Scala analysis: glamma
Glamma = reca1c2, <12 19 27 34|-epimorphic
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: 10/7 617.487807 Euler's tritone 7: 35/24 653.184619 septimal semi-diminished fifth 8: 3/2 701.955001 perfect fifth 9: 5/3 884.358713 major sixth, BP sixth 10: 12/7 933.129094 septimal major sixth 11: 7/4 968.825906 harmonic seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 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: 8/7 231.1741 septimal whole tone 7: 49/48 35.6968 slendro diesis, septimal 1/6-tone 8: 36/35 48.7704 septimal diesis, 1/4-tone 9: 10/9 182.4037 minor whole tone 10: 36/35 48.7704 septimal diesis, 1/4-tone 11: 49/48 35.6968 slendro diesis, septimal 1/6-tone 12: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 256/245 76.034 cents septimal minor semitone 1: 2 21/20 84.467 cents minor semitone 1: 1 10/9 182.404 cents minor whole tone 1: 2 8/7 231.174 cents septimal whole tone 2: 2 21/20 84.467 cents minor semitone 2: 2 35/32 155.140 cents septimal neutral second 2: 2 192/175 160.502 cents septimal 4/5-tone 2: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 2 25/21 301.847 cents BP second, quasi-equal minor third 3: 2 8/7 231.174 cents septimal whole tone 3: 1 144/125 244.969 cents classic diminished third 3: 2 7/6 266.871 cents septimal minor third 3: 1 288/245 279.944 cents 3: 2 6/5 315.641 cents minor third 3: 2 175/144 337.543 cents 3: 2 5/4 386.314 cents major third 4: 4 6/5 315.641 cents minor third 4: 2 5/4 386.314 cents major third 4: 2 245/192 422.011 cents 4: 2 64/49 462.348 cents 2 septatones or septatonic major third 4: 2 4/3 498.045 cents perfect fourth 5: 1 49/40 351.338 cents larger approximation to neutral third 5: 1 5/4 386.314 cents major third 5: 2 21/16 470.781 cents narrow fourth 5: 2 4/3 498.045 cents perfect fourth 5: 4 48/35 546.815 cents septimal semi-augmented fourth 5: 2 25/18 568.717 cents classic augmented fourth 6: 2 48/35 546.815 cents septimal semi-augmented fourth 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 35/24 653.185 cents septimal semi-diminished fifth 7: 2 36/25 631.283 cents classic diminished fifth 7: 4 35/24 653.185 cents septimal semi-diminished fifth 7: 2 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 7: 1 8/5 813.686 cents minor sixth 7: 1 80/49 848.662 cents smaller approximation to neutral sixth 8: 2 3/2 701.955 cents perfect fifth 8: 2 49/32 737.652 cents 8: 2 384/245 777.989 cents 8: 2 8/5 813.686 cents minor sixth 8: 4 5/3 884.359 cents major sixth, BP sixth 9: 2 8/5 813.686 cents minor sixth 9: 2 288/175 862.457 cents 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 245/144 920.056 cents 9: 2 12/7 933.129 cents septimal major sixth 9: 1 125/72 955.031 cents classic augmented sixth 9: 2 7/4 968.826 cents harmonic seventh 10: 2 42/25 898.153 cents quasi-equal major sixth 10: 2 12/7 933.129 cents septimal major sixth 10: 2 7/4 968.826 cents harmonic seventh 10: 2 175/96 1039.498 cents 10: 2 64/35 1044.860 cents septimal neutral seventh 10: 2 40/21 1115.533 cents acute major seventh 11: 2 7/4 968.826 cents harmonic seventh 11: 1 9/5 1017.596 cents just minor seventh, BP seventh 11: 2 40/21 1115.533 cents acute major seventh 11: 1 245/128 1123.966 cents 11: 2 48/25 1129.328 cents classic diminished octave 11: 2 35/18 1151.230 cents septimal semi-diminished octave 11: 2 96/49 1164.303 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 70.7 155.1 231.2 315.6 386.3 617.5 653.2 702.0 884.4 933.1 968.8 1200.0 70.7 : 84.5 160.5 245.0 315.6 546.8 582.5 631.3 813.7 862.5 898.2 1129.3 1200.0 155.1 : 76.0 160.5 231.2 462.3 498.0 546.8 729.2 778.0 813.7 1044.9 1115.5 1200.0 231.2 : 84.5 155.1 386.3 422.0 470.8 653.2 702.0 737.7 968.8 1039.5 1124.0 1200.0 315.6 : 70.7 301.8 337.5 386.3 568.7 617.5 653.2 884.4 955.0 1039.5 1115.5 1200.0 386.3 : 231.2 266.9 315.6 498.0 546.8 582.5 813.7 884.4 968.8 1044.9 1129.3 1200.0 617.5 : 35.7 84.5 266.9 315.6 351.3 582.5 653.2 737.7 813.7 898.2 968.8 1200.0 653.2 : 48.8 231.2 279.9 315.6 546.8 617.5 702.0 778.0 862.5 933.1 1164.3 1200.0 702.0 : 182.4 231.2 266.9 498.0 568.7 653.2 729.2 813.7 884.4 1115.5 1151.2 1200.0 884.4 : 48.8 84.5 315.6 386.3 470.8 546.8 631.3 702.0 933.1 968.8 1017.6 1200.0 933.1 : 35.7 266.9 337.5 422.0 498.0 582.5 653.2 884.4 920.1 968.8 1151.2 1200.0 968.8 : 231.2 301.8 386.3 462.3 546.8 617.5 848.7 884.4 933.1 1115.5 1164.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 231.1741 cents 384/343, 195.4773 cents 49/48, 35.6968 cents 2: 84.4672 .. 301.8465 cents 500/441, 217.3793 cents 147/160,-146.7069 cents 3: 231.1741 .. 386.3137 cents 35/32, 155.1396 cents 24/25,-70.6724 cents 4: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 24/25,-70.6724 cents 5: 351.3381 .. 568.7174 cents 500/441, 217.3793 cents 147/160,-146.7069 cents 6: 546.8154 .. 653.1846 cents 1225/1152, 106.3692 cents 864/875,-21.9020 cents 7: 631.2826 .. 848.6619 cents 500/441, 217.3793 cents 864/875,-21.9020 cents 8: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 147/160,-146.7069 cents 9: 813.6863 .. 968.8259 cents 35/32, 155.1396 cents 24/25,-70.6724 cents 10: 898.1535 .. 1115.5328 cents 500/441, 217.3793 cents 24/25,-70.6724 cents 11: 968.8259 .. 1164.3032 cents 384/343, 195.4773 cents 147/160,-146.7069 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.801371 Largest / Average step : 2.311741 Largest / Smallest step : 6.476043 Median interval of one step : 73.35345 cents, amount: 0 Least squares average step : 93.09088 cents, oct.: 1117.09054 cents Scale is not proper Step pattern alph. order: ABCBADEFGFED Step pattern size order : CEDECGABFBAG Scale is not a Constant Structure Scale diversity : 1.428531 Lumma stability : 0.059495 Lumma impropriety factor : 0.702808 Rothenberg efficiency : 0.310853 redundancy: 0.689147 Efficiency x scale size : 3.730231 Number of different interval sizes : 48 = 4.36364 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.00000 = 6 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 6144/6125, 5.3620 cents Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 3 5 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 41.6667% Scale is n-1 differentially coherent in interval class 1 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 Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties -- Prime limit : 7 Odd number limit : 245 (O: 245 U: 245) Highest odd numerator or denominator: 35 Scale harmonicity : 0.018831 Average absolute harmonicity : 0.168874 Specific harmonicity : 0.119897 Fundamental : 1/3360, -11.7142 octaves, 0.0779 Hz. Guide tone : 4200, 12.0362 octaves, 1098827.374 Hz. Exponens Consonantiae : 1.411200E+07, 23.75042 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 136.5, average 11.37500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.44050, average 0.87004 Sum of Tenney's harmonic distance : 20.74980, average 1.72915 Vogel's harmonic complexity : 21.83333 Wille's k value : 1837 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 259.11698, average 3.32201 Lattice compactness (without 2's) : 130.32634, average 1.67085 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -0.66667 24 1 3: -1 .. 1 0.00000 6 1 5: -1 .. 2 0.50000 8 4 7: -1 .. 1 0.00000 6 6 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 20 / 12 = 1.66667 Scale is weakly epimorphic with val: <12 17 25 34| Scale is weakly epimorphic with val: <12 17 27 32| Scale is weakly epimorphic with val: <12 17 31 37| Scale is weakly epimorphic with val: <12 18 29 34| Scale is weakly epimorphic with val: <12 19 27 34| Scale is weakly epimorphic with val: <12 19 29 32| Scale is weakly epimorphic with val: <12 19 29 35| Scale is weakly epimorphic with val: <12 20 25 33| Scale is weakly epimorphic with val: <12 20 27 35| Scale is weakly epimorphic with val: <12 20 29 37| Scale is weakly epimorphic with val: <12 21 29 34| Scale is weakly epimorphic with val: <12 21 31 32|
FIT/MODE
12: 1 1 0 1 1 2 1 0 2 0 1 2 N T3 SD: 27.5253 c. M:-46.8154 c. 14: 1 1 1 1 1 2 1 0 2 1 0 3 N SD: 23.8570 c. M:-42.2577 c. 15: 1 1 1 1 1 3 0 1 2 1 0 3 N SD: 13.6016 c. M:-26.8709 c. 22: 1 2 1 2 1 4 1 1 3 1 1 4 N SD: 10.6206 c. M: 17.4878 c. 26: 1 2 2 2 1 5 1 1 4 1 1 5 N SD: 12.3539 c. M: 24.5186 c. 27: 2 2 1 2 2 5 1 1 4 1 1 5 N SD: 11.2584 c. M:-22.6382 c. 30: 2 2 2 2 2 5 1 2 4 1 1 6 N SD: 11.0657 c. M:-18.0450 c. 31: 2 2 2 2 2 6 1 1 5 1 1 6 N SD: 3.9857 c. M:-6.7469 c. 46: 3 3 3 3 3 9 1 2 7 2 1 9 N SD: 4.4782 c. M:-8.5991 c. 53: 3 4 3 4 3 10 2 2 8 2 2 10 N SD: 3.4482 c. M: 6.1671 c. 68: 4 5 4 5 4 13 2 3 10 3 2 13 N SD: 2.0761 c. M:-3.9274 c. 99: 6 7 6 7 6 19 3 4 15 4 3 19 N SD: 1.2293 c. M:-2.4361 c. 140: 8 10 9 10 8 27 4 6 21 6 4 27 N SD: 1.1364 c. M: 2.1010 c. 171: 10 12 11 12 10 33 5 7 26 7 5 33 N SD: 0.3763 c. M: 0.7537 c. 270: 16 19 17 19 16 52 8 11 41 11 8 52 N SD: 0.2470 c. M:-0.4387 c. 441: 26 31 28 31 26 85 13 18 67 18 13 85 N SD: 0.1102 c. M:-0.2042 c. 935: 55 66 59 66 55 180 28 38 142 38 28 180 N SD: 0.1074 c. M: 0.1616 c. 1106: 65 78 70 78 65 213 33 45 168 45 33 213 N SD: 0.0771 c. M: 0.1480 c. 1137: 67 80 72 80 67 219 34 46 173 46 34 219 N SD: 0.0756 c. M: 0.1476 c. 1308: 77 92 83 92 77 252 39 53 199 53 39 252 N SD: 0.0637 c. M: 0.1201 c. 1376: 81 97 87 97 81 265 41 56 209 56 41 265 N SD: 0.0540 c. M:-0.0929 c. 1547: 91 109 98 109 91 298 46 63 235 63 46 298 N SD: 0.0446 c. M: 0.0842 c. 1578: 93 111 100 111 93 304 47 64 240 64 47 304 N SD: 0.0360 c. M: 0.0539 c. 1749: 103 123 111 123 103 337 52 71 266 71 52 337 N SD: 0.0398 c. M: 0.0796 c. 2019: 119 142 128 142 119 389 60 82 307 82 60 389 N SD: 0.0305 c. M:-0.0557 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 x 3 x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 37.2438 cents 4 x x x x 5 x x 6 x x 7:8 S SD: 0.0000 cents 5 x x x 6 x 7 x x 8 x 9:10 S SD: 18.5434 cents 6 x x 7 x 8 x x 9:10 x 11:12 S SD: 23.7138 cents 7 x x 8 x 9:10 x 11 x 12 x 14 S SD: 15.6921 cents 8 x x 9 x 10:11 x 12:13 x 14:16 S SD: 11.9889 cents 9 x 10 x 11 x x 13:14:15 x 16:18 SD: 11.7233 cents 10 x 11 x 12:13:14 x 15 x 17:18:20 SD: 11.5376 cents 11 x 12 x 13:14 x 16:17:18:19 x 22 SD: 9.3233 cents 12 x 13:14 x 15:17 x 18:20 x 21:24 SD: 5.2420 cents 13 x 14:15 x 16 x 19:20 x 22:23:26 SD: 8.3927 cents 14 x 15:16:17:18:20 x 21:23:24:25:28 SD: 7.6918 cents 15:16 x 17:18:19:21:22:23:25 x 26:30 SD: 7.3922 cents 16:17 x 18:19:20:23 x 24:27 x 28:32 SD: 5.9068 cents 17:18:19 x 20:21:24:25:26:28:29:30:34 SD: 7.1909 cents 18:19:20:21:22:23 x 26:27:30:31:32:36 SD: 7.0898 cents 19:20:21:22:23:24:27:28:29:32 x 33:38 SD: 5.4125 cents 20:21:22:23:24:25 x 29:30:33:34:35:40 SD: 2.8963 cents 25:26:27:29:30:31:36 x 38:42:43:44:50 SD: 4.4369 cents 26:27:28:30:31:33:37:38:39:43:45:46:52 SD: 4.3430 cents 27:28:30:31:32:34 x 39:41:45:46:47:54 SD: 4.4698 cents 28:29:31:32:34:35:40:41:42:47:48:49:56 SD: 2.8428 cents 35:36:38:40:42:44:50:51:53:58:60:61:70 SD: 2.8380 cents 40:42:44:46:48:50:57:58:60:67:69:70:80 SD: 2.2237 cents 44:46:48:50:53:55:63:64:66:73:75:77:88 SD: 1.6565 cents 56:58:61:64:67:70:80:82:84:93:96:98:112 SD: 1.3522 cents 64:67:70:73:77:80:91:93:96:107:110:112:128 SD: 1.3444 cents 72:75:79:82:86:90:103:105:108:120:123:126:144 SD: 1.0959 cents 76:79:83:87:91:95:109:111:114:127:130:133:152 SD: 0.9541 cents 96:100:105:110:115:120:137:140:144:160:165:168:192 SD: 0.6058 cents 120:125:131:137:144:150:171:175:180:200:206:210:240 SD: 0.5184 cents 140:146:153:160:168:175:200:204:210:233:240:245:280 SD: 0.3122 cents 216:225:236:247:259:270:309:315:324:360:370:378:432 SD: 0.3085 cents 224:233:245:256:269:280:320:327:336:373:384:392:448 SD: 0.3038 cents 244:254:267:279:293:305:349:356:366:407:418:427:488 SD: 0.2973 cents 264:275:289:302:317:330:377:385:396:440:453:462:528 SD: 0.2533 cents 288:300:315:329:346:360:411:420:432:480:494:504:576 SD: 0.2477 cents 308:321:337:352:370:385:440:449:462:513:528:539:616 SD: 0.2109 cents 336:350:368:384:403:420:480:490:504:560:576:588:672 SD: 0.2088 cents 360:375:394:411:432:450:514:525:540:600:617:630:720 SD: 0.1963 cents 364:379:398:416:437:455:520:531:546:607:624:637:728 SD: 0.1370 cents 480:500:525:549:576:600:686:700:720:800:823:840:960 SD: 0.1301 cents 504:525:551:576:605:630:720:735:756:840:864:882:1008 SD: 0.0810 cents