Scala analysis: sengic7
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: 811.775 cents 811.775000 5: 941.301 cents 941.301000 6: 1070.827 cents 1070.827000 7: 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: 315.6270 cents 315.6270 5: 129.5260 cents 129.5260 6: 129.5260 cents 129.5260 7: 129.5260 cents 129.5260
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 129.52600 cents 1: 1 237.09600 cents 1: 1 315.62700 cents 2: 3 259.05200 cents 2: 2 366.62200 cents 2: 2 445.15300 cents 3: 1 388.57800 cents 3: 3 496.14800 cents 3: 3 574.67900 cents 4: 3 625.67400 cents 4: 3 704.20500 cents 4: 1 811.77500 cents 5: 2 755.20000 cents 5: 2 833.73100 cents 5: 3 941.30100 cents 6: 1 884.72600 cents 6: 1 963.25700 cents 6: 5 1070.82700 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 0.0 : 237.1 366.6 496.1 811.8 941.3 1070.8 1200.4 237.1 : 129.5 259.1 574.7 704.2 833.7 963.3 1200.4 366.6 : 129.5 445.2 574.7 704.2 833.7 1070.8 1200.4 496.1 : 315.6 445.2 574.7 704.2 941.3 1070.8 1200.4 811.8 : 129.5 259.1 388.6 625.7 755.2 884.7 1200.4 941.3 : 129.5 259.1 496.1 625.7 755.2 1070.8 1200.4 1070.8: 129.5 366.6 496.1 625.7 941.3 1070.8 1200.4 1200.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 129.5260 .. 315.6270 cents 186.10100 cents 129.52600 cents 2: 259.0520 .. 445.1530 cents 186.10100 cents -56.57500 cents 3: 388.5780 .. 574.6790 cents 186.10100 cents -56.57500 cents 4: 625.6740 .. 811.7750 cents 186.10100 cents 50.99500 cents 5: 755.2000 .. 941.3010 cents 186.10100 cents -56.57500 cents 6: 884.7260 .. 1070.8270 cents 186.10100 cents -56.57500 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 129.52600 cents, class 1 Average step (divided formal octave): 171.4790 cents Largest one step interval : 315.62700 cents Average / Smallest step : 1.323896 Largest / Average step : 1.840616 Largest / Smallest step : 2.436785 Median interval of one step : 129.52600 cents, amount: 5 Most common interval of one step : 129.52600 cents, amount: 5 Least squares average step : 180.28444 cents, oct.: 1261.99110 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABBCBBB Step pattern size order : MSSLSSS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 21.95600 cents Scale diversity : 1.387403 Lumma stability : 0.258297 Lumma impropriety factor : 0.188528 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 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: 5 Scale is a chain of 3 triads 0.0 496.148 1070.827 cents Number of recognisable fifths : 3, average 704.2050 cents Number of recognisable fourths : 3, average 496.1480 cents Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 47.9308 c. M: 83.9060 c. 8: 1 1 1 2 1 1 1 P M ME I SD: 53.4738 c. M: 87.0519 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 22.6861 c. M:-37.3422 c. 10: 2 1 1 3 1 1 1 N T3 SD: 14.9693 c. M:-28.4721 c. 19: 4 2 2 5 2 2 2 N T3 SD: 9.4500 c. M:-15.6099 c. 27: 5 3 3 7 3 3 3 N T3 SD: 9.2367 c. M: 14.8084 c. 29: 6 3 3 8 3 3 3 N T3 SD: 8.9658 c. M:-16.0547 c. 34: 7 3 4 9 4 3 4 N SD: 9.0036 c. M: 13.5770 c. 36: 7 4 4 9 4 4 4 N T3 SD: 5.8163 c. M: 11.5397 c. 37: 7 4 4 10 4 4 4 N T3 SD: 6.4001 c. M: 10.0022 c. 46: 9 5 5 12 5 5 5 N T3 SD: 1.6648 c. M: 2.8415 c. 102: 20 11 11 27 11 11 11 N T3 SD: 1.1897 c. M: 1.8850 c. 111: 22 12 12 29 12 12 12 N T3 SD: 0.7808 c. M:-1.2956 c. 121: 24 13 13 32 13 13 13 N T3 SD: 0.8953 c. M:-1.6874 c. 157: 31 17 17 41 17 17 17 N T3 SD: 0.7190 c. M: 1.3456 c. 167: 33 18 18 44 18 18 18 N T3 SD: 0.2238 c. M:-0.4399 c. 213: 42 23 23 56 23 23 23 N T3 SD: 0.2479 c. M: 0.4067 c. 278: 55 30 30 73 30 30 30 N T3 SD: 0.2572 c. M:-0.4009 c. 324: 64 35 35 85 35 35 35 N T3 SD: 0.2364 c. M: 0.4253 c. 380: 75 41 41 100 41 41 41 N T3 SD: 0.1317 c. M: 0.2127 c. 491: 97 53 53 129 53 53 53 N T3 SD: 0.0862 c. M: 0.1310 c. 658: 130 71 71 173 71 71 71 N T3 SD: 0.0342 c. M:-0.0558 c. 871: 172 94 94 229 94 94 94 N T3 SD: 0.0377 c. M: 0.0573 c. 1038: 205 112 112 273 112 112 112 N T3 SD: 0.0291 c. M: 0.0483 c. 1529: 302 165 165 402 165 165 165 N T3 SD: 0.0128 c. M: 0.0255 c. 1696: 335 183 183 446 183 183 183 N T3 SD: 0.0107 c. M:-0.0203 c. 2187: 432 236 236 575 236 236 236 N T3 SD: 0.0122 c. M:-0.0199 c. 2354: 465 254 254 619 254 254 254 N T3 SD: 0.0117 c. M:-0.0185 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.3530 cents 2 x x x 3 x x 4 S SD: 54.9103 cents 3 x x 4 x 5 x 6 S SD: 18.9917 cents 4 x 5 x 6:7 x 8 S SD: 28.7293 cents 5 x 6:7:8 x 9:10 S SD: 22.7113 cents 6:7 x 8 x 10:11:12 S SD: 13.5549 cents 7:8 x 9:11:12:13:14 SD: 11.4128 cents 12:14:15:16:19:21:22:24 SD: 7.5042 cents 13:15:16:17:21:22:24:26 SD: 7.1876 cents 15:17:19:20:24:26:28:30 SD: 7.0788 cents 18:21:22:24:29:31:33:36 SD: 6.2486 cents 20:23:25:27:32:34:37:40 SD: 5.5512 cents 21:24:26:28:34:36:39:42 SD: 3.5509 cents 33:38:41:44:53:57:61:66 SD: 2.4173 cents 42:48:52:56:67:72:78:84 SD: 1.6077 cents 54:62:67:72:86:93:100:108 SD: 1.4886 cents 55:63:68:73:88:95:102:110 SD: 1.1992 cents 69:79:85:92:110:119:128:138 SD: 1.1777 cents 75:86:93:100:120:129:139:150 SD: 1.0486 cents 90:103:111:120:144:155:167:180 SD: 0.8174 cents 97:111:120:129:155:167:180:194 SD: 0.7049 cents 102:117:126:136:163:176:189:204 SD: 0.6928 cents 136:156:168:181:217:234:252:272 SD: 0.6914 cents 144:165:178:192:230:248:267:288 SD: 0.4675 cents 169:194:209:225:270:291:314:338 SD: 0.4137 cents 199:228:246:265:318:343:369:398 SD: 0.3970 cents 217:249:268:289:347:374:403:434 SD: 0.3333 cents 238:273:294:317:380:410:442:476 SD: 0.3128 cents 259:297:320:345:414:446:481:518 SD: 0.1682 cents 361:414:446:481:577:622:670:722 SD: 0.1667 cents 368:422:455:490:588:634:683:736 SD: 0.1664 cents 403:462:498:537:644:694:748:806 SD: 0.1640 cents 458:525:566:610:732:789:850:916 SD: 0.1315 cents 530:608:655:706:847:913:984:1060 SD: 0.1253 cents 572:656:707:762:914:985:1062:1144 SD: 0.1250 cents