Scala analysis: xen18-erlich-passion-12
1L 11s MOS for Passion, L=115.91, s=98.40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 98.400 cents 98.400000 2: 196.800 cents 196.800000 3: 295.200 cents 295.200000 4: 393.600 cents 393.600000 5: 492.000 cents 492.000000 6: 607.910 cents 607.910000 7: 706.310 cents 706.310000 8: 804.710 cents 804.710000 9: 903.110 cents 903.110000 10: 1001.510 cents 1001.510000 11: 1099.910 cents 1099.910000 12: 1198.310 cents 1198.310000
SHOW/INTERVAL
0: 98.4000 cents 98.4000 1: 98.4000 cents 98.4000 2: 98.4000 cents 98.4000 3: 98.4000 cents 98.4000 4: 98.4000 cents 98.4000 5: 98.4000 cents 98.4000 6: 115.9100 cents 115.9100 7: 98.4000 cents 98.4000 8: 98.4000 cents 98.4000 9: 98.4000 cents 98.4000 10: 98.4000 cents 98.4000 11: 98.4000 cents 98.4000 12: 98.4000 cents 98.4000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 98.40000 cents 1: 1 115.91000 cents 2: 10 196.80000 cents 2: 2 214.31000 cents 3: 9 295.20000 cents 3: 3 312.71000 cents 4: 8 393.60000 cents 4: 4 411.11000 cents 5: 7 492.00000 cents 5: 5 509.51000 cents 6: 6 590.40000 cents 6: 6 607.91000 cents 7: 5 688.80000 cents 7: 7 706.31000 cents 8: 4 787.20000 cents 8: 8 804.71000 cents 9: 3 885.60000 cents 9: 9 903.11000 cents 10: 2 984.00000 cents 10: 10 1001.51000 cents 11: 1 1082.40000 cents 11: 11 1099.91000 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 0.0 : 98.4 196.8 295.2 393.6 492.0 607.9 706.3 804.7 903.1 1001.5 1099.9 1198.3 98.4 : 98.4 196.8 295.2 393.6 509.5 607.9 706.3 804.7 903.1 1001.5 1099.9 1198.3 196.8 : 98.4 196.8 295.2 411.1 509.5 607.9 706.3 804.7 903.1 1001.5 1099.9 1198.3 295.2 : 98.4 196.8 312.7 411.1 509.5 607.9 706.3 804.7 903.1 1001.5 1099.9 1198.3 393.6 : 98.4 214.3 312.7 411.1 509.5 607.9 706.3 804.7 903.1 1001.5 1099.9 1198.3 492.0 : 115.9 214.3 312.7 411.1 509.5 607.9 706.3 804.7 903.1 1001.5 1099.9 1198.3 607.9 : 98.4 196.8 295.2 393.6 492.0 590.4 688.8 787.2 885.6 984.0 1082.4 1198.3 706.3 : 98.4 196.8 295.2 393.6 492.0 590.4 688.8 787.2 885.6 984.0 1099.9 1198.3 804.7 : 98.4 196.8 295.2 393.6 492.0 590.4 688.8 787.2 885.6 1001.5 1099.9 1198.3 903.1 : 98.4 196.8 295.2 393.6 492.0 590.4 688.8 787.2 903.1 1001.5 1099.9 1198.3 1001.5: 98.4 196.8 295.2 393.6 492.0 590.4 688.8 804.7 903.1 1001.5 1099.9 1198.3 1099.9: 98.4 196.8 295.2 393.6 492.0 590.4 706.3 804.7 903.1 1001.5 1099.9 1198.3 1198.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.4000 .. 115.9100 cents 17.51000 cents 98.40000 cents 2: 196.8000 .. 214.3100 cents 17.51000 cents 80.89000 cents 3: 295.2000 .. 312.7100 cents 17.51000 cents 80.89000 cents 4: 393.6000 .. 411.1100 cents 17.51000 cents 80.89000 cents 5: 492.0000 .. 509.5100 cents 17.51000 cents 80.89000 cents 6: 590.4000 .. 607.9100 cents 17.51000 cents 80.89000 cents 7: 688.8000 .. 706.3100 cents 17.51000 cents 80.89000 cents 8: 787.2000 .. 804.7100 cents 17.51000 cents 80.89000 cents 9: 885.6000 .. 903.1100 cents 17.51000 cents 80.89000 cents 10: 984.0000 .. 1001.5100 cents 17.51000 cents 80.89000 cents 11: 1082.4000 .. 1099.9100 cents 17.51000 cents 80.89000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 98.40000 cents, class 1 Average step (divided formal octave): 99.8592 cents Largest one step interval : 115.91000 cents Average / Smallest step : 1.014829 Largest / Average step : 1.160735 Largest / Smallest step : 1.177947 Median interval of one step : 98.40000 cents, amount: 11 Most common interval of one step : 98.40000 cents, amount: 11 Least squares average step : 100.09712 cents, oct.: 1201.16548 cents Scale is strictly proper Scale has Myhill's property chromas: 17.51000 cents and 80.89000 cents, ratio: 4.619646 generators: 1 of 98.40000 cents and 11 of 1099.91000 cents ET pair of linear temperament : 12&61 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1437-tone equal temperament with octave 1198.310 cents degrees: 118 236 354 472 590 729 847 965 1083 1201 1319 1437 generators: 118 and 1319 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAAABAAAAAA Step pattern size order : SSSSSLSSSSSS Scale is a Constant Structure, by a margin of 80.89000 cents Scale diversity : 1.124412 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.839265 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 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 : 17.51000 cents Most common intervals : 98.40000 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 492.000 1099.910 cents Number of recognisable fifths : 12, average 699.0142 cents Number of appreciable fifths : 7, average 706.3100 cents Number of recognisable fourths : 12, average 499.2958 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.0897 c. M: 8.7550 c. Twelve-tone Chromatic (1/11-comma) 37: 3 3 3 3 3 4 3 3 3 3 3 3 SP M ME SD: 4.3243 c. M:-7.4384 c. 49: 4 4 4 4 4 5 4 4 4 4 4 4 SP M ME SD: 2.0188 c. M:-3.4727 c. 61: 5 5 5 5 5 6 5 5 5 5 5 5 SP M ME SD: 0.6204 c. M:-1.0672 c. 73: 6 6 6 6 6 7 6 6 6 6 6 6 SP M ME SD: 0.3182 c. M: 0.5474 c. 134: 11 11 11 11 11 13 11 11 11 11 11 11 SP M DE SD: 0.1091 c. M:-0.1876 c. 207: 17 17 17 17 17 20 17 17 17 17 17 17 SP M DE SD: 0.0416 c. M: 0.0716 c. 341: 28 28 28 28 28 33 28 28 28 28 28 28 SP M DE SD: 0.0176 c. M:-0.0303 c. 548: 45 45 45 45 45 53 45 45 45 45 45 45 SP M DE SD: 0.0048 c. M: 0.0082 c. 889: 73 73 73 73 73 86 73 73 73 73 73 73 SP M DE SD: 0.0038 c. M:-0.0065 c. 1437: 118 118 118 118 118 139 118 118 118 118 118 118 SP M DE SD: 0.0005 c. M:-0.0009 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 1.6900 cents 2 x x x x x x 3 x x x x 4 S SD: 2.3357 cents 3 x x x x 4 x x x 5 x x 6 S SD: 6.5913 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.4527 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.4969 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.8635 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.2893 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.5319 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.9894 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.5050 cents 11 x 12:13:14:15:16:17:18:19:20:21:22 S SD: 10.8775 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.2675 cents 13:14 x 15:16:17:18:20:21:22:23:25:26 SD: 9.3385 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.7620 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.3497 cents 16:17:18:19:20:21:23:24:25:27:29:30:32 SD: 4.5635 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 4.2326 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 4.0767 cents 27:29:30:32:34:36:38:41:43:45:48:51:54 SD: 3.5857 cents 28:30:31:33:35:37:40:42:45:47:50:53:56 SD: 3.3195 cents 31:33:35:37:39:41:44:47:49:52:55:59:62 SD: 2.8477 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.6610 cents 34:36:38:40:43:45:48:51:54:57:61:64:68 SD: 2.3344 cents 36:38:40:43:45:48:51:54:57:61:64:68:72 SD: 2.2539 cents 42:44:47:50:53:56:60:63:67:71:75:79:84 SD: 2.1926 cents 47:50:53:56:59:62:67:71:75:79:84:89:94 SD: 2.0451 cents 48:51:54:57:60:64:68:72:76:81:86:91:96 SD: 1.7613 cents 50:53:56:59:63:66:71:75:80:84:89:94:100 SD: 1.7488 cents 52:55:58:62:65:69:74:78:83:88:93:98:104 SD: 1.5622 cents 64:68:72:76:80:85:91:96:102:108:114:121:128 SD: 1.1798 cents 66:70:74:78:83:88:94:99:105:111:118:125:132 SD: 1.1767 cents 74:78:83:88:93:98:105:111:118:125:132:140:148 SD: 1.1406 cents 82:87:92:97:103:109:116:123:131:138:146:155:164 SD: 1.1091 cents 83:88:93:98:104:110:118:125:132:140:148:157:166 SD: 0.9326 cents 86:91:96:102:108:114:122:129:137:145:153:162:172 SD: 0.9129 cents 91:96:102:108:114:121:129:137:145:153:162:172:182 SD: 0.8394 cents 98:104:110:116:123:130:139:147:156:165:175:185:196 SD: 0.7698 cents 107:113:120:127:134:142:152:161:170:180:191:202:214 SD: 0.6731 cents 125:132:140:148:157:166:178:188:199:211:223:236:250 SD: 0.6289 cents 133:141:149:158:167:177:189:200:212:224:237:251:266 SD: 0.4994 cents 152:161:170:180:191:202:216:229:242:256:271:287:304 SD: 0.4904 cents 167:177:187:198:210:222:237:251:266:281:298:315:334 SD: 0.4768 cents 183:194:205:217:230:243:260:275:291:308:326:345:366 SD: 0.4696 cents 188:199:211:223:236:250:267:283:299:317:335:355:376 SD: 0.4070 cents 204:216:229:242:256:271:290:307:325:344:364:385:408 SD: 0.4026 cents 216:229:242:256:271:287:307:325:344:364:385:408:432 SD: 0.3453 cents 240:254:269:285:301:319:341:361:382:404:428:453:480 SD: 0.3122 cents 258:273:289:306:324:343:367:388:411:435:460:487:515 SD: 0.3045 cents 274:290:307:325:344:364:389:412:436:462:489:517:547 SD: 0.2382 cents 340:360:381:403:427:452:483:511:541:573:606:642:679 SD: 0.2097 cents 356:377:399:422:447:473:506:535:567:600:635:672:711 SD: 0.2023 cents 375:397:420:445:471:498:533:564:597:632:669:708:749 SD: 0.1936 cents 392:415:439:465:492:521:557:589:624:660:699:740:783 SD: 0.1860 cents 407:431:456:483:511:541:578:612:648:686:726:768:813 SD: 0.1785 cents 447:473:501:530:561:594:635:672:712:753:797:844:893 SD: 0.1476 cents 463:490:519:549:581:615:658:696:737:780:826:874:925 SD: 0.1363 cents 532:563:596:631:668:707:756:800:847:896:949:1004:1063 SD: 0.1091 cents