Scala analysis: xen15-gilson-generalized-just-2
Scale based on product (25/24)**2 * (21/20)**3 * 16/15 * (8/7)**3 = 2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 6/5 315.641287 minor third 3: 5/4 386.313714 major third 4: 10/7 617.487807 Euler's tritone 5: 3/2 701.955001 perfect fifth 6: 25/16 772.627428 classic augmented fifth 7: 25/14 1003.801521 middle minor seventh 8: 15/8 1088.268715 classic major seventh 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 8/7 231.1741 septimal whole tone 2: 21/20 84.4672 minor semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 8/7 231.1741 septimal whole tone 5: 21/20 84.4672 minor semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 8/7 231.1741 septimal whole tone 8: 21/20 84.4672 minor semitone 9: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 3 8/7 231.174 cents septimal whole tone 2: 2 35/32 155.140 cents septimal neutral second 2: 1 28/25 196.198 cents middle second 2: 2 25/21 301.847 cents BP second, quasi-equal minor third 2: 3 6/5 315.641 cents minor third 2: 1 128/105 342.905 cents septimal neutral third 3: 6 5/4 386.314 cents major third 3: 3 32/25 427.373 cents classic diminished fourth 4: 1 125/96 456.986 cents classic augmented third 4: 2 21/16 470.781 cents narrow fourth 4: 2 4/3 498.045 cents perfect fourth 4: 1 168/125 511.840 cents 4: 2 10/7 617.488 cents Euler's tritone 4: 1 256/175 658.547 cents 5: 1 175/128 541.453 cents 5: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 1 125/84 688.160 cents 5: 2 3/2 701.955 cents perfect fifth 5: 2 32/21 729.219 cents wide fifth 5: 1 192/125 743.014 cents classic diminished sixth 6: 3 25/16 772.627 cents classic augmented fifth 6: 6 8/5 813.686 cents minor sixth 7: 1 105/64 857.095 cents septimal neutral sixth 7: 3 5/3 884.359 cents major sixth, BP sixth 7: 2 42/25 898.153 cents quasi-equal major sixth 7: 1 25/14 1003.802 cents middle minor seventh 7: 2 64/35 1044.860 cents septimal neutral seventh 8: 3 7/4 968.826 cents harmonic seventh 8: 1 15/8 1088.269 cents classic major seventh 8: 3 40/21 1115.533 cents acute major seventh 8: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.25000 = 17/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 231.2 315.6 386.3 617.5 702.0 772.6 1003.8 1088.3 1200.0 231.2 : 84.5 155.1 386.3 470.8 541.5 772.6 857.1 968.8 1200.0 315.6 : 70.7 301.8 386.3 457.0 688.2 772.6 884.4 1115.5 1200.0 386.3 : 231.2 315.6 386.3 617.5 702.0 813.7 1044.9 1129.3 1200.0 617.5 : 84.5 155.1 386.3 470.8 582.5 813.7 898.2 968.8 1200.0 702.0 : 70.7 301.8 386.3 498.0 729.2 813.7 884.4 1115.5 1200.0 772.6 : 231.2 315.6 427.4 658.5 743.0 813.7 1044.9 1129.3 1200.0 1003.8: 84.5 196.2 427.4 511.8 582.5 813.7 898.2 968.8 1200.0 1088.3: 111.7 342.9 427.4 498.0 729.2 813.7 884.4 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 231.1741 cents 192/175, 160.5017 cents 25/24, 70.6724 cents 2: 155.1396 .. 342.9054 cents 4096/3675, 187.7658 cents 245/256,-76.0345 cents 3: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 525/512, 43.4083 cents 4: 456.9861 .. 658.5467 cents 24576/21875, 201.5605 cents 3125/3072, 29.6136 cents 5: 541.4533 .. 743.0139 cents 24576/21875, 201.5605 cents 30625/32768,-117.0933 cents 6: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 3125/3072, 29.6136 cents 7: 857.0946 .. 1044.8604 cents 4096/3675, 187.7658 cents 525/512, 43.4083 cents 8: 968.8259 .. 1129.3276 cents 192/175, 160.5017 cents 245/256,-76.0345 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.886639 Largest / Average step : 1.733806 Largest / Smallest step : 3.271065 Median interval of one step : 21/20, 84.4672 cents, amount: 3 Least squares average step : 137.43736 cents, oct.: 1236.93628 cents Scale is not proper Step pattern alph. order: ABCABCABD Step pattern size order : DBADBADBC Scale is a Constant Structure, by a margin of 29.61357 cents Scale diversity : 1.522233 Lumma stability : 0.239491 Lumma impropriety factor : 0.224302 Rothenberg efficiency : 0.410053 redundancy: 0.589947 Efficiency x scale size : 3.690476 Number of different interval sizes : 34 = 4.25000 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.25000 = 17/4 Median interval variety : 3 Lowest interval variety : 2 Smallest interval difference : 126/125, 13.7948 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 6 Most common triad is 0.0 386.314 813.686 cents, amount: 3 Number of recognisable fifths : 3, average 697.3567 cents Number of appreciable fifths : 2, average 701.9550 cents Scale contains two identical conjunct tetrachords All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 11.1111% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 175 (O: 175 U: 175) Highest odd numerator or denominator: 25 Scale harmonicity : 0.025541 Average absolute harmonicity : 0.200759 Specific harmonicity : 0.141844 Fundamental : 1/560, -9.1293 octaves, 0.4672 Hz. Guide tone : 600, 9.2288 octaves, 156975.339 Hz. Exponens Consonantiae : 3.360000E+05, 18.35810 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 81.5, average 9.05556 Mersenne's string divisions : 103159485 Sum of van Prooijen's expressibility: 7.53723, average 0.83747 Sum of Tenney's harmonic distance : 14.67593, average 1.63066 Vogel's harmonic complexity : 17.44444 Wille's k value : 437 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 140.24476, average 3.11655 Lattice compactness (without 2's) : 69.87120, average 1.55269 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 3 -0.55556 17 1 3: 0 .. 1 0.33333 3 1 5: -1 .. 2 0.66667 8 4 7: -1 .. 0 -0.33333 3 3 Average exponent except 2's : 6 / 9 = 0.66667 Average absolute exponent except 2's: 14 / 9 = 1.55556 Scale is weakly epimorphic with val: <9 13 21 25| Scale is weakly epimorphic with val: <9 14 21 23| Scale is JI-epimorphic with val: <9 14 21 26|
FIT/MODE
9: 2 0 1 2 0 1 2 0 1 N B D3 SD: 37.5312 c. M:-62.8651 c. 10: 2 1 0 2 1 0 2 1 1 N SD: 30.0482 c. M: 52.6274 c. 11: 2 1 1 2 0 1 2 1 1 N D3 SD: 27.8909 c. M:-50.0499 c. 12: 2 1 1 2 1 1 2 1 1 P B ME S SD: 17.0449 c. M: 31.1741 c. Messiaen mode 3 inverse, Tcherepnin Nonatonic mode 2 19: 4 1 1 4 1 1 4 1 2 N SD: 11.7396 c. M:-21.4575 c. 22: 4 2 1 4 2 1 4 2 2 N SD: 11.7951 c. M: 21.9833 c. 25: 5 2 1 5 2 1 5 2 2 N SD: 11.3150 c. M:-20.3587 c. 26: 5 2 1 5 2 2 5 2 2 N SD: 12.4781 c. M:-19.4236 c. 28: 5 2 2 5 2 2 5 2 3 N SD: 13.7921 c. M: 18.0872 c. 29: 6 2 1 6 2 2 5 2 3 N SD: 11.4886 c. M:-17.1018 c. 30: 6 2 2 5 3 1 6 2 3 N SD: 11.3428 c. M:-18.0450 c. 31: 6 2 2 6 2 2 6 2 3 N SD: 3.2745 c. M: 5.9639 c. 53: 10 4 3 10 4 3 10 4 5 N SD: 3.8291 c. M: 7.5751 c. 56: 11 4 3 11 4 3 11 4 5 N SD: 3.8088 c. M:-5.7873 c. 68: 13 5 4 13 5 4 13 5 6 N SD: 2.9736 c. M:-5.8489 c. 84: 16 6 5 16 6 5 16 6 8 N SD: 2.2475 c. M: 3.8015 c. 87: 17 6 5 17 6 5 17 6 8 N SD: 2.0425 c. M:-3.3087 c. 99: 19 7 6 19 7 6 19 7 9 N SD: 1.7307 c. M:-3.1301 c. 115: 22 8 7 22 8 7 22 8 11 N SD: 1.9581 c. M: 3.0513 c. 118: 23 8 7 23 8 7 23 8 11 N SD: 1.6578 c. M:-2.9781 c. 130: 25 9 8 25 9 8 25 9 12 N SD: 1.5081 c. M:-2.7572 c. 140: 27 10 8 27 10 8 27 10 13 N SD: 0.8187 c. M:-1.5016 c. 171: 33 12 10 33 12 10 33 12 16 N SD: 0.3690 c. M: 0.6976 c. 270: 52 19 16 52 19 16 52 19 25 N SD: 0.4200 c. M:-0.7059 c. 354: 68 25 21 68 25 21 68 25 33 N SD: 0.3679 c. M: 0.6656 c. 410: 79 29 24 79 29 24 79 29 38 N SD: 0.2840 c. M:-0.5118 c. 441: 85 31 26 85 31 26 85 31 41 N SD: 0.1491 c. M:-0.2801 c. 612: 118 43 36 118 43 36 118 43 57 N SD: 0.1000 c. M:-0.1985 c. 935: 180 66 55 180 66 55 180 66 87 N SD: 0.1034 c. M: 0.1652 c. 966: 186 68 57 186 68 57 186 68 90 N SD: 0.0798 c. M: 0.1182 c. 1137: 219 80 67 219 80 67 219 80 106 N SD: 0.0828 c. M: 0.1421 c. 1376: 265 97 81 265 97 81 265 97 128 N SD: 0.0582 c. M:-0.1034 c. 1407: 271 99 83 271 99 83 271 99 131 N SD: 0.0453 c. M:-0.0805 c. 1547: 298 109 91 298 109 91 298 109 144 N SD: 0.0388 c. M:-0.0665 c. 1578: 304 111 93 304 111 93 304 111 147 N SD: 0.0312 c. M: 0.0558 c. 1988: 383 140 117 383 140 117 383 140 185 N SD: 0.0347 c. M:-0.0613 c. 2019: 389 142 119 389 142 119 389 142 188 N SD: 0.0337 c. M:-0.0618 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x 4 x x 5 x x 6 S SD: 52.6706 cents 4 x x 5 x 6 x 7 x 8 S SD: 8.7439 cents 5 x 6 x 7 x 8:9 x 10 S SD: 11.1345 cents 6:7 x 8 x 9 x x 11:12 SD: 24.7158 cents 7:8 x 9:10 x 11 x 13:14 SD: 8.7406 cents 8:9 x 10:11:12:13:14:15:16 S SD: 13.0836 cents 9:10:11 x 13 x 14:16:17:18 SD: 9.0754 cents 11 x 13:14:16 x 17:20:21:22 SD: 10.0525 cents 12:14 x 15:17:18:19:21:23:24 SD: 8.5523 cents 13:15 x 16:19 x 20:23:24:26 SD: 9.3172 cents 14:16:17:18:20:21:22:25:26:28 SD: 6.2560 cents 15:17:18:19:21 x 23:27:28:30 SD: 7.1512 cents 16:18:19:20:23:24:25:29:30:32 SD: 4.7826 cents 20:23:24:25:29:30:31:36:38:40 SD: 4.5680 cents 24:27:29:30:34:36:38:43:45:48 SD: 4.5212 cents 28:32:34:35:40:42:44:50:53:56 SD: 3.1158 cents 35:40:42:44:50:53:55:63:66:70 SD: 3.0460 cents 36:41:43:45:51:54:56:64:68:72 SD: 2.7054 cents 40:46:48:50:57:60:63:71:75:80 SD: 2.3147 cents 44:50:53:55:63:66:69:79:83:88 SD: 2.2033 cents 48:55:58:60:69:72:75:86:90:96 SD: 1.9669 cents 55:63:66:69:79:83:86:98:103:110 SD: 1.8370 cents 56:64:67:70:80:84:88:100:105:112 SD: 1.2370 cents 64:73:77:80:91:96:100:114:120:128 SD: 1.2002 cents 80:91:96:100:114:120:125:143:150:160 SD: 1.0420 cents 84:96:101:105:120:126:131:150:158:168 SD: 0.8072 cents 96:110:115:120:137:144:150:171:180:192 SD: 0.7963 cents 112:128:134:140:160:168:175:200:210:224 SD: 0.5734 cents 140:160:168:175:200:210:219:250:263:280 SD: 0.4269 cents 196:224:235:245:280:294:306:350:368:392 SD: 0.3462 cents 224:256:269:280:320:336:350:400:420:448 SD: 0.1431 cents 336:384:403:420:480:504:525:600:630:672 SD: 0.0954 cents 560:640:672:700:800:840:875:1000:1050:1120 S SD: 0.0000 cents