Scala analysis: cx4
Fourth 10/4 scale <10 16 23 28| epimorphic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 35/32 155.139620 septimal neutral second 2: 9/8 203.910002 major whole tone 3: 5/4 386.313714 major third 4: 21/16 470.780907 narrow fourth 5: 35/24 653.184619 septimal semi-diminished fifth 6: 3/2 701.955001 perfect fifth 7: 105/64 857.094621 septimal neutral sixth 8: 7/4 968.825906 harmonic seventh 9: 15/8 1088.268715 classic major seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 35/32 155.1396 septimal neutral second 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 10/9 182.4037 minor whole tone 4: 21/20 84.4672 minor semitone 5: 10/9 182.4037 minor whole tone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 35/32 155.1396 septimal neutral second 8: 16/15 111.7313 minor diatonic semitone 9: 15/14 119.4428 major diatonic semitone 10: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 2 35/32 155.140 cents septimal neutral second 1: 2 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 4 8/7 231.174 cents septimal whole tone 2: 4 7/6 266.871 cents septimal minor third 3: 4 6/5 315.641 cents minor third 3: 1 128/105 342.905 cents septimal neutral third 3: 4 5/4 386.314 cents major third 3: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 4: 2 9/7 435.084 cents septimal major third, BP third 4: 2 21/16 470.781 cents narrow fourth 4: 6 4/3 498.045 cents perfect fourth 5: 3 48/35 546.815 cents septimal semi-augmented fourth 5: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 2 10/7 617.488 cents Euler's tritone 5: 3 35/24 653.185 cents septimal semi-diminished fifth 6: 6 3/2 701.955 cents perfect fifth 6: 2 32/21 729.219 cents wide fifth 6: 2 14/9 764.916 cents septimal minor sixth 7: 1 54/35 750.725 cents septimal semi-augmented fifth 7: 4 8/5 813.686 cents minor sixth 7: 1 105/64 857.095 cents septimal neutral sixth 7: 4 5/3 884.359 cents major sixth, BP sixth 8: 4 12/7 933.129 cents septimal major sixth 8: 4 7/4 968.826 cents harmonic seventh 8: 2 16/9 996.090 cents Pythagorean minor seventh 9: 2 9/5 1017.596 cents just minor seventh, BP seventh 9: 2 64/35 1044.860 cents septimal neutral seventh 9: 1 28/15 1080.557 cents grave major seventh 9: 2 15/8 1088.269 cents classic major seventh 9: 1 40/21 1115.533 cents acute major seventh 9: 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: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 155.1 203.9 386.3 470.8 653.2 702.0 857.1 968.8 1088.3 1200.0 155.1 : 48.8 231.2 315.6 498.0 546.8 702.0 813.7 933.1 1044.9 1200.0 203.9 : 182.4 266.9 449.3 498.0 653.2 764.9 884.4 996.1 1151.2 1200.0 386.3 : 84.5 266.9 315.6 470.8 582.5 702.0 813.7 968.8 1017.6 1200.0 470.8 : 182.4 231.2 386.3 498.0 617.5 729.2 884.4 933.1 1115.5 1200.0 653.2 : 48.8 203.9 315.6 435.1 546.8 702.0 750.7 933.1 1017.6 1200.0 702.0 : 155.1 266.9 386.3 498.0 653.2 702.0 884.4 968.8 1151.2 1200.0 857.1 : 111.7 231.2 342.9 498.0 546.8 729.2 813.7 996.1 1044.9 1200.0 968.8 : 119.4 231.2 386.3 435.1 617.5 702.0 884.4 933.1 1088.3 1200.0 1088.3: 111.7 266.9 315.6 498.0 582.5 764.9 813.7 968.8 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 182.4037 cents 175/162, 133.6333 cents 36/35, 48.7704 cents 2: 203.9100 .. 266.8709 cents 28/27, 62.9609 cents 81/80, 21.5063 cents 3: 315.6413 .. 449.2746 cents 175/162, 133.6333 cents 36/35, 48.7704 cents 4: 435.0841 .. 498.0450 cents 28/27, 62.9609 cents 243/245,-14.1905 cents 5: 546.8154 .. 653.1846 cents 1225/1152, 106.3692 cents 36/35, 48.7704 cents 6: 701.9550 .. 764.9159 cents 28/27, 62.9609 cents 36/35, 48.7704 cents 7: 750.7254 .. 884.3587 cents 175/162, 133.6333 cents 243/245,-14.1905 cents 8: 933.1291 .. 996.0900 cents 28/27, 62.9609 cents 36/35, 48.7704 cents 9: 1017.5963 .. 1151.2296 cents 175/162, 133.6333 cents 81/80, 21.5063 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 2.460510 Largest / Average step : 1.520031 Largest / Smallest step : 3.740051 Median interval of one step : 115.58705 cents, amount: 0 Least squares average step : 121.11004 cents, oct.: 1211.10040 cents Scale is not proper Step pattern alph. order: ABCDCBAEFE Step pattern size order : EAFBFAECDC Scale is a Constant Structure, by a margin of 14.19052 cents Scale diversity : 1.514718 Lumma stability : 0.279696 Lumma impropriety factor : 0.023651 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 : 6 Highest interval variety : 6 Mean interval variety : 4.00000 = 4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 6, average 701.9550 cents Length of longest harmonic part : 2 at degree 8 Length of longest subharmonic part : 2 at degree 7 Formal octave complements present : 1 = 10.0000% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined Scale is n-1 differentially coherent in interval classes 6 and 7 combined Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 8-9 -- Rational properties -- Prime limit : 7 Odd number limit : 105 (O: 105 U: 105) Highest odd numerator or denominator: 105 Scale harmonicity : 0.031560 Average absolute harmonicity : 0.186532 Specific harmonicity : 0.157571 Fundamental : 1/192, -7.5850 octaves, 1.3626 Hz. Guide tone : 630, 9.2992 octaves, 164824.106 Hz. Exponens Consonantiae : 1.209600E+05, 16.88417 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 200.0, average 20.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.58307, average 1.05831 Sum of Tenney's harmonic distance : 20.09109, average 2.00911 Vogel's harmonic complexity : 13.70000 Wille's k value : 157 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 166.20399, average 3.02189 Lattice compactness (without 2's) : 80.88634, average 1.47066 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 1 -2.80000 30 1 3: -1 .. 2 0.50000 7 2 5: 0 .. 1 0.50000 5 2 7: 0 .. 1 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 16 21 28| Scale is JI-epimorphic with val: <10 16 23 28| = patent Scale is weakly epimorphic with val: <10 16 25 28| 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 17 25 31| 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: 26.2819 c. M: 53.1846 c. 12: 2 0 2 1 2 0 2 1 1 1 N D3 SD: 28.6612 c. M:-46.8154 c. 15: 2 1 2 1 2 1 2 1 2 1 SP B ME SD: 19.2544 c. M:-36.0900 c. Archytas Clan-10 17: 2 1 2 2 2 1 2 2 1 2 P M ME SD: 18.9604 c. M: 33.3725 c. 18: 2 1 3 1 3 1 2 2 1 2 N D3 SD: 18.4160 c. M:-31.3783 c. 19: 2 1 3 1 3 1 2 2 2 2 P D3 SD: 20.9925 c. M: 36.0420 c. 21: 3 1 3 1 3 1 3 2 2 2 P SD: 14.5935 c. M:-24.6614 c. 22: 3 1 3 2 3 1 3 2 2 2 P D3 SD: 10.8359 c. M:-20.1282 c. 25: 3 1 4 2 4 1 3 2 3 2 N SD: 11.8700 c. M:-18.8154 c. 28: 4 1 4 2 4 1 4 3 2 3 P SD: 11.4586 c. M:-16.8884 c. 29: 4 1 4 2 5 1 4 2 3 3 N SD: 11.0541 c. M: 17.1018 c. 31: 4 1 5 2 5 1 4 3 3 3 N SD: 4.9853 c. M: 10.3616 c. 41: 5 2 6 3 6 2 5 4 4 4 P SD: 5.5800 c. M: 9.2822 c. 46: 6 2 7 3 7 2 6 4 5 4 P SD: 3.7381 c. M:-7.3835 c. 53: 7 2 8 4 8 2 7 5 5 5 N SD: 2.8728 c. M:-4.7590 c. 77: 10 3 12 5 12 3 10 7 8 7 N SD: 1.9904 c. M:-3.2967 c. 94: 12 4 14 7 14 4 12 9 9 9 N SD: 1.9254 c. M: 3.3350 c. 99: 13 4 15 7 15 4 13 9 10 9 N SD: 1.9967 c. M:-3.5114 c. 118: 15 5 18 8 18 5 15 11 12 11 N SD: 1.9254 c. M: 2.9843 c. 125: 16 5 19 9 19 5 16 12 12 12 N SD: 1.8595 c. M: 3.4687 c. 130: 17 5 20 9 20 5 17 12 13 12 N SD: 1.1725 c. M:-2.2000 c. 140: 18 6 21 10 21 6 18 13 14 13 N SD: 0.9391 c. M:-1.8043 c. 171: 22 7 26 12 26 7 22 16 17 16 N SD: 0.5422 c. M: 0.9543 c. 224: 29 9 34 16 34 9 29 21 22 21 N SD: 0.4878 c. M:-0.8170 c. 270: 35 11 41 19 41 11 35 25 27 25 N SD: 0.4051 c. M:-0.6832 c. 301: 39 12 46 21 46 12 39 28 30 28 N SD: 0.3534 c. M:-0.6360 c. 395: 51 16 60 28 60 16 51 37 39 37 N SD: 0.3386 c. M: 0.6738 c. 441: 57 18 67 31 67 18 57 41 44 41 N SD: 0.1026 c. M:-0.1716 c. 836: 108 34 127 59 127 34 108 78 83 78 N SD: 0.1214 c. M: 0.2304 c. 935: 121 38 142 66 142 38 121 87 93 87 N SD: 0.1410 c. M:-0.2351 c. 966: 125 39 147 68 147 39 125 90 96 90 N SD: 0.1173 c. M:-0.2315 c. 1053: 136 43 160 74 160 43 136 98 105 98 N SD: 0.1129 c. M: 0.1932 c. 1106: 143 45 168 78 168 45 143 103 110 103 N SD: 0.0535 c. M:-0.1052 c. 1277: 165 52 194 90 194 52 165 119 127 119 N SD: 0.0646 c. M: 0.0960 c. 1407: 182 57 214 99 214 57 182 131 140 131 N SD: 0.0583 c. M:-0.1203 c. 1547: 200 63 235 109 235 63 200 144 154 144 N SD: 0.0476 c. M:-0.0978 c. 1848: 239 75 281 130 281 75 239 172 184 172 N SD: 0.0372 c. M:-0.0621 c. 2019: 261 82 307 142 307 82 261 188 201 188 N SD: 0.0288 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: 0.0000 cents 3 x x x 4 x x 5 x x 6 S SD: 12.8524 cents 4 x x 5 x x 6 x 7 x 8 S SD: 0.0000 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 23.8764 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 13.9088 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 14.5729 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 10.2779 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 10.3088 cents 10:11 x x 13 x 15:16:18:19:20 SD: 10.2623 cents 11:12 x 14 x 16:17:18:19:21:22 SD: 9.0054 cents 12:13:14:15:16 x 18:20:21:23:24 SD: 9.4104 cents 13:14:15:16:17:19:20:21:23:24:26 SD: 8.4481 cents 14:15:16 x 18:20:21:23:25:26:28 SD: 8.6563 cents 15:16:17:19:20:22:23:25:26:28:30 SD: 7.7066 cents 16 x 18:20:21:23:24:26:28:30:32 SD: 3.3240 cents 17 x 19:21:22:25:26:28:30:32:34 SD: 5.8654 cents 18 x 20:23:24:26:27:30:32:34:36 SD: 7.5179 cents 19:21 x 24:25:28:29:31:33:36:38 SD: 5.5580 cents 20:22:23:25:26:29:30:33:35:38:40 SD: 5.0410 cents 22:24:25:28:29:32:33:36:39:41:44 SD: 4.4748 cents 23:25:26:29:30:34:35:38:40:43:46 SD: 4.4595 cents 24:26:27:30:32:35:36:39:42:45:48 SD: 3.5948 cents 27 x 30:34:35:39:41:44:47:51:54 SD: 5.2082 cents 28:31:32:35:37:41:42:46:49:53:56 SD: 4.0615 cents 30:33:34:38:39:44:45:49:53:56:60 SD: 3.9324 cents 31:34:35:39:41:45:47:51:54:58:62 SD: 2.9463 cents 32:35:36:40:42:47:48:53:56:60:64 SD: 2.0521 cents 48:53:54:60:63:70:72:79:84:90:96 SD: 1.7303 cents 55:60:62:69:72:80:83:90:96:103:110 SD: 1.6337 cents 56:61:63:70:74:82:84:92:98:105:112 SD: 1.5594 cents 63:69:71:79:83:92:95:103:110:118:126 SD: 1.5224 cents 64:70:72:80:84:93:96:105:112:120:128 SD: 0.6194 cents 96:105:108:120:126:140:144:158:168:180:192 SD: 0.5487 cents 128:140:144:160:168:187:192:210:224:240:256 SD: 0.3089 cents 192:210:216:240:252:280:288:315:336:360:384 SD: 0.0000 cents