Scala analysis: xen18-erlich-amity-11
7L 4s MOS for Amity, L=158.03, s=23.41
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 158.030 cents 158.030000 2: 181.440 cents 181.440000 3: 339.470 cents 339.470000 4: 497.500 cents 497.500000 5: 520.910 cents 520.910000 6: 678.940 cents 678.940000 7: 702.350 cents 702.350000 8: 860.380 cents 860.380000 9: 1018.410 cents 1018.410000 10: 1041.820 cents 1041.820000 11: 1199.850 cents 1199.850000
SHOW/INTERVAL
0: 158.0300 cents 158.0300 1: 158.0300 cents 158.0300 2: 23.4100 cents 23.4100 3: 158.0300 cents 158.0300 4: 158.0300 cents 158.0300 5: 23.4100 cents 23.4100 6: 158.0300 cents 158.0300 7: 23.4100 cents 23.4100 8: 158.0300 cents 158.0300 9: 158.0300 cents 158.0300 10: 23.4100 cents 23.4100 11: 158.0300 cents 158.0300
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 23.41000 cents 1: 7 158.03000 cents 2: 8 181.44000 cents 2: 3 316.06000 cents 3: 1 204.85000 cents 3: 10 339.47000 cents 4: 5 362.88000 cents 4: 6 497.50000 cents 5: 9 520.91000 cents 5: 2 655.53000 cents 6: 2 544.32000 cents 6: 9 678.94000 cents 7: 6 702.35000 cents 7: 5 836.97000 cents 8: 10 860.38000 cents 8: 1 995.00000 cents 9: 3 883.79000 cents 9: 8 1018.41000 cents 10: 7 1041.82000 cents 10: 4 1176.44000 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 0.0 : 158.0 181.4 339.5 497.5 520.9 678.9 702.3 860.4 1018.4 1041.8 1199.8 158.0 : 23.4 181.4 339.5 362.9 520.9 544.3 702.3 860.4 883.8 1041.8 1199.8 181.4 : 158.0 316.1 339.5 497.5 520.9 678.9 837.0 860.4 1018.4 1176.4 1199.8 339.5 : 158.0 181.4 339.5 362.9 520.9 678.9 702.3 860.4 1018.4 1041.8 1199.9 497.5 : 23.4 181.4 204.8 362.9 520.9 544.3 702.3 860.4 883.8 1041.8 1199.8 520.9 : 158.0 181.4 339.5 497.5 520.9 678.9 837.0 860.4 1018.4 1176.4 1199.8 678.9 : 23.4 181.4 339.5 362.9 520.9 678.9 702.3 860.4 1018.4 1041.8 1199.8 702.3 : 158.0 316.1 339.5 497.5 655.5 678.9 837.0 995.0 1018.4 1176.4 1199.8 860.4 : 158.0 181.4 339.5 497.5 520.9 678.9 837.0 860.4 1018.4 1041.8 1199.8 1018.4: 23.4 181.4 339.5 362.9 520.9 678.9 702.3 860.4 883.8 1041.8 1199.8 1041.8: 158.0 316.1 339.5 497.5 655.5 678.9 837.0 860.4 1018.4 1176.4 1199.8 1199.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 23.4100 .. 158.0300 cents 134.62000 cents 23.41000 cents 2: 181.4400 .. 316.0600 cents 134.62000 cents 23.41000 cents 3: 204.8500 .. 339.4700 cents 134.62000 cents -111.21000 cents 4: 362.8800 .. 497.5000 cents 134.62000 cents 23.41000 cents 5: 520.9100 .. 655.5300 cents 134.62000 cents 23.41000 cents 6: 544.3200 .. 678.9400 cents 134.62000 cents -111.21000 cents 7: 702.3500 .. 836.9700 cents 134.62000 cents 23.41000 cents 8: 860.3800 .. 995.0000 cents 134.62000 cents 23.41000 cents 9: 883.7900 .. 1018.4100 cents 134.62000 cents -111.21000 cents 10: 1041.8200 .. 1176.4400 cents 134.62000 cents 23.41000 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 23.41000 cents, class 1 Average step (divided formal octave): 109.0773 cents Largest one step interval : 158.03000 cents Average / Smallest step : 4.659431 Largest / Average step : 1.448789 Largest / Smallest step : 6.750534 Median interval of one step : 158.03000 cents, amount: 7 Most common interval of one step : 158.03000 cents, amount: 7 Least squares average step : 108.27913 cents, oct.: 1191.07043 cents Scale is not proper Scale has Myhill's property chromas: 134.62000 cents and 111.21000 cents, ratio: 1.210503 generators: 3 of 339.47000 cents and 8 of 860.38000 cents ET pair of linear temperament : 46&53 Scale is distributional even Scale is a mode of a 205-tone equal temperament with octave 1199.850 cents degrees: 27 31 58 85 89 116 120 147 174 178 205 generators: 58 and 147 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABABAABA Step pattern size order : LSLLSLSLLSL Scale is a Constant Structure, by a margin of 23.41000 cents Scale diversity : 1.045820 Lumma stability : 0.156086 Lumma impropriety factor : 0.278060 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 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 : 23.41000 cents Most common intervals : 339.47000 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 497.500 860.380 cents Most common triad is 0.0 339.470 860.380 cents, amount: 9 Number of recognisable fifths : 6, average 702.3500 cents Number of recognisable fourths : 6, average 497.5000 cents Scale contains two identical disjunct pentachords Formal octave complements present : 11 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties --
FIT/MODE
11: 1 0 2 1 0 2 0 1 2 0 2 N T3 SD: 57.1418 c. M: 96.8391 c. 12: 2 0 1 2 0 2 0 2 1 0 2 N I SD: 27.3348 c. M:-41.9450 c. 14: 2 0 2 2 0 2 0 2 2 0 2 N M DE I SD: 10.5756 c. M:-16.7214 c. 21: 3 0 3 3 0 3 0 3 3 0 3 N M DE I SD: 10.5756 c. M:-16.7214 c. 31: 4 1 4 4 0 5 0 4 4 1 4 N I SD: 10.2877 c. M: 17.7471 c. 32: 4 1 4 4 1 4 1 4 4 1 4 N M DE I SD: 6.3631 c. M:-10.0609 c. 39: 5 1 5 5 1 5 1 5 5 1 5 N M DE I SD: 3.3228 c. M:-5.2538 c. 46: 6 1 6 6 1 6 1 6 6 1 6 N M DE I SD: 1.2079 c. M: 1.9098 c. 53: 7 1 7 7 1 7 1 7 7 1 7 N M DE I SD: 0.3484 c. M:-0.5509 c. 152: 20 3 20 20 3 20 3 20 20 3 20 N M DE I SD: 0.1225 c. M:-0.1938 c. 205: 27 4 27 27 4 27 4 27 27 4 27 N M DE I SD: 0.0008 c. M:-0.0012 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.1500 cents 2 x x x x x x 3 x x x 4 S SD: 0.2113 cents 3 x x x 4 x x x 5 x x 6 S SD: 7.9951 cents 4 x x 5 x x x 6 x 7 x 8 S SD: 17.0534 cents 5 x x 6 x 7 x x 8:9 x 10 S SD: 16.1785 cents 6 x x 7:8 x x 9:10 x 11:12 S SD: 12.8051 cents 7 x 8 x 9 x 10 x 12 x 13:14 S SD: 21.2988 cents 8 x 9:10 x 11 x 12:13:14:15:16 S SD: 11.6151 cents 9 x 10:11:12 x 13:14:15:16 x 18 S SD: 10.3404 cents 10:11 x 12:13:14 x 15:16:18 x 20 S SD: 11.5014 cents 11:12 x 13 x 15:16:17:18 x 20:22 SD: 10.0710 cents 12:13 x 15:16 x x 18:20 x 22:24 SD: 8.0879 cents 13:14 x 16:17:18:19:20:21:23:24:26 SD: 9.3716 cents 14:15:16:17 x 19 x 21:23:25:26:28 SD: 7.9671 cents 15:16:17:18:20 x 22:23:25:27 x 30 SD: 8.7490 cents 16 x 18:19:21:22 x 24:26:29 x 32 SD: 8.3131 cents 17 x 19:21 x 23:25:26:28 x 31:34 SD: 5.6871 cents 18 x 20:22:24 x x 27:30:32:33:36 S SD: 4.3201 cents 19 x 21:23:25:26:28:29:31:34:35:38 SD: 5.1078 cents 20:22 x 24 x 27 x 30:33:36:37:40 SD: 4.3322 cents 21:23 x 26:28 x 31:32:35:38 x 42 SD: 6.0019 cents 22:24 x 27:29:30 x 33:36 x 40:44 SD: 3.9861 cents 23:25:26:28 x 31:34:35:38:41:42:46 SD: 4.6374 cents 24:26:27:29:32 x x 36:39:43:44:48 SD: 4.3796 cents 26:28:29:32 x 35:38:39:43:47 x 52 SD: 4.9933 cents 27 x 30:33:36 x 40:41:44 x 49:54 SD: 3.5895 cents 28 x 31:34:37:38:41:42:46:50:51:56 SD: 3.0028 cents 29 x 32:35 x 39:43:44:48:52:53:58 SD: 3.4568 cents 30:33 x 37:40:41:44:45:49:54:55:60 SD: 3.7851 cents 31:34 x 38:41:42:46:47:51:56:57:62 SD: 3.0246 cents 32:35:36:39 x 43:47:48:53:58 x 64 SD: 3.6652 cents 33:36:37:40:44:45:49:50:54:59:60:66 SD: 3.1658 cents 34:37:38:41:45:46:50:51:56:61:62:68 SD: 2.6268 cents 35:38:39:43 x 47:52:53:58:63:64:70 SD: 3.4389 cents 36:39:40:44:48:49:53:54:59:65:66:72 SD: 2.5689 cents 37 x 41:45:49:50:55:56:61:67:68:74 SD: 2.6068 cents 38 x 42:46 x 51:56:57:62:68:69:76 SD: 2.9439 cents 39:43 x 47:52:53:58:59:64:70:71:78 SD: 2.8788 cents 40:44 x 49:53:54:59:60:66:72:73:80 SD: 1.9464 cents 41:45:46:50:55 x 61:62:67:74:75:82 SD: 2.9340 cents 42:46:47:51:56:57:62:63:69:76:77:84 SD: 1.8134 cents 44:48:49:54:59 x 65:66:72:79:80:88 SD: 2.3646 cents 45:49:50:55:60:61:67:68:74:81:82:90 SD: 1.9835 cents 46:50:51:56:61:62:68:69:76:83:84:92 SD: 1.7904 cents 48 x 53:58:64:65:71:72:79:86:88:96 SD: 1.9898 cents 49:54 x 60:65:66:73:74:81:88:89:98 SD: 2.7770 cents 50:55:56:61:67:68:74:75:82:90:91:100 SD: 2.1250 cents 51:56:57:62:68:69:75:77:84:92:93:102 SD: 1.8541 cents 52:57:58:63:69:70:77:78:85:94:95:104 SD: 1.7027 cents 54:59:60:66:72:73:80:81:89:97:99:108 SD: 1.2451 cents 58 x 64:71:77:78:86:87:95:104:106:116 SD: 2.1302 cents 60:66:67:73:80:81:89:90:99:108:110:120 SD: 1.4586 cents 62:68:69:75:83:84:92:93:102:112:113:124 SD: 1.4453 cents 64:70:71:78:85:86:95:96:105:115:117:128 SD: 1.2979 cents 73:80:81:89:97:99:108:110:120:131:133:146 SD: 1.2589 cents 74:81:82:90:99:100:110:111:122:133:135:148 SD: 1.1169 cents 82:90:91:100:109:111:121:123:135:148:150:164 SD: 1.0228 cents 92:101:102:112:123:124:136:138:151:166:168:184 SD: 0.8624 cents 96:105:107:117:128:130:142:144:158:173:175:192 SD: 0.8495 cents 102:112:113:124:136:138:151:153:168:184:186:204 SD: 0.7289 cents 116:127:129:141:155:157:172:174:191:209:212:232 SD: 0.7079 cents 125:137:139:152:167:169:185:188:205:225:228:250 SD: 0.7041 cents 126:138:140:153:168:170:187:189:207:227:230:252 SD: 0.5822 cents 144:158:160:175:192:195:213:216:237:259:263:288 SD: 0.5715 cents 148:162:164:180:197:200:219:222:243:267:270:296 SD: 0.5542 cents 154:169:171:187:205:208:228:231:253:277:281:308 SD: 0.5044 cents 156:171:173:190:208:211:231:234:256:281:285:312 SD: 0.4559 cents 171:187:190:208:228:231:253:257:281:308:312:342 SD: 0.4256 cents 180:197:200:219:240:243:266:270:296:324:329:360 SD: 0.4155 cents 190:208:211:231:253:257:281:285:312:342:347:380 SD: 0.3749 cents 208:228:231:253:277:281:308:312:342:375:380:416 SD: 0.2919 cents 262:287:291:319:349:354:388:393:431:472:478:524 SD: 0.2423 cents 333:365:370:405:444:450:493:500:547:600:608:666 SD: 0.2351 cents 336:368:373:409:448:454:497:504:552:605:613:672 SD: 0.2058 cents 379:415:421:461:505:512:561:569:623:683:692:758 SD: 0.1962 cents 387:424:430:471:516:523:573:581:636:697:706:774 SD: 0.1922 cents 388:425:431:472:517:524:574:582:638:699:708:776 SD: 0.1699 cents 396:434:440:482:528:535:586:594:651:713:723:792 SD: 0.1539 cents 462:506:513:562:616:624:684:693:759:832:843:924 SD: 0.1458 cents 481:527:534:585:641:650:712:722:791:866:878:962 SD: 0.1384 cents 544:596:604:662:725:735:805:816:894:980:993:1088 SD: 0.1010 cents