Scala analysis: sengic9
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: 129.526 cents 129.526000 2: 259.052 cents 259.052000 3: 388.578 cents 388.578000 4: 518.104 cents 518.104000 5: 704.205 cents 704.205000 6: 833.731 cents 833.731000 7: 963.257 cents 963.257000 8: 1092.783 cents 1092.783000 9: 1200.353 cents 1200.353000
SHOW/INTERVAL
0: 107.5700 cents 107.5700 1: 129.5260 cents 129.5260 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 9: 107.5700 cents 107.5700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 107.57000 cents 1: 7 129.52600 cents 1: 1 186.10100 cents 2: 2 237.09600 cents 2: 5 259.05200 cents 2: 2 315.62700 cents 3: 3 366.62200 cents 3: 3 388.57800 cents 3: 3 445.15300 cents 4: 4 496.14800 cents 4: 1 518.10400 cents 4: 4 574.67900 cents 5: 4 625.67400 cents 5: 1 682.24900 cents 5: 4 704.20500 cents 6: 3 755.20000 cents 6: 3 811.77500 cents 6: 3 833.73100 cents 7: 2 884.72600 cents 7: 5 941.30100 cents 7: 2 963.25700 cents 8: 1 1014.25200 cents 8: 7 1070.82700 cents 8: 1 1092.78300 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 129.5 259.1 388.6 518.1 704.2 833.7 963.3 1092.8 1200.4 129.5 : 129.5 259.1 388.6 574.7 704.2 833.7 963.3 1070.8 1200.4 259.1 : 129.5 259.1 445.2 574.7 704.2 833.7 941.3 1070.8 1200.4 388.6 : 129.5 315.6 445.2 574.7 704.2 811.8 941.3 1070.8 1200.4 518.1 : 186.1 315.6 445.2 574.7 682.2 811.8 941.3 1070.8 1200.4 704.2 : 129.5 259.1 388.6 496.1 625.7 755.2 884.7 1014.3 1200.4 833.7 : 129.5 259.1 366.6 496.1 625.7 755.2 884.7 1070.8 1200.4 963.3 : 129.5 237.1 366.6 496.1 625.7 755.2 941.3 1070.8 1200.4 1092.8: 107.6 237.1 366.6 496.1 625.7 811.8 941.3 1070.8 1200.4 1200.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 107.5700 .. 186.1010 cents 78.53100 cents 107.57000 cents 2: 237.0960 .. 315.6270 cents 78.53100 cents 50.99500 cents 3: 366.6220 .. 445.1530 cents 78.53100 cents 50.99500 cents 4: 496.1480 .. 574.6790 cents 78.53100 cents 50.99500 cents 5: 625.6740 .. 704.2050 cents 78.53100 cents 50.99500 cents 6: 755.2000 .. 833.7310 cents 78.53100 cents 50.99500 cents 7: 884.7260 .. 963.2570 cents 78.53100 cents 50.99500 cents 8: 1014.2520 .. 1092.7830 cents 78.53100 cents 50.99500 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 107.57000 cents, class 1 Average step (divided formal octave): 133.3726 cents Largest one step interval : 186.10100 cents Average / Smallest step : 1.239868 Largest / Average step : 1.395347 Largest / Smallest step : 1.730046 Median interval of one step : 129.52600 cents, amount: 7 Most common interval of one step : 129.52600 cents, amount: 7 Least squares average step : 135.78046 cents, oct.: 1222.02414 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: AAAABAAAC Step pattern size order : MMMMLMMMS Scale is a Constant Structure, by a margin of 50.99500 cents Scale diversity : 1.370791 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.476614 Rothenberg efficiency : 0.525132 redundancy: 0.474868 Efficiency x scale size : 4.726190 Number of different interval sizes : 24 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 21.95600 cents Most common intervals : 129.52600 cents & inv., amount: 7 Scale is a chain of 4 triads 0.0 574.679 1070.827 cents Most common triad is 0.0 129.526 1070.827 cents, amount: 5 Number of recognisable fifths : 4, average 704.2050 cents Number of recognisable fourths : 4, average 496.1480 cents Formal octave complements present : 1 = 11.1111% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
9: 1 1 1 1 1 1 1 1 1 SP B ME I SD: 22.3734 c. M: 37.3422 c. Pelog Nawanada: Sunda 10: 1 1 1 1 2 1 1 1 1 P M ME I SD: 18.7531 c. M: 37.9628 c. Yoyo & Latrizo-9 16: 2 1 2 2 2 2 2 2 1 P D3 S SD: 20.8823 c. M: 33.9858 c. 19: 2 2 2 2 3 2 2 2 2 SP M ME I SD: 11.2497 c. M: 18.7829 c. Negri-9 27: 3 3 3 3 4 3 3 3 2 SP T3 SD: 11.4599 c. M:-18.6550 c. 30: 3 3 4 3 5 3 3 3 3 P SD: 10.8045 c. M: 18.9814 c. 32: 3 4 3 4 5 3 4 3 3 P SD: 9.6954 c. M: 16.9929 c. 34: 4 3 4 4 5 4 3 4 3 P SD: 8.8293 c. M:-13.5770 c. 36: 4 4 4 4 5 4 4 4 3 SP T3 SD: 7.6768 c. M:-15.3862 c. 37: 4 4 4 4 6 4 4 4 3 SP T3 SD: 6.6047 c. M:-10.2441 c. 46: 5 5 5 5 7 5 5 5 4 SP T3 SD: 2.2096 c. M:-3.7886 c. 56: 6 6 6 6 9 6 6 6 5 SP T3 SD: 2.1591 c. M: 3.6670 c. 65: 7 7 7 7 10 7 7 7 6 SP T3 SD: 1.9640 c. M: 3.2318 c. 102: 11 11 11 11 16 11 11 11 9 SP T3 SD: 1.1900 c. M:-1.8850 c. 111: 12 12 12 12 17 12 12 12 10 SP T3 SD: 0.7837 c. M: 1.2956 c. 167: 18 18 18 18 26 18 18 18 15 SP T3 SD: 0.2897 c. M: 0.5865 c. 213: 23 23 23 23 33 23 23 23 19 SP T3 SD: 0.2990 c. M:-0.4963 c. 278: 30 30 30 30 43 30 30 30 25 SP T3 SD: 0.2593 c. M: 0.4009 c. 380: 41 41 41 41 59 41 41 41 34 SP T3 SD: 0.1306 c. M:-0.2127 c. 491: 53 53 53 53 76 53 53 53 44 SP T3 SD: 0.0958 c. M:-0.1747 c. 658: 71 71 71 71 102 71 71 71 59 SP T3 SD: 0.0368 c. M: 0.0604 c. 1038: 112 112 112 112 161 112 112 112 93 SP T3 SD: 0.0290 c. M:-0.0483 c. 1529: 165 165 165 165 237 165 165 165 137 SP T3 SD: 0.0170 c. M:-0.0340 c. 1696: 183 183 183 183 263 183 183 183 152 SP T3 SD: 0.0134 c. M: 0.0271 c. 2187: 236 236 236 236 339 236 236 236 196 SP T3 SD: 0.0125 c. M: 0.0199 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.3530 cents 2 x x x x 3 x x x 4 S SD: 1.1388 cents 3 x x x 4 x 5 x x 6 S SD: 18.1526 cents 4 x x 5 x 6 x 7 x 8 S SD: 1.6071 cents 5 x 6 x 7 x 8:9 x 10 S SD: 20.6934 cents 6 x 7 x 8:9:10 x 11:12 S SD: 11.6871 cents 7 x 8:9 x x 11:12:13:14 SD: 13.8621 cents 8 x 9:10:11:12:13:14:15:16 S SD: 8.1506 cents 9:10 x 11:12:14:15:16:17:18 S SD: 13.8568 cents 10:11:12 x 13:15:16:17:19:20 SD: 13.2757 cents 11:12:13:14:15:17:18:19:21:22 SD: 8.8539 cents 12:13:14:15:16:18:19:21:23:24 SD: 6.2544 cents 20:22:23:25:27:30:32:35:38:40 SD: 5.3693 cents 23:25:27:29:31:35:37:40:43:46 SD: 4.2641 cents 24:26:28:30:32:36:39:42:45:48 S SD: 2.8398 cents 36:39:42:45:49:54:58:63:68:72 SD: 2.6344 cents 40:43:46:50:54:60:65:70:75:80 SD: 2.2792 cents 48:52:56:60:65:72:78:84:90:96 SD: 1.9145 cents 51:55:59:64:69:77:83:89:96:102 SD: 1.8285 cents 52:56:60:65:70:78:84:91:98:104 SD: 1.6251 cents 60:65:70:75:81:90:97:105:113:120 SD: 1.5746 cents 63:68:73:79:85:95:102:110:118:126 SD: 1.2399 cents 68:73:79:85:92:102:110:119:128:136 SD: 1.2162 cents 74:80:86:93:100:111:120:129:139:148 SD: 1.1631 cents 75:81:87:94:101:113:121:131:141:150 SD: 1.1038 cents 86:93:100:108:116:129:139:150:162:172 SD: 1.0934 cents 91:98:106:114:123:137:147:159:171:182 SD: 0.9940 cents 92:99:107:115:124:138:149:160:173:184 SD: 0.8098 cents 100:108:116:125:135:150:162:174:188:200 SD: 0.7989 cents 118:127:137:148:159:177:191:206:222:236 SD: 0.6148 cents 143:154:166:179:193:215:231:249:269:286 SD: 0.6037 cents 155:167:180:194:209:233:251:270:291:310 SD: 0.4243 cents 167:180:194:209:225:251:270:291:314:334 SD: 0.4067 cents 191:206:222:239:258:287:309:333:359:382 SD: 0.3895 cents 215:232:250:269:290:323:348:375:404:430 SD: 0.3604 cents 223:240:259:279:301:335:361:389:419:446 SD: 0.3221 cents 235:253:273:294:317:353:380:410:442:470 SD: 0.3124 cents 243:262:282:304:328:365:393:424:457:486 SD: 0.3055 cents 247:266:287:309:333:371:400:431:464:494 SD: 0.2812 cents 267:288:310:334:360:401:432:466:502:534 SD: 0.2649 cents 309:333:359:387:417:464:500:539:581:618 SD: 0.1899 cents 422:455:490:528:569:634:683:736:793:844 SD: 0.1807 cents 464:500:539:581:626:697:751:809:872:928 SD: 0.1556 cents 490:528:569:613:661:736:793:855:921:980 SD: 0.1327 cents 516:556:599:646:696:775:835:900:970:1032 SD: 0.1267 cents 556:599:646:696:750:835:900:970:1045:1112 SD: 0.1211 cents 564:608:655:706:761:847:913:984:1060:1128 SD: 0.1153 cents