Scala analysis: cv9
Ninth 12/5 scale <12 19 28 34| epimorphic
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: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 10/7 617.487807 Euler's tritone 7: 32/21 729.219093 wide fifth 8: 8/5 813.686286 minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 25/14 1003.801521 middle minor seventh 11: 40/21 1115.532807 acute major seventh 12: 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: 49/48 35.6968 slendro diesis, septimal 1/6-tone 4: 15/14 119.4428 major diatonic semitone 5: 16/15 111.7313 minor diatonic 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: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 15/14 119.4428 major diatonic semitone 11: 16/15 111.7313 minor diatonic semitone 12: 21/20 84.4672 minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 21/20 84.467 cents minor semitone 1: 4 16/15 111.731 cents minor diatonic semitone 1: 4 15/14 119.443 cents major diatonic semitone 2: 1 49/45 147.428 cents BP minor semitone 2: 2 35/32 155.140 cents septimal neutral second 2: 1 125/112 190.115 cents classic augmented semitone 2: 2 28/25 196.198 cents middle second 2: 1 9/8 203.910 cents major whole tone 2: 5 8/7 231.174 cents septimal whole tone 3: 4 7/6 266.871 cents septimal minor third 3: 1 75/64 274.582 cents classic augmented second 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 4 6/5 315.641 cents minor third 3: 1 128/105 342.905 cents septimal neutral third 3: 1 60/49 350.617 cents smaller approximation to neutral third 4: 1 49/40 351.338 cents larger approximation to neutral third 4: 1 56/45 378.602 cents septimal narrow major third 4: 6 5/4 386.314 cents major third 4: 2 32/25 427.373 cents classic diminished fourth 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 64/49 462.348 cents 2 septatones or septatonic major third 5: 1 98/75 463.069 cents 5: 2 21/16 470.781 cents narrow fourth 5: 5 4/3 498.045 cents perfect fourth 5: 2 75/56 505.757 cents marvelous fourth 5: 2 48/35 546.815 cents septimal semi-augmented fourth 6: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 45/32 590.224 cents diatonic tritone 6: 1 64/45 609.776 cents 2nd tritone 6: 5 10/7 617.488 cents Euler's tritone 7: 2 35/24 653.185 cents septimal semi-diminished fifth 7: 2 112/75 694.243 cents marvelous fifth 7: 5 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 7: 1 75/49 736.931 cents BP fifth 8: 1 49/32 737.652 cents 8: 1 14/9 764.916 cents septimal minor sixth 8: 2 25/16 772.627 cents classic augmented fifth 8: 6 8/5 813.686 cents minor sixth 8: 1 45/28 821.398 cents septimale wide minor sixth 8: 1 80/49 848.662 cents smaller approximation to neutral sixth 9: 1 49/30 849.383 cents larger approximation to neutral sixth 9: 1 105/64 857.095 cents septimal neutral sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 1 128/75 925.418 cents diminished seventh 9: 4 12/7 933.129 cents septimal major sixth 10: 5 7/4 968.826 cents harmonic seventh 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 2 25/14 1003.802 cents middle minor seventh 10: 1 224/125 1009.885 cents 10: 2 64/35 1044.860 cents septimal neutral seventh 10: 1 90/49 1052.572 cents 11: 4 28/15 1080.557 cents grave major seventh 11: 4 15/8 1088.269 cents classic major seventh 11: 2 40/21 1115.533 cents acute major seventh 11: 1 48/25 1129.328 cents classic diminished octave 11: 1 96/49 1164.303 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.45455 = 60/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 119.4 231.2 266.9 386.3 498.0 617.5 729.2 813.7 884.4 1003.8 1115.5 1200.0 119.4 : 111.7 147.4 266.9 378.6 498.0 609.8 694.2 764.9 884.4 996.1 1080.6 1200.0 231.2 : 35.7 155.1 266.9 386.3 498.0 582.5 653.2 772.6 884.4 968.8 1088.3 1200.0 266.9 : 119.4 231.2 350.6 462.3 546.8 617.5 736.9 848.7 933.1 1052.6 1164.3 1200.0 386.3 : 111.7 231.2 342.9 427.4 498.0 617.5 729.2 813.7 933.1 1044.9 1080.6 1200.0 498.0 : 119.4 231.2 315.6 386.3 505.8 617.5 702.0 821.4 933.1 968.8 1088.3 1200.0 617.5 : 111.7 196.2 266.9 386.3 498.0 582.5 702.0 813.7 849.4 968.8 1080.6 1200.0 729.2 : 84.5 155.1 274.6 386.3 470.8 590.2 702.0 737.7 857.1 968.8 1088.3 1200.0 813.7 : 70.7 190.1 301.8 386.3 505.8 617.5 653.2 772.6 884.4 1003.8 1115.5 1200.0 884.4 : 119.4 231.2 315.6 435.1 546.8 582.5 702.0 813.7 933.1 1044.9 1129.3 1200.0 1003.8: 111.7 196.2 315.6 427.4 463.1 582.5 694.2 813.7 925.4 1009.9 1080.6 1200.0 1115.5: 84.5 203.9 315.6 351.3 470.8 582.5 702.0 813.7 898.2 968.8 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 119.4428 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 2: 147.4281 .. 231.1741 cents 360/343, 83.7460 cents 686/675, 27.9853 cents 3: 266.8709 .. 350.6169 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 4: 351.3381 .. 462.3482 cents 2560/2401, 111.0101 cents 2401/2400, 0.7212 cents 5: 463.0694 .. 546.8154 cents 360/343, 83.7460 cents 2401/2400, 0.7212 cents 6: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 49/48, 35.6968 cents 7: 653.1846 .. 736.9306 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 8: 737.6518 .. 848.6619 cents 2560/2401, 111.0101 cents 2401/2400, 0.7212 cents 9: 849.3831 .. 933.1291 cents 360/343, 83.7460 cents 2401/2400, 0.7212 cents 10: 968.8259 .. 1052.5719 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 11: 1080.5572 .. 1164.3032 cents 360/343, 83.7460 cents 686/675, 27.9853 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 15/14, 119.4428 cents Average / Smallest step : 2.801371 Largest / Average step : 1.194428 Largest / Smallest step : 3.346036 Median interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 100.62298 cents, oct.: 1207.47579 cents Scale is strictly proper Step pattern alph. order: ABCABABDEABD Step pattern size order : EDAEDEDCBEDC Scale is a Constant Structure, by a margin of 0.72120 cents Scale diversity : 1.511514 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.227530 Rothenberg efficiency : 0.274886 redundancy: 0.725114 Efficiency x scale size : 3.298629 Number of different interval sizes : 60 = 5.45455 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.45455 = 60/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 6 Number of recognisable fifths : 7, average 699.7517 cents Best fifths form a closed circle Scale contains a complete diamond : 1 5 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 3 = 25.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 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 -- Rational properties -- Prime limit : 7 Odd number limit : 125 (O: 125 U: 125) Highest odd numerator or denominator: 25 Scale harmonicity : 0.019192 Average absolute harmonicity : 0.162049 Specific harmonicity : 0.129353 Fundamental : 1/420, -8.7142 octaves, 0.6229 Hz. Guide tone : 16800, 14.0362 octaves, 4395309.497 Hz. Exponens Consonantiae : 7.056000E+06, 22.75042 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 133.5, average 11.12500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.32780, average 0.86065 Sum of Tenney's harmonic distance : 21.29386, average 1.77449 Vogel's harmonic complexity : 16.66667 Wille's k value : 262 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 241.07051, average 3.09065 Lattice compactness (without 2's) : 123.94224, average 1.58900 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 5 1.08333 23 1 3: -1 .. 1 -0.33333 6 1 5: -1 .. 2 0.50000 8 3 7: -1 .. 1 -0.41667 7 7 Average exponent except 2's :-3 / 12 =-0.25000 Average absolute exponent except 2's: 21 / 12 = 1.75000 Scale is JI-epimorphic with val: <12 19 28 34| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 19.3343 c. M:-33.1291 c. Twelve-tone Chromatic (1/11-comma) 18: 2 1 1 2 1 2 2 1 1 2 2 1 P D3 S SD: 17.0565 c. M: 31.3783 c. 19: 2 2 0 2 2 2 2 1 1 2 2 1 N SD: 14.1163 c. M:-28.6756 c. 20: 2 2 0 2 2 2 2 2 1 2 2 1 N SD: 18.2738 c. M: 26.8709 c. 22: 2 2 1 2 2 2 2 2 1 2 2 2 SP B ME SD: 13.9566 c. M: 24.6237 c. Jubilee-12 26: 3 2 1 2 3 2 3 2 1 3 2 2 P SD: 12.1855 c. M:-19.0187 c. 27: 3 2 1 3 2 3 2 2 2 3 2 2 P D3 SD: 11.0352 c. M:-18.4207 c. 30: 3 3 1 3 2 3 3 2 2 3 3 2 P T3 SD: 10.7821 c. M: 18.0450 c. 31: 3 3 1 3 3 3 3 2 2 3 3 2 P SD: 4.0000 c. M:-7.0478 c. 68: 7 6 2 7 6 7 6 5 4 7 6 5 P SD: 2.9191 c. M: 5.6897 c. 72: 7 7 2 7 7 7 7 5 4 7 7 5 P SD: 2.3873 c. M:-4.1142 c. 99: 10 9 3 10 9 10 9 7 6 10 9 7 P SD: 1.2827 c. M:-2.2591 c. 130: 13 12 4 13 12 13 12 9 8 13 12 9 P SD: 1.1818 c. M:-2.3523 c. 140: 14 13 4 14 13 14 13 10 8 14 13 10 P SD: 0.8409 c. M: 1.5016 c. 171: 17 16 5 17 16 17 16 12 10 17 16 12 P SD: 0.2963 c. M:-0.6055 c. 410: 41 38 12 41 38 41 38 29 24 41 38 29 P SD: 0.3432 c. M:-0.5572 c. 441: 44 41 13 44 41 44 41 31 26 44 41 31 P SD: 0.1553 c. M:-0.2851 c. 612: 61 57 18 61 57 61 57 43 36 61 57 43 P SD: 0.1335 c. M: 0.2042 c. 935: 93 87 28 93 87 93 87 66 55 93 87 66 SP SD: 0.1344 c. M: 0.2387 c. 966: 96 90 29 96 90 96 90 68 57 96 90 68 SP SD: 0.1046 c. M:-0.2098 c. 1106: 110 103 33 110 103 110 103 78 65 110 103 78 SP SD: 0.0996 c. M: 0.1849 c. 1137: 113 106 34 113 106 113 106 80 67 113 106 80 SP SD: 0.0907 c. M: 0.1816 c. 1236: 123 115 37 123 115 123 115 87 73 123 115 87 SP SD: 0.0769 c. M:-0.1194 c. 1376: 137 128 41 137 128 137 128 97 81 137 128 97 SP SD: 0.0692 c. M: 0.1493 c. 1407: 140 131 42 140 131 140 131 99 83 140 131 99 SP SD: 0.0435 c. M:-0.0801 c. 1547: 154 144 46 154 144 154 144 109 91 154 144 109 SP SD: 0.0449 c. M: 0.0835 c. 1578: 157 147 47 157 147 157 147 111 93 157 147 111 SP SD: 0.0380 c. M:-0.0585 c. 2019: 201 188 60 201 188 201 188 142 119 201 188 142 SP SD: 0.0382 c. M:-0.0690 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 13.6320 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 11.0867 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 12.3161 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 8.8493 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.4960 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 10.4670 cents 9 x 10 x 11:12:13:14 x 15:16:17:18 S SD: 8.4633 cents 10:11 x 12 x 13:14:15:16:17:18:19:20 S SD: 9.8623 cents 11:12 x 13:14:15:16:17 x 18:20:21:22 S SD: 8.6752 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 4.9689 cents 13:14:15 x 16:17:19:20:21:22:23:25:26 SD: 6.7685 cents 14:15:16 x 18:19:20:21:22:23:25:27:28 SD: 7.1101 cents 15:16:17:18:19:20:21:23:24:25:27:29:30 SD: 6.1056 cents 17:18:19:20:21:23:24:26:27:28:30:32:34 SD: 5.9290 cents 18:19 x 21:23:24:26:27:29:30:32:34:36 SD: 5.4830 cents 19:20 x 22:24:25:27:29:30:32:34:36:38 SD: 4.9850 cents 20:21:23 x 25:27:29:30:32:33:36:38:40 SD: 5.5460 cents 21:23:24:25:26:28:30:32:34:35:38:40:42 SD: 5.1983 cents 23:25:26:27:29:31:33:35:37:38:41:44:46 SD: 3.8302 cents 25:27 x 29:31:33:36:38:40:42:45:48:50 SD: 3.5961 cents 26:28:30 x 33:35:37:40:42:43:46:50:52 SD: 4.6625 cents 27:29:31:32:34:36:39:41:43:45:48:51:54 SD: 3.4609 cents 28:30:32:33:35:37:40:43:45:47:50:53:56 SD: 2.7139 cents 32:34 x 37:40:43:46:49:51:53:57:61:64 SD: 2.8809 cents 36:39:41:42:45:48:51:55:58:60:64:69:72 SD: 2.5708 cents 40:43:46:47:50:53:57:61:64:67:71:76:80 SD: 2.1109 cents 42:45:48:49:53:56:60:64:67:70:75:80:84 SD: 1.4335 cents 65:70:74:76:81:87:93:99:104:108:116:124:130 SD: 1.3293 cents 71:76:81:83:89:95:101:108:114:118:127:135:142 SD: 1.2544 cents 72:77:82:84:90:96:103:110:115:120:129:137:144 SD: 0.9056 cents 84:90:96:98:105:112:120:128:134:140:150:160:168 SD: 0.4300 cents 168:180:192:196:210:224:240:256:269:280:300:320:336 SD: 0.1073 cents 252:270:288:294:315:336:360:384:403:420:450:480:504 SD: 0.0716 cents 420:450:480:490:525:560:600:640:672:700:750:800:840 S SD: 0.0000 cents