Scala analysis: xen10-wolf-sands
Scale from 'Trio: The Sands'
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 28/25 196.198479 middle second 3: 6/5 315.641287 minor third 4: 32/25 427.372572 classic diminished fourth 5: 21/16 470.780907 narrow fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 42/25 898.153480 quasi-equal major sixth 10: 7/4 968.825906 harmonic seventh 11: 48/25 1129.327573 classic diminished octave 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 21/20 84.4672 minor semitone 2: 16/15 111.7313 minor diatonic semitone 3: 15/14 119.4428 major diatonic semitone 4: 16/15 111.7313 minor diatonic semitone 5: 525/512 43.4083 Avicenna enharmonic diesis 6: 16/15 111.7313 minor diatonic semitone 7: 15/14 119.4428 major diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 21/20 84.4672 minor semitone 10: 25/24 70.6724 classic chromatic semitone, minor chroma 11: 192/175 160.5017 septimal 4/5-tone 12: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 525/512 43.408 cents Avicenna enharmonic diesis 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 21/20 84.467 cents minor semitone 1: 4 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 192/175 160.502 cents septimal 4/5-tone 2: 4 35/32 155.140 cents septimal neutral second 2: 2 28/25 196.198 cents middle second 2: 6 8/7 231.174 cents septimal whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 2 75/64 274.582 cents classic augmented second 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 4 6/5 315.641 cents minor third 3: 2 128/105 342.905 cents septimal neutral third 4: 8 5/4 386.314 cents major third 4: 4 32/25 427.373 cents classic diminished fourth 5: 3 21/16 470.781 cents narrow fourth 5: 6 4/3 498.045 cents perfect fourth 5: 1 75/56 505.757 cents marvelous fourth 5: 2 48/35 546.815 cents septimal semi-augmented fourth 6: 2 175/128 541.453 cents 6: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 4 10/7 617.488 cents Euler's tritone 6: 2 256/175 658.547 cents 7: 2 35/24 653.185 cents septimal semi-diminished fifth 7: 1 112/75 694.243 cents marvelous fifth 7: 6 3/2 701.955 cents perfect fifth 7: 3 32/21 729.219 cents wide fifth 8: 4 25/16 772.627 cents classic augmented fifth 8: 8 8/5 813.686 cents minor sixth 9: 2 105/64 857.095 cents septimal neutral sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 2 128/75 925.418 cents diminished seventh 9: 3 12/7 933.129 cents septimal major sixth 10: 6 7/4 968.826 cents harmonic seventh 10: 2 25/14 1003.802 cents middle minor seventh 10: 4 64/35 1044.860 cents septimal neutral seventh 11: 1 175/96 1039.498 cents 11: 2 28/15 1080.557 cents grave major seventh 11: 4 15/8 1088.269 cents classic major seventh 11: 2 40/21 1115.533 cents acute major seventh 11: 2 48/25 1129.328 cents classic diminished octave 11: 1 1024/525 1156.592 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 84.5 196.2 315.6 427.4 470.8 582.5 702.0 813.7 898.2 968.8 1129.3 1200.0 84.5 : 111.7 231.2 342.9 386.3 498.0 617.5 729.2 813.7 884.4 1044.9 1115.5 1200.0 196.2 : 119.4 231.2 274.6 386.3 505.8 617.5 702.0 772.6 933.1 1003.8 1088.3 1200.0 315.6 : 111.7 155.1 266.9 386.3 498.0 582.5 653.2 813.7 884.4 968.8 1080.6 1200.0 427.4 : 43.4 155.1 274.6 386.3 470.8 541.5 702.0 772.6 857.1 968.8 1088.3 1200.0 470.8 : 111.7 231.2 342.9 427.4 498.0 658.5 729.2 813.7 925.4 1044.9 1156.6 1200.0 582.5 : 119.4 231.2 315.6 386.3 546.8 617.5 702.0 813.7 933.1 1044.9 1088.3 1200.0 702.0 : 111.7 196.2 266.9 427.4 498.0 582.5 694.2 813.7 925.4 968.8 1080.6 1200.0 813.7 : 84.5 155.1 315.6 386.3 470.8 582.5 702.0 813.7 857.1 968.8 1088.3 1200.0 898.2 : 70.7 231.2 301.8 386.3 498.0 617.5 729.2 772.6 884.4 1003.8 1115.5 1200.0 968.8 : 160.5 231.2 315.6 427.4 546.8 658.5 702.0 813.7 933.1 1044.9 1129.3 1200.0 1129.3: 70.7 155.1 266.9 386.3 498.0 541.5 653.2 772.6 884.4 968.8 1039.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.4083 .. 160.5017 cents 32768/30625, 117.0933 cents 525/512, 43.4083 cents 2: 155.1396 .. 231.1741 cents 256/245, 76.0345 cents 6125/6144,-5.3620 cents 3: 266.8709 .. 342.9054 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 4: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 525/512, 43.4083 cents 5: 470.7809 .. 546.8154 cents 256/245, 76.0345 cents 525/512, 43.4083 cents 6: 541.4533 .. 658.5467 cents 32768/30625, 117.0933 cents 6125/6144,-5.3620 cents 7: 653.1846 .. 729.2191 cents 256/245, 76.0345 cents 6125/6144,-5.3620 cents 8: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 525/512, 43.4083 cents 9: 857.0946 .. 933.1291 cents 256/245, 76.0345 cents 525/512, 43.4083 cents 10: 968.8259 .. 1044.8604 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 11: 1039.4983 .. 1156.5917 cents 32768/30625, 117.0933 cents 6125/6144,-5.3620 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 525/512, 43.4083 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 192/175, 160.5017 cents Average / Smallest step : 2.303705 Largest / Average step : 1.605017 Largest / Smallest step : 3.697485 Median interval of one step : 16/15, 111.7313 cents, amount: 4 Most common interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 99.99950 cents, oct.: 1199.99400 cents Scale is not proper Step pattern alph. order: ABCBDBCBAEFE Step pattern size order : CDEDADEDCBFB Scale is a Constant Structure, by a margin of 5.36205 cents Scale diversity : 1.444575 Lumma stability : 0.276536 Lumma impropriety factor : 0.017873 Rothenberg efficiency : 0.356421 redundancy: 0.643579 Efficiency x scale size : 4.277056 Number of different interval sizes : 44 = 4.00000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.00000 = 4 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 6144/6125, 5.3620 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 8 Most common triad is 0.0 386.314 813.686 cents, amount: 4 Number of recognisable fifths : 7, average 700.8534 cents Best fifths form a closed circle Scale is a complete genus musicum : 2^m 3^1 5^2 7^1 Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 8.3333% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 10-11 -- Rational properties -- Prime limit : 7 Odd number limit : 525 (O: 525 U: 525) Highest odd numerator or denominator: 25 Scale harmonicity : 0.028775 Average absolute harmonicity : 0.159199 Specific harmonicity : 0.133872 Fundamental : 1/400, -8.6439 octaves, 0.6541 Hz. Guide tone : 672, 9.3923 octaves, 175812.380 Hz. Exponens Consonantiae : 2.688000E+05, 18.03617 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 191.5, average 15.95833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.80146, average 0.98345 Sum of Tenney's harmonic distance : 24.14774, average 2.01231 Vogel's harmonic complexity : 14.66667 Wille's k value : 262 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 271.71730, average 3.48356 Lattice compactness (without 2's) : 118.55192, average 1.51990 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.66667 26 1 3: 0 .. 1 0.50000 6 1 5: -2 .. 0 -1.00000 12 4 7: 0 .. 1 0.50000 6 6 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 24 / 12 = 2.00000 Scale is weakly epimorphic with val: <12 17 28 34| Scale is weakly epimorphic with val: <12 18 25 33| Scale is weakly epimorphic with val: <12 18 26 31| Scale is weakly epimorphic with val: <12 18 26 33| Scale is weakly epimorphic with val: <12 18 26 35| Scale is weakly epimorphic with val: <12 18 26 37| Scale is weakly epimorphic with val: <12 18 28 31| Scale is weakly epimorphic with val: <12 18 28 33| Scale is weakly epimorphic with val: <12 18 28 35| Scale is weakly epimorphic with val: <12 18 28 37| Scale is weakly epimorphic with val: <12 18 29 33| Scale is weakly epimorphic with val: <12 18 31 33| Scale is JI-epimorphic with val: <12 19 28 34| = patent Scale is weakly epimorphic with val: <12 21 28 34|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 19.2260 c. M:-31.1741 c. Twelve-tone Chromatic (1/11-comma) 15: 1 1 2 1 1 1 2 1 1 1 2 1 P B ME SD: 17.5540 c. M: 36.1985 c. Augene-12 16: 1 2 1 2 0 2 1 2 1 1 2 1 P D3 SD: 16.6541 c. M:-28.8015 c. 19: 1 2 2 2 0 2 2 2 1 1 3 1 N SD: 14.5914 c. M: 28.6756 c. 20: 1 2 2 2 1 2 2 2 1 1 3 1 N D3 SD: 15.1770 c. M:-26.3137 c. 25: 2 2 3 2 1 2 3 2 2 1 4 1 N SD: 12.3442 c. M:-22.6724 c. 28: 2 3 2 3 1 3 2 3 2 2 3 2 SP D3 SD: 11.7617 c. M:-18.0872 c. 31: 2 3 3 3 1 3 3 3 2 2 4 2 P SD: 4.7690 c. M: 7.8309 c. 53: 4 5 5 5 2 5 5 5 4 3 7 3 P SD: 4.5906 c. M:-7.5751 c. 56: 4 5 6 5 2 5 6 5 4 3 8 3 N SD: 3.6019 c. M:-6.3867 c. 68: 5 6 7 6 3 6 7 6 5 4 9 4 P SD: 2.8190 c. M:-5.6897 c. 84: 6 8 8 8 3 8 8 8 6 5 11 5 P SD: 1.9341 c. M:-3.8015 c. 87: 6 8 9 8 3 8 9 8 6 5 12 5 N SD: 1.9858 c. M: 3.3087 c. 99: 7 9 10 9 4 9 10 9 7 6 13 6 P SD: 1.5691 c. M: 3.1301 c. 115: 8 11 11 11 4 11 11 11 8 7 15 7 P SD: 1.6796 c. M: 2.8246 c. 130: 9 12 13 12 5 12 13 12 9 8 17 8 P SD: 1.8078 c. M: 3.1737 c. 140: 10 13 14 13 5 13 14 13 10 8 19 8 N SD: 1.1453 c. M:-2.1010 c. 171: 12 16 17 16 6 16 17 16 12 10 23 10 N SD: 0.3664 c. M:-0.6976 c. 270: 19 25 27 25 10 25 27 25 19 16 36 16 N SD: 0.3704 c. M: 0.7059 c. 354: 25 33 35 33 13 33 35 33 25 21 47 21 N SD: 0.3797 c. M:-0.6656 c. 410: 29 38 41 38 15 38 41 38 29 24 55 24 N SD: 0.3103 c. M:-0.4840 c. 441: 31 41 44 41 16 41 44 41 31 26 59 26 N SD: 0.1384 c. M: 0.2801 c. 612: 43 57 61 57 22 57 61 57 43 36 82 36 N SD: 0.1189 c. M: 0.1985 c. 966: 68 90 96 90 35 90 96 90 68 57 129 57 N SD: 0.0773 c. M: 0.1350 c. 1137: 80 106 113 106 41 106 113 106 80 67 152 67 N SD: 0.0639 c. M: 0.1080 c. 1376: 97 128 137 128 50 128 137 128 97 81 184 81 N SD: 0.0761 c. M:-0.1493 c. 1407: 99 131 140 131 51 131 140 131 99 83 188 83 N SD: 0.0566 c. M: 0.1165 c. 1547: 109 144 154 144 56 144 154 144 109 91 207 91 N SD: 0.0586 c. M:-0.1012 c. 1578: 111 147 157 147 57 147 157 147 111 93 211 93 N SD: 0.0385 c. M: 0.0585 c. 1988: 140 185 198 185 72 185 198 185 140 117 266 117 N SD: 0.0344 c. M:-0.0571 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 10.1851 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.2647 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.7541 cents 6 x x 7 x 8 x 9 x 10 x x 12 S SD: 11.5103 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.7960 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.9483 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 10.5305 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.6140 cents 11 x 12:13:14 x 15:17:18 x 19:21:22 SD: 10.9667 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 8.4711 cents 13:14:15:16 x 17:18:20:21:22:23:25:26 SD: 8.9194 cents 14:15:16:17:18 x 20:21:22:24:25:27:28 SD: 7.9400 cents 15:16:17:18:19:20:21:23:24:25:26:29:30 SD: 5.4589 cents 17:18:19:20:22 x 24:26:27:29:30:33:34 SD: 6.1210 cents 18:19:20:22:23:24:25:27:29:30:32:35:36 SD: 5.1251 cents 20:21:22:24 x 26:28:30:32:34:35:38:40 SD: 4.0615 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 4.0496 cents 24:25:27:29:31:32:34:36:38:40:42:46:48 SD: 4.0235 cents 25:26:28:30:32:33:35:38:40:42:44:48:50 SD: 2.6285 cents 27:28:30:32 x 35:38:41:43:45:47:52:54 SD: 4.5274 cents 28:29:31:34:36:37:39:42:45:47:49:54:56 SD: 3.5144 cents 32:34:36:38:41:42:45:48:51:54:56:61:64 SD: 2.8018 cents 35:37:39:42:45:46:49:53:56:59:61:67:70 SD: 2.1438 cents 40:42:45:48:51:53:56:60:64:67:70:77:80 SD: 1.7110 cents 57:60:64:68:73:75:80:86:91:96:100:109:114 SD: 1.6280 cents 58:61:65:70:74:76:81:87:93:97:102:111:116 SD: 1.5466 cents 60:63:67:72:77:79:84:90:96:101:105:115:120 SD: 0.8243 cents 100:105:112:120:128:131:140:150:160:168:175:192:200 SD: 0.2751 cents 160:168:179:192:205:210:224:240:256:269:280:307:320 SD: 0.2572 cents 240:252:269:288:307:315:336:360:384:403:420:461:480 SD: 0.1714 cents 300:315:336:360:384:394:420:450:480:504:525:576:600 SD: 0.0916 cents 400:420:448:480:512:525:560:600:640:672:700:768:800 SD: 0.0000 cents