Scala analysis: xen18-ayers-table-54
7 Iterated First Unnamed Means between 1/1 and 2/1, Weighted by Ratio 3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 2: 13/9 636.617660 tridecimal diminished fifth 3: 43/27 805.652703 4: 5/3 884.358713 major sixth, BP sixth 5: 49/27 1031.786810 6: 17/9 1101.045408 septendecimal major seventh 7: 53/27 1167.639543 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 54/53 32.3605 1: 35/27 449.2746 septimal semi-diminished fourth, 9/4-tone 2: 39/35 187.3430 3: 43/39 169.0350 4: 45/43 78.7060 5: 49/45 147.4281 BP minor semitone 6: 51/49 69.2586 7: 53/51 66.5941 8: 54/53 32.3605
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 54/53 32.360 cents 1: 1 53/51 66.594 cents 1: 1 51/49 69.259 cents 1: 1 45/43 78.706 cents 1: 1 49/45 147.428 cents BP minor semitone 1: 1 43/39 169.035 cents 1: 1 39/35 187.343 cents 1: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 18/17 98.955 cents Arabic lute index finger 2: 1 53/49 135.853 cents 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 49/43 226.134 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 43/35 356.378 cents 2: 1 70/53 481.635 cents 2: 1 13/9 636.618 cents tridecimal diminished fifth 3: 1 54/49 168.213 cents Zalzal's mujannab 3: 1 53/45 283.281 cents 3: 1 51/43 295.393 cents 3: 1 49/39 395.169 cents 3: 1 9/7 435.084 cents septimal major third, BP third 3: 1 70/51 548.229 cents 3: 1 78/53 668.978 cents 3: 1 43/27 805.653 cents 4: 1 6/5 315.641 cents minor third 4: 1 53/43 361.987 cents 4: 1 17/13 464.428 cents 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 10/7 617.488 cents Euler's tritone 4: 1 26/17 735.572 cents 4: 1 86/53 838.013 cents 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 54/43 394.347 cents 5: 1 53/39 531.022 cents 5: 1 51/35 651.771 cents 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 78/49 804.831 cents 5: 1 86/51 904.607 cents 5: 1 90/53 916.719 cents 5: 1 49/27 1031.787 cents 6: 1 18/13 563.382 cents tridecimal augmented fourth 6: 1 53/35 718.365 cents 6: 1 70/43 843.622 cents 6: 1 26/15 952.259 cents tridecimal semi-augmented sixth 6: 1 86/49 973.866 cents 6: 1 30/17 983.313 cents septendecimal minor seventh 6: 1 98/53 1064.147 cents 6: 1 17/9 1101.045 cents septendecimal major seventh 7: 1 54/35 750.725 cents septimal semi-augmented fifth 7: 1 70/39 1012.657 cents 7: 1 78/43 1030.965 cents 7: 1 90/49 1052.572 cents 7: 1 86/45 1121.294 cents 7: 1 98/51 1130.741 cents 7: 1 102/53 1133.406 cents 7: 1 53/27 1167.640 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 8.00000 = 8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 449.3 636.6 805.7 884.4 1031.8 1101.0 1167.6 1200.0 449.3 : 187.3 356.4 435.1 582.5 651.8 718.4 750.7 1200.0 636.6 : 169.0 247.7 395.2 464.4 531.0 563.4 1012.7 1200.0 805.7 : 78.7 226.1 295.4 362.0 394.3 843.6 1031.0 1200.0 884.4 : 147.4 216.7 283.3 315.6 764.9 952.3 1121.3 1200.0 1031.8: 69.3 135.9 168.2 617.5 804.8 973.9 1052.6 1200.0 1101.0: 66.6 99.0 548.2 735.6 904.6 983.3 1130.7 1200.0 1167.6: 32.4 481.6 669.0 838.0 916.7 1064.1 1133.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 32.3605 .. 449.2746 cents 1855/1458, 416.9142 cents 54/53, 32.3605 cents 2: 98.9546 .. 636.6177 cents 221/162, 537.6631 cents 486/595,-350.3200 cents 3: 168.2132 .. 805.6527 cents 2107/1458, 637.4395 cents 486/637,-468.4045 cents 4: 315.6413 .. 884.3587 cents 25/18, 568.7174 cents 162/215,-490.0114 cents 5: 394.3473 .. 1031.7868 cents 2107/1458, 637.4395 cents 162/215,-490.0114 cents 6: 563.3823 .. 1101.0454 cents 221/162, 537.6631 cents 486/637,-468.4045 cents 7: 750.7254 .. 1167.6395 cents 1855/1458, 416.9142 cents 486/595,-350.3200 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 54/53, 32.3605 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 35/27, 449.2746 cents Average / Smallest step : 4.635287 Largest / Average step : 2.995164 Largest / Smallest step : 13.883445 Median interval of one step : 113.06705 cents, amount: 0 Least squares average step : 182.42934 cents, oct.: 1459.43475 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : HGFDECBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.82185 cents Scale diversity : 1.795077 Lumma stability : 0.053934 Lumma impropriety factor : 0.835076 Rothenberg efficiency : 0.250000 redundancy: 0.750000 Efficiency x scale size : 2.000000 Number of different interval sizes : 56 = 8.00000 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 8.00000 = 8 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 2107/2106, 0.8219 cents Number of recognisable fifths : 1, average 718.3649 cents Number of appreciable fifths : 0 Formal octave complements present : 1 = 12.5000% -- Rational properties -- Prime limit : 53 Odd number limit : 53 (O: 53 U: 53) Highest odd numerator or denominator: 53 Scale harmonicity : 0.011332 Fundamental : 1/27, -4.7549 octaves, 9.6898 Hz. Guide tone : 246792910, 27.8787 octaves, 64567334591.029 Hz. Exponens Consonantiae : 6.663409E+09, 32.63361 octaves Euler's gradus suavitatis : 146 Sum of Mann's harmonic distance : 173.5, average 21.68750 Mersenne's string divisions : 141501360 Sum of van Prooijen's expressibility: 9.63537, average 1.20442 Sum of Tenney's harmonic distance : 18.04746, average 2.25593 Vogel's harmonic complexity : 22.37500 Wille's k value : 26 Wilson's harmonic complexity : 154 Rectangular lattice diameter : 10 Triangular lattice diameter : 3 Lattice compactness : 77.35486, average 2.14875 Lattice compactness (without 2's) : 75.00204, average 2.08339 Number of different primes : 8 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.12500 1 1 3: -3 .. 0 -2.12500 17 5: 0 .. 1 0.25000 2 1 7: 0 .. 2 0.37500 3 2 13: 0 .. 1 0.12500 1 1 17: 0 .. 1 0.12500 1 1 43: 0 .. 1 0.12500 1 1 53: 0 .. 1 0.12500 1 1 Average exponent except 2's :-8 / 8 =-1.00000 Average absolute exponent except 2's: 26 / 8 = 3.25000 Scale is weakly epimorphic with val: <8 12 19 21 29 34 45 47| Scale is weakly epimorphic with val: <8 12 19 21 29 35 45 46| Scale is weakly epimorphic with val: <8 13 18 23 29 35 43 45| Scale is weakly epimorphic with val: <8 13 18 23 30 35 42 45| Scale is weakly epimorphic with val: <8 13 19 22 29 35 43 46| Scale is weakly epimorphic with val: <8 13 19 22 30 35 42 46| Scale is weakly epimorphic with val: <8 13 20 21 30 35 44 45| Scale is weakly epimorphic with val: <8 13 20 21 31 35 43 45| Scale is weakly epimorphic with val: <8 13 20 22 30 35 41 45| Scale is weakly epimorphic with val: <8 14 18 22 29 33 41 45| Scale is weakly epimorphic with val: <8 14 18 22 29 35 45 47| Scale is weakly epimorphic with val: <8 14 18 22 31 35 43 47| Scale is weakly epimorphic with val: <8 14 19 22 29 34 45 46| Scale is weakly epimorphic with val: <8 14 19 22 31 34 43 46| Scale is weakly epimorphic with val: <8 14 20 23 30 33 41 45| Scale is weakly epimorphic with val: <8 14 20 23 30 35 45 47| Scale is weakly epimorphic with val: <8 14 20 23 31 35 44 47|
FIT/MODE
8: 3 1 1 1 1 0 1 0 N SD: 32.9162 c. M: 55.6527 c. 9: 3 2 1 1 1 0 1 0 N SD: 33.9247 c. M: 49.2746 c. 11: 4 2 1 1 1 1 1 0 N SD: 27.4672 c. M: 49.9686 c. 13: 5 2 2 1 1 1 1 0 N SD: 21.5977 c. M:-38.7182 c. 15: 6 2 2 1 2 1 1 0 N SD: 17.6081 c. M:-32.3605 c. 19: 7 3 3 1 2 1 1 1 N SD: 17.5467 c. M: 30.7974 c. 21: 8 3 3 1 3 1 1 1 N SD: 14.8276 c. M: 27.2159 c. 22: 8 4 3 1 3 1 1 1 N SD: 13.2110 c. M: 22.1850 c. 24: 9 4 3 2 3 1 1 1 N SD: 11.7270 c. M:-18.2132 c. 27: 10 4 4 2 3 2 1 1 N SD: 8.8166 c. M: 14.3954 c. 34: 13 5 5 2 4 2 2 1 N SD: 5.6910 c. M:-9.5489 c. 45: 17 7 6 3 6 2 3 1 N SD: 5.4568 c. M:-8.2132 c. 49: 18 8 7 3 6 3 3 1 N SD: 4.4521 c. M: 8.4583 c. 62: 23 10 9 4 7 4 3 2 N SD: 4.8768 c. M:-7.2505 c. 64: 24 10 9 4 8 4 3 2 N SD: 2.8530 c. M:-5.2046 c. 72: 27 11 10 5 9 4 4 2 N SD: 2.4685 c. M: 5.6527 c. 85: 32 13 12 6 10 5 5 2 N SD: 2.5703 c. M:-5.0531 c. 98: 37 15 14 6 12 6 5 3 N SD: 2.7053 c. M: 4.3742 c. 106: 40 16 15 7 13 6 6 3 N SD: 2.2005 c. M:-3.5556 c. 107: 40 17 15 7 13 6 6 3 N SD: 1.5382 c. M:-2.6347 c. 149: 56 23 21 10 18 9 8 4 N SD: 1.2151 c. M:-2.3103 c. 155: 58 24 22 10 19 9 9 4 N SD: 1.4086 c. M: 2.1094 c. 171: 64 27 24 11 21 10 9 5 N SD: 1.3137 c. M: 2.7273 c. 179: 67 28 25 12 22 10 10 5 N SD: 0.8720 c. M: 1.6041 c. 228: 85 36 32 15 28 13 13 6 N SD: 0.8370 c. M: 1.9062 c. 256: 96 40 36 17 31 15 14 7 N SD: 0.7837 c. M:-1.5788 c. 270: 101 42 38 18 33 16 15 7 N SD: 0.8765 c. M:-1.2493 c. 292: 109 46 41 19 36 17 16 8 N SD: 0.6143 c. M: 1.3294 c. 305: 114 48 43 20 37 18 17 8 N SD: 0.7759 c. M: 0.9671 c. 307: 115 48 43 20 38 18 17 8 N SD: 0.7238 c. M:-1.2347 c. 326: 122 51 46 21 40 19 18 9 N SD: 0.6298 c. M: 1.1120 c. 328: 123 51 46 22 40 19 18 9 N SD: 0.5589 c. M:-1.0071 c. 377: 141 59 53 25 46 22 21 10 N SD: 0.3889 c. M:-0.5302 c. 486: 182 76 68 32 60 28 27 13 N SD: 0.3651 c. M: 0.7144 c. 556: 208 87 78 37 68 32 31 15 N SD: 0.3390 c. M: 0.6167 c. 593: 222 93 83 39 73 34 33 16 N SD: 0.3250 c. M:-0.8191 c. 620: 232 97 87 41 76 36 34 17 N SD: 0.3030 c. M: 0.5428 c. 737: 276 115 104 48 91 42 41 20 N SD: 0.2742 c. M:-0.5063 c. 742: 278 116 104 49 91 43 41 20 N SD: 0.2907 c. M:-0.5791 c. 764: 286 119 108 50 94 44 42 21 N SD: 0.2901 c. M: 0.6238 c. 775: 290 121 109 51 95 45 43 21 N SD: 0.3093 c. M: 0.5610 c. 779: 292 121 110 51 96 45 43 21 N SD: 0.2975 c. M:-0.5328 c. 786: 294 123 111 51 97 45 44 21 N SD: 0.3120 c. M:-0.4542 c. 791: 296 124 111 52 97 46 44 21 N SD: 0.3109 c. M:-0.5505 c. 812: 304 127 114 53 100 47 45 22 N SD: 0.2817 c. M: 0.6149 c. 822: 308 128 116 54 101 47 46 22 N SD: 0.2610 c. M:-0.3604 c. 852: 319 133 120 56 105 49 47 23 N SD: 0.2561 c. M:-0.6076 c. 886: 332 138 125 58 109 51 49 24 N SD: 0.1945 c. M:-0.3868 c. 897: 336 140 126 59 110 52 50 24 N SD: 0.2133 c. M: 0.3487 c. 935: 350 146 132 61 115 54 52 25 N SD: 0.1685 c. M:-0.3366 c. 1007: 377 157 142 66 124 58 56 27 N SD: 0.1489 c. M: 0.2721 c. 1114: 417 174 157 73 137 64 62 30 N SD: 0.0926 c. M:-0.1701 c. 1263: 473 197 178 83 155 73 70 34 N SD: 0.1043 c. M:-0.2019 c. 1491: 558 233 210 98 183 86 83 40 N SD: 0.1027 c. M: 0.1801 c. 1555: 582 243 219 102 191 90 86 42 N SD: 0.0838 c. M:-0.1765 c. 1661: 622 259 234 109 204 96 92 45 N SD: 0.1012 c. M: 0.1501 c. 1734: 649 271 244 114 213 100 96 47 N SD: 0.0944 c. M: 0.1655 c. 1889: 707 295 266 124 232 109 105 51 N SD: 0.1106 c. M: 0.1481 c. 1966: 736 307 277 129 241 114 109 53 N SD: 0.0985 c. M: 0.2507 c. 2011: 753 314 283 132 247 116 112 54 N SD: 0.0788 c. M:-0.1377 c. 2075: 777 324 292 136 255 120 115 56 N SD: 0.0748 c. M: 0.1177 c. 2377: 890 371 335 156 292 137 132 64 N SD: 0.0641 c. M:-0.1175 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x 3 x x x x x 4 S SD: 32.6687 cents 3:4 x x 5 x x x 6 S SD: 16.2568 cents 4:5:6 x x 7 x x 8 S SD: 27.6101 cents 5 x 7:8 x 9 x x 10 SD: 14.1273 cents 6:8:9 x 10:11 x x 12 S SD: 16.6811 cents 7:9:10:11:12 x 13 x 14 SD: 10.9840 cents 8:10:12:13 x x 15 x 16 SD: 19.6087 cents 9:12:13:14:15:16:17 x 18 S SD: 10.4122 cents 10:13:14:16:17:18:19 x 20 SD: 9.5790 cents 11:14:16 x 18:20:21 x 22 SD: 8.3555 cents 12:16:17:19:20:22:23 x 24 SD: 9.6450 cents 13:17:19:21:22:24:25 x 26 SD: 8.7961 cents 14:18:20:22:23:25:26:27:28 SD: 8.2014 cents 15:19:22:24:25:27:28:29:30 SD: 7.5829 cents 16:21:23:25:27:29:30:31:32 SD: 6.5722 cents 17:22:25:27:28:31:32:33:34 SD: 5.4389 cents 18:23:26:29:30:33:34:35:36 SD: 4.9989 cents 20:26:29:32:33:36:38:39:40 SD: 3.6910 cents 27:35:39:43:45:49:51:53:54 SD: 0.0000 cents