Scala analysis: xen18-erlich-doublewide-10
4L 6s MOS for Doublewide, L=217.68, s=54.64
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 54.640 cents 54.640000 2: 272.320 cents 272.320000 3: 326.960 cents 326.960000 4: 544.640 cents 544.640000 5: 599.280 cents 599.280000 6: 653.920 cents 653.920000 7: 871.600 cents 871.600000 8: 926.240 cents 926.240000 9: 1143.920 cents 1143.920000 10: 1198.560 cents 1198.560000
SHOW/INTERVAL
0: 54.6400 cents 54.6400 1: 54.6400 cents 54.6400 2: 217.6800 cents 217.6800 3: 54.6400 cents 54.6400 4: 217.6800 cents 217.6800 5: 54.6400 cents 54.6400 6: 54.6400 cents 54.6400 7: 217.6800 cents 217.6800 8: 54.6400 cents 54.6400 9: 217.6800 cents 217.6800 10: 54.6400 cents 54.6400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 54.64000 cents 1: 4 217.68000 cents 2: 2 109.28000 cents 2: 8 272.32000 cents 3: 8 326.96000 cents 3: 2 490.00000 cents 4: 4 381.60000 cents 4: 6 544.64000 cents 5: 10 599.28000 cents 6: 6 653.92000 cents 6: 4 816.96000 cents 7: 2 708.56000 cents 7: 8 871.60000 cents 8: 8 926.24000 cents 8: 2 1089.28000 cents 9: 4 980.88000 cents 9: 6 1143.92000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.88889 = 17/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 54.6 272.3 327.0 544.6 599.3 653.9 871.6 926.2 1143.9 1198.6 54.6 : 217.7 272.3 490.0 544.6 599.3 817.0 871.6 1089.3 1143.9 1198.6 272.3 : 54.6 272.3 327.0 381.6 599.3 653.9 871.6 926.2 980.9 1198.6 327.0 : 217.7 272.3 327.0 544.6 599.3 817.0 871.6 926.2 1143.9 1198.6 544.6 : 54.6 109.3 327.0 381.6 599.3 653.9 708.6 926.2 980.9 1198.6 599.3 : 54.6 272.3 327.0 544.6 599.3 653.9 871.6 926.2 1143.9 1198.6 653.9 : 217.7 272.3 490.0 544.6 599.3 817.0 871.6 1089.3 1143.9 1198.6 871.6 : 54.6 272.3 327.0 381.6 599.3 653.9 871.6 926.2 980.9 1198.6 926.2 : 217.7 272.3 327.0 544.6 599.3 817.0 871.6 926.2 1143.9 1198.6 1143.9: 54.6 109.3 327.0 381.6 599.3 653.9 708.6 926.2 980.9 1198.6 1198.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.6400 .. 217.6800 cents 163.04000 cents 54.64000 cents 2: 109.2800 .. 272.3200 cents 163.04000 cents -108.40000 cents 3: 326.9600 .. 490.0000 cents 163.04000 cents 54.64000 cents 4: 381.6000 .. 544.6400 cents 163.04000 cents -108.40000 cents 5: 599.2800 .. 599.2800 cents 1/1, 0.0000 cents 54.64000 cents 6: 653.9200 .. 816.9600 cents 163.04000 cents 54.64000 cents 7: 708.5600 .. 871.6000 cents 163.04000 cents -108.40000 cents 8: 926.2400 .. 1089.2800 cents 163.04000 cents 54.64000 cents 9: 980.8800 .. 1143.9200 cents 163.04000 cents -108.40000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 54.64000 cents, class 1 Average step (divided formal octave): 119.8560 cents Largest one step interval : 217.68000 cents Average / Smallest step : 2.193558 Largest / Average step : 1.816179 Largest / Smallest step : 3.983895 Median interval of one step : 54.64000 cents, amount: 6 Most common interval of one step : 54.64000 cents, amount: 6 Least squares average step : 120.70296 cents, oct.: 1207.02961 cents Scale is not proper Scale has 2 repeating blocks of 5 notes Blocks have Myhill's property chromas: 163.04000 cents and 108.40000 cents, ratio: 1.504059 generators: 2 of 272.32000 cents and 3 of 326.96000 cents ET pair of linear temperament : 22&1360 Scale is distributional even Scale is a mode of a 1316-tone equal temperament with octave 1198.560 cents degrees: 60 299 359 598 658 718 957 1017 1256 1316 Least number of segments generator : 659 of 600.191 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 957 of 871.597 cents and inv. generated superset size: 663 = 653 more = 6630.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABABA Step pattern size order : SLSLSSLSLS Scale is a Constant Structure, by a margin of 54.64000 cents Scale diversity : 1.209668 Lumma stability : 0.273528 Lumma impropriety factor : 0.361767 Rothenberg efficiency (ambiguous key): 0.513333 redundancy: 0.486667 Efficiency x scale size : 5.133333 Number of different interval sizes : 17 = 1.88889 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.88889 = 17/9 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 54.64000 cents Most common intervals : 599.28000 cents & inv., amount: 10 Number of recognisable fifths : 2, average 708.5600 cents Number of recognisable fourths : 2, average 490.0000 cents Scale contains two identical disjunct pentachords Formal octave complements present : 10 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 5 Limited inverse transpositions : 5 Inversional symmetry on degrees : 0 5 Inversional symmetry on intervals : 2-3 7-8 -- Rational properties --
FIT/MODE
10: 0 2 0 2 1 0 2 0 2 1 N B D3 SD: 56.4166 c. M: 87.2480 c. 11: 0 2 1 2 0 1 2 0 2 1 N D3 SD: 38.5233 c. M: 54.6400 c. 13: 0 3 0 3 0 1 2 1 2 1 N SD: 33.1514 c. M: 54.6400 c. 14: 1 2 1 2 1 1 2 1 2 1 P B ME I SD: 21.9001 c. M: 30.9714 c. Decimal-10 16: 1 3 0 3 1 1 3 0 3 1 N B D3 I SD: 21.5152 c. M: 27.3200 c. 17: 1 3 1 3 0 1 3 1 3 1 N SD: 19.9803 c. M: 35.2518 c. 18: 1 3 1 3 1 1 3 1 3 1 N B DE I SD: 8.4476 c. M:-11.9467 c. 22: 1 4 1 4 1 1 4 1 4 1 N B DE I SD: 0.1131 c. M:-0.1600 c. Doublewide-10 700: 32 127 32 127 32 32 127 32 127 32 N B DE I SD: 0.1070 c. M: 0.1513 c. 722: 33 131 33 131 33 33 131 33 131 33 N B DE I SD: 0.1003 c. M:-0.1418 c. 744: 34 135 34 135 34 34 135 34 135 34 N B DE I SD: 0.0940 c. M: 0.1329 c. 766: 35 139 35 139 35 35 139 35 139 35 N B DE I SD: 0.0880 c. M: 0.1245 c. 788: 36 143 36 143 36 36 143 36 143 36 N B DE I SD: 0.0824 c. M:-0.1165 c. 810: 37 147 37 147 37 37 147 37 147 37 N B DE I SD: 0.0771 c. M: 0.1090 c. 832: 38 151 38 151 38 38 151 38 151 38 N B DE I SD: 0.0721 c. M:-0.1019 c. 854: 39 155 39 155 39 39 155 39 155 39 N B DE I SD: 0.0673 c. M:-0.0952 c. 876: 40 159 40 159 40 40 159 40 159 40 N B DE I SD: 0.0628 c. M: 0.0888 c. 898: 41 163 41 163 41 41 163 41 163 41 N B DE I SD: 0.0585 c. M:-0.0827 c. 920: 42 167 42 167 42 42 167 42 167 42 N B DE I SD: 0.0544 c. M:-0.0769 c. 942: 43 171 43 171 43 43 171 43 171 43 N B DE I SD: 0.0504 c. M: 0.0713 c. 964: 44 175 44 175 44 44 175 44 175 44 N B DE I SD: 0.0467 c. M: 0.0661 c. 986: 45 179 45 179 45 45 179 45 179 45 N B DE I SD: 0.0431 c. M: 0.0610 c. 1008: 46 183 46 183 46 46 183 46 183 46 N B DE I SD: 0.0397 c. M: 0.0562 c. 1030: 47 187 47 187 47 47 187 47 187 47 N B DE I SD: 0.0365 c. M: 0.0516 c. 1052: 48 191 48 191 48 48 191 48 191 48 N B DE I SD: 0.0333 c. M: 0.0471 c. 1074: 49 195 49 195 49 49 195 49 195 49 N B DE I SD: 0.0303 c. M: 0.0429 c. 1096: 50 199 50 199 50 50 199 50 199 50 N B DE I SD: 0.0275 c. M:-0.0388 c. 1118: 51 203 51 203 51 51 203 51 203 51 N B DE I SD: 0.0247 c. M:-0.0349 c. 1140: 52 207 52 207 52 52 207 52 207 52 N B DE I SD: 0.0220 c. M:-0.0312 c. 1162: 53 211 53 211 53 53 211 53 211 53 N B DE I SD: 0.0195 c. M:-0.0275 c. 1184: 54 215 54 215 54 54 215 54 215 54 N B DE I SD: 0.0170 c. M:-0.0241 c. 1206: 55 219 55 219 55 55 219 55 219 55 N B DE I SD: 0.0146 c. M:-0.0207 c. 1228: 56 223 56 223 56 56 223 56 223 56 N B DE I SD: 0.0123 c. M: 0.0175 c. 1250: 57 227 57 227 57 57 227 57 227 57 N B DE I SD: 0.0101 c. M: 0.0143 c. 1272: 58 231 58 231 58 58 231 58 231 58 N B DE I SD: 0.0080 c. M:-0.0113 c. 1294: 59 235 59 235 59 59 235 59 235 59 N B DE I SD: 0.0059 c. M:-0.0084 c. 1316: 60 239 60 239 60 60 239 60 239 60 N B DE I SD: 0.0040 c. M: 0.0056 c. 1338: 61 243 61 243 61 61 243 61 243 61 N B DE I SD: 0.0020 c. M: 0.0029 c. 1360: 62 247 62 247 62 62 247 62 247 62 N B DE I SD: 0.0002 c. M:-0.0002 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 1.4400 cents 2 x x x x x 3 x x x 4 S SD: 24.0283 cents 3 x x x 4 x x 5 x x 6 S SD: 16.1106 cents 4 x x 5 x x 6 x 7 x 8 S SD: 21.8601 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 22.0103 cents 6 x 7 x 8 x 9:10 x x 12 S SD: 13.6719 cents 7 x 8 x x 10 x x 12 x 14 S SD: 11.3854 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 16.0239 cents 9 x x 11:12 x 13:15 x 17:18 SD: 11.6567 cents 10 x x 12 x 14:15 x 17:19:20 SD: 10.3375 cents 11:12:13 x 15 x 16:18:19:21:22 SD: 13.0785 cents 12:13:14:15:16:17:18:20 x 23:24 SD: 13.8618 cents 13:14:15:16:18 x 19 x 22:25:26 SD: 11.0594 cents 14:15:16:17:19:20 x 23:24:27:28 SD: 9.1672 cents 15:16 x 18 x 21:22:25:26:29:30 SD: 8.4786 cents 16:17:19 x 22 x 23:26:27:31:32 SD: 9.0593 cents 17:18:20:21:23:24:25:28:29:33:34 SD: 6.5488 cents 18:19:21:22:25 x 26:30:31:35:36 SD: 6.3682 cents 19:20:22:23:26:27:28:31:32:37:38 SD: 5.6177 cents 21:22 x 25:29:30:31:35:36:41:42 SD: 5.7363 cents 22:23:26:27:30:31:32:36:38:43:44 SD: 5.1850 cents 24:25:28:29:33:34:35:40:41:46:48 SD: 2.8663 cents 29:30:34:35:40:41:42:48:50:56:58 SD: 2.5355 cents 34:35:40:41:47:48:50:56:58:66:68 SD: 2.5317 cents 35:36:41:42:48:49:51:58:60:68:70 SD: 2.3409 cents 48:50:56:58:66:68:70:79:82:93:96 SD: 2.0774 cents 52:54:61:63:71:74:76:86:89:101:104 SD: 1.9475 cents 54:56:63:65:74:76:79:89:92:105:108 SD: 1.8161 cents 57:59:67:69:78:81:83:94:97:110:114 SD: 1.7107 cents 58:60:68:70:79:82:85:96:99:112:116 SD: 1.4378 cents 63:65:74:76:86:89:92:104:108:122:126 SD: 1.2121 cents 82:85:96:99:112:116:120:136:140:159:164 SD: 1.1753 cents 87:90:102:105:119:123:127:144:149:168:174 SD: 0.9288 cents 92:95:108:111:126:130:134:152:157:178:184 SD: 0.7180 cents 116:120:136:140:159:164:169:192:198:225:232 SD: 0.6895 cents 124:128:145:150:170:175:181:205:212:240:248 SD: 0.5433 cents 130:134:152:157:178:184:190:215:222:252:260 SD: 0.5319 cents 154:159:180:186:211:218:225:255:263:298:308 SD: 0.4810 cents 157:162:184:190:215:222:229:260:268:304:314 SD: 0.4763 cents 159:164:186:192:218:225:232:263:271:308:318 SD: 0.4547 cents 187:193:219:226:256:264:273:309:319:362:374 SD: 0.4346 cents 211:218:247:255:289:298:308:349:360:409:422 SD: 0.3946 cents 216:223:253:261:296:305:315:357:369:418:432 SD: 0.3809 cents 222:229:260:268:304:314:324:367:379:430:444 SD: 0.2997 cents 246:254:288:297:337:348:359:407:420:476:492 SD: 0.2608 cents 312:322:365:377:427:441:455:516:533:604:623 SD: 0.2552 cents 341:352:399:412:467:482:498:564:582:660:681 SD: 0.2459 cents 346:357:405:418:474:489:505:572:591:670:691 SD: 0.2089 cents 370:382:433:447:507:523:540:612:632:716:739 SD: 0.1941 cents 438:452:513:529:600:619:639:725:748:848:875 SD: 0.1783 cents 457:472:535:552:626:646:667:756:780:885:913 SD: 0.1769 cents 471:486:551:569:645:666:687:779:804:912:941 SD: 0.1392 cents 530:547:620:640:726:749:773:877:905:1026:1059 SD: 0.1297 cents 558:576:653:674:764:789:814:923:953:1080:1115 SD: 0.1250 cents 592:611:693:715:811:837:864:979:1011:1146:1183 SD: 0.1223 cents