Scala analysis: abacbadabc
7-limit scale with mean variety four
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 8/7 231.174094 septimal whole tone 3: 128/105 342.905379 septimal neutral third 4: 4/3 498.044999 perfect fourth 5: 10/7 617.487807 Euler's tritone 6: 32/21 729.219093 wide fifth 7: 8/5 813.686286 minor sixth 8: 128/75 925.417571 diminished seventh 9: 64/35 1044.860380 septimal neutral seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 35/32 155.1396 septimal neutral second 1: 16/15 111.7313 minor diatonic semitone 2: 15/14 119.4428 major diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 35/32 155.1396 septimal neutral second 5: 15/14 119.4428 major diatonic semitone 6: 16/15 111.7313 minor diatonic semitone 7: 21/20 84.4672 minor semitone 8: 16/15 111.7313 minor diatonic semitone 9: 15/14 119.4428 major diatonic semitone 10: 35/32 155.1396 septimal neutral second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 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 1: 2 35/32 155.140 cents septimal neutral second 2: 2 28/25 196.198 cents middle second 2: 4 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 2 75/64 274.582 cents classic augmented second 3: 1 448/375 307.930 cents 3: 2 6/5 315.641 cents minor third 3: 1 128/105 342.905 cents septimal neutral third 3: 6 5/4 386.314 cents major third 4: 2 32/25 427.373 cents classic diminished fourth 4: 2 21/16 470.781 cents narrow fourth 4: 4 4/3 498.045 cents perfect fourth 4: 2 75/56 505.757 cents marvelous fourth 5: 1 48/35 546.815 cents septimal semi-augmented fourth 5: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 4 10/7 617.488 cents Euler's tritone 5: 1 35/24 653.185 cents septimal semi-diminished fifth 6: 2 112/75 694.243 cents marvelous fifth 6: 4 3/2 701.955 cents perfect fifth 6: 2 32/21 729.219 cents wide fifth 6: 2 25/16 772.627 cents classic augmented fifth 7: 6 8/5 813.686 cents minor sixth 7: 1 105/64 857.095 cents septimal neutral sixth 7: 2 5/3 884.359 cents major sixth, BP sixth 7: 1 375/224 892.070 cents 8: 2 128/75 925.418 cents diminished seventh 8: 2 12/7 933.129 cents septimal major sixth 8: 4 7/4 968.826 cents harmonic seventh 8: 2 25/14 1003.802 cents middle minor seventh 9: 2 64/35 1044.860 cents septimal neutral seventh 9: 3 28/15 1080.557 cents grave major seventh 9: 4 15/8 1088.269 cents classic major seventh 9: 1 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 111.7 231.2 342.9 498.0 617.5 729.2 813.7 925.4 1044.9 1200.0 111.7 : 119.4 231.2 386.3 505.8 617.5 702.0 813.7 933.1 1088.3 1200.0 231.2 : 111.7 266.9 386.3 498.0 582.5 694.2 813.7 968.8 1080.6 1200.0 342.9 : 155.1 274.6 386.3 470.8 582.5 702.0 857.1 968.8 1088.3 1200.0 498.0 : 119.4 231.2 315.6 427.4 546.8 702.0 813.7 933.1 1044.9 1200.0 617.5 : 111.7 196.2 307.9 427.4 582.5 694.2 813.7 925.4 1080.6 1200.0 729.2 : 84.5 196.2 315.6 470.8 582.5 702.0 813.7 968.8 1088.3 1200.0 813.7 : 111.7 231.2 386.3 498.0 617.5 729.2 884.4 1003.8 1115.5 1200.0 925.4 : 119.4 274.6 386.3 505.8 617.5 772.6 892.1 1003.8 1088.3 1200.0 1044.9: 155.1 266.9 386.3 498.0 653.2 772.6 884.4 968.8 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 155.1396 cents 25/24, 70.6724 cents 21/20, 84.4672 cents 2: 196.1985 .. 274.5824 cents 1875/1792, 78.3839 cents 128/125, 41.0589 cents 3: 307.9298 .. 386.3137 cents 1875/1792, 78.3839 cents 28672/28125, 33.3473 cents 4: 427.3726 .. 505.7565 cents 1875/1792, 78.3839 cents 128/125, 41.0589 cents 5: 546.8154 .. 653.1846 cents 1225/1152, 106.3692 cents 128/125, 41.0589 cents 6: 694.2435 .. 772.6274 cents 1875/1792, 78.3839 cents 128/125, 41.0589 cents 7: 813.6863 .. 892.0702 cents 1875/1792, 78.3839 cents 128/125, 41.0589 cents 8: 925.4176 .. 1003.8015 cents 1875/1792, 78.3839 cents 28672/28125, 33.3473 cents 9: 1044.8604 .. 1115.5328 cents 25/24, 70.6724 cents 128/125, 41.0589 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 35/32, 155.1396 cents Average / Smallest step : 1.420670 Largest / Average step : 1.292830 Largest / Smallest step : 1.836685 Median interval of one step : 115.58705 cents, amount: 0 Most common interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 118.33927 cents, oct.: 1183.39265 cents Scale is strictly proper Step pattern alph. order: ABACBADABC Step pattern size order : BCBDCBABCD Scale is a Constant Structure, by a margin of 33.34734 cents Scale diversity : 1.455960 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.401652 Rothenberg efficiency : 0.366587 redundancy: 0.633413 Efficiency x scale size : 3.665873 Number of different interval sizes : 36 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 6 Most common triad is 0.0 386.314 813.686 cents, amount: 2 Number of recognisable fifths : 6, average 699.3845 cents Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 10.0000% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 6-7 -- Rational properties -- Prime limit : 7 Odd number limit : 375 (O: 375 U: 375) Highest odd numerator or denominator: 105 Scale harmonicity : 0.025541 Average absolute harmonicity : 0.171125 Specific harmonicity : 0.138989 Fundamental : 1/525, -9.0362 octaves, 0.4983 Hz. Guide tone : 640, 9.3219 octaves, 167440.362 Hz. Exponens Consonantiae : 3.360000E+05, 18.35810 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 337.0, average 33.70000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.80492, average 1.08049 Sum of Tenney's harmonic distance : 23.24406, average 2.32441 Vogel's harmonic complexity : 16.40000 Wille's k value : 262 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 187.71364, average 3.41298 Lattice compactness (without 2's) : 80.80457, average 1.46917 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 7 3.90000 39 1 3: -1 .. 0 -0.50000 5 1 5: -2 .. 1 -0.50000 7 3 7: -1 .. 0 -0.50000 5 5 Average exponent except 2's :-15 / 10 =-1.50000 Average absolute exponent except 2's: 17 / 10 = 1.70000 Scale is weakly epimorphic with val: <10 15 22 26| Scale is weakly epimorphic with val: <10 15 23 29| Scale is JI-epimorphic with val: <10 16 23 28| = patent Scale is weakly epimorphic with val: <10 17 21 25| Scale is weakly epimorphic with val: <10 17 22 26| Scale is weakly epimorphic with val: <10 18 24 25| Scale is weakly epimorphic with val: <10 18 24 27| Scale is weakly epimorphic with val: <10 18 24 29| Scale is weakly epimorphic with val: <10 18 24 31|
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 20.6835 c. M:-35.1396 c. 17: 2 1 2 2 2 1 2 1 2 2 P D3 SD: 18.9490 c. M:-33.3725 c. 21: 2 2 2 3 2 2 1 2 2 3 P SD: 10.7818 c. M: 16.2890 c. 22: 2 2 2 3 2 2 2 2 2 3 SP D3 SD: 11.3044 c. M: 20.1282 c. Standard Pentachordal Minor 25: 2 3 2 3 3 2 2 2 3 3 P D3 SD: 10.6562 c. M: 18.0450 c. 31: 3 3 3 4 3 3 2 3 3 4 SP SD: 3.6593 c. M:-6.2648 c. 53: 5 5 5 7 5 5 4 5 5 7 SP SD: 3.4231 c. M: 6.1671 c. 56: 5 6 5 7 6 5 4 5 6 7 SP SD: 3.5668 c. M: 5.1879 c. 74: 7 7 7 10 7 7 5 7 7 10 SP SD: 3.2912 c. M: 7.0225 c. 77: 7 8 7 10 8 7 5 7 8 10 SP SD: 3.2553 c. M: 5.9371 c. 84: 8 8 8 11 8 8 6 8 8 11 SP SD: 2.0522 c. M: 3.2021 c. 87: 8 9 8 11 9 8 6 8 9 11 SP SD: 2.1367 c. M:-3.4155 c. 99: 9 10 9 13 10 9 7 9 10 13 SP SD: 2.2706 c. M: 4.2055 c. 109: 10 11 10 14 11 10 8 10 11 14 SP SD: 1.4983 c. M: 2.6322 c. 130: 12 13 12 17 13 12 9 12 13 17 SP SD: 1.2099 c. M: 2.3406 c. 140: 13 14 13 18 14 13 10 13 14 18 SP SD: 0.5184 c. M: 0.9021 c. 171: 16 17 16 22 17 16 12 16 17 22 SP SD: 0.5730 c. M:-0.9543 c. 270: 25 27 25 35 27 25 19 25 27 35 SP SD: 0.4862 c. M: 0.9731 c. 301: 28 30 28 39 30 28 21 28 30 39 SP SD: 0.3089 c. M: 0.5006 c. 410: 38 41 38 53 41 38 29 38 41 53 SP SD: 0.3472 c. M: 0.5395 c. 441: 41 44 41 57 44 41 31 41 44 57 SP SD: 0.1271 c. M: 0.2475 c. 612: 57 61 57 79 61 57 43 57 61 79 SP SD: 0.1484 c. M:-0.2377 c. 913: 85 91 85 118 91 85 64 85 91 118 SP SD: 0.1424 c. M:-0.2559 c. 935: 87 93 87 121 93 87 66 87 93 121 SP SD: 0.1415 c. M: 0.2351 c. 966: 90 96 90 125 96 90 68 90 96 125 SP SD: 0.0787 c. M: 0.1399 c. 1106: 103 110 103 143 110 103 78 103 110 143 SP SD: 0.0680 c. M: 0.1280 c. 1407: 131 140 131 182 140 131 99 131 140 182 SP SD: 0.0404 c. M: 0.0843 c. 1547: 144 154 144 200 154 144 109 144 154 200 SP SD: 0.0347 c. M: 0.0659 c. 1578: 147 157 147 204 157 147 111 147 157 204 SP SD: 0.0406 c. M:-0.0604 c. 1988: 185 198 185 257 198 185 140 185 198 257 SP SD: 0.0402 c. M: 0.0655 c. 2019: 188 201 188 261 201 188 142 188 201 261 SP SD: 0.0286 c. M:-0.0528 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 13.6320 cents 3 x x x 4 x x x 5 x 6 S SD: 13.6863 cents 4 x x 5 x x 6 x 7 x 8 S SD: 16.7927 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 10.4114 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 10.1703 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 10.8016 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 12.9289 cents 9 x 10:11:12:13:14 x 15:16:18 S SD: 11.2524 cents 10:11 x 12:13:14:15:16:17:18:20 S SD: 10.0973 cents 11:12 x 13:15:16:17:18:19:20:22 SD: 10.8426 cents 12:13:14:15:16:17:18:19:20:22:24 S SD: 8.2867 cents 13:14:15:16:17:19:20:21:22:24:26 SD: 6.7460 cents 14:15:16:17:19:20:21:22:24:26:28 SD: 5.9503 cents 17:18:19:21:23:24:26:27:29:31:34 SD: 5.8868 cents 18:19:21:22:24:26:27:29:31:33:36 SD: 5.6063 cents 19:20:22:23:25:27:29:30:32:35:38 SD: 5.4931 cents 21:22:24:26:28:30:32:34:36:38:42 SD: 5.0014 cents 23:25:26:28:31:33:35:37:39:42:46 SD: 4.5378 cents 27:29:31:33:36:39:41:43:46:49:54 SD: 2.9572 cents 28:30:32:34:37:40:43:45:48:51:56 SD: 2.6322 cents 40:43:46:49:53:57:61:64:68:73:80 SD: 2.3765 cents 42:45:48:51:56:60:64:67:72:77:84 SD: 1.4552 cents 63:67:72:77:84:90:96:101:108:115:126 SD: 1.1278 cents 75:80:86:91:100:107:114:120:128:137:150 SD: 1.1257 cents 77:82:88:94:103:110:117:123:131:141:154 SD: 1.0649 cents 78:83:89:95:104:111:119:125:133:143:156 SD: 1.0331 cents 90:96:103:110:120:129:137:144:154:165:180 SD: 1.0151 cents 91:97:104:111:121:130:139:146:155:166:182 SD: 0.9700 cents 92:98:105:112:123:131:140:147:157:168:184 SD: 0.9344 cents 105:112:120:128:140:150:160:168:179:192:210 SD: 0.1933 cents 273:291:312:333:364:390:416:437:466:499:546 SD: 0.1922 cents 315:336:360:384:420:450:480:504:538:576:630 SD: 0.1288 cents 420:448:480:512:560:600:640:672:717:768:840 SD: 0.0483 cents 525:560:600:640:700:750:800:840:896:960:1050 SD: 0.0000 cents