Scala analysis: xen13-mclaren-factorable-numbers
Factorable numbers scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 5/4 386.313714 major third 3: 13/10 454.213948 tridecimal semi-diminished fourth 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 5/3 884.358713 major sixth, BP sixth
SHOW/INTERVAL
0: 25/21 301.8465 BP second, quasi-equal minor third 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 25/22 221.3095 undecimal acute whole tone 3: 26/25 67.9002 tridecimal 1/3-tone 4: 14/13 128.2982 2/3-tone 5: 25/21 301.8465 BP second, quasi-equal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 26/25 67.900 cents tridecimal 1/3-tone 1: 1 14/13 128.298 cents 2/3-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 25/22 221.309 cents undecimal acute whole tone 1: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 28/25 196.198 cents middle second 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 5/4 386.314 cents major third 2: 1 50/39 430.145 cents 2: 1 55/42 466.851 cents 3: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 13/10 454.214 cents tridecimal semi-diminished fourth 3: 1 4/3 498.045 cents perfect fourth 3: 1 55/39 595.149 cents 3: 1 125/84 688.160 cents 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 22/15 663.049 cents undecimal diminished fifth 4: 1 50/33 719.354 cents 3 pentatones 4: 1 65/42 756.060 cents 4: 1 125/78 816.458 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 165.0 386.3 454.2 582.5 884.4 165.0: 221.3 289.2 417.5 719.4 884.4 386.3: 67.9 196.2 498.0 663.0 884.4 454.2: 128.3 430.1 595.1 816.5 884.4 582.5: 301.8 466.9 688.2 756.1 884.4 884.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9002 .. 301.8465 cents 625/546, 233.9463 cents 26/25, 67.9002 cents 2: 196.1985 .. 466.8507 cents 1375/1176, 270.6523 cents 588/625,-105.6480 cents 3: 417.5080 .. 688.1602 cents 1375/1176, 270.6523 cents 588/605,-49.3428 cents 4: 582.5122 .. 816.4585 cents 625/546, 233.9463 cents 588/625,-105.6480 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 26/25, 67.9002 cents, class 1 Average step (divided formal octave): 176.8717 cents Largest one step interval : 25/21, 301.8465 cents Average / Smallest step : 2.604877 Largest / Average step : 1.706584 Largest / Smallest step : 4.445442 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 164.58392 cents, oct.: 822.91962 cents Scale is not proper Step pattern alph. order: ABCDE Step pattern size order : CDABE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 12.63680 cents Scale diversity : 1.485584 Lumma stability : 0.153558 Lumma impropriety factor : 0.294721 Rothenberg efficiency : 0.400000 redundancy: 0.600000 Efficiency x scale size : 2.000000 Number of different interval sizes : 20 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 5.00000 = 5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 275/273, 12.6368 cents Number of recognisable fifths : 2, average 703.7574 cents Number of appreciable fifths : 0 Number of recognisable fourths : 1, average 498.0450 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 20.0000% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 13 Odd number limit : 125 (O: 125 U: 39) Highest odd numerator or denominator: 13 Scale harmonicity : 0.014687 Average absolute harmonicity : 0.072440 Specific harmonicity : 0.092487 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 5005, 12.2892 octaves, 1309435.954 Hz. Exponens Consonantiae : 3.003000E+05, 18.19604 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 36.5, average 7.30000 Mersenne's string divisions : 11592 Sum of van Prooijen's expressibility: 4.39837, average 0.87967 Sum of Tenney's harmonic distance : 8.17653, average 1.63531 Vogel's harmonic complexity : 13.80000 Wille's k value : 37 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 31.28295, average 2.08553 Lattice compactness (without 2's) : 25.95617, average 1.73041 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -2 .. 0 -0.80000 4 3: -1 .. 0 -0.20000 1 5: -1 .. 1 -0.20000 5 2 7: 0 .. 1 0.20000 1 1 11: 0 .. 1 0.20000 1 1 13: 0 .. 1 0.20000 1 1 Average exponent except 2's : 1 / 5 = 0.20000 Average absolute exponent except 2's: 9 / 5 = 1.80000 Scale is weakly epimorphic with val: <7 11 15 20 24 25| Scale is weakly epimorphic with val: <7 11 16 19 22 24| Scale is JI-epimorphic with val: <7 11 16 20 24 26| Scale is weakly epimorphic with val: <7 12 15 20 24 26| Scale is weakly epimorphic with val: <7 12 17 18 23 26| Scale is weakly epimorphic with val: <7 12 17 19 23 25|
FIT/MODE
5: 1 1 1 0 2 N T3 SD: 44.1183 c. M:-76.4013 c. 6: 1 2 0 1 2 N T3 SD: 26.9288 c. M:-55.8656 c. 8: 1 2 1 1 3 N T3 SD: 37.3839 c. M: 54.6792 c. 9: 2 2 1 1 3 N SD: 22.2029 c. M:-37.0964 c. 10: 2 2 1 2 3 P T3 SD: 23.1585 c. M:-36.5389 c. 11: 2 3 1 1 4 N SD: 17.0059 c. M:-28.1635 c. 12: 2 3 1 2 4 N SD: 12.8279 c. M: 17.8309 c. 16: 3 4 1 3 5 N SD: 12.6119 c. M:-25.4844 c. 18: 3 5 1 3 6 N SD: 10.4899 c. M: 17.6111 c. 20: 4 5 1 3 7 N SD: 9.8011 c. M: 12.0346 c. 21: 4 5 2 3 7 N SD: 6.2680 c. M:-9.0216 c. 27: 5 7 2 4 9 N SD: 4.8080 c. M:-7.0603 c. 37: 7 9 3 5 13 N SD: 4.4542 c. M: 8.8741 c. 39: 7 10 3 6 13 N SD: 4.2512 c. M:-7.0603 c. 41: 8 10 3 6 14 N SD: 3.5328 c. M:-7.5536 c. 43: 8 11 3 6 15 N SD: 3.6693 c. M: 6.6507 c. 48: 9 12 4 7 16 N SD: 4.2822 c. M:-7.0603 c. 49: 9 12 4 7 17 N SD: 4.3295 c. M: 7.3028 c. 50: 9 13 4 7 17 N SD: 3.8740 c. M: 5.8197 c. 52: 10 13 4 7 18 N SD: 4.2930 c. M:-5.0648 c. 53: 10 13 4 8 18 N SD: 2.2692 c. M: 3.6916 c. 64: 12 16 5 9 22 N SD: 1.3285 c. M: 2.1518 c. 76: 14 19 6 11 26 N SD: 1.4423 c. M: 2.3159 c. 103: 19 26 8 15 35 N SD: 1.0954 c. M: 1.8701 c. 117: 22 29 9 17 40 N SD: 0.7829 c. M:-1.2854 c. 140: 26 35 11 20 48 N SD: 0.8688 c. M: 1.3622 c. 144: 27 36 11 21 49 N SD: 0.6195 c. M:-0.9189 c. 199: 37 50 15 29 68 N SD: 0.5302 c. M: 0.9246 c. 208: 39 52 16 30 71 N SD: 0.5537 c. M:-0.8130 c. 220: 41 55 17 32 75 N SD: 0.2596 c. M: 0.4117 c. 284: 53 71 22 41 97 N SD: 0.2259 c. M:-0.4212 c. 401: 75 100 31 58 137 N SD: 0.2798 c. M:-0.3995 c. 407: 76 102 31 59 139 N SD: 0.2313 c. M:-0.4574 c. 419: 78 105 32 61 143 N SD: 0.2556 c. M: 0.4261 c. 428: 80 107 33 62 146 N SD: 0.2260 c. M:-0.3630 c. 483: 90 121 37 70 165 N SD: 0.1642 c. M: 0.2636 c. 563: 105 141 43 82 192 N SD: 0.1697 c. M: 0.2536 c. 627: 117 157 48 91 214 N SD: 0.0718 c. M:-0.1525 c. 847: 158 212 65 123 289 N SD: 0.0489 c. M:-0.0996 c. 1131: 211 283 87 164 386 N SD: 0.0445 c. M:-0.0853 c. 1474: 275 369 113 214 503 N SD: 0.0441 c. M:-0.0682 c. 1538: 287 385 118 223 525 N SD: 0.0474 c. M:-0.0901 c. 1614: 301 404 124 234 551 N SD: 0.0466 c. M: 0.0774 c. 1758: 328 440 135 255 600 N SD: 0.0226 c. M:-0.0386 c.
FIT/HARMONIC
1 x x x x 2 S SD: 315.6413 cents 2 x x x 3 x S SD: 119.4428 cents 3 x x 4 x 5 S SD: 21.9155 cents 4 x 5 x 6:7 S SD: 48.7639 cents 5 x 6 x 7:8 S SD: 33.3153 cents 6:7 x 8 x 10 S SD: 36.9654 cents 7:8 x 9:10:12 S SD: 22.8394 cents 8:9:10 x 11:13 SD: 16.5980 cents 9:10:11:12:13:15 SD: 16.3278 cents 10:11 x 13:14:17 SD: 8.5707 cents 11:12:14 x 15:18 S SD: 16.3257 cents 12:13:15:16:17:20 SD: 11.0264 cents 14:15 x 18:20:23 SD: 16.3661 cents 15:17:19:20:21:25 SD: 14.3081 cents 16:18:20:21:22:27 SD: 11.3556 cents 17:19:21:22:24:28 SD: 8.6493 cents 18:20 x 23:25:30 SD: 9.3007 cents 19:21:24:25:27:32 SD: 8.5559 cents 20:22:25:26:28:33 SD: 3.4799 cents 40:44:50:52:56:67 SD: 1.7269 cents 60:66:75:78:84:100 SD: 0.0000 cents