Scala analysis: xen15-gilson-generalized-just-1
Ten note just scale, two rows and five columns of chart on p.119
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75/64 274.582429 classic augmented second 2: 6/5 315.641287 minor third 3: 5/4 386.313714 major third 4: 32/25 427.372572 classic diminished fourth 5: 3/2 701.955001 perfect fifth 6: 25/16 772.627428 classic augmented fifth 7: 8/5 813.686286 minor sixth 8: 15/8 1088.268715 classic major seventh 9: 48/25 1129.327573 classic diminished octave 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 75/64 274.5824 classic augmented second 2: 128/125 41.0589 minor diesis, diesis 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 128/125 41.0589 minor diesis, diesis 5: 75/64 274.5824 classic augmented second 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 128/125 41.0589 minor diesis, diesis 8: 75/64 274.5824 classic augmented second 9: 128/125 41.0589 minor diesis, diesis 10: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 128/125 41.059 cents minor diesis, diesis 1: 3 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 75/64 274.582 cents classic augmented second 2: 4 16/15 111.731 cents minor diatonic semitone 2: 4 6/5 315.641 cents minor third 2: 2 625/512 345.255 cents classic neutral third 3: 1 2048/1875 152.790 cents double diminished third 3: 1 768/625 356.700 cents 3: 8 5/4 386.314 cents major third 4: 6 32/25 427.373 cents classic diminished fourth 4: 2 125/96 456.986 cents classic augmented third 4: 2 375/256 660.896 cents double augmented fourth 5: 5 4/3 498.045 cents perfect fourth 5: 5 3/2 701.955 cents perfect fifth 6: 2 512/375 539.104 cents double diminished fifth 6: 2 192/125 743.014 cents classic diminished sixth 6: 6 25/16 772.627 cents classic augmented fifth 7: 8 8/5 813.686 cents minor sixth 7: 1 625/384 843.300 cents 7: 1 1875/1024 1047.210 cents double augmented sixth 8: 2 1024/625 854.745 cents two (classic diminished fourth) 8: 4 5/3 884.359 cents major sixth, BP sixth 8: 4 15/8 1088.269 cents classic major seventh 9: 3 128/75 925.418 cents diminished seventh 9: 3 48/25 1129.328 cents classic diminished octave 9: 4 125/64 1158.941 cents classic augmented seventh, octave - minor diesis Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.88889 = 26/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 274.6 315.6 386.3 427.4 702.0 772.6 813.7 1088.3 1129.3 1200.0 274.6 : 41.1 111.7 152.8 427.4 498.0 539.1 813.7 854.7 925.4 1200.0 315.6 : 70.7 111.7 386.3 457.0 498.0 772.6 813.7 884.4 1158.9 1200.0 386.3 : 41.1 315.6 386.3 427.4 702.0 743.0 813.7 1088.3 1129.3 1200.0 427.4 : 274.6 345.3 386.3 660.9 702.0 772.6 1047.2 1088.3 1158.9 1200.0 702.0 : 70.7 111.7 386.3 427.4 498.0 772.6 813.7 884.4 925.4 1200.0 772.6 : 41.1 315.6 356.7 427.4 702.0 743.0 813.7 854.7 1129.3 1200.0 813.7 : 274.6 315.6 386.3 660.9 702.0 772.6 813.7 1088.3 1158.9 1200.0 1088.3: 41.1 111.7 386.3 427.4 498.0 539.1 813.7 884.4 925.4 1200.0 1129.3: 70.7 345.3 386.3 457.0 498.0 772.6 843.3 884.4 1158.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 274.5824 cents 9375/8192, 233.5236 cents 128/125, 41.0589 cents 2: 111.7313 .. 345.2549 cents 9375/8192, 233.5236 cents 1024/1125,-162.8511 cents 3: 152.7901 .. 386.3137 cents 9375/8192, 233.5236 cents 1048576/1171875,-192.4647 cents 4: 427.3726 .. 660.8961 cents 9375/8192, 233.5236 cents 128/125, 41.0589 cents 5: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 1024/1125,-162.8511 cents 6: 539.1039 .. 772.6274 cents 9375/8192, 233.5236 cents 1024/1125,-162.8511 cents 7: 813.6863 .. 1047.2099 cents 9375/8192, 233.5236 cents 128/125, 41.0589 cents 8: 854.7451 .. 1088.2687 cents 9375/8192, 233.5236 cents 1048576/1171875,-192.4647 cents 9: 925.4176 .. 1158.9411 cents 9375/8192, 233.5236 cents 1024/1125,-162.8511 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 128/125, 41.0589 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 75/64, 274.5824 cents Average / Smallest step : 2.922634 Largest / Average step : 2.288187 Largest / Smallest step : 6.687532 Median interval of one step : 25/24, 70.6724 cents, amount: 3 Most common interval of one step : 128/125, 41.0589 cents, amount: 4 Least squares average step : 125.93698 cents, oct.: 1259.36982 cents Scale is not proper Scale is 3-distributional even Step pattern alph. order: ABCBACBABC Step pattern size order : LSMSLMSLSM Scale is a Constant Structure, by a margin of 11.44529 cents Scale diversity : 1.281110 Lumma stability : 0.136863 Lumma impropriety factor : 0.559131 Rothenberg efficiency : 0.526429 redundancy: 0.473571 Efficiency x scale size : 5.264286 Number of different interval sizes : 26 = 2.88889 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.88889 = 26/9 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 393216/390625, 11.4453 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 8 Most common triad is 0.0 386.314 813.686 cents, amount: 6 Number of recognisable fifths : 5, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale is a complete genus musicum : 2^m 3^1 5^4 Scale contains a complete diamond : 1 5 25 Formal octave complements present : 5 = 50.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 4 and 5 combined Scale is differentially coherent in interval class 5 Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 7-8 -- Rational properties -- Prime limit : 5 Odd number limit : 1875 (O: 1875 U: 1875) Highest odd numerator or denominator: 75 Scale harmonicity : 0.025467 Average absolute harmonicity : 0.189402 Specific harmonicity : 0.135225 Fundamental : 1/1600, -10.6439 octaves, 0.1635 Hz. Guide tone : 2400, 11.2288 octaves, 627901.357 Hz. Exponens Consonantiae : 3.840000E+06, 21.87267 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 187.0, average 18.70000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.81900, average 0.98190 Sum of Tenney's harmonic distance : 19.80415, average 1.98041 Vogel's harmonic complexity : 17.30000 Wille's k value : 937 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 252.02334, average 4.58224 Lattice compactness (without 2's) : 104.92600, average 1.90775 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 5 -0.20000 30 1 3: 0 .. 1 0.50000 5 1 5: -2 .. 2 0.00000 12 8 Average exponent except 2's : 5 / 10 = 0.50000 Average absolute exponent except 2's: 17 / 10 = 1.70000 Scale is weakly epimorphic with val: <10 15 21| Scale is weakly epimorphic with val: <10 15 22| Scale is JI-epimorphic with val: <10 15 23| Scale is weakly epimorphic with val: <10 15 24| Scale is weakly epimorphic with val: <10 17 22| Scale is weakly epimorphic with val: <10 17 24|
FIT/MODE
10: 2 1 0 1 2 0 1 2 0 1 N T3 SD: 35.9374 c. M:-52.6274 c. 11: 2 1 0 1 2 1 0 3 0 1 N SD: 36.3310 c. M: 59.0410 c. 12: 3 0 1 0 3 1 0 3 0 1 N D3 SD: 19.4046 c. M: 29.3276 c. 17: 4 0 1 1 4 1 0 4 1 1 N SD: 21.3991 c. M: 37.2157 c. 18: 4 1 1 0 5 1 0 4 1 1 N SD: 19.2772 c. M:-31.3783 c. 19: 4 1 1 1 4 1 1 4 1 1 N M DE SD: 11.6007 c. M: 21.9508 c. Magic-10 22: 5 1 1 1 5 1 1 5 1 1 N M DE SD: 8.1167 c. M:-16.1270 c. Magic-10 31: 7 1 2 1 7 2 1 7 1 2 N D3 SD: 3.8271 c. M: 6.7469 c. 53: 12 2 3 2 12 3 2 12 2 3 N D3 SD: 1.9919 c. M: 2.8843 c. 65: 15 2 4 2 15 4 2 15 2 4 N D3 SD: 1.9717 c. M: 3.1737 c. 84: 19 3 5 3 19 5 3 19 3 5 N D3 SD: 1.6216 c. M: 3.1539 c. 87: 20 3 5 3 20 5 3 20 3 5 N D3 SD: 1.0667 c. M:-1.7069 c. 118: 27 4 7 4 27 7 4 27 4 7 N D3 SD: 0.2570 c. M: 0.5140 c. 323: 74 11 19 11 74 19 11 74 11 19 N D3 SD: 0.1752 c. M:-0.3402 c. 441: 101 15 26 15 101 26 15 101 15 26 N D3 SD: 0.1294 c. M:-0.2475 c. 494: 113 17 29 17 113 29 17 113 17 29 N D3 SD: 0.1219 c. M:-0.2271 c. 559: 128 19 33 19 128 33 19 128 19 33 N D3 SD: 0.1284 c. M:-0.1940 c. 612: 140 21 36 21 140 36 21 140 21 36 N D3 SD: 0.0556 c. M:-0.0842 c. 730: 167 25 43 25 167 43 25 167 25 43 N D3 SD: 0.0316 c. M: 0.0619 c. 1053: 241 36 62 36 241 62 36 241 36 62 N D3 SD: 0.0319 c. M:-0.0614 c. 1171: 268 40 69 40 268 69 40 268 40 69 N D3 SD: 0.0328 c. M:-0.0546 c. 1665: 381 57 98 57 381 98 57 381 57 98 N D3 SD: 0.0218 c. M:-0.0418 c. 1783: 408 61 105 61 408 105 61 408 61 105 N D3 SD: 0.0060 c. M:-0.0110 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x 4 x x 5 x x 6 S SD: 33.3153 cents 4 x x 5 x 6 x x x x 8 S SD: 0.0000 cents 5 x 6 x x x x 8:9 x 10 S SD: 17.6681 cents 6:7 x x 8:9 x 10:11 x 12 S SD: 17.9214 cents 7:8 x x 9 x 11 x 13 x 14 SD: 9.6240 cents 8:9 x 10 x 12 x 13:15 x 16 SD: 12.5997 cents 9 x 11 x 12 x 14 x 17 x 18 SD: 15.7815 cents 10 x 12 x 13:15 x 16 x 19:20 SD: 5.3983 cents 11:13 x x 14 x 17:18 x 21:22 SD: 7.9632 cents 12:14 x 15 x 18 x 19 x 23:24 SD: 3.3214 cents 13:15 x 16:17 x 20:21:24:25:26 SD: 8.4197 cents 14:16:17 x 18:21:22 x 26:27:28 SD: 6.6082 cents 15 x 18 x 19 x 23:24:28:29:30 SD: 5.7068 cents 16 x 19:20 x 24:25:26:30:31:32 SD: 4.4997 cents 17:20 x 21:22:26 x 27:32:33:34 SD: 6.2827 cents 18:21:22 x 23:27:28:29:34:35:36 SD: 4.8732 cents 19:22:23:24 x 29:30 x 36 x 38 SD: 7.2179 cents 20:23:24:25:26:30:31:32 x 38:40 SD: 5.3364 cents 21 x 25:26:27:32:33:34:39:40:42 SD: 5.2698 cents 22:26 x x 28:33:34:35:41:42:44 SD: 3.9077 cents 23:27:28:29 x 35:36:37:43:44:46 SD: 4.4950 cents 24:28:29:30:31:36 x 38:45:46:48 SD: 3.1179 cents 26:30:31 x 33:39:41:42:49:50:52 SD: 4.5433 cents 27:32 x 34:35:41:42:43:51:52:54 SD: 4.7038 cents 28:33:34:35:36:42:44:45:53:54:56 SD: 3.2590 cents 30:35:36 x 38:45:47:48:56:58:60 SD: 2.7496 cents 32 x 38:40:41:48:50:51:60:61:64 SD: 2.5633 cents 35:41:42:44:45:53:55:56:66:67:70 SD: 2.5451 cents 36:42:43:45:46:54:56:58:68:69:72 SD: 2.2547 cents 40:47:48:50:51:60:63:64:75:77:80 SD: 1.6665 cents 60:70:72:75:77:90:94:96:113:115:120 SD: 1.3000 cents 64:75:77:80:82:96:100:102:120:123:128 SD: 0.8479 cents 100:117:120:125:128:150:156:160:188:192:200 SD: 0.6052 cents 128:150:154:160:164:192:200:205:240:246:256 SD: 0.5370 cents 140:164:168:175:179:210:219:224:263:269:280 SD: 0.4538 cents 176:206:211:220:225:264:275:282:330:338:352 SD: 0.4236 cents 192:225:230:240:246:288:300:307:360:369:384 SD: 0.4004 cents 200:234:240:250:256:300:313:320:375:384:400 SD: 0.3917 cents 210:246:252:263:269:315:328:336:394:403:420 SD: 0.3915 cents 215:252:258:269:275:323:336:344:403:413:430 SD: 0.3545 cents 240:281:288:300:307:360:375:384:450:461:480 SD: 0.2051 cents 320:375:384:400:410:480:500:512:600:614:640 SD: 0.2031 cents 336:394:403:420:430:504:525:538:630:645:672 SD: 0.1952 cents 360:422:432:450:461:540:563:576:675:691:720 SD: 0.1856 cents 400:469:480:500:512:600:625:640:750:768:800 SD: 0.0923 cents 560:656:672:700:717:840:875:896:1050:1075:1120 SD: 0.0879 cents