Scala analysis: deporcy
A 15-note chord-based detempering of 7-limit porcupine
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 35/32 155.139620 septimal neutral second 3: 8/7 231.174094 septimal whole tone 4: 6/5 315.641287 minor third 5: 5/4 386.313714 major third 6: 4/3 498.044999 perfect fourth 7: 48/35 546.815381 septimal semi-augmented fourth 8: 35/24 653.184619 septimal semi-diminished fifth 9: 3/2 701.955001 perfect fifth 10: 8/5 813.686286 minor sixth 11: 5/3 884.358713 major sixth, BP sixth 12: 7/4 968.825906 harmonic seventh 13: 64/35 1044.860380 septimal neutral seventh 14: 48/25 1129.327573 classic diminished octave 15: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 21/20 84.4672 minor semitone 3: 256/245 76.0345 septimal minor semitone 4: 21/20 84.4672 minor semitone 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 16/15 111.7313 minor diatonic semitone 7: 36/35 48.7704 septimal diesis, 1/4-tone 8: 1225/1152 106.3692 9: 36/35 48.7704 septimal diesis, 1/4-tone 10: 16/15 111.7313 minor diatonic semitone 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 21/20 84.4672 minor semitone 13: 256/245 76.0345 septimal minor semitone 14: 21/20 84.4672 minor semitone 15: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 4 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 256/245 76.034 cents septimal minor semitone 1: 4 21/20 84.467 cents minor semitone 1: 1 1225/1152 106.369 cents 1: 2 16/15 111.731 cents minor diatonic semitone 2: 1 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 2: 6 35/32 155.140 cents septimal neutral second 2: 6 192/175 160.502 cents septimal 4/5-tone 2: 2 10/9 182.404 cents minor whole tone 3: 1 9/8 203.910 cents major whole tone 3: 2 875/768 225.812 cents 3: 6 8/7 231.174 cents septimal whole tone 3: 2 144/125 244.969 cents classic diminished third 3: 4 7/6 266.871 cents septimal minor third 4: 2 25/21 301.847 cents BP second, quasi-equal minor third 4: 1 1225/1024 310.279 cents two (septimal neutral second) 4: 8 6/5 315.641 cents minor third 4: 2 175/144 337.543 cents 4: 2 128/105 342.905 cents septimal neutral third 5: 8 5/4 386.314 cents major third 5: 2 1536/1225 391.676 cents 5: 2 245/192 422.011 cents 5: 3 32/25 427.373 cents classic diminished fourth 6: 2 125/96 456.986 cents classic augmented third 6: 1 64/49 462.348 cents 2 septatones or septatonic major third 6: 4 21/16 470.781 cents narrow fourth 6: 2 1152/875 476.143 cents 6: 6 4/3 498.045 cents perfect fourth 7: 2 175/128 541.453 cents 7: 6 48/35 546.815 cents septimal semi-augmented fourth 7: 3 25/18 568.717 cents classic augmented fourth 7: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 8: 4 10/7 617.488 cents Euler's tritone 8: 3 36/25 631.283 cents classic diminished fifth 8: 6 35/24 653.185 cents septimal semi-diminished fifth 8: 2 256/175 658.547 cents 9: 6 3/2 701.955 cents perfect fifth 9: 2 875/576 723.857 cents 9: 4 32/21 729.219 cents wide fifth 9: 1 49/32 737.652 cents 9: 2 192/125 743.014 cents classic diminished sixth 10: 3 25/16 772.627 cents classic augmented fifth 10: 2 384/245 777.989 cents 10: 2 1225/768 808.324 cents 10: 8 8/5 813.686 cents minor sixth 11: 2 105/64 857.095 cents septimal neutral sixth 11: 2 288/175 862.457 cents 11: 8 5/3 884.359 cents major sixth, BP sixth 11: 1 2048/1225 889.721 cents 11: 2 42/25 898.153 cents quasi-equal major sixth 12: 4 12/7 933.129 cents septimal major sixth 12: 2 125/72 955.031 cents classic augmented sixth 12: 6 7/4 968.826 cents harmonic seventh 12: 2 1536/875 974.188 cents 12: 1 16/9 996.090 cents Pythagorean minor seventh 13: 2 9/5 1017.596 cents just minor seventh, BP seventh 13: 6 175/96 1039.498 cents 13: 6 64/35 1044.860 cents septimal neutral seventh 13: 1 1152/625 1058.655 cents 14: 2 15/8 1088.269 cents classic major seventh 14: 1 2304/1225 1093.631 cents two (septimal semi-augmented fourth) 14: 4 40/21 1115.533 cents acute major seventh 14: 2 245/128 1123.966 cents 14: 4 48/25 1129.328 cents classic diminished octave 14: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.71429 = 33/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 70.7 155.1 231.2 315.6 386.3 498.0 546.8 653.2 702.0 813.7 884.4 968.8 1044.9 1129.3 1200.0 70.7 : 84.5 160.5 245.0 315.6 427.4 476.1 582.5 631.3 743.0 813.7 898.2 974.2 1058.7 1129.3 1200.0 155.1 : 76.0 160.5 231.2 342.9 391.7 498.0 546.8 658.5 729.2 813.7 889.7 974.2 1044.9 1115.5 1200.0 231.2 : 84.5 155.1 266.9 315.6 422.0 470.8 582.5 653.2 737.7 813.7 898.2 968.8 1039.5 1124.0 1200.0 315.6 : 70.7 182.4 231.2 337.5 386.3 498.0 568.7 653.2 729.2 813.7 884.4 955.0 1039.5 1115.5 1200.0 386.3 : 111.7 160.5 266.9 315.6 427.4 498.0 582.5 658.5 743.0 813.7 884.4 968.8 1044.9 1129.3 1200.0 498.0 : 48.8 155.1 203.9 315.6 386.3 470.8 546.8 631.3 702.0 772.6 857.1 933.1 1017.6 1088.3 1200.0 546.8 : 106.4 155.1 266.9 337.5 422.0 498.0 582.5 653.2 723.9 808.3 884.4 968.8 1039.5 1151.2 1200.0 653.2 : 48.8 160.5 231.2 315.6 391.7 476.1 546.8 617.5 702.0 778.0 862.5 933.1 1044.9 1093.6 1200.0 702.0 : 111.7 182.4 266.9 342.9 427.4 498.0 568.7 653.2 729.2 813.7 884.4 996.1 1044.9 1151.2 1200.0 813.7 : 70.7 155.1 231.2 315.6 386.3 457.0 541.5 617.5 702.0 772.6 884.4 933.1 1039.5 1088.3 1200.0 884.4 : 84.5 160.5 245.0 315.6 386.3 470.8 546.8 631.3 702.0 813.7 862.5 968.8 1017.6 1129.3 1200.0 968.8 : 76.0 160.5 231.2 301.8 386.3 462.3 546.8 617.5 729.2 778.0 884.4 933.1 1044.9 1115.5 1200.0 1044.9: 84.5 155.1 225.8 310.3 386.3 470.8 541.5 653.2 702.0 808.3 857.1 968.8 1039.5 1124.0 1200.0 1129.3: 70.7 141.3 225.8 301.8 386.3 457.0 568.7 617.5 723.9 772.6 884.4 955.0 1039.5 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 111.7313 cents 28/27, 62.9609 cents 36/35, 48.7704 cents 2: 141.3449 .. 182.4037 cents 128/125, 41.0589 cents 3125/3072, 29.6136 cents 3: 203.9100 .. 266.8709 cents 28/27, 62.9609 cents 81/80, 21.5063 cents 4: 301.8465 .. 342.9054 cents 128/125, 41.0589 cents 50/49, 34.9756 cents 5: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 525/512, 43.4083 cents 6: 456.9861 .. 498.0450 cents 128/125, 41.0589 cents 3125/3072, 29.6136 cents 7: 541.4533 .. 582.5122 cents 128/125, 41.0589 cents 525/512, 43.4083 cents 8: 617.4878 .. 658.5467 cents 128/125, 41.0589 cents 50/49, 34.9756 cents 9: 701.9550 .. 743.0139 cents 128/125, 41.0589 cents 525/512, 43.4083 cents 10: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 3125/3072, 29.6136 cents 11: 857.0946 .. 898.1535 cents 128/125, 41.0589 cents 525/512, 43.4083 cents 12: 933.1291 .. 996.0900 cents 28/27, 62.9609 cents 50/49, 34.9756 cents 13: 1017.5963 .. 1058.6551 cents 128/125, 41.0589 cents 81/80, 21.5063 cents 14: 1088.2687 .. 1151.2296 cents 28/27, 62.9609 cents 3125/3072, 29.6136 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.640340 Largest / Average step : 1.396641 Largest / Smallest step : 2.290966 Median interval of one step : 256/245, 76.0345 cents, amount: 2 Least squares average step : 80.25173 cents, oct.: 1203.77598 cents Scale is strictly proper Step pattern alph. order: ABCBADEFEDABCBA Step pattern size order : BDCDBFAEAFBDCDB Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.404376 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.447973 Number of different interval sizes : 66 = 4.71429 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.71429 = 33/7 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 6144/6125, 5.3620 cents Number of recognisable fifths : 6, average 701.9550 cents Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 5 35 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 15 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 7-8 -- Rational properties -- Prime limit : 7 Odd number limit : 1225 (O: 1225 U: 1225) Highest odd numerator or denominator: 35 Scale harmonicity : 0.015999 Average absolute harmonicity : 0.157467 Specific harmonicity : 0.107279 Fundamental : 1/16800, -14.0362 octaves, 0.0156 Hz. Guide tone : 33600, 15.0362 octaves, 8790618.994 Hz. Exponens Consonantiae : 5.644800E+08, 29.07235 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 256.0, average 17.06667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.41247, average 0.96083 Sum of Tenney's harmonic distance : 29.31640, average 1.95443 Vogel's harmonic complexity : 25.53333 Wille's k value : 9187 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 501.67912, average 4.18066 Lattice compactness (without 2's) : 220.63241, average 1.83860 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 6 0.53333 40 1 3: -1 .. 1 0.00000 8 2 5: -2 .. 2 0.00000 12 6 7: -1 .. 1 0.00000 6 6 Average exponent except 2's : 0 / 15 = 0.00000 Average absolute exponent except 2's: 26 / 15 = 1.73333 Scale is weakly epimorphic with val: <15 22 33 40| Scale is weakly epimorphic with val: <15 22 35 41| Scale is weakly epimorphic with val: <15 22 36 43| Scale is weakly epimorphic with val: <15 23 33 41| Scale is weakly epimorphic with val: <15 23 36 44| Scale is JI-epimorphic with val: <15 24 35 42| = patent Scale is weakly epimorphic with val: <15 25 32 42| Scale is weakly epimorphic with val: <15 25 33 43| Scale is weakly epimorphic with val: <15 25 34 44| Scale is weakly epimorphic with val: <15 26 32 40| Scale is weakly epimorphic with val: <15 26 33 44| Scale is weakly epimorphic with val: <15 26 35 43|
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.9197 c. M:-18.0450 c. 22: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 P M ME I SD: 9.7252 c. M:-16.1270 c. 31: 2 2 2 2 2 3 1 3 1 3 2 2 2 2 2 P D3 I SD: 4.2209 c. M: 6.7469 c. 46: 3 3 3 3 3 4 2 4 2 4 3 3 3 3 3 SP D3 I SD: 3.8457 c. M: 7.5884 c. 53: 3 4 3 4 3 5 2 5 2 5 3 4 3 4 3 SP I SD: 2.7544 c. M:-4.7590 c. 68: 4 5 4 5 4 6 3 6 3 6 4 5 4 5 4 SP I SD: 2.3060 c. M:-3.9274 c. 84: 5 6 5 6 5 8 3 8 3 8 5 6 5 6 5 SP I SD: 2.0991 c. M: 3.9582 c. 99: 6 7 6 7 6 9 4 9 4 9 6 7 6 7 6 SP I SD: 1.4883 c. M:-2.4361 c. 140: 8 10 9 10 8 13 6 12 6 13 8 10 9 10 8 SP I SD: 1.2501 c. M: 2.1010 c. 156: 9 11 10 11 9 15 6 14 6 15 9 11 10 11 9 SP I SD: 1.2179 c. M: 1.9550 c. 171: 10 12 11 12 10 16 7 15 7 16 10 12 11 12 10 SP I SD: 0.4425 c. M: 0.7537 c. 270: 16 19 17 19 16 25 11 24 11 25 16 19 17 19 16 SP I SD: 0.2816 c. M:-0.4387 c. 441: 26 31 28 31 26 41 18 39 18 41 26 31 28 31 26 SP I SD: 0.0819 c. M:-0.1234 c. 1106: 65 78 70 78 65 103 45 98 45 103 65 78 70 78 65 SP I SD: 0.0733 c. M: 0.1480 c. 1137: 67 80 72 80 67 106 46 101 46 106 67 80 72 80 67 SP I SD: 0.0677 c. M:-0.1135 c. 1308: 77 92 83 92 77 122 53 116 53 122 77 92 83 92 77 SP I SD: 0.0662 c. M:-0.1201 c. 1376: 81 97 87 97 81 128 56 122 56 128 81 97 87 97 81 SP I SD: 0.0575 c. M:-0.0929 c. 1547: 91 109 98 109 91 144 63 137 63 144 91 109 98 109 91 SP I SD: 0.0476 c. M: 0.0842 c. 1578: 93 111 100 111 93 147 64 140 64 147 93 111 100 111 93 SP I SD: 0.0372 c. M:-0.0539 c. 2019: 119 142 128 142 119 188 82 179 82 188 119 142 128 142 119 SP I SD: 0.0297 c. M: 0.0557 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 0.0000 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 0.0000 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 0.0000 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 8.9835 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 5.9966 cents 7 x x 8 x 9 x x 10 x 11 x 12:13 x 14 S SD: 11.6239 cents 8 x x 9 x 10 x 11 x 12:13 x 14 x 15:16 S SD: 7.0377 cents 9 x 10 x 11 x 12 x 13 x 14:15:16 x 17:18 S SD: 8.5697 cents 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20 S SD: 7.4431 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 7.1562 cents 12 x 13:14 x 15:16 x x 18:19:20:21:22:23:24 S SD: 3.9696 cents 13 x 14:15 x 16:17:18:19:20:21:22:23:24:25:26 S SD: 6.2818 cents 14 x 15:16:17:18 x 19:20:21:22:23:25:26:27:28 SD: 7.4071 cents 15:16 x 17:18:19:20:21:22:23:24:25:26:27:29:30 SD: 5.7153 cents 16:17 x 18:19:20:21:22:23:24:26:27:28:29:31:32 SD: 5.1975 cents 17:18:19 x 20:21 x 23:25:26:27:28:30:31:33:34 SD: 6.3728 cents 18:19:20:21:22:23:24:25:26:27:29:30:32:33:35:36 SD: 5.6338 cents 19:20:21:22:23:24:25:26:28:29:30:32:33:35:36:38 SD: 4.8148 cents 20:21:22:23:24:25:27 x 29:30:32:33:35:37:38:40 SD: 3.1969 cents 24:25:26:27:29:30:32:33:35:36:38:40:42:44:46:48 SD: 2.6158 cents 35:36:38:40:42:44:47:48:51:53:56:58:61:64:67:70 SD: 2.4388 cents 40:42:44:46:48:50:53:55:58:60:64:67:70:73:77:80 SD: 1.8218 cents 48:50:53:55:58:60:64:66:70:72:77:80:84:88:92:96 SD: 1.4951 cents 63:66:69:72:76:79:84:86:92:95:101:105:110:115:121:126 SD: 1.3442 cents 64:67:70:73:77:80:85:88:93:96:102:107:112:117:123:128 SD: 1.1333 cents 72:75:79:82:86:90:96:99:105:108:115:120:126:132:138:144 SD: 0.9179 cents 75:78:82:86:90:94:100:103:109:113:120:125:131:137:144:150 SD: 0.8864 cents 76:79:83:87:91:95:101:104:111:114:122:127:133:139:146:152 SD: 0.8177 cents 96:100:105:110:115:120:128:132:140:144:154:160:168:176:184:192 SD: 0.6640 cents 116:121:127:133:139:145:155:159:169:174:186:193:203:212:223:232 SD: 0.6398 cents 120:125:131:137:144:150:160:165:175:180:192:200:210:219:230:240 SD: 0.4941 cents 140:146:153:160:168:175:187:192:204:210:224:233:245:256:269:280 SD: 0.3349 cents 216:225:236:247:259:270:288:296:315:324:346:360:378:395:415:432 SD: 0.2434 cents 264:275:289:302:317:330:352:362:385:396:422:440:462:483:507:528 SD: 0.2098 cents 288:300:315:329:346:360:384:395:420:432:461:480:504:527:553:576 SD: 0.1721 cents 360:375:394:411:432:450:480:494:525:540:576:600:630:658:691:720 SD: 0.1671 cents 384:400:420:439:461:480:512:527:560:576:614:640:672:702:737:768 SD: 0.1375 cents 460:479:503:526:552:575:613:631:671:690:736:767:805:841:883:920 SD: 0.1241 cents 480:500:525:549:576:600:640:658:700:720:768:800:840:878:922:960 SD: 0.1206 cents 504:525:551:576:605:630:672:691:735:756:806:840:882:922:968:1008 SD: 0.1121 cents 552:575:604:631:662:690:736:757:805:828:883:920:966:1009:1060:1104 SD: 0.1031 cents 576:600:630:658:691:720:768:790:840:864:922:960:1008:1053:1106:1152 SD: 0.0841 cents 600:625:656:686:720:750:800:823:875:900:960:1000:1050:1097:1152:1200 SD: 0.0698 cents