Scala analysis: decab
(10/9) <=> (16/15) transform of decaa
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: 28/25 196.198479 middle second 3: 6/5 315.641287 minor third 4: 4/3 498.044999 perfect fourth 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 3/2 701.955001 perfect fifth 7: 8/5 813.686286 minor sixth 8: 42/25 898.153480 quasi-equal major sixth 9: 28/15 1080.557192 grave major seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 21/20 84.4672 minor semitone 2: 16/15 111.7313 minor diatonic semitone 3: 15/14 119.4428 major diatonic semitone 4: 10/9 182.4037 minor whole tone 5: 21/20 84.4672 minor semitone 6: 15/14 119.4428 major diatonic semitone 7: 16/15 111.7313 minor diatonic semitone 8: 21/20 84.4672 minor semitone 9: 10/9 182.4037 minor whole tone 10: 15/14 119.4428 major diatonic 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 : 84.5 196.2 315.6 498.0 582.5 702.0 813.7 898.2 1080.6 1200.0 84.5 : 111.7 231.2 413.6 498.0 617.5 729.2 813.7 996.1 1115.5 1200.0 196.2 : 119.4 301.8 386.3 505.8 617.5 702.0 884.4 1003.8 1088.3 1200.0 315.6 : 182.4 266.9 386.3 498.0 582.5 764.9 884.4 968.8 1080.6 1200.0 498.0 : 84.5 203.9 315.6 400.1 582.5 702.0 786.4 898.2 1017.6 1200.0 582.5 : 119.4 231.2 315.6 498.0 617.5 702.0 813.7 933.1 1115.5 1200.0 702.0 : 111.7 196.2 378.6 498.0 582.5 694.2 813.7 996.1 1080.6 1200.0 813.7 : 84.5 266.9 386.3 470.8 582.5 702.0 884.4 968.8 1088.3 1200.0 898.2 : 182.4 301.8 386.3 498.0 617.5 799.9 884.4 1003.8 1115.5 1200.0 1080.6: 119.4 203.9 315.6 435.1 617.5 702.0 821.4 933.1 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 : 117.26313 cents, oct.: 1172.63131 cents Scale is not proper Step pattern alph. order: ABCDACBADC Step pattern size order : ABCDACBADC 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 5 Length of longest subharmonic part : 2 at degree 1 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: 25 Scale harmonicity : 0.029923 Average absolute harmonicity : 0.192357 Specific harmonicity : 0.147626 Fundamental : 1/300, -8.2288 octaves, 0.8721 Hz. Guide tone : 168, 7.3923 octaves, 43953.095 Hz. Exponens Consonantiae : 5.040000E+04, 15.62114 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 127.5, average 12.75000 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 : 17.89440, average 1.78944 Vogel's harmonic complexity : 15.50000 Wille's k value : 157 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 0.90000 15 1 3: -1 .. 1 0.20000 6 2 5: -2 .. 0 -0.90000 9 2 7: 0 .. 1 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. 11: 1 1 1 2 0 1 1 1 2 1 N D3 SD: 32.1747 c. M: 50.0499 c. 12: 1 1 1 2 1 1 1 1 2 1 P B ME S SD: 11.7583 c. M:-19.4428 c. 19: 1 2 2 3 1 2 2 1 3 2 N D3 SD: 10.4786 c. M: 21.3093 c. 27: 2 2 3 4 2 3 2 2 4 3 P SD: 10.1763 c. M: 18.4207 c. 28: 2 3 2 5 2 2 3 2 4 3 N SD: 12.2221 c. M:-18.0872 c. 29: 2 3 3 4 2 3 3 2 4 3 P D3 SD: 8.5610 c. M:-15.3932 c. 31: 2 3 3 5 2 3 3 2 5 3 N SD: 4.7154 c. M: 7.8309 c. 41: 3 4 4 6 3 4 4 3 6 4 P SD: 5.0836 c. M:-9.1636 c. 43: 3 4 4 7 3 4 4 3 7 4 N SD: 4.8177 c. M: 8.6645 c. 53: 4 5 5 8 4 5 5 4 8 5 P SD: 4.8128 c. M:-7.5751 c. 56: 4 5 6 8 4 6 5 4 8 6 P SD: 4.5019 c. M: 9.1286 c. 57: 4 5 6 9 4 5 6 4 8 6 N SD: 5.9163 c. M:-7.3663 c. 58: 4 5 6 9 4 6 5 4 9 6 N SD: 5.3468 c. M: 9.9916 c. 60: 4 6 6 9 4 6 6 4 9 6 N SD: 3.3308 c. M:-6.3137 c. 68: 5 6 7 10 5 7 6 5 10 7 P SD: 2.7790 c. M: 4.0866 c. 72: 5 7 7 11 5 7 7 5 11 7 N SD: 2.1238 c. M:-3.8015 c. 99: 7 9 10 15 7 10 9 7 15 10 N SD: 1.2355 c. M: 2.2591 c. 130: 9 12 13 20 9 13 12 9 20 13 N SD: 1.4786 c. M: 2.7689 c. 140: 10 13 14 21 10 14 13 10 21 14 N SD: 1.0261 c. M:-1.8465 c. 159: 11 15 16 24 11 16 15 11 24 16 N SD: 0.9753 c. M: 1.4483 c. 171: 12 16 17 26 12 17 16 12 26 17 N SD: 0.2020 c. M:-0.3488 c. 441: 31 41 44 67 31 44 41 31 67 44 N SD: 0.1647 c. M: 0.2851 c. 612: 43 57 61 93 43 61 57 43 93 61 N SD: 0.1036 c. M: 0.1650 c. 783: 55 73 78 119 55 78 73 55 119 78 N SD: 0.0916 c. M: 0.1760 c. 966: 68 90 96 147 68 96 90 68 147 96 N SD: 0.0899 c. M:-0.1881 c. 1065: 75 99 106 162 75 106 99 75 162 106 N SD: 0.0938 c. M: 0.1652 c. 1137: 80 106 113 173 80 113 106 80 173 113 N SD: 0.0901 c. M:-0.1816 c. 1236: 87 115 123 188 87 123 115 87 188 123 N SD: 0.0611 c. M: 0.1073 c. 1407: 99 131 140 214 99 140 131 99 214 140 N SD: 0.0439 c. M: 0.0763 c. 1578: 111 147 157 240 111 157 147 111 240 157 N SD: 0.0416 c. M: 0.0565 c. 2019: 142 188 201 307 142 201 188 142 307 201 N SD: 0.0462 c. M: 0.0851 c. 2159: 152 201 215 328 152 215 201 152 328 215 N SD: 0.0353 c. M:-0.0604 c. 2330: 164 217 232 354 164 232 217 164 354 232 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 x 5 x 6 S SD: 4.5983 cents 4 x x 5 x x 6 x 7 x 8 S SD: 24.9865 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 12.5922 cents 6 x x 7:8 x 9 x 10:11:12 S SD: 9.9190 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 13.3137 cents 8 x 9:10 x 11:12:13 x 15:16 SD: 11.7864 cents 9 x 10:11:12:13 x 14:15:17:18 SD: 10.5441 cents 10 x 11:12:13:14:15:16:17:19:20 SD: 7.2461 cents 11 x 12:13:15 x 17:18 x 21:22 SD: 14.2761 cents 12:13 x 14:16:17:18:19:20:22:24 S SD: 9.4397 cents 14:15:16:17:19:20:21:22:24:26:28 SD: 8.5460 cents 15:16:17:18:20:21:23:24:25:28:30 SD: 5.2927 cents 18:19:20:22:24:25:27:29:30:34:36 SD: 4.7189 cents 20:21:22:24:27:28:30:32:34:37:40 SD: 4.5787 cents 22:23:25:26:29:31:33:35:37:41:44 SD: 4.4848 cents 24:25:27:29:32:34:36:38:40:45:48 SD: 3.7302 cents 25:26:28:30:33:35:38:40:42:47:50 SD: 3.5424 cents 32:34:36:38:43:45:48:51:54:60:64 SD: 3.4838 cents 34:36:38:41:45:48:51:54:57:63:68 SD: 3.1744 cents 35:37:39:42:47:49:53:56:59:65:70 SD: 2.7391 cents 40:42:45:48:53:56:60:64:67:75:80 SD: 1.6229 cents 60:63:67:72:80:84:90:96:101:112:120 SD: 0.6197 cents 100:105:112:120:133:140:150:160:168:187:200 SD: 0.5322 cents 140:147:157:168:187:196:210:224:235:261:280 SD: 0.4633 cents 160:168:179:192:213:224:240:256:269:299:320 SD: 0.4056 cents 200:210:224:240:267:280:300:320:336:373:400 SD: 0.2659 cents 240:252:269:288:320:336:360:384:403:448:480 SD: 0.1548 cents 300:315:336:360:400:420:450:480:504:560:600 S SD: 0.0000 cents