Scala analysis: xen18-secor-13-limit-2-tempered
13-limit tempered scale, enharmonic alteration
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 144.856 cents 144.856000 2: 278.339 cents 278.339000 3: 492.780 cents 492.780000 4: 707.220 cents 707.220000 5: 849.233 cents 849.233000 6: 985.559 cents 985.559000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 214.4410 cents 214.4410 1: 144.8560 cents 144.8560 2: 133.4830 cents 133.4830 3: 214.4410 cents 214.4410 4: 214.4400 cents 214.4400 5: 142.0130 cents 142.0130 6: 136.3260 cents 136.3260 7: 214.4410 cents 214.4410
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 133.48300 cents 1: 1 136.32600 cents 1: 1 142.01300 cents 1: 1 144.85600 cents 1: 1 214.44000 cents 1: 2 214.44100 cents 2: 2 278.33900 cents 2: 1 347.92400 cents 2: 1 350.76700 cents 2: 1 356.45300 cents 2: 1 359.29700 cents 2: 1 428.88100 cents 3: 1 492.77900 cents 3: 3 492.78000 cents 3: 1 495.62300 cents 3: 1 562.36400 cents 3: 1 570.89400 cents 4: 1 629.10600 cents 4: 1 637.63600 cents 4: 1 704.37700 cents 4: 3 707.22000 cents 4: 1 707.22100 cents 5: 1 771.11900 cents 5: 1 840.70300 cents 5: 1 843.54700 cents 5: 1 849.23300 cents 5: 1 852.07600 cents 5: 2 921.66100 cents 6: 2 985.55900 cents 6: 1 985.56000 cents 6: 1 1055.14400 cents 6: 1 1057.98700 cents 6: 1 1063.67400 cents 6: 1 1066.51700 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.66667 = 17/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 144.9 278.3 492.8 707.2 849.2 985.6 1200.0 144.9 : 133.5 347.9 562.4 704.4 840.7 1055.1 1200.0 278.3 : 214.4 428.9 570.9 707.2 921.7 1066.5 1200.0 492.8 : 214.4 356.5 492.8 707.2 852.1 985.6 1200.0 707.2 : 142.0 278.3 492.8 637.6 771.1 985.6 1200.0 849.2 : 136.3 350.8 495.6 629.1 843.5 1058.0 1200.0 985.6 : 214.4 359.3 492.8 707.2 921.7 1063.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.4830 .. 214.4410 cents 80.95800 cents 133.48300 cents 2: 278.3390 .. 428.8810 cents 150.54200 cents 63.89800 cents 3: 492.7790 .. 570.8940 cents 78.11500 cents 63.89800 cents 4: 629.1060 .. 707.2210 cents 78.11500 cents 58.21200 cents 5: 771.1190 .. 921.6610 cents 150.54200 cents 63.89800 cents 6: 985.5590 .. 1066.5170 cents 80.95800 cents 63.89800 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 133.48300 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 214.44100 cents Average / Smallest step : 1.284273 Largest / Average step : 1.250906 Largest / Smallest step : 1.606504 Median interval of one step : 144.85600 cents, amount: 1 Most common interval of one step : 214.44100 cents, amount: 2 Least squares average step : 168.34481 cents, oct.: 1178.41365 cents Scale is strictly proper Scale is a mode of a 845-tone equal temperament with octave 1200.000 cents degrees: 102 196 347 498 598 694 845 Least number of segments generator : 423 of 600.710 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 696 of 988.402 cents and inv. generated superset size: 47 = 40 more = 671.429% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFC Step pattern size order : DAFECBF Scale is a Constant Structure, by a margin of 58.21200 cents Scale diversity : 1.404277 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.483975 Rothenberg efficiency : 0.341497 redundancy: 0.658503 Efficiency x scale size : 2.390476 Number of different interval sizes : 34 = 5.66667 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.66667 = 17/3 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 0.00100 cents Most common intervals : 492.78000 cents & inv., amount: 3 Number of recognisable fifths : 5, average 706.6516 cents Best fifths form a closed circle Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 150.5420 cents: 6 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.1799 c. M:-64.5181 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 39.4350 c. M:-64.4410 c. 10: 1 1 2 2 1 1 2 P D3 S SD: 21.2229 c. M: 38.3390 c. 17: 2 2 3 3 2 2 3 SP D3 S SD: 2.5388 c. M:-4.0139 c. 73: 9 8 13 13 9 8 13 SP SD: 2.4651 c. M:-5.5615 c. 83: 10 9 15 15 10 9 15 SP SD: 2.2817 c. M:-3.7790 c. 90: 11 10 16 16 11 10 16 SP SD: 1.8780 c. M:-4.1003 c. 100: 12 11 18 18 12 11 18 SP SD: 1.5815 c. M:-2.7670 c. 107: 13 12 19 19 13 12 19 SP SD: 1.5772 c. M:-3.1034 c. 117: 14 13 21 21 14 13 21 SP SD: 1.1429 c. M:-2.0491 c. 134: 16 15 24 24 16 15 24 SP SD: 0.8979 c. M: 1.5724 c. 151: 18 17 27 27 18 17 27 SP SD: 0.8056 c. M: 1.8096 c. 229: 28 25 41 41 27 26 41 SP SD: 0.7762 c. M:-1.8689 c. 246: 30 27 44 44 29 28 44 SP SD: 0.6038 c. M:-1.4855 c. 263: 32 29 47 47 31 30 47 SP SD: 0.4847 c. M:-1.1516 c. 280: 34 31 50 50 33 32 50 SP SD: 0.4250 c. M:-0.8583 c. 297: 36 33 53 53 35 34 53 SP SD: 0.4232 c. M: 0.7482 c. 363: 44 40 65 65 43 41 65 SP SD: 0.4130 c. M: 0.6530 c. 380: 46 42 68 68 45 43 68 SP SD: 0.2810 c. M: 0.4443 c. 397: 48 44 71 71 47 45 71 SP SD: 0.1602 c. M: 0.2534 c. 414: 50 46 74 74 49 47 74 SP SD: 0.0494 c. M: 0.0781 c. 845: 102 94 151 151 100 96 151 SP SD: 0.0027 c. M:-0.0042 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 2.6325 cents 3 x x 4 x 5 x 6 S SD: 11.8394 cents 4 x x 5:6 x 7:8 S SD: 26.9754 cents 5 x 6:7 x 8:9:10 S SD: 21.6641 cents 6 x 7:8:9:10:11:12 S SD: 12.3510 cents 7 x 8:9 x 11:12:14 SD: 22.5890 cents 8:9 x 11:12:13:14:16 SD: 14.2376 cents 10:11:12:13:15:16:18:20 SD: 10.6928 cents 12:13:14:16:18:20:21:24 S SD: 5.9595 cents 21:23:25:28:32:34:37:42 SD: 5.4878 cents 22:24:26:29:33:36:39:44 SD: 2.9722 cents 33:36:39:44:50:54:58:66 SD: 2.9398 cents 34:37:40:45:51:56:60:68 SD: 2.5351 cents 46:50:54:61:69:75:81:92 SD: 1.3600 cents 57:62:67:76:86:93:101:114 SD: 1.2780 cents 69:75:81:92:104:113:122:138 SD: 1.1230 cents 79:86:93:105:119:129:140:158 SD: 1.0214 cents 91:99:107:121:137:149:161:182 SD: 0.7952 cents 103:112:121:137:155:168:182:206 SD: 0.3664 cents 194:211:228:258:292:317:343:388 SD: 0.3114 cents 218:237:256:290:328:356:385:436 SD: 0.2306 cents 240:261:282:319:361:392:424:480 SD: 0.1581 cents 343:373:403:456:516:560:606:686 SD: 0.1514 cents 458:498:538:609:689:748:809:916 SD: 0.1323 cents