Scala analysis: sengic8
A distributionally even scale in sengic temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 237.096 cents 237.096000 2: 366.622 cents 366.622000 3: 496.148 cents 496.148000 4: 625.674 cents 625.674000 5: 811.775 cents 811.775000 6: 941.301 cents 941.301000 7: 1070.827 cents 1070.827000 8: 1200.353 cents 1200.353000
SHOW/INTERVAL
0: 129.5260 cents 129.5260 1: 237.0960 cents 237.0960 2: 129.5260 cents 129.5260 3: 129.5260 cents 129.5260 4: 129.5260 cents 129.5260 5: 186.1010 cents 186.1010 6: 129.5260 cents 129.5260 7: 129.5260 cents 129.5260 8: 129.5260 cents 129.5260
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 129.52600 cents 1: 1 186.10100 cents 1: 1 237.09600 cents 2: 4 259.05200 cents 2: 2 315.62700 cents 2: 2 366.62200 cents 3: 2 388.57800 cents 3: 3 445.15300 cents 3: 3 496.14800 cents 4: 4 574.67900 cents 4: 4 625.67400 cents 5: 3 704.20500 cents 5: 3 755.20000 cents 5: 2 811.77500 cents 6: 2 833.73100 cents 6: 2 884.72600 cents 6: 4 941.30100 cents 7: 1 963.25700 cents 7: 1 1014.25200 cents 7: 6 1070.82700 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.85714 = 20/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 237.1 366.6 496.1 625.7 811.8 941.3 1070.8 1200.4 237.1 : 129.5 259.1 388.6 574.7 704.2 833.7 963.3 1200.4 366.6 : 129.5 259.1 445.2 574.7 704.2 833.7 1070.8 1200.4 496.1 : 129.5 315.6 445.2 574.7 704.2 941.3 1070.8 1200.4 625.7 : 186.1 315.6 445.2 574.7 811.8 941.3 1070.8 1200.4 811.8 : 129.5 259.1 388.6 625.7 755.2 884.7 1014.3 1200.4 941.3 : 129.5 259.1 496.1 625.7 755.2 884.7 1070.8 1200.4 1070.8: 129.5 366.6 496.1 625.7 755.2 941.3 1070.8 1200.4 1200.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 129.5260 .. 237.0960 cents 107.57000 cents 129.52600 cents 2: 259.0520 .. 366.6220 cents 107.57000 cents 21.95600 cents 3: 388.5780 .. 496.1480 cents 107.57000 cents 21.95600 cents 4: 574.6790 .. 625.6740 cents 50.99500 cents 78.53100 cents 5: 704.2050 .. 811.7750 cents 107.57000 cents 78.53100 cents 6: 833.7310 .. 941.3010 cents 107.57000 cents 21.95600 cents 7: 963.2570 .. 1070.8270 cents 107.57000 cents 21.95600 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 129.52600 cents, class 1 Average step (divided formal octave): 150.0441 cents Largest one step interval : 237.09600 cents Average / Smallest step : 1.158409 Largest / Average step : 1.580175 Largest / Smallest step : 1.830490 Median interval of one step : 129.52600 cents, amount: 6 Most common interval of one step : 129.52600 cents, amount: 6 Least squares average step : 155.71948 cents, oct.: 1245.75584 cents Scale is strictly proper Scale is 3-distributional even Step pattern alph. order: ABBBCBBB Step pattern size order : LSSSMSSS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 21.95600 cents Scale diversity : 1.359320 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.419825 Rothenberg efficiency : 0.546429 redundancy: 0.453571 Efficiency x scale size : 4.371429 Number of different interval sizes : 20 = 2.85714 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.85714 = 20/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 21.95600 cents Most common intervals : 129.52600 cents & inv., amount: 6 Most common triad is 0.0 129.526 1070.827 cents, amount: 3 Number of recognisable fifths : 3, average 704.2050 cents Number of recognisable fourths : 3, average 496.1480 cents Formal octave complements present : 1 = 12.5000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 4-5 -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 50.8260 c. M: 87.0519 c. 9: 2 1 1 1 1 1 1 1 P M ME SD: 25.7370 c. M:-41.1888 c. 10: 2 1 1 1 2 1 1 1 P B ME SD: 16.6534 c. M:-28.4721 c. 17: 3 2 2 2 2 2 2 2 SP M ME SD: 18.8296 c. M: 35.0760 c. 19: 4 2 2 2 3 2 2 2 P D3 SD: 9.0982 c. M:-15.6099 c. 27: 5 3 3 3 4 3 3 3 SP D3 SD: 8.7171 c. M: 14.8084 c. 29: 6 3 3 3 5 3 3 3 P D3 SD: 8.5569 c. M:-16.0547 c. 34: 7 3 4 4 5 4 3 4 P SD: 9.1079 c. M: 13.5770 c. 36: 7 4 4 4 5 4 4 4 SP D3 SD: 6.1070 c. M: 11.5397 c. 37: 7 4 4 4 6 4 4 4 SP D3 SD: 6.8262 c. M: 10.0022 c. 46: 9 5 5 5 7 5 5 5 SP D3 SD: 1.5715 c. M: 2.8415 c. 102: 20 11 11 11 16 11 11 11 SP D3 SD: 1.3112 c. M: 1.9612 c. 111: 22 12 12 12 17 12 12 12 SP D3 SD: 0.9104 c. M:-1.5375 c. 121: 24 13 13 13 19 13 13 13 SP D3 SD: 0.8730 c. M:-1.6874 c. 157: 31 17 17 17 24 17 17 17 SP D3 SD: 0.8071 c. M: 1.3456 c. 167: 33 18 18 18 26 18 18 18 SP D3 SD: 0.2415 c. M:-0.4399 c. 213: 42 23 23 23 33 23 23 23 SP D3 SD: 0.2369 c. M: 0.4067 c. 380: 75 41 41 41 59 41 41 41 SP D3 SD: 0.1470 c. M: 0.2269 c. 445: 88 48 48 48 69 48 48 48 SP D3 SD: 0.1625 c. M:-0.2772 c. 491: 97 53 53 53 76 53 53 53 SP D3 SD: 0.1010 c. M:-0.1720 c. 658: 130 71 71 71 102 71 71 71 SP D3 SD: 0.0353 c. M:-0.0558 c. 871: 172 94 94 94 135 94 94 94 SP D3 SD: 0.0353 c. M: 0.0573 c. 1038: 205 112 112 112 161 112 112 112 SP D3 SD: 0.0337 c. M: 0.0565 c. 1529: 302 165 165 165 237 165 165 165 SP D3 SD: 0.0134 c. M: 0.0255 c. 1696: 335 183 183 183 263 183 183 183 SP D3 SD: 0.0119 c. M:-0.0203 c. 2354: 465 254 254 254 365 254 254 254 SP D3 SD: 0.0110 c. M:-0.0185 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.3530 cents 2 x x x 3 x x x 4 S SD: 38.1409 cents 3 x x 4 x x 5 x 6 S SD: 18.9917 cents 4 x 5 x 6 x 7 x 8 S SD: 20.8631 cents 5 x 6 x 7:8 x 9:10 S SD: 17.0871 cents 6:7 x 8:9 x 10:11:12 S SD: 17.0067 cents 7:8 x 9:10:11:12:13:14 S SD: 9.8520 cents 8:9:10:11 x 13:14:15:16 SD: 11.4477 cents 12:14:15:16:17:19:21:22:24 SD: 7.1517 cents 14:16:17:19:20:22:24:26:28 SD: 6.8646 cents 18:21:22:24:26:29:31:33:36 SD: 5.6360 cents 20:23:25:27:29:32:34:37:40 SD: 5.3317 cents 21:24:26:28:30:34:36:39:42 SD: 3.2712 cents 30:34:37:40:43:48:52:56:60 SD: 3.2043 cents 33:38:41:44:47:53:57:61:66 SD: 2.7012 cents 34:39:42:45:49:54:59:63:68 SD: 2.6890 cents 39:45:48:52:56:62:67:72:78 SD: 2.3784 cents 42:48:52:56:60:67:72:78:84 SD: 1.7396 cents 48:55:59:64:69:77:83:89:96 SD: 1.7313 cents 55:63:68:73:79:88:95:102:110 SD: 1.0605 cents 69:79:85:92:99:110:119:128:138 SD: 1.0339 cents 90:103:111:120:129:144:155:167:180 SD: 0.7768 cents 97:111:120:129:139:155:167:180:194 SD: 0.7117 cents 115:132:142:153:165:184:198:213:230 SD: 0.6513 cents 136:156:168:181:195:217:234:252:272 SD: 0.6469 cents 144:165:178:192:207:230:248:267:288 SD: 0.5225 cents 165:189:204:220:237:264:284:306:330 SD: 0.5179 cents 177:203:219:236:254:283:305:329:354 SD: 0.4778 cents 190:218:235:253:273:304:327:353:380 SD: 0.4709 cents 199:228:246:265:286:318:343:369:398 SD: 0.4447 cents 204:234:252:272:293:326:351:379:408 SD: 0.4238 cents 211:242:261:281:303:337:363:392:422 SD: 0.4146 cents 216:248:267:288:310:345:372:401:432 SD: 0.3850 cents 232:266:287:309:333:371:400:431:464 SD: 0.3793 cents 237:272:293:316:340:379:408:440:474 SD: 0.3671 cents 246:282:304:328:353:393:424:457:492 SD: 0.3606 cents 259:297:320:345:372:414:446:481:518 SD: 0.2054 cents 356:408:440:474:511:569:613:661:712 SD: 0.1797 cents 361:414:446:481:518:577:622:670:722 SD: 0.1602 cents 530:608:655:706:761:847:913:984:1060 SD: 0.1336 cents 551:632:681:734:791:881:949:1023:1102 SD: 0.1332 cents 572:656:707:762:821:914:985:1062:1144 SD: 0.1094 cents