Scala analysis: decac
inversion of decaa
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: 8/7 231.174094 septimal whole tone 3: 6/5 315.641287 minor third 4: 4/3 498.044999 perfect fourth 5: 10/7 617.487807 Euler's tritone 6: 3/2 701.955001 perfect fifth 7: 8/5 813.686286 minor sixth 8: 12/7 933.129094 septimal major sixth 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: 16/15 111.7313 minor diatonic semitone 3: 21/20 84.4672 minor semitone 4: 10/9 182.4037 minor whole tone 5: 15/14 119.4428 major diatonic semitone 6: 21/20 84.4672 minor semitone 7: 16/15 111.7313 minor diatonic semitone 8: 15/14 119.4428 major diatonic semitone 9: 10/9 182.4037 minor whole tone 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 : 119.4 231.2 315.6 498.0 617.5 702.0 813.7 933.1 1115.5 1200.0 119.4 : 111.7 196.2 378.6 498.0 582.5 694.2 813.7 996.1 1080.6 1200.0 231.2 : 84.5 266.9 386.3 470.8 582.5 702.0 884.4 968.8 1088.3 1200.0 315.6 : 182.4 301.8 386.3 498.0 617.5 799.9 884.4 1003.8 1115.5 1200.0 498.0 : 119.4 203.9 315.6 435.1 617.5 702.0 821.4 933.1 1017.6 1200.0 617.5 : 84.5 196.2 315.6 498.0 582.5 702.0 813.7 898.2 1080.6 1200.0 702.0 : 111.7 231.2 413.6 498.0 617.5 729.2 813.7 996.1 1115.5 1200.0 813.7 : 119.4 301.8 386.3 505.8 617.5 702.0 884.4 1003.8 1088.3 1200.0 933.1 : 182.4 266.9 386.3 498.0 582.5 764.9 884.4 968.8 1080.6 1200.0 1115.5: 84.5 203.9 315.6 400.1 582.5 702.0 786.4 898.2 1017.6 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 : 119.53428 cents, oct.: 1195.34275 cents Scale is not proper Step pattern alph. order: ABCDACBADC Step pattern size order : CBADCABCDA 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 Most common triad is 0.0 498.045 701.955 cents, amount: 2 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 0 Length of longest subharmonic part : 2 at degree 6 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 -- Rational properties -- Prime limit : 7 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 21 Scale harmonicity : 0.030846 Average absolute harmonicity : 0.198529 Specific harmonicity : 0.152002 Fundamental : 1/210, -7.7142 octaves, 1.2458 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 2.520000E+04, 14.62114 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 90.0, average 9.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.38579, average 0.73858 Sum of Tenney's harmonic distance : 16.00161, average 1.60016 Vogel's harmonic complexity : 15.00000 Wille's k value : 157 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 137.13944, average 2.49344 Lattice compactness (without 2's) : 84.32583, average 1.53320 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.40000 18 1 3: -1 .. 1 0.20000 6 2 5: -1 .. 1 0.10000 5 2 7: -1 .. 0 -0.50000 5 5 Average exponent except 2's :-2 / 10 =-0.20000 Average absolute exponent except 2's: 16 / 10 = 1.60000 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: 23.8328 c. M:-44.3587 c. 12: 1 1 1 2 1 1 1 1 2 1 P B ME S SD: 18.5313 c. M: 33.1291 c. 18: 2 1 2 2 2 2 1 2 3 1 N T3 SD: 20.6325 c. M: 31.3783 c. 19: 2 2 1 3 2 1 2 2 3 1 N D3 SD: 12.3351 c. M:-21.4575 c. 22: 2 2 2 3 2 2 2 2 3 2 SP B ME S SD: 12.1645 c. M: 24.6237 c. Static Symmetrical Minor, Pajara-10 26: 3 2 2 4 2 2 3 2 4 2 P T3 SD: 11.6768 c. M:-19.0187 c. 27: 3 2 2 4 3 2 2 3 4 2 P SD: 8.3102 c. M:-13.8905 c. 31: 3 3 2 5 3 2 3 3 5 2 N SD: 4.1468 c. M:-7.0478 c. 41: 4 4 3 6 4 3 4 4 6 3 P SD: 3.4627 c. M:-6.3099 c. 53: 5 5 4 8 5 4 5 5 8 4 P SD: 4.0478 c. M: 6.2353 c. 58: 6 5 4 9 6 4 5 6 9 4 N SD: 3.6206 c. M: 6.7897 c. 68: 7 6 5 10 7 5 6 7 10 5 P SD: 2.7799 c. M:-4.0866 c. 72: 7 7 5 11 7 5 7 7 11 5 N SD: 1.7874 c. M:-2.9804 c. 99: 10 9 7 15 10 7 9 10 15 7 N SD: 0.9777 c. M:-1.7693 c. 130: 13 12 9 20 13 9 12 13 20 9 N SD: 0.9747 c. M: 1.7951 c. 140: 14 13 10 21 14 10 13 14 21 10 N SD: 0.8734 c. M:-1.5016 c. 171: 17 16 12 26 17 12 16 17 26 12 N SD: 0.2280 c. M:-0.4049 c. 441: 44 41 31 67 44 31 41 44 67 31 N SD: 0.1452 c. M:-0.2851 c. 612: 61 57 43 93 61 43 57 61 93 43 N SD: 0.1268 c. M:-0.2042 c. 935: 93 87 66 142 93 66 87 93 142 66 N SD: 0.1184 c. M: 0.2387 c. 966: 96 90 68 147 96 68 90 96 147 68 N SD: 0.1153 c. M: 0.2098 c. 1065: 106 99 75 162 106 75 99 106 162 75 N SD: 0.1081 c. M: 0.1882 c. 1106: 110 103 78 168 110 78 103 110 168 78 N SD: 0.0847 c. M: 0.1621 c. 1236: 123 115 87 188 123 87 115 123 188 87 N SD: 0.0686 c. M: 0.1194 c. 1277: 127 119 90 194 127 90 119 127 194 90 N SD: 0.0715 c. M: 0.1060 c. 1376: 137 128 97 209 137 97 128 137 209 97 N SD: 0.0637 c. M: 0.1258 c. 1407: 140 131 99 214 140 99 131 140 214 99 N SD: 0.0458 c. M: 0.0801 c. 1547: 154 144 109 235 154 109 144 154 235 109 N SD: 0.0438 c. M: 0.0835 c. 1578: 157 147 111 240 157 111 147 157 240 111 N SD: 0.0410 c. M:-0.0565 c. 1718: 171 160 121 261 171 121 160 171 261 121 N SD: 0.0393 c. M:-0.0747 c. 1848: 184 172 130 281 184 130 172 184 281 130 N SD: 0.0348 c. M: 0.0569 c. 2019: 201 188 142 307 201 142 188 201 307 142 N SD: 0.0334 c. M:-0.0690 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 x 5 x 6 S SD: 16.2568 cents 4 x x 5 x x 6 x 7 x 8 S SD: 19.7940 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 18.2844 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 14.9362 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 11.8307 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 13.2959 cents 9 x 10:11:12:13 x 14:15:17:18 SD: 11.6730 cents 10:11 x 12:13:14:15:16:17:19:20 SD: 8.2019 cents 11:12 x 13:15:16:17:18:19:21:22 SD: 10.2616 cents 12:13:14 x 16:17:18:19:21:23:24 SD: 6.6382 cents 14:15:16:17:19:20:21:22:24:27:28 SD: 5.2861 cents 20:21:23:24:27:29:30:32:34:38:40 SD: 5.1915 cents 24:26:27:29:32:34:36:38:41:46:48 SD: 4.4090 cents 26:28:30:31:35:37:39:42:45:50:52 SD: 4.0239 cents 28:30:32:34:37:40:42:45:48:53:56 SD: 2.8950 cents 30:32:34:36:40:43:45:48:51:57:60 SD: 2.3048 cents 40:43:46:48:53:57:60:64:69:76:80 SD: 2.0525 cents 42:45:48:50:56:60:63:67:72:80:84 SD: 1.4728 cents 56:60:64:67:75:80:84:90:96:107:112 SD: 1.3219 cents 70:75:80:84:93:100:105:112:120:133:140 SD: 0.7559 cents 84:90:96:101:112:120:126:134:144:160:168 SD: 0.6197 cents 126:135:144:151:168:180:189:202:216:240:252 SD: 0.4126 cents 140:150:160:168:187:200:210:224:240:267:280 SD: 0.3771 cents 168:180:192:202:224:240:252:269:288:320:336 SD: 0.3665 cents 210:225:240:252:280:300:315:336:360:400:420 S SD: 0.0000 cents