Scala analysis: xen18-ayers-table-59
7 Iterated Second 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: 28/27 62.960904 Archytas' 1/3-tone 2: 10/9 182.403712 minor whole tone 3: 32/27 294.134997 Pythagorean minor third 4: 4/3 498.044999 perfect fourth 5: 38/27 591.648014 6: 14/9 764.915905 septimal minor sixth 7: 46/27 922.409345 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 27/23 277.5907 vicesimotertial minor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 15/14 119.4428 major diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 19/18 93.6030 undevicesimal semitone 6: 21/19 173.2679 7: 23/21 157.4934 8: 27/23 277.5907 vicesimotertial minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 19/18 93.603 cents undevicesimal semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 23/21 157.493 cents 1: 1 21/19 173.268 cents 1: 1 9/8 203.910 cents major whole tone 1: 1 27/23 277.591 cents vicesimotertial minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 19/16 297.513 cents 19th harmonic 2: 1 6/5 315.641 cents minor third 2: 1 23/19 330.761 cents 2: 1 28/23 340.552 cents 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 32/27 294.135 cents Pythagorean minor third 3: 1 19/15 409.244 cents undevicesimal ditone 3: 1 23/18 424.364 cents vicesimotertial major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 1 30/23 459.994 cents 3: 1 21/16 470.781 cents narrow fourth 3: 1 4/3 498.045 cents perfect fourth 3: 1 27/19 608.352 cents 4: 1 4/3 498.045 cents perfect fourth 4: 1 19/14 528.687 cents 4: 1 32/23 571.726 cents 23rd subharmonic 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 23/16 628.274 cents 23rd harmonic 4: 1 28/19 671.313 cents 4: 1 3/2 701.955 cents perfect fifth 5: 1 38/27 591.648 cents 5: 1 3/2 701.955 cents perfect fifth 5: 1 32/21 729.219 cents wide fifth 5: 1 23/15 740.006 cents 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 36/23 775.636 cents 5: 1 30/19 790.756 cents smaller undevicesimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 1 14/9 764.916 cents septimal minor sixth 6: 1 23/14 859.448 cents 6: 1 38/23 869.239 cents 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 32/19 902.487 cents 19th subharmonic 6: 1 12/7 933.129 cents septimal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 7: 1 46/27 922.409 cents 7: 1 16/9 996.090 cents Pythagorean minor seventh 7: 1 38/21 1026.732 cents 7: 1 42/23 1042.507 cents 7: 1 28/15 1080.557 cents grave major seventh 7: 1 15/8 1088.269 cents classic major seventh 7: 1 36/19 1106.397 cents smaller undevicesimal major seventh 7: 1 27/14 1137.039 cents septimal major seventh 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 : 63.0 182.4 294.1 498.0 591.6 764.9 922.4 1200.0 63.0 : 119.4 231.2 435.1 528.7 702.0 859.4 1137.0 1200.0 182.4 : 111.7 315.6 409.2 582.5 740.0 1017.6 1080.6 1200.0 294.1 : 203.9 297.5 470.8 628.3 905.9 968.8 1088.3 1200.0 498.0 : 93.6 266.9 424.4 702.0 764.9 884.4 996.1 1200.0 591.6 : 173.3 330.8 608.4 671.3 790.8 902.5 1106.4 1200.0 764.9 : 157.5 435.1 498.0 617.5 729.2 933.1 1026.7 1200.0 922.4 : 277.6 340.6 460.0 571.7 775.6 869.2 1042.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 277.5907 cents 729/644, 214.6298 cents 28/27, 62.9609 cents 2: 182.4037 .. 435.0841 cents 81/70, 252.6804 cents 230/243,-95.1869 cents 3: 294.1350 .. 608.3520 cents 729/608, 314.2170 cents 224/243,-140.9491 cents 4: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 76/81,-110.3070 cents 5: 591.6480 .. 905.8650 cents 729/608, 314.2170 cents 76/81,-110.3070 cents 6: 764.9159 .. 1017.5963 cents 81/70, 252.6804 cents 224/243,-140.9491 cents 7: 922.4093 .. 1137.0391 cents 729/644, 214.6298 cents 230/243,-95.1869 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 27/23, 277.5907 cents Average / Smallest step : 2.382431 Largest / Average step : 1.850604 Largest / Smallest step : 4.408937 Median interval of one step : 138.46812 cents, amount: 0 Least squares average step : 131.89683 cents, oct.: 1055.17468 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : ADCGBFEH Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.716681 Lumma stability : 0.104935 Lumma impropriety factor : 0.563485 Rothenberg efficiency : 0.267857 redundancy: 0.732143 Efficiency x scale size : 2.142857 Number of different interval sizes : 52 = 7.42857 / 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 : 513/512, 3.3780 cents Number of recognisable fifths : 2, average 701.9550 cents Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 12.5000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 23 Odd number limit : 27 (O: 27 U: 27) Highest odd numerator or denominator: 27 Scale harmonicity : 0.009445 Average absolute harmonicity : 0.190248 Specific harmonicity : 0.081537 Fundamental : 1/27, -4.7549 octaves, 9.6898 Hz. Guide tone : 489440, 18.9008 octaves, 128050016.681 Hz. Exponens Consonantiae : 1.321488E+07, 23.65566 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 152.0, average 19.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.11106, average 1.01388 Sum of Tenney's harmonic distance : 17.35513, average 2.16939 Vogel's harmonic complexity : 12.00000 Wille's k value : 13 Wilson's harmonic complexity : 63 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 95.60185, average 2.65561 Lattice compactness (without 2's) : 68.60010, average 1.90556 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 1 .. 5 1.75000 14 1 3: -3 .. 0 -2.12500 17 2 5: 0 .. 1 0.12500 1 1 7: 0 .. 1 0.25000 2 2 19: 0 .. 1 0.12500 1 1 23: 0 .. 1 0.12500 1 1 Average exponent except 2's :-12 / 8 =-1.50000 Average absolute exponent except 2's: 22 / 8 = 2.75000 Scale is weakly epimorphic with val: <8 13 20 22 36 37| Scale is weakly epimorphic with val: <8 14 19 23 35 38|
FIT/MODE
8: 0 1 1 1 1 1 1 2 N T3 SD: 31.9202 c. M: 62.9609 c. 12: 1 1 1 2 1 2 1 3 N SD: 20.9838 c. M:-37.0391 c. 14: 1 1 1 3 1 2 2 3 N SD: 18.7104 c. M: 36.9921 c. 16: 1 1 2 3 1 2 2 4 N SD: 18.5416 c. M: 32.4037 c. 17: 1 2 1 3 1 3 2 4 N SD: 15.6387 c. M:-29.3610 c. 19: 1 2 2 3 1 3 3 4 N SD: 14.9281 c. M:-24.9591 c. 20: 1 2 2 3 2 3 2 5 N SD: 12.1142 c. M: 22.4093 c. 21: 1 2 2 4 1 3 3 5 N SD: 13.4647 c. M: 22.0588 c. 22: 1 2 2 4 2 3 3 5 N SD: 11.3319 c. M: 21.4077 c. 25: 1 3 2 4 2 4 3 6 N SD: 11.4122 c. M: 18.0450 c. 29: 1 3 3 5 2 4 4 7 N SD: 13.5763 c. M: 21.5816 c. 31: 2 3 3 5 2 5 4 7 N SD: 10.3239 c. M:-15.5424 c. 32: 2 3 3 5 3 4 5 7 N SD: 10.2254 c. M:-15.0907 c. 33: 2 3 3 6 2 5 4 8 N SD: 7.9356 c. M: 13.3184 c. 34: 2 3 3 6 3 5 4 8 N SD: 7.6939 c. M: 11.7821 c. 36: 2 4 3 6 3 5 5 8 N SD: 8.3197 c. M:-17.5963 c. 38: 2 4 3 7 3 5 5 9 N SD: 6.7407 c. M: 9.9245 c. 39: 2 4 4 6 3 6 5 9 N SD: 6.0431 c. M:-13.5573 c. 41: 2 4 4 7 3 6 5 10 N SD: 6.6223 c. M: 15.0923 c. 44: 2 5 4 7 4 6 6 10 N SD: 6.3593 c. M:-8.5054 c. 52: 3 5 5 9 4 7 7 12 N SD: 5.6267 c. M:-9.6473 c. 53: 3 5 5 9 4 8 7 12 N SD: 3.4242 c. M:-5.8925 c. 77: 4 8 7 13 6 11 10 18 N SD: 2.1351 c. M:-4.6093 c. 91: 5 9 8 16 7 13 12 21 N SD: 2.3131 c. M: 4.0251 c. 94: 5 9 9 16 7 14 12 22 N SD: 2.3926 c. M: 4.4140 c. 99: 5 10 9 17 8 14 13 23 N SD: 1.7948 c. M: 3.2259 c. 113: 6 11 11 19 9 16 15 26 N SD: 1.8400 c. M:-3.2101 c. 118: 6 12 11 20 9 17 16 27 N SD: 1.6629 c. M:-3.0144 c. 130: 7 13 12 22 10 19 17 30 N SD: 1.2306 c. M:-2.2117 c. 152: 8 15 14 26 12 22 20 35 N SD: 0.9934 c. M: 2.0297 c. 176: 9 18 16 30 14 25 23 41 N SD: 1.3332 c. M: 1.9548 c. 190: 10 19 18 32 15 27 25 44 N SD: 1.2984 c. M:-2.7071 c. 191: 10 19 18 32 15 28 25 44 N SD: 1.0765 c. M: 1.7099 c. 229: 12 23 21 39 18 33 30 53 N SD: 0.4765 c. M:-1.0024 c. 342: 18 34 32 58 27 49 45 79 N SD: 0.5458 c. M:-1.3344 c. 347: 18 35 32 59 27 50 46 80 N SD: 0.5816 c. M:-0.9336 c. 359: 19 36 33 61 28 52 47 83 N SD: 0.5804 c. M:-1.4403 c. 367: 19 37 34 62 29 53 48 85 N SD: 0.5576 c. M: 1.0423 c. 381: 20 38 35 65 30 55 50 88 N SD: 0.5403 c. M: 1.2216 c. 395: 21 39 37 67 31 57 52 91 N SD: 0.6460 c. M:-1.1350 c. 400: 21 40 37 68 31 58 52 93 N SD: 0.5906 c. M: 1.4093 c. 403: 21 40 38 68 32 58 53 93 N SD: 0.6313 c. M:-0.9078 c. 416: 22 41 39 71 32 60 55 96 N SD: 0.5567 c. M:-0.9935 c. 420: 22 42 39 71 33 61 55 97 N SD: 0.4923 c. M: 0.9021 c. 436: 23 43 41 74 34 63 57 101 N SD: 0.3603 c. M: 0.7523 c. 515: 27 51 48 88 40 74 68 119 N SD: 0.4516 c. M: 0.6561 c. 527: 28 52 49 90 41 76 69 122 N SD: 0.4273 c. M:-0.7962 c. 535: 28 53 50 91 42 77 70 124 N SD: 0.3863 c. M: 0.7215 c. 552: 29 55 51 94 43 80 72 128 N SD: 0.3851 c. M: 0.6702 c. 554: 29 55 52 94 43 80 73 128 N SD: 0.3059 c. M: 0.4543 c. 631: 33 63 59 107 49 91 83 146 N SD: 0.3032 c. M:-0.6352 c. 645: 34 64 60 110 50 93 85 149 N SD: 0.2862 c. M:-0.5597 c. 653: 34 65 61 111 51 94 86 151 N SD: 0.2921 c. M: 0.4800 c. 665: 35 66 62 113 52 96 87 154 N SD: 0.1752 c. M: 0.3041 c. 783: 41 78 73 133 61 113 103 181 N SD: 0.1138 c. M:-0.1960 c. 1012: 53 101 94 172 79 146 133 234 N SD: 0.1035 c. M:-0.2050 c. 1335: 70 133 124 227 104 193 175 309 N SD: 0.1193 c. M: 0.2024 c. 1448: 76 144 135 246 113 209 190 335 N SD: 0.0465 c. M: 0.0833 c. 2231: 117 222 208 379 174 322 293 516 N SD: 0.0478 c. M:-0.0828 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x 4 S SD: 31.4805 cents 3 x x x 4 x x 5:6 S SD: 12.6835 cents 4 x x 5 x x 6:7:8 S SD: 30.2236 cents 5 x x 6 x 7:8:9:10 S SD: 21.8953 cents 6 x x 7:8 x 9:10:12 S SD: 15.6911 cents 7 x 8 x 9:10:11:12:14 S SD: 14.3703 cents 8 x 9 x x 11:12:14:16 SD: 18.1192 cents 9 x 10:11:12:13:14:15:18 S SD: 11.3462 cents 10 x 11:12:13:14:16:17:20 SD: 10.2645 cents 11 x 12:13:15 x 17:19:22 SD: 9.4868 cents 12 x 13:14:16:17:19:20:24 SD: 10.2819 cents 13 x 14:15:17:18:20:22:26 SD: 12.3799 cents 14:15:16:17:19:20:22:24:28 SD: 12.0952 cents 15:16:17:18:20:21:23:26:30 SD: 9.3636 cents 16:17:18:19:21:23:25:27:32 SD: 8.5289 cents 17:18:19:20:23:24:26:29:34 SD: 6.9544 cents 18:19:20:21:24:25:28:31:36 SD: 6.3226 cents 20:21:22:24:27:28:31:34:40 SD: 5.3419 cents 24:25:27:28:32:34:37:41:48 SD: 5.0888 cents 25:26:28:30:33:35:39:43:50 SD: 4.6088 cents 26:27:29:31:35:37:40:44:52 SD: 4.5074 cents 27:28:30:32:36:38:42:46:54 SD: 0.0000 cents