Scala analysis: xen18-erlich-keemun-11
4L 7s MOS for Keemun, L=181.50, s=68.17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68.170 cents 68.170000 2: 249.670 cents 249.670000 3: 317.840 cents 317.840000 4: 386.010 cents 386.010000 5: 567.510 cents 567.510000 6: 635.680 cents 635.680000 7: 817.180 cents 817.180000 8: 885.350 cents 885.350000 9: 953.520 cents 953.520000 10: 1135.020 cents 1135.020000 11: 1203.190 cents 1203.190000
SHOW/INTERVAL
0: 68.1700 cents 68.1700 1: 68.1700 cents 68.1700 2: 181.5000 cents 181.5000 3: 68.1700 cents 68.1700 4: 68.1700 cents 68.1700 5: 181.5000 cents 181.5000 6: 68.1700 cents 68.1700 7: 181.5000 cents 181.5000 8: 68.1700 cents 68.1700 9: 68.1700 cents 68.1700 10: 181.5000 cents 181.5000 11: 68.1700 cents 68.1700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 68.17000 cents 1: 4 181.50000 cents 2: 3 136.34000 cents 2: 8 249.67000 cents 3: 10 317.84000 cents 3: 1 431.17000 cents 4: 6 386.01000 cents 4: 5 499.34000 cents 5: 2 454.18000 cents 5: 9 567.51000 cents 6: 9 635.68000 cents 6: 2 749.01000 cents 7: 5 703.85000 cents 7: 6 817.18000 cents 8: 1 772.02000 cents 8: 10 885.35000 cents 9: 8 953.52000 cents 9: 3 1066.85000 cents 10: 4 1021.69000 cents 10: 7 1135.02000 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 : 68.2 249.7 317.8 386.0 567.5 635.7 817.2 885.3 953.5 1135.0 1203.2 68.2 : 181.5 249.7 317.8 499.3 567.5 749.0 817.2 885.3 1066.8 1135.0 1203.2 249.7 : 68.2 136.3 317.8 386.0 567.5 635.7 703.8 885.4 953.5 1021.7 1203.2 317.8 : 68.2 249.7 317.8 499.3 567.5 635.7 817.2 885.3 953.5 1135.0 1203.2 386.0 : 181.5 249.7 431.2 499.3 567.5 749.0 817.2 885.3 1066.8 1135.0 1203.2 567.5 : 68.2 249.7 317.8 386.0 567.5 635.7 703.8 885.4 953.5 1021.7 1203.2 635.7 : 181.5 249.7 317.8 499.3 567.5 635.7 817.2 885.3 953.5 1135.0 1203.2 817.2 : 68.2 136.3 317.8 386.0 454.2 635.7 703.8 772.0 953.5 1021.7 1203.2 885.3 : 68.2 249.7 317.8 386.0 567.5 635.7 703.9 885.3 953.5 1135.0 1203.2 953.5 : 181.5 249.7 317.8 499.3 567.5 635.7 817.2 885.4 1066.8 1135.0 1203.2 1135.0: 68.2 136.3 317.8 386.0 454.2 635.7 703.8 885.3 953.5 1021.7 1203.2 1203.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 68.1700 .. 181.5000 cents 113.33000 cents 68.17000 cents 2: 136.3400 .. 249.6700 cents 113.33000 cents -45.16000 cents 3: 317.8400 .. 431.1700 cents 113.33000 cents 68.17000 cents 4: 386.0100 .. 499.3400 cents 113.33000 cents -45.16000 cents 5: 454.1800 .. 567.5100 cents 113.33000 cents -45.16000 cents 6: 635.6800 .. 749.0100 cents 113.33000 cents 68.17000 cents 7: 703.8500 .. 817.1800 cents 113.33000 cents -45.16000 cents 8: 772.0200 .. 885.3500 cents 113.33000 cents -45.16000 cents 9: 953.5200 .. 1066.8500 cents 113.33000 cents 68.17000 cents 10: 1021.6900 .. 1135.0200 cents 113.33000 cents -45.16000 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 68.17000 cents, class 1 Average step (divided formal octave): 109.3809 cents Largest one step interval : 181.50000 cents Average / Smallest step : 1.604531 Largest / Average step : 1.659339 Largest / Smallest step : 2.662461 Median interval of one step : 68.17000 cents, amount: 7 Most common interval of one step : 68.17000 cents, amount: 7 Least squares average step : 110.05283 cents, oct.: 1210.58109 cents Scale is not proper Scale has Myhill's property chromas: 113.33000 cents and 45.16000 cents, ratio: 2.509522 generators: 3 of 317.84000 cents and 8 of 885.35000 cents ET pair of linear temperament : 15&19 Scale is distributional even Scale is a mode of a 1306-tone equal temperament with octave 1203.190 cents degrees: 74 271 345 419 616 690 887 961 1035 1232 1306 generators: 345 and 961 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABABAABA Step pattern size order : SLSSLSLSSLS Scale is a Constant Structure, by a margin of 23.01000 cents Scale diversity : 1.239234 Lumma stability : 0.283289 Lumma impropriety factor : 0.225201 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 : 23.01000 cents Most common intervals : 317.84000 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 386.010 885.350 cents Most common triad is 0.0 317.840 885.350 cents, amount: 9 Number of recognisable fifths : 5, average 703.8500 cents Number of recognisable fourths : 5, average 499.3400 cents Scale contains two identical conjunct hexachords 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 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 32.5801 c. M: 51.5136 c. 13: 1 2 0 1 2 1 2 1 0 2 1 N T3 I SD: 24.8290 c. M: 40.1808 c. 15: 1 2 1 1 2 1 2 1 1 2 1 P M ME I SD: 9.5206 c. M: 15.0533 c. 19: 1 3 1 1 3 1 3 1 1 3 1 N M DE I SD: 3.8297 c. M: 6.0553 c. 34: 2 5 2 2 5 2 5 2 2 5 2 N M DE I SD: 2.0601 c. M: 3.2574 c. 53: 3 8 3 3 8 3 8 3 3 8 3 N M DE I SD: 0.0513 c. M: 0.0811 c. 723: 41 109 41 41 109 41 109 41 41 109 41 N M DE I SD: 0.0480 c. M: 0.0759 c. 776: 44 117 44 44 117 44 117 44 44 117 44 N M DE I SD: 0.0412 c. M: 0.0651 c. 829: 47 125 47 47 125 47 125 47 47 125 47 N M DE I SD: 0.0353 c. M: 0.0558 c. 882: 50 133 50 50 133 50 133 50 50 133 50 N M DE I SD: 0.0301 c. M: 0.0476 c. 935: 53 141 53 53 141 53 141 53 53 141 53 N M DE I SD: 0.0255 c. M:-0.0403 c. 988: 56 149 56 56 149 56 149 56 56 149 56 N M DE I SD: 0.0213 c. M: 0.0338 c. 1041: 59 157 59 59 157 59 157 59 59 157 59 N M DE I SD: 0.0176 c. M:-0.0279 c. 1094: 62 165 62 62 165 62 165 62 62 165 62 N M DE I SD: 0.0143 c. M: 0.0226 c. 1147: 65 173 65 65 173 65 173 65 65 173 65 N M DE I SD: 0.0113 c. M: 0.0178 c. 1200: 68 181 68 68 181 68 181 68 68 181 68 N M DE I SD: 0.0085 c. M: 0.0135 c. 1253: 71 189 71 71 189 71 189 71 71 189 71 N M DE I SD: 0.0060 c. M: 0.0095 c. 1306: 74 197 74 74 197 74 197 74 74 197 74 N M DE I SD: 0.0037 c. M: 0.0058 c. 1359: 77 205 77 77 205 77 205 77 77 205 77 N M DE I SD: 0.0015 c. M: 0.0024 c. 1412: 80 213 80 80 213 80 213 80 80 213 80 N M DE I SD: 0.0005 c. M: 0.0007 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 3.1900 cents 2 x x x x x 3 x x x x 4 S SD: 33.1759 cents 3 x x x x 4 x x 5 x x 6 S SD: 23.1818 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 17.0237 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 13.2031 cents 6 x 7 x x 8:9 x 10 x x 12 S SD: 19.5190 cents 7 x 8 x 9 x 10:11 x 12:13:14 S SD: 13.3399 cents 8 x 9 x 10:11:12:13 x 14:15:16 S SD: 12.3262 cents 9 x 10:11 x x 13:14:15:16:17:18 SD: 13.1749 cents 10 x x 12:13:14 x 16:17 x 19:20 SD: 11.5880 cents 11:12 x 13:14:15:16 x 18:19:21:22 SD: 11.7034 cents 12:13:14 x 15 x 17:19:20:21:23:24 SD: 9.3684 cents 13:14:15 x 16:18:19:21:22:23:25:26 SD: 8.2478 cents 15:16:17:18:19:21:22:24:25:26:29:30 SD: 6.1448 cents 17:18:20 x 21:24:25:27:28:29:33:34 SD: 7.7463 cents 18:19:21:22:23:25:26:29:30:31:35:36 SD: 5.5966 cents 19:20:22:23:24:26:27:30:32:33:37:38 SD: 5.4977 cents 20:21:23:24:25:28:29:32:33:35:39:40 SD: 3.6980 cents 25:26:29:30:31:35:36:40:42:43:48:50 SD: 2.7575 cents 39:41:45:47:49:54:56:63:65:68:75:78 SD: 2.6165 cents 40:42:46:48:50:56:58:64:67:69:77:80 SD: 2.5503 cents 41:43:47:49:51:57:59:66:68:71:79:82 SD: 2.4532 cents 43:45:50:52:54:60:62:69:72:75:83:86 SD: 2.3910 cents 44:46:51:53:55:61:64:71:73:76:85:88 SD: 2.2203 cents 45:47:52:54:56:62:65:72:75:78:87:90 SD: 1.6697 cents 52:54:60:62:65:72:75:83:87:90:100:104 SD: 1.6595 cents 56:58:65:67:70:78:81:90:93:97:108:112 SD: 1.6195 cents 64:67:74:77:80:89:92:103:107:111:123:128 SD: 1.5427 cents 65:68:75:78:81:90:94:104:108:113:125:130 SD: 1.4215 cents 69:72:80:83:86:96:100:111:115:120:133:138 SD: 1.3729 cents 70:73:81:84:87:97:101:112:117:121:135:140 SD: 1.3277 cents 72:75:83:87:90:100:104:115:120:125:139:144 SD: 1.2432 cents 75:78:87:90:94:104:108:120:125:130:144:150 SD: 1.1542 cents 79:82:91:95:99:110:114:127:132:137:152:158 SD: 1.0785 cents 93:97:107:112:116:129:134:149:155:161:179:186 SD: 1.0613 cents 95:99:110:114:119:132:137:152:158:165:183:190 SD: 0.9275 cents 103:107:119:124:129:143:149:165:172:179:198:206 SD: 0.8325 cents 108:112:125:130:135:150:156:173:180:187:208:216 SD: 0.7831 cents 121:126:140:145:151:168:175:194:202:210:233:242 SD: 0.7303 cents 124:129:143:149:155:172:179:199:207:215:239:248 SD: 0.4754 cents 180:187:208:216:225:250:260:289:300:312:347:361 SD: 0.4575 cents 193:201:223:232:241:268:279:309:322:335:372:387 SD: 0.4458 cents 199:207:230:239:249:276:287:319:332:345:383:399 SD: 0.3563 cents 219:228:253:263:274:304:316:351:365:380:422:439 SD: 0.2888 cents 252:262:291:303:315:350:364:404:420:437:485:505 SD: 0.2659 cents 297:309:343:357:371:412:429:476:495:515:572:595 SD: 0.2054 cents 421:438:486:506:526:584:608:675:702:730:811:844 SD: 0.1918 cents 446:464:515:536:557:619:644:715:744:774:859:894 SD: 0.1796 cents 451:469:521:542:564:626:651:723:752:782:869:904 SD: 0.1489 cents 476:495:550:572:595:661:687:763:794:826:917:954 SD: 0.1471 cents 516:537:596:620:645:716:745:827:860:895:994:1034 SD: 0.1417 cents 521:542:602:626:651:723:752:835:869:904:1004:1044 SD: 0.1228 cents 572:595:661:687:715:794:826:917:954:992:1102:1146 SD: 0.1140 cents