186:190:206 SD: 0.6659 cents 124:135:137:149:152:165:168:183:186:202:206:224:228:248 SD: 0.6514 cents 129:140:143:155:158:172:175:190:194:210:215:233:237:258 SD: 0.6091 cents 133:144:147:160:163:177:180:196:200:217:221:240:245:266 SD: 0.6071 cents 138:150:153:166:169:184:187:203:207:225:229:249:254:276 SD: 0.5980 cents 139:151:154:167:170:185:189:205:209:227:231:251:256:278 SD: 0.5148 cents 160:174:177:192:196:213:217:236:240:261:266:289:295:320 SD: 0.4788 cents 163:177:180:196:200:217:221:240:245:266:271:294:300:326 SD: 0.4444 cents 187:203:207:225:229:249:254:275:281:305:311:338:344:374 SD: 0.3918 cents 199:216:220:239:244:265:270:293:299:325:331:359:366:398 SD: 0.3713 cents 222:241:246:267:272:295:301:327:333:362:369:401:409:444 SD: 0.3563 cents 233:253:258:280:286:310:316:343:350:380:387:421:429:466 SD: 0.3126 cents 243:264:269:292:298:323:330:358:365:396:404:439:447:486 SD: 0.2931 cents 271:294:300:326:332:361:368:399:407:442:451:489:499:542 SD: 0.2930 cents 279:303:309:335:342:371:379:411:419:455:464:504:514:558 SD: 0.2738 cents 302:328:334:363:370:402:410:445:454:493:502:545:556:604 SD: 0.2671 cents 315:342:349:379:386:419:427:464:473:514:524:569:580:630 SD: 0.2577 cents 317:344:351:381:389:422:430:467:476:517:527:572:584:634 SD: 0.2463 cents 327:355:362:393:401:435:444:482:491:533:544:590:602:654 SD: 0.2172 cents 336:365:372:404:412:447:456:495:505:548:559:607:619:672 SD: 0.1995 cents 372:404:412:447:456:495:505:548:559:607:619:672:685:744 SD: 0.1840 cents 412:447:456:495:505:548:559:607:619:672:685:744:759:824 SD: 0.1774 cents 420:456:465:505:515:559:570:619:631:685:698:758:773:840 SD: 0.1727 cents 421:457:466:506:516:560:571:620:632:687:700:760:775:842 SD: 0.1695 cents 466:506:516:560:571:620:632:686:700:760:775:841:858:931 SD: 0.1575 cents 505:548:559:607:619:672:685:744:759:824:840:912:930:1009 SD: 0.1506 cents 514:558:569:618:630:684:697:757:772:838:855:928:946:1027 SD: 0.1361 cents 550:597:609:661:674:732:746:810:826:897:915:993:1013:1099 SD: 0.1233 cents 560:608:620:673:686:745:760:825:841:913:931:1011:1031:1119 SD: 0.1172 cents