Scala analysis: xen18-erlich-orson-13
9L 4s MOS for Orson, L=113.64, s=44.37
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 113.640 cents 113.640000 2: 158.010 cents 158.010000 3: 271.650 cents 271.650000 4: 385.290 cents 385.290000 5: 429.660 cents 429.660000 6: 543.300 cents 543.300000 7: 656.940 cents 656.940000 8: 770.580 cents 770.580000 9: 814.950 cents 814.950000 10: 928.590 cents 928.590000 11: 1042.230 cents 1042.230000 12: 1086.600 cents 1086.600000 13: 1200.240 cents 1200.240000
SHOW/INTERVAL
0: 113.6400 cents 113.6400 1: 113.6400 cents 113.6400 2: 44.3700 cents 44.3700 3: 113.6400 cents 113.6400 4: 113.6400 cents 113.6400 5: 44.3700 cents 44.3700 6: 113.6400 cents 113.6400 7: 113.6400 cents 113.6400 8: 113.6400 cents 113.6400 9: 44.3700 cents 44.3700 10: 113.6400 cents 113.6400 11: 113.6400 cents 113.6400 12: 44.3700 cents 44.3700 13: 113.6400 cents 113.6400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 44.37000 cents 1: 9 113.64000 cents 2: 8 158.01000 cents 2: 5 227.28000 cents 3: 12 271.65000 cents 3: 1 340.92000 cents 4: 3 316.02000 cents 4: 10 385.29000 cents 5: 7 429.66000 cents 5: 6 498.93000 cents 6: 11 543.30000 cents 6: 2 612.57000 cents 7: 2 587.67000 cents 7: 11 656.94000 cents 8: 6 701.31000 cents 8: 7 770.58000 cents 9: 10 814.95000 cents 9: 3 884.22000 cents 10: 1 859.32000 cents 10: 12 928.59000 cents 11: 5 972.96000 cents 11: 8 1042.23000 cents 12: 9 1086.60000 cents 12: 4 1155.87000 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 : 113.6 158.0 271.6 385.3 429.7 543.3 656.9 770.6 814.9 928.6 1042.2 1086.6 1200.2 113.6 : 44.4 158.0 271.6 316.0 429.7 543.3 656.9 701.3 814.9 928.6 973.0 1086.6 1200.2 158.0 : 113.6 227.3 271.6 385.3 498.9 612.6 656.9 770.6 884.2 928.6 1042.2 1155.9 1200.2 271.6 : 113.6 158.0 271.6 385.3 498.9 543.3 656.9 770.6 814.9 928.6 1042.2 1086.6 1200.2 385.3 : 44.4 158.0 271.7 385.3 429.7 543.3 656.9 701.3 815.0 928.6 973.0 1086.6 1200.2 429.7 : 113.6 227.3 340.9 385.3 498.9 612.6 656.9 770.6 884.2 928.6 1042.2 1155.9 1200.2 543.3 : 113.6 227.3 271.7 385.3 498.9 543.3 656.9 770.6 815.0 928.6 1042.2 1086.6 1200.2 656.9 : 113.6 158.0 271.6 385.3 429.7 543.3 656.9 701.3 814.9 928.6 973.0 1086.6 1200.2 770.6 : 44.4 158.0 271.6 316.0 429.7 543.3 587.7 701.3 814.9 859.3 973.0 1086.6 1200.2 814.9 : 113.6 227.3 271.6 385.3 498.9 543.3 656.9 770.6 815.0 928.6 1042.2 1155.9 1200.2 928.6 : 113.6 158.0 271.6 385.3 429.7 543.3 656.9 701.3 814.9 928.6 1042.2 1086.6 1200.2 1042.2: 44.4 158.0 271.7 316.0 429.7 543.3 587.7 701.3 815.0 928.6 973.0 1086.6 1200.2 1086.6: 113.6 227.3 271.7 385.3 498.9 543.3 656.9 770.6 884.2 928.6 1042.2 1155.9 1200.2 1200.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.3700 .. 113.6400 cents 69.27000 cents 44.37000 cents 2: 158.0100 .. 227.2800 cents 69.27000 cents 44.37000 cents 3: 271.6500 .. 340.9200 cents 69.27000 cents 44.37000 cents 4: 316.0200 .. 385.2900 cents 69.27000 cents -24.90000 cents 5: 429.6600 .. 498.9300 cents 69.27000 cents 44.37000 cents 6: 543.3000 .. 612.5700 cents 69.27000 cents 44.37000 cents 7: 587.6700 .. 656.9400 cents 69.27000 cents -24.90000 cents 8: 701.3100 .. 770.5800 cents 69.27000 cents 44.37000 cents 9: 814.9500 .. 884.2200 cents 69.27000 cents 44.37000 cents 10: 859.3200 .. 928.5900 cents 69.27000 cents -24.90000 cents 11: 972.9600 .. 1042.2300 cents 69.27000 cents 44.37000 cents 12: 1086.6000 .. 1155.8700 cents 69.27000 cents 44.37000 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 44.37000 cents, class 1 Average step (divided formal octave): 92.3262 cents Largest one step interval : 113.64000 cents Average / Smallest step : 2.080824 Largest / Average step : 1.230854 Largest / Smallest step : 2.561190 Median interval of one step : 113.64000 cents, amount: 9 Most common interval of one step : 113.64000 cents, amount: 9 Least squares average step : 92.41073 cents, oct.: 1201.33952 cents Scale is not proper Scale has Myhill's property chromas: 69.27000 cents and 24.90000 cents, ratio: 2.781928 generators: 3 of 271.65000 cents and 10 of 928.59000 cents ET pair of linear temperament : 22&31 Scale is distributional even Scale is a mode of a 1109-tone equal temperament with octave 1200.240 cents degrees: 105 146 251 356 397 502 607 712 753 858 963 1004 1109 generators: 251 and 858 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAAABAABA Step pattern size order : LSLLSLLLSLLSL Scale is a Constant Structure, by a margin of 24.90000 cents Scale diversity : 1.225333 Lumma stability : 0.369676 Lumma impropriety factor : 0.062238 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 : 24.90000 cents Most common intervals : 271.65000 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 429.660 928.590 cents Most common triad is 0.0 271.650 928.590 cents, amount: 11 Number of recognisable fifths : 6, average 701.3100 cents Number of recognisable fourths : 6, average 498.9300 cents Scale contains two identical disjunct heptachords 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: 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 19.9373 c. M:-31.9708 c. 18: 2 0 2 2 0 2 2 2 0 2 2 0 2 N M DE I SD: 18.4464 c. M:-29.5800 c. 20: 2 1 2 1 1 2 2 2 1 1 2 1 2 N D3 I SD: 17.8492 c. M:-28.4100 c. 22: 2 1 2 2 1 2 2 2 1 2 2 1 2 P M ME I SD: 4.2349 c. M:-6.7909 c. 31: 3 1 3 3 1 3 3 3 1 3 3 1 3 N M DE I SD: 2.3500 c. M:-3.7684 c. 53: 5 2 5 5 2 5 5 5 2 5 5 2 5 N M DE I SD: 0.3833 c. M:-0.6147 c. 137: 13 5 13 13 5 13 13 13 5 13 13 5 13 N M DE I SD: 0.2352 c. M:-0.3771 c. 190: 18 7 18 18 7 18 18 18 7 18 18 7 18 N M DE I SD: 0.0626 c. M:-0.1004 c. 243: 23 9 23 23 9 23 23 23 9 23 23 9 23 N M DE I SD: 0.0346 c. M:-0.0556 c. 433: 41 16 41 41 16 41 41 41 16 41 41 16 41 N M DE I SD: 0.0080 c. M:-0.0129 c. 676: 64 25 64 64 25 64 64 64 25 64 64 25 64 N M DE I SD: 0.0073 c. M:-0.0117 c. 1109: 105 41 105 105 41 105 105 105 41 105 105 41 105 N M DE I SD: 0.0013 c. M:-0.0021 c. 1542: 146 57 146 146 57 146 146 146 57 146 146 57 146 N M DE I SD: 0.0013 c. M:-0.0021 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.2400 cents 2 x x x x x x 3 x x x x x 4 S SD: 22.5078 cents 3 x x x x x 4 x x x 5 x x 6 S SD: 21.0937 cents 4 x x x 5 x x 6 x x 7 x x 8 S SD: 15.0963 cents 5 x x 6 x x 7 x x 8 x 9 x 10 S SD: 12.7770 cents 6 x x 7 x x 8:9 x x 10:11 x 12 S SD: 13.0219 cents 7 x x 8 x 9 x 10:11 x 12 x 13:14 S SD: 8.5818 cents 8 x 9 x 10 x 11:12 x 13:14 x 15:16 S SD: 10.0580 cents 9 x 10 x 11 x 12:13:14 x 15:16:17:18 S SD: 10.4333 cents 10 x 11:12 x 13:14:15 x 16:17:18:19:20 S SD: 8.6392 cents 11 x 12:13 x 14:15:16:17:18:19:20:21:22 S SD: 5.5783 cents 12 x 13:14:15 x 16:18 x 19:21:22 x 24 SD: 8.9732 cents 13:14 x 15:16:17:18:19:20:21:22:24 x 26 S SD: 6.1654 cents 14:15 x 16:17:18:19:20:22 x 24 x 26:28 S SD: 7.9200 cents 15:16 x 18 x 19:21:22:23:24:26:27:28:30 SD: 7.0831 cents 16:17:18:19:20:21:22:23:25:26:27:29:30:32 SD: 6.3278 cents 17:18:19:20:21:22:23:25 x 27:29:31:32:34 SD: 4.5373 cents 19:20:21:22:24 x 26:28:30 x 32:35:36:38 SD: 5.3468 cents 20:21:22:23:25:26:27:29:31:32:34 x 37:40 SD: 5.1659 cents 21:22:23:25:26:27:29:31:33:34:36:38:39:42 SD: 4.7500 cents 22:23:24:26:27:28:30:32:34:35:38:40:41:44 SD: 4.7177 cents 23 x 25:27:29 x 31:34:36:37:39:42:43:46 SD: 3.9438 cents 24 x 26:28:30:31:33:35:37:38:41:44:45:48 SD: 3.2715 cents 25:27 x 29:31:32:34:37:39:40:43:46:47:50 SD: 3.4295 cents 26:28 x 30:32:33:36:38:41:42:44:47:49:52 SD: 4.8764 cents 27:29:30:32:34:35:37:39:42:43:46:49:51:54 SD: 3.9744 cents 28:30:31:33:35:36:38:41:44:45:48:51:52:56 SD: 2.6943 cents 32:34:35:37:40:41:44:47:50:51:55:58:60:64 SD: 2.3692 cents 40:43:44:47:50:51:55:58:62:64:68:73:75:80 SD: 2.2009 cents 41:44:45:48:51:53:56:60:64:66:70:75:77:82 SD: 1.7207 cents 52:56:57:61:65:67:71:76:81:83:89:95:97:104 SD: 1.6063 cents 57:61:62:67:71:73:78:83:89:91:97:104:107:114 SD: 1.5616 cents 60:64:66:70:75:77:82:88:94:96:103:110:112:120 SD: 1.3468 cents 63:67:69:74:79:81:86:92:98:101:108:115:118:126 SD: 1.2174 cents 71:76:78:83:89:91:97:104:111:114:121:130:133:142 SD: 1.0602 cents 76:81:83:89:95:97:104:111:119:122:130:139:142:152 SD: 1.0332 cents 85:91:93:99:106:109:116:124:133:136:145:155:159:170 SD: 1.0241 cents 87:93:95:102:109:112:119:127:136:139:149:159:163:174 SD: 1.0087 cents 92:98:101:108:115:118:126:134:144:147:157:168:172:184 SD: 0.9914 cents 93:99:102:109:116:119:127:136:145:149:159:170:174:186 SD: 0.7174 cents 116:124:127:136:145:149:159:170:181:186:198:212:217:232 SD: 0.7140 cents 117:125:128:137:146:150:160:171:183:187:200:214:219:234 SD: 0.5489 cents 148:158:162:173:185:190:203:216:231:237:253:270:277:296 SD: 0.4737 cents 160:171:175:187:200:205:219:234:250:256:274:292:300:320 SD: 0.4403 cents 176:188:193:206:220:226:241:257:275:282:301:321:330:352 SD: 0.4224 cents 177:189:194:207:221:227:242:259:276:283:303:323:332:354 SD: 0.4182 cents 188:201:206:220:235:241:257:275:293:301:321:343:352:376 SD: 0.3922 cents 189:202:207:221:236:242:259:276:295:303:323:345:354:378 SD: 0.3376 cents 230:246:252:269:287:295:315:336:359:368:393:420:431:460 SD: 0.3345 cents 241:257:264:282:301:309:330:352:376:386:412:440:451:482 SD: 0.2630 cents 253:270:277:296:316:324:346:370:395:405:433:462:474:506 SD: 0.2583 cents 293:313:321:343:366:376:401:428:457:469:501:535:549:586 SD: 0.2276 cents 323:345:354:378:404:414:442:472:504:517:552:590:605:646 SD: 0.2078 cents 366:391:401:428:457:469:501:535:571:586:626:668:686:732 SD: 0.1613 cents 401:428:439:469:501:514:549:586:626:642:686:732:751:802 SD: 0.1602 cents 458:489:502:536:572:587:627:669:715:733:783:836:858:916 SD: 0.1468 cents 472:504:517:552:590:605:646:690:737:756:807:862:884:944 SD: 0.1369 cents 542:579:594:634:677:695:742:792:846:868:927:990:1015:1084 SD: 0.1365 cents 546:583:598:639:682:700:747:798:852:874:934:997:1023:1092 SD: 0.1254 cents 589:629:645:689:736:755:806:861:919:943:1007:1075:1103:1178 SD: 0.1084 cents