Scala analysis: decad
inversion of decab
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 25/21 301.846520 BP second, quasi-equal minor third 3: 5/4 386.313714 major third 4: 4/3 498.044999 perfect fourth 5: 10/7 617.487807 Euler's tritone 6: 3/2 701.955001 perfect fifth 7: 5/3 884.358713 major sixth, BP sixth 8: 25/14 1003.801521 middle minor seventh 9: 40/21 1115.532807 acute major seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21/20 84.4672 minor semitone 1: 15/14 119.4428 major diatonic semitone 2: 10/9 182.4037 minor whole tone 3: 21/20 84.4672 minor semitone 4: 16/15 111.7313 minor diatonic semitone 5: 15/14 119.4428 major diatonic semitone 6: 21/20 84.4672 minor semitone 7: 10/9 182.4037 minor whole tone 8: 15/14 119.4428 major diatonic semitone 9: 16/15 111.7313 minor diatonic semitone 10: 21/20 84.4672 minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 3 15/14 119.443 cents major diatonic semitone 1: 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: 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: 4 6/5 315.641 cents minor third 3: 1 56/45 378.602 cents septimal narrow major third 3: 4 5/4 386.314 cents major third 3: 1 80/63 413.578 cents wide major third 4: 1 63/50 400.108 cents quasi-equal major third 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 21/16 470.781 cents narrow fourth 4: 6 4/3 498.045 cents perfect fourth 4: 1 75/56 505.757 cents marvelous fourth 5: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 5 10/7 617.488 cents Euler's tritone 6: 1 112/75 694.243 cents marvelous fifth 6: 6 3/2 701.955 cents perfect fifth 6: 1 32/21 729.219 cents wide fifth 6: 1 14/9 764.916 cents septimal minor sixth 6: 1 100/63 799.892 cents quasi-equal minor sixth 7: 1 63/40 786.422 cents narrow minor sixth 7: 4 8/5 813.686 cents minor sixth 7: 1 45/28 821.398 cents septimale wide minor sixth 7: 4 5/3 884.359 cents major sixth, BP sixth 8: 2 42/25 898.153 cents quasi-equal major sixth 8: 2 12/7 933.129 cents septimal major sixth 8: 2 7/4 968.826 cents harmonic seventh 8: 2 16/9 996.090 cents Pythagorean minor seventh 8: 2 25/14 1003.802 cents middle minor seventh 9: 2 9/5 1017.596 cents just minor seventh, BP seventh 9: 3 28/15 1080.557 cents grave major seventh 9: 2 15/8 1088.269 cents classic major seventh 9: 3 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.22222 = 38/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 119.4 301.8 386.3 498.0 617.5 702.0 884.4 1003.8 1115.5 1200.0 119.4 : 182.4 266.9 378.6 498.0 582.5 764.9 884.4 996.1 1080.6 1200.0 301.8 : 84.5 196.2 315.6 400.1 582.5 702.0 813.7 898.2 1017.6 1200.0 386.3 : 111.7 231.2 315.6 498.0 617.5 729.2 813.7 933.1 1115.5 1200.0 498.0 : 119.4 203.9 386.3 505.8 617.5 702.0 821.4 1003.8 1088.3 1200.0 617.5 : 84.5 266.9 386.3 498.0 582.5 702.0 884.4 968.8 1080.6 1200.0 702.0 : 182.4 301.8 413.6 498.0 617.5 799.9 884.4 996.1 1115.5 1200.0 884.4 : 119.4 231.2 315.6 435.1 617.5 702.0 813.7 933.1 1017.6 1200.0 1003.8: 111.7 196.2 315.6 498.0 582.5 694.2 813.7 898.2 1080.6 1200.0 1115.5: 84.5 203.9 386.3 470.8 582.5 702.0 786.4 968.8 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 182.4037 cents 200/189, 97.9365 cents 21/20, 84.4672 cents 2: 196.1985 .. 301.8465 cents 625/588, 105.6480 cents 126/125, 13.7948 cents 3: 315.6413 .. 413.5778 cents 200/189, 97.9365 cents 126/125, 13.7948 cents 4: 400.1085 .. 505.7565 cents 625/588, 105.6480 cents 3969/4000,-13.4693 cents 5: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 392/375, 76.7557 cents 6: 694.2435 .. 799.8915 cents 625/588, 105.6480 cents 392/375, 76.7557 cents 7: 786.4222 .. 884.3587 cents 200/189, 97.9365 cents 3969/4000,-13.4693 cents 8: 898.1535 .. 1003.8015 cents 625/588, 105.6480 cents 126/125, 13.7948 cents 9: 1017.5963 .. 1115.5328 cents 200/189, 97.9365 cents 126/125, 13.7948 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 : 10/9, 182.4037 cents Average / Smallest step : 1.420670 Largest / Average step : 1.520031 Largest / Smallest step : 2.159462 Median interval of one step : 115.58705 cents, amount: 0 Least squares average step : 123.20557 cents, oct.: 1232.05570 cents Scale is not proper Step pattern alph. order: ABCDACBADC Step pattern size order : CDABCADCBA Scale is a Constant Structure, by a margin of 13.46933 cents Scale diversity : 1.394628 Lumma stability : 0.314687 Lumma impropriety factor : 0.022449 Rothenberg efficiency : 0.362698 redundancy: 0.637302 Efficiency x scale size : 3.626984 Number of different interval sizes : 38 = 4.22222 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.22222 = 38/9 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Number of recognisable fifths : 7, average 700.8534 cents Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 7 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 3 = 30.0000% Scale is 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 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 differentially coherent in interval classes 6 and 7 combined Scale is n-1 differentially coherent in interval classes 7 and 8 combined -- Rational properties -- Prime limit : 7 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 25 Scale harmonicity : 0.029923 Average absolute harmonicity : 0.194712 Specific harmonicity : 0.147626 Fundamental : 1/84, -6.3923 octaves, 3.1146 Hz. Guide tone : 600, 9.2288 octaves, 156975.339 Hz. Exponens Consonantiae : 5.040000E+04, 15.62114 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 112.0, average 11.20000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.49147, average 0.84915 Sum of Tenney's harmonic distance : 16.99131, average 1.69913 Vogel's harmonic complexity : 12.60000 Wille's k value : 52 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 137.45535, average 2.49919 Lattice compactness (without 2's) : 86.59717, average 1.57449 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.20000 12 1 3: -1 .. 1 -0.20000 6 2 5: 0 .. 2 0.90000 9 2 7: -1 .. 0 -0.50000 5 5 Average exponent except 2's : 2 / 10 = 0.20000 Average absolute exponent except 2's: 20 / 10 = 2.00000 Scale is JI-epimorphic with val: <10 16 23 28| = patent Scale is weakly epimorphic with val: <10 17 21 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: 32.5939 c. M: 61.8465 c. 12: 1 2 1 1 1 1 2 1 1 1 P B ME S SD: 11.7583 c. M: 19.4428 c. 19: 2 3 1 2 2 1 3 2 2 1 N D3 SD: 10.4786 c. M:-21.3093 c. 27: 3 4 2 2 3 2 4 3 2 2 P SD: 10.1763 c. M:-18.4207 c. 29: 3 4 2 3 3 2 4 3 3 2 P D3 SD: 8.5610 c. M: 15.3932 c. 31: 3 5 2 3 3 2 5 3 3 2 N SD: 4.7154 c. M:-7.8309 c. 41: 4 6 3 4 4 3 6 4 4 3 P SD: 5.0836 c. M: 9.1636 c. 43: 4 7 3 4 4 3 7 4 4 3 N SD: 4.8177 c. M:-8.6645 c. 53: 5 8 4 5 5 4 8 5 5 4 P SD: 4.8128 c. M: 7.5751 c. 56: 6 8 4 5 6 4 8 6 5 4 P SD: 4.5019 c. M:-9.1286 c. 60: 6 9 4 6 6 4 9 6 6 4 N SD: 3.3308 c. M: 6.3137 c. 68: 7 10 5 6 7 5 10 7 6 5 P SD: 2.7790 c. M:-4.0866 c. 72: 7 11 5 7 7 5 11 7 7 5 N SD: 2.1238 c. M: 3.8015 c. 99: 10 15 7 9 10 7 15 10 9 7 N SD: 1.2355 c. M:-2.2591 c. 130: 13 20 9 12 13 9 20 13 12 9 N SD: 1.4786 c. M:-2.7689 c. 140: 14 21 10 13 14 10 21 14 13 10 N SD: 1.0261 c. M: 1.8465 c. 159: 16 24 11 15 16 11 24 16 15 11 N SD: 0.9753 c. M:-1.4483 c. 171: 17 26 12 16 17 12 26 17 16 12 N SD: 0.2020 c. M: 0.3488 c. 441: 44 67 31 41 44 31 67 44 41 31 N SD: 0.1647 c. M:-0.2851 c. 612: 61 93 43 57 61 43 93 61 57 43 N SD: 0.1036 c. M:-0.1650 c. 783: 78 119 55 73 78 55 119 78 73 55 N SD: 0.0916 c. M:-0.1760 c. 966: 96 147 68 90 96 68 147 96 90 68 N SD: 0.0899 c. M: 0.1881 c. 1065: 106 162 75 99 106 75 162 106 99 75 N SD: 0.0938 c. M:-0.1652 c. 1137: 113 173 80 106 113 80 173 113 106 80 N SD: 0.0901 c. M: 0.1816 c. 1236: 123 188 87 115 123 87 188 123 115 87 N SD: 0.0611 c. M:-0.1073 c. 1407: 140 214 99 131 140 99 214 140 131 99 N SD: 0.0439 c. M:-0.0763 c. 1578: 157 240 111 147 157 111 240 157 147 111 N SD: 0.0416 c. M:-0.0565 c. 2019: 201 307 142 188 201 142 307 201 188 142 N SD: 0.0462 c. M:-0.0851 c. 2159: 215 328 152 201 215 152 328 215 201 152 N SD: 0.0353 c. M: 0.0604 c. 2330: 232 354 164 217 232 164 354 232 217 164 N SD: 0.0351 c. M: 0.0669 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: 0.0000 cents 4 x x 5 x x 6 x 7 x 8 S SD: 8.7439 cents 5 x 6 x x 7 x 8:9 x 10 S SD: 16.2462 cents 6 x 7 x 8 x 9:10:11 x 12 S SD: 9.5730 cents 7 x 8:9 x 10:11:12 x 13:14 S SD: 19.2508 cents 8:9 x 10:11 x 12:13:14:15:16 S SD: 14.7163 cents 9:10 x 11:12:13:14:15:16:17:18 S SD: 11.1539 cents 10:11:12 x 13:14:15:17:18:19:20 SD: 9.1591 cents 12:13:14:15:16:17:18:20:21:23:24 SD: 5.6025 cents 16:17:19:20:21:23:24:27:29:30:32 SD: 5.4393 cents 23:25:27:29:31:33:35:38:41:44:46 SD: 5.2487 cents 24:26:29:30:32:34:36:40:43:46:48 SD: 3.7280 cents 27:29:32:34:36:39:41:45:48:51:54 SD: 3.6435 cents 28:30:33:35:37:40:42:47:50:53:56 SD: 2.8521 cents 32:34:38:40:43:46:48:53:57:61:64 SD: 2.5787 cents 40:43:48:50:53:57:60:67:71:76:80 SD: 2.3706 cents 42:45:50:53:56:60:63:70:75:80:84 SD: 1.6410 cents 52:56:62:65:69:74:78:87:93:99:104 SD: 1.5861 cents 56:60:67:70:75:80:84:93:100:107:112 SD: 1.4197 cents 68:73:81:85:91:97:102:113:121:130:136 SD: 1.2776 cents 72:77:86:90:96:103:108:120:129:137:144 SD: 0.9258 cents 84:90:100:105:112:120:126:140:150:160:168 S SD: 0.0000 cents