Scala analysis: xen18-secor-13-limit-1-tempered
13-limit tempered scale
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: 1057.987 cents 1057.987000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 142.0130 cents 142.0130 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: 208.7540 cents 208.7540 7: 142.0130 cents 142.0130
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 133.48300 cents 1: 2 142.01300 cents 1: 1 144.85600 cents 1: 1 208.75400 cents 1: 1 214.44000 cents 1: 1 214.44100 cents 2: 1 278.33900 cents 2: 1 286.86900 cents 2: 1 347.92400 cents 2: 2 350.76700 cents 2: 1 356.45300 cents 2: 1 428.88100 cents 3: 1 420.35200 cents 3: 2 492.78000 cents 3: 1 495.62300 cents 3: 1 562.36400 cents 3: 1 565.20700 cents 3: 1 570.89400 cents 4: 1 629.10600 cents 4: 1 634.79300 cents 4: 1 637.63600 cents 4: 1 704.37700 cents 4: 2 707.22000 cents 4: 1 779.64800 cents 5: 1 771.11900 cents 5: 1 843.54700 cents 5: 2 849.23300 cents 5: 1 852.07600 cents 5: 1 913.13100 cents 5: 1 921.66100 cents 6: 1 985.55900 cents 6: 1 985.56000 cents 6: 1 991.24600 cents 6: 1 1055.14400 cents 6: 2 1057.98700 cents 6: 1 1066.51700 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 144.9 278.3 492.8 707.2 849.2 1058.0 1200.0 144.9 : 133.5 347.9 562.4 704.4 913.1 1055.1 1200.0 278.3 : 214.4 428.9 570.9 779.6 921.7 1066.5 1200.0 492.8 : 214.4 356.5 565.2 707.2 852.1 985.6 1200.0 707.2 : 142.0 350.8 492.8 637.6 771.1 985.6 1200.0 849.2 : 208.8 350.8 495.6 629.1 843.5 1058.0 1200.0 1058.0: 142.0 286.9 420.4 634.8 849.2 991.2 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: 420.3520 .. 570.8940 cents 150.54200 cents -8.52900 cents 4: 629.1060 .. 779.6480 cents 150.54200 cents 58.21200 cents 5: 771.1190 .. 921.6610 cents 150.54200 cents -8.52900 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 : 142.01300 cents, amount: 2 Least squares average step : 171.44886 cents, oct.: 1200.14205 cents Scale is not proper Scale is a mode of a 845-tone equal temperament with octave 1200.000 cents degrees: 102 196 347 498 598 745 845 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: ABCDEFE Step pattern size order : CAFEBDB Scale is a Constant Structure, by a margin of 8.52900 cents Scale diversity : 1.432030 Lumma stability : 0.377478 Lumma impropriety factor : 0.014215 Rothenberg efficiency : 0.326531 redundancy: 0.673469 Efficiency x scale size : 2.285714 Number of different interval sizes : 36 = 6.00000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 6.00000 = 6 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 0.00100 cents Number of recognisable fifths : 3, average 706.2723 cents Best fifths form a closed circle Formal octave complements present : 3 = 42.8571% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 30.9874 c. M:-64.5181 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 31.1609 c. M:-50.7670 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 29.4167 c. M: 49.2330 c. 10: 1 1 2 2 1 2 1 N D3 SD: 20.6473 c. M: 38.3390 c. 14: 2 1 3 2 2 2 2 P T3 SD: 20.7303 c. M: 29.4156 c. 17: 2 2 3 3 2 3 2 P D3 SD: 2.3500 c. M:-4.0139 c. 83: 10 9 15 15 10 14 10 N SD: 2.3033 c. M:-3.7790 c. 92: 11 10 17 16 11 16 11 N SD: 2.4528 c. M: 4.4260 c. 100: 12 11 18 18 12 17 12 N SD: 1.6486 c. M:-2.7670 c. 117: 14 13 21 21 14 20 14 N SD: 1.2386 c. M:-2.0491 c. 134: 16 15 24 24 16 23 16 N SD: 1.0017 c. M: 1.5724 c. 151: 18 17 27 27 18 26 18 N SD: 0.8940 c. M: 1.8096 c. 168: 20 19 30 30 20 29 20 N SD: 0.8752 c. M: 1.9989 c. 229: 28 25 41 41 27 40 27 N SD: 0.7867 c. M:-1.8689 c. 246: 30 27 44 44 29 43 29 N SD: 0.6343 c. M:-1.4855 c. 263: 32 29 47 47 31 46 31 N SD: 0.5301 c. M:-1.1516 c. 280: 34 31 50 50 33 49 33 N SD: 0.4754 c. M:-0.8583 c. 297: 36 33 53 53 35 52 35 N SD: 0.4664 c. M: 0.7482 c. 363: 44 40 65 65 43 63 43 N SD: 0.3824 c. M: 0.6530 c. 380: 46 42 68 68 45 66 45 N SD: 0.2601 c. M: 0.4443 c. 397: 48 44 71 71 47 69 47 N SD: 0.1484 c. M: 0.2534 c. 414: 50 46 74 74 49 72 49 N SD: 0.0458 c. M: 0.0781 c. 845: 102 94 151 151 100 147 100 N SD: 0.0024 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: 34.7423 cents 5 x 6:7 x 8:9:10 S SD: 22.2156 cents 6 x 7:8:9:10:11:12 S SD: 6.4445 cents 7 x 8:9 x 11:13:14 SD: 20.1948 cents 8:9 x 11:12:13:15:16 SD: 14.8460 cents 10:11:12:13:15:16:18:20 SD: 11.2553 cents 11:12:13:15:17:18:20:22 SD: 9.8945 cents 12:13:14:16:18:20:22:24 S SD: 5.5963 cents 22:24:26:29:33:36:41:44 SD: 4.0199 cents 24:26:28:32:36:39:44:48 SD: 2.7723 cents 33:36:39:44:50:54:61:66 SD: 2.7460 cents 36:39:42:48:54:59:66:72 SD: 2.6231 cents 45:49:53:60:68:73:83:90 SD: 2.2798 cents 46:50:54:61:69:75:85:92 SD: 1.2742 cents 57:62:67:76:86:93:105:114 SD: 1.0772 cents 79:86:93:105:119:129:146:158 SD: 1.0440 cents 91:99:107:121:137:149:168:182 SD: 0.8810 cents 103:112:121:137:155:168:190:206 SD: 0.4681 cents 115:125:135:153:173:188:212:230 SD: 0.3732 cents 218:237:256:290:328:356:402:436 SD: 0.2810 cents 240:261:282:319:361:392:442:480 SD: 0.1872 cents 343:373:403:456:516:560:632:686 SD: 0.1482 cents 355:386:417:472:534:580:654:710 SD: 0.1347 cents 458:498:538:609:689:748:844:916 SD: 0.1078 cents