Scala analysis: hanson7
Hanson[7] in 53-et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 67.925 cents 67.924528 2: 316.981 cents 316.981132 3: 384.906 cents 384.905660 4: 633.962 cents 633.962264 5: 701.887 cents 701.886792 6: 950.943 cents 950.943396 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 249.0566 cents 249.0566 1: 67.9245 cents 67.9245 2: 249.0566 cents 249.0566 3: 67.9245 cents 67.9245 4: 249.0566 cents 249.0566 5: 67.9245 cents 67.9245 6: 249.0566 cents 249.0566 7: 249.0566 cents 249.0566
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 67.92453 cents 1: 4 249.05660 cents 2: 6 316.98113 cents 2: 1 498.11321 cents 3: 2 384.90566 cents 3: 5 566.03774 cents 4: 5 633.96226 cents 4: 2 815.09434 cents 5: 1 701.88679 cents 5: 6 883.01887 cents 6: 4 950.94340 cents 6: 3 1132.07547 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 0.0 : 67.9 317.0 384.9 634.0 701.9 950.9 1200.0 67.9 : 249.1 317.0 566.0 634.0 883.0 1132.1 1200.0 317.0 : 67.9 317.0 384.9 634.0 883.0 950.9 1200.0 384.9 : 249.1 317.0 566.0 815.1 883.0 1132.1 1200.0 634.0 : 67.9 317.0 566.0 634.0 883.0 950.9 1200.0 701.9 : 249.1 498.1 566.0 815.1 883.0 1132.1 1200.0 950.9 : 249.1 317.0 566.0 634.0 883.0 950.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9245 .. 249.0566 cents 181.13208 cents 67.92453 cents 2: 316.9811 .. 498.1132 cents 181.13208 cents 67.92453 cents 3: 384.9057 .. 566.0377 cents 181.13208 cents -113.20755 cents 4: 633.9623 .. 815.0943 cents 181.13208 cents 67.92453 cents 5: 701.8868 .. 883.0189 cents 181.13208 cents -113.20755 cents 6: 950.9434 .. 1132.0755 cents 181.13208 cents 67.92453 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 67.92453 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 249.05660 cents Average / Smallest step : 2.523810 Largest / Average step : 1.452830 Largest / Smallest step : 3.666667 Median interval of one step : 249.05660 cents, amount: 4 Most common interval of one step : 249.05660 cents, amount: 4 Least squares average step : 157.19677 cents, oct.: 1100.37736 cents Scale is not proper Scale has Myhill's property chromas: 181.13208 cents and 113.20755 cents, ratio: 1.600000 generators: 2 of 316.98113 cents and 883.01887 cents ET pair of linear temperament : 15&19 Scale is distributional even Scale is a mode of a 53-tone equal temperament with octave 1200.000 cents degrees: 3 14 17 28 31 42 53 generators: 14 and 39 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABB Step pattern size order : SLSLSLL Interval vector is [ 0 0 3 0 0 0 0 0 0 0 4 0 0 6 0 0 2 0 0 0 0 1 0 0 5 0 ] Scale is a Constant Structure, by a margin of 67.92453 cents Scale diversity : 1.225008 Lumma stability : 0.283019 Lumma impropriety factor : 0.188679 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 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 : 67.92453 cents Most common intervals : 316.98113 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 316.981 633.962 cents Most common triad is 0.0 316.981 883.019 cents, amount: 5 Number of recognisable fifths : 1, average 701.8868 cents Formal octave complements present : 1 = 14.2857% Limited inverse transpositions : 5 Inversional symmetry on degrees : 6 Inversional symmetry on intervals : 2-3 -- Rational properties --
FIT/MODE
7: 0 2 0 2 0 2 1 N T3 SD: 47.8350 c. M:-77.6280 c. 9: 1 1 1 2 0 2 2 N T3 SD: 37.1442 c. M:-65.4088 c. 10: 1 2 0 2 1 2 2 N T3 S SD: 31.0445 c. M:-52.0755 c. 12: 1 2 1 2 1 3 2 N T3 SD: 27.0148 c. M:-49.0566 c. 13: 1 2 1 3 1 2 3 N T3 SD: 25.9334 c. M: 40.0581 c. 14: 1 3 0 3 1 3 3 N T3 S SD: 24.5953 c. M: 42.0485 c. 15: 1 3 1 3 1 3 3 N M DE S SD: 10.8847 c. M:-18.1132 c. Kleismic-7, Triolic Diatonic 19: 1 4 1 4 1 4 4 N M DE S SD: 4.2966 c. M: 7.1499 c. Kleismic-7 34: 2 7 2 7 2 7 7 N M DE S SD: 2.4010 c. M:-3.9956 c. Kleismic-7 53: 3 11 3 11 3 11 11 N M DE S SD: 0.0000 c. M:-0.0000 c. Kleismic-7
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 0.0341 cents 3 x x 4 x x 5:6 S SD: 43.7595 cents 4 x x 5 x 6:7:8 S SD: 4.4845 cents 5 x 6 x 7:8:9:10 S SD: 27.9933 cents 6 x 7:8 x 9:10:12 S SD: 28.1034 cents 7 x 8:9:10:11:12:14 S SD: 21.7094 cents 8 x x 10 x 12:14:16 S SD: 4.4845 cents 9:10:11 x 13:14:16:18 SD: 23.5992 cents 10:11:12 x 14:15:17:20 SD: 19.0881 cents 11:12:13:14:16:17:19:22 SD: 15.3815 cents 12:13:14:15:17:18:21:24 SD: 13.3879 cents 13:14 x 16:19:20:23:26 SD: 15.0033 cents 14:15:17 x 20:21:24:28 SD: 10.0133 cents 15:16:18:19:22:23:26:30 SD: 9.9119 cents 16:17:19:20:23:24:28:32 SD: 6.5534 cents 18:19:22 x 26:27:31:36 SD: 6.8488 cents 20:21:24:25:29:30:35:40 SD: 3.7355 cents 36:37:43:45:52:54:62:72 SD: 3.5374 cents 40:42:48:50:58:60:69:80 SD: 2.9044 cents 44:46:53:55:63:66:76:88 SD: 2.4351 cents 45:47:54:56:65:67:78:90 SD: 2.3404 cents 48:50:58:60:69:72:83:96 SD: 1.8253 cents 56:58:67:70:81:84:97:112 SD: 1.5716 cents 68:71:82:85:98:102:118:136 SD: 1.5088 cents 70:73:84:87:101:105:121:140 SD: 1.4918 cents 74:77:89:92:107:111:128:148 SD: 1.3995 cents 76:79:91:95:110:114:132:152 SD: 1.3577 cents 80:83:96:100:115:120:139:160 SD: 1.3065 cents 96:100:115:120:138:144:166:192 SD: 1.1860 cents 100:104:120:125:144:150:173:200 SD: 0.5539 cents 104:108:125:130:150:156:180:208 SD: 0.5010 cents 124:129:149:155:179:186:215:248 SD: 0.4322 cents 204:212:245:255:294:306:353:408 SD: 0.4042 cents 224:233:269:280:323:336:388:448 SD: 0.2111 cents 378:393:454:472:545:567:655:756 SD: 0.1698 cents 398:414:478:497:574:597:689:796 SD: 0.1403 cents 522:543:627:652:753:783:904:1044 SD: 0.0920 cents