Scala analysis: even12a
first maximally even {15/14,16/15,21/20,25/24} scale
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: 35/32 155.139620 septimal neutral second 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 21/16 470.780907 narrow fourth 6: 45/32 590.223716 diatonic tritone 7: 3/2 701.955001 perfect fifth 8: 25/16 772.627428 classic augmented fifth 9: 105/64 857.094621 septimal neutral sixth 10: 7/4 968.825906 harmonic seventh 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 21/20 84.4672 minor semitone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 16/15 111.7313 minor diatonic semitone 4: 15/14 119.4428 major diatonic semitone 5: 21/20 84.4672 minor semitone 6: 15/14 119.4428 major diatonic semitone 7: 16/15 111.7313 minor diatonic semitone 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 21/20 84.4672 minor semitone 10: 16/15 111.7313 minor diatonic semitone 11: 15/14 119.4428 major diatonic semitone 12: 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: 4 16/15 111.731 cents minor diatonic semitone 1: 3 15/14 119.443 cents major diatonic semitone 2: 2 35/32 155.140 cents septimal neutral second 2: 2 10/9 182.404 cents minor whole tone 2: 2 28/25 196.198 cents middle second 2: 2 9/8 203.910 cents major whole tone 2: 4 8/7 231.174 cents septimal whole tone 3: 4 7/6 266.871 cents septimal minor third 3: 2 25/21 301.847 cents BP second, quasi-equal minor third 3: 4 6/5 315.641 cents minor third 3: 1 135/112 323.353 cents septimal wide minor third 3: 1 128/105 342.905 cents septimal neutral third 4: 2 56/45 378.602 cents septimal narrow major third 4: 6 5/4 386.314 cents major third 4: 2 32/25 427.373 cents classic diminished fourth 4: 2 9/7 435.084 cents septimal major third, BP third 5: 2 21/16 470.781 cents narrow fourth 5: 6 4/3 498.045 cents perfect fourth 5: 2 75/56 505.757 cents marvelous fourth 5: 1 168/125 511.840 cents 5: 1 48/35 546.815 cents septimal semi-augmented fourth 6: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 2 45/32 590.224 cents diatonic tritone 6: 2 64/45 609.776 cents 2nd tritone 6: 4 10/7 617.488 cents Euler's tritone 7: 1 35/24 653.185 cents septimal semi-diminished fifth 7: 1 125/84 688.160 cents 7: 2 112/75 694.243 cents marvelous fifth 7: 6 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 8: 2 14/9 764.916 cents septimal minor sixth 8: 2 25/16 772.627 cents classic augmented fifth 8: 6 8/5 813.686 cents minor sixth 8: 2 45/28 821.398 cents septimale wide minor sixth 9: 1 105/64 857.095 cents septimal neutral sixth 9: 1 224/135 876.647 cents narrow septimal major sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 2 42/25 898.153 cents quasi-equal major sixth 9: 4 12/7 933.129 cents septimal major sixth 10: 4 7/4 968.826 cents harmonic seventh 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 2 25/14 1003.802 cents middle minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 64/35 1044.860 cents septimal neutral seventh 11: 3 28/15 1080.557 cents grave major seventh 11: 4 15/8 1088.269 cents classic major seventh 11: 3 40/21 1115.533 cents acute major seventh 11: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.54545 = 50/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 84.5 155.1 266.9 386.3 470.8 590.2 702.0 772.6 857.1 968.8 1088.3 1200.0 84.5 : 70.7 182.4 301.8 386.3 505.8 617.5 688.2 772.6 884.4 1003.8 1115.5 1200.0 155.1 : 111.7 231.2 315.6 435.1 546.8 617.5 702.0 813.7 933.1 1044.9 1129.3 1200.0 266.9 : 119.4 203.9 323.4 435.1 505.8 590.2 702.0 821.4 933.1 1017.6 1088.3 1200.0 386.3 : 84.5 203.9 315.6 386.3 470.8 582.5 702.0 813.7 898.2 968.8 1080.6 1200.0 470.8 : 119.4 231.2 301.8 386.3 498.0 617.5 729.2 813.7 884.4 996.1 1115.5 1200.0 590.2 : 111.7 182.4 266.9 378.6 498.0 609.8 694.2 764.9 876.6 996.1 1080.6 1200.0 702.0 : 70.7 155.1 266.9 386.3 498.0 582.5 653.2 764.9 884.4 968.8 1088.3 1200.0 772.6 : 84.5 196.2 315.6 427.4 511.8 582.5 694.2 813.7 898.2 1017.6 1129.3 1200.0 857.1 : 111.7 231.2 342.9 427.4 498.0 609.8 729.2 813.7 933.1 1044.9 1115.5 1200.0 968.8 : 119.4 231.2 315.6 386.3 498.0 617.5 702.0 821.4 933.1 1003.8 1088.3 1200.0 1088.3: 111.7 196.2 266.9 378.6 498.0 582.5 702.0 813.7 884.4 968.8 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 119.4428 cents 36/35, 48.7704 cents 25/24, 70.6724 cents 2: 155.1396 .. 231.1741 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 3: 266.8709 .. 342.9054 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 4: 378.6022 .. 435.0841 cents 405/392, 56.4819 cents 49/48, 35.6968 cents 5: 470.7809 .. 546.8154 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 6: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 49/48, 35.6968 cents 7: 653.1846 .. 729.2191 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 8: 764.9159 .. 821.3978 cents 405/392, 56.4819 cents 49/48, 35.6968 cents 9: 857.0946 .. 933.1291 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 10: 968.8259 .. 1044.8604 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 11: 1080.5572 .. 1129.3276 cents 36/35, 48.7704 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 15/14, 119.4428 cents Average / Smallest step : 1.414979 Largest / Average step : 1.194428 Largest / Smallest step : 1.690091 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 : 97.69790 cents, oct.: 1172.37474 cents Scale is strictly proper Step pattern alph. order: ABCDADCBACDC Step pattern size order : BACDBDCABCDC Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.440723 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.415261 Rothenberg efficiency : 0.297499 redundancy: 0.702501 Efficiency x scale size : 3.569986 Number of different interval sizes : 50 = 4.54545 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.54545 = 50/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 3136/3125, 6.0832 cents Number of recognisable fifths : 9, average 698.7086 cents Number of appreciable fifths : 8, average 700.0271 cents Best fifths form a closed circle All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 5 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 1 = 8.3333% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 10-11 -- Rational properties -- Prime limit : 7 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 105 Scale harmonicity : 0.022479 Average absolute harmonicity : 0.161531 Specific harmonicity : 0.138026 Fundamental : 1/960, -9.9069 octaves, 0.2725 Hz. Guide tone : 3150, 11.6211 octaves, 824120.531 Hz. Exponens Consonantiae : 3.024000E+06, 21.52803 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 248.0, average 20.66667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.30323, average 1.10860 Sum of Tenney's harmonic distance : 25.31640, average 2.10970 Vogel's harmonic complexity : 18.66667 Wille's k value : 787 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 244.76407, average 3.13800 Lattice compactness (without 2's) : 126.18857, average 1.61780 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 1 -2.83333 36 1 3: -1 .. 2 0.50000 8 1 5: -1 .. 2 0.50000 8 4 7: 0 .. 1 0.50000 6 6 Average exponent except 2's : 18 / 12 = 1.50000 Average absolute exponent except 2's: 22 / 12 = 1.83333 Scale is JI-epimorphic with val: <12 19 28 34| = patent Scale is weakly epimorphic with val: <12 20 26 31| Scale is weakly epimorphic with val: <12 20 26 33| Scale is weakly epimorphic with val: <12 20 26 35| Scale is weakly epimorphic with val: <12 20 26 37|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 26.1268 c. M:-44.8604 c. Twelve-tone Chromatic (1/11-comma) 14: 1 1 1 2 0 2 1 1 1 1 2 1 P D3 SD: 21.6812 c. M:-42.2577 c. 15: 1 1 1 2 1 1 2 1 1 1 2 1 P D3 SD: 19.6548 c. M:-31.7313 c. 17: 1 1 2 1 2 1 2 1 1 2 1 2 P M ME SD: 18.9548 c. M: 33.3725 c. 18: 1 1 2 2 1 2 2 1 1 2 1 2 N D3 SD: 19.0530 c. M:-31.3783 c. 19: 1 1 2 2 1 2 2 1 1 2 2 2 P D3 SD: 20.5768 c. M: 36.0420 c. 20: 1 2 1 2 2 2 2 1 1 2 2 2 P D3 SD: 17.3930 c. M: 26.8709 c. 21: 1 2 2 2 1 2 2 2 1 2 2 2 SP B ME SD: 16.1243 c. M:-27.3726 c. August-12 22: 2 1 2 2 2 2 2 1 2 2 2 2 SP B ME SD: 12.1986 c. M:-24.6237 c. 24: 2 1 2 3 1 3 2 1 2 2 3 2 P T3 SD: 13.9201 c. M: 22.6274 c. 25: 2 1 3 2 2 2 3 1 2 2 3 2 P D3 SD: 11.9592 c. M:-21.1291 c. 26: 2 1 3 2 2 3 2 2 2 2 3 2 P T3 SD: 12.6521 c. M:-19.8285 c. 28: 2 2 2 3 2 3 2 2 2 3 2 3 SP B D3 SD: 10.3758 c. M:-16.8884 c. 31: 2 2 3 3 2 3 3 2 2 3 3 3 SP D3 SD: 4.8133 c. M: 9.5786 c. 53: 4 3 5 5 4 5 5 3 4 5 5 5 SP SD: 3.4356 c. M:-6.0988 c. 77: 5 5 7 8 5 8 7 5 5 7 8 7 SP SD: 3.2919 c. M:-6.5934 c. 84: 6 5 8 8 6 8 8 5 6 8 8 8 SP SD: 2.3455 c. M:-4.5577 c. 87: 6 5 8 9 6 9 8 5 6 8 9 8 SP SD: 2.3819 c. M: 4.8019 c. 99: 7 6 9 10 7 10 9 6 7 9 10 9 SP SD: 2.1829 c. M:-3.7157 c. 118: 8 7 11 12 8 12 11 7 8 11 12 11 SP SD: 1.9856 c. M: 3.1113 c. 130: 9 8 12 13 9 13 12 8 9 12 13 12 SP SD: 1.2490 c. M:-2.7572 c. 140: 10 8 13 14 10 14 13 8 10 13 14 13 SP SD: 0.8298 c. M:-1.2471 c. 171: 12 10 16 17 12 17 16 10 12 16 17 16 SP SD: 0.5500 c. M: 0.9543 c. 270: 19 16 25 27 19 27 25 16 19 25 27 25 SP SD: 0.4709 c. M:-0.8874 c. 301: 21 18 28 30 21 30 28 18 21 28 30 28 SP SD: 0.3852 c. M:-0.7945 c. 441: 31 26 41 44 31 44 41 26 31 41 44 41 SP SD: 0.1307 c. M:-0.2525 c. 612: 43 36 57 61 43 61 57 36 43 57 61 57 SP SD: 0.1477 c. M: 0.2377 c. 935: 66 55 87 93 66 93 87 55 66 87 93 87 SP SD: 0.1459 c. M:-0.2387 c. 966: 68 57 90 96 68 96 90 57 68 90 96 90 SP SD: 0.1010 c. M:-0.2098 c. 1053: 74 62 98 105 74 105 98 62 74 98 105 98 SP SD: 0.1129 c. M: 0.2042 c. 1106: 78 65 103 110 78 110 103 65 78 103 110 103 SP SD: 0.0732 c. M:-0.1621 c. 1407: 99 83 131 140 99 140 131 83 99 131 140 131 SP SD: 0.0494 c. M:-0.0843 c. 1547: 109 91 144 154 109 154 144 91 109 144 154 144 SP SD: 0.0468 c. M:-0.0835 c. 1848: 130 109 172 184 130 184 172 109 130 172 184 172 SP SD: 0.0446 c. M:-0.0998 c. 2019: 142 119 188 201 142 201 188 119 142 188 201 188 SP SD: 0.0327 c. M: 0.0690 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: 12.8524 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.0000 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 16.1275 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.1292 cents 7 x x 8 x 9:10 x 11 x 12:13:14 S SD: 10.0386 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.0687 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 9.2042 cents 10 x 11:12 x 13:14:15:16 x 18:19:20 S SD: 9.5581 cents 11 x 12:13:14 x 15 x 17:18:19:21:22 SD: 8.7464 cents 12 x 13:14:15:16:17:18:19:20:21:23:24 SD: 5.6758 cents 13 x 14:15:16:17:18 x 20:21:23:24:26 SD: 7.1324 cents 14:15 x 16 x 18:20:21:22:23:25:26:28 SD: 7.8203 cents 15:16 x 18:19:20:21 x 23:25:26:28:30 SD: 8.1191 cents 16:17:18:19:20:21:23:24:25:26:28:30:32 SD: 6.1574 cents 17:18:19:20:21:22:24:26:27:28:30:32:34 S SD: 5.9591 cents 19:20:21:22:24:25:27:29:30:31:33:36:38 SD: 4.5798 cents 20:21:22:23:25:26:28:30:31:33:35:38:40 SD: 3.6019 cents 25:26:27:29:31:33:35:38:39:41:44:47:50 SD: 3.5894 cents 32:34:35:37:40:42:45:48:50:53:56:60:64 SD: 2.5415 cents 36:38:39:42:45:47:51:54:56:59:63:68:72 SD: 2.4031 cents 41:43:45:48:51:54:58:62:64:67:72:77:82 SD: 2.0084 cents 42:44:46:49:53:55:59:63:66:69:74:79:84 SD: 2.0066 cents 44:46:48:51:55:58:62:66:69:72:77:83:88 SD: 1.7504 cents 55:58:60:64:69:72:77:83:86:90:96:103:110 SD: 1.6066 cents 60:63:66:70:75:79:84:90:94:98:105:113:120 SD: 1.5059 cents 61:64:67:71:76:80:86:92:95:100:107:114:122 SD: 1.4357 cents 64:67:70:75:80:84:90:96:100:105:112:120:128 SD: 0.7732 cents 96:101:105:112:120:126:135:144:150:158:168:180:192 SD: 0.5393 cents 128:134:140:149:160:168:180:192:200:210:224:240:256 SD: 0.5374 cents 140:147:153:163:175:184:197:210:219:230:245:263:280 SD: 0.5372 cents 160:168:175:187:200:210:225:240:250:263:280:300:320 SD: 0.3763 cents 180:189:197:210:225:236:253:270:281:295:315:338:360 SD: 0.3496 cents 192:202:210:224:240:252:270:288:300:315:336:360:384 SD: 0.2860 cents 256:269:280:299:320:336:360:384:400:420:448:480:512 SD: 0.1934 cents 320:336:350:373:400:420:450:480:500:525:560:600:640 SD: 0.1289 cents 384:403:420:448:480:504:540:576:600:630:672:720:768 SD: 0.0716 cents 576:605:630:672:720:756:810:864:900:945:1008:1080:1152 SD: 0.0477 cents