Scala analysis: cv7
Seventh 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: 21/20 84.467193 minor semitone 2: 9/8 203.910002 major whole tone 3: 6/5 315.641287 minor third 4: 9/7 435.084095 septimal major third, BP third 5: 21/16 470.780907 narrow fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 12/7 933.129094 septimal major sixth 10: 9/5 1017.596288 just minor seventh, BP seventh 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 21/20 84.4672 minor semitone 2: 15/14 119.4428 major diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 15/14 119.4428 major diatonic semitone 5: 49/48 35.6968 slendro diesis, septimal 1/6-tone 6: 16/15 111.7313 minor diatonic semitone 7: 15/14 119.4428 major diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 15/14 119.4428 major diatonic semitone 10: 21/20 84.4672 minor semitone 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 16/15 111.7313 minor diatonic 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 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 2: 2 9/8 203.910 cents major whole tone 2: 5 8/7 231.174 cents septimal whole tone 3: 5 7/6 266.871 cents septimal minor third 3: 1 75/64 274.582 cents classic augmented second 3: 3 6/5 315.641 cents minor third 3: 1 128/105 342.905 cents septimal neutral third 3: 2 60/49 350.617 cents smaller approximation to neutral third 4: 1 49/40 351.338 cents larger approximation to neutral third 4: 2 56/45 378.602 cents septimal narrow major third 4: 5 5/4 386.314 cents major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 2 9/7 435.084 cents septimal major third, BP third 4: 1 64/49 462.348 cents 2 septatones or septatonic major third 5: 3 21/16 470.781 cents narrow fourth 5: 6 4/3 498.045 cents perfect fourth 5: 1 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: 1 112/75 694.243 cents marvelous fifth 7: 6 3/2 701.955 cents perfect fifth 7: 3 32/21 729.219 cents wide fifth 8: 1 49/32 737.652 cents 8: 2 14/9 764.916 cents septimal minor sixth 8: 1 25/16 772.627 cents classic augmented fifth 8: 5 8/5 813.686 cents minor sixth 8: 2 45/28 821.398 cents septimale wide minor sixth 8: 1 80/49 848.662 cents smaller approximation to neutral sixth 9: 2 49/30 849.383 cents larger approximation to neutral sixth 9: 1 105/64 857.095 cents septimal neutral sixth 9: 3 5/3 884.359 cents major sixth, BP sixth 9: 1 128/75 925.418 cents diminished seventh 9: 5 12/7 933.129 cents septimal major sixth 10: 5 7/4 968.826 cents harmonic seventh 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 1 25/14 1003.802 cents middle minor seventh 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 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: 5.09091 = 56/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 84.5 203.9 315.6 435.1 470.8 582.5 702.0 813.7 933.1 1017.6 1088.3 1200.0 84.5 : 119.4 231.2 350.6 386.3 498.0 617.5 729.2 848.7 933.1 1003.8 1115.5 1200.0 203.9 : 111.7 231.2 266.9 378.6 498.0 609.8 729.2 813.7 884.4 996.1 1080.6 1200.0 315.6 : 119.4 155.1 266.9 386.3 498.0 617.5 702.0 772.6 884.4 968.8 1088.3 1200.0 435.1 : 35.7 147.4 266.9 378.6 498.0 582.5 653.2 764.9 849.4 968.8 1080.6 1200.0 470.8 : 111.7 231.2 342.9 462.3 546.8 617.5 729.2 813.7 933.1 1044.9 1164.3 1200.0 582.5 : 119.4 231.2 350.6 435.1 505.8 617.5 702.0 821.4 933.1 1052.6 1088.3 1200.0 702.0 : 111.7 231.2 315.6 386.3 498.0 582.5 702.0 813.7 933.1 968.8 1080.6 1200.0 813.7 : 119.4 203.9 274.6 386.3 470.8 590.2 702.0 821.4 857.1 968.8 1088.3 1200.0 933.1 : 84.5 155.1 266.9 351.3 470.8 582.5 702.0 737.7 849.4 968.8 1080.6 1200.0 1017.6: 70.7 182.4 266.9 386.3 498.0 617.5 653.2 764.9 884.4 996.1 1115.5 1200.0 1088.3: 111.7 196.2 315.6 427.4 546.8 582.5 694.2 813.7 925.4 1044.9 1129.3 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: 470.7809 .. 546.8154 cents 256/245, 76.0345 cents 1029/1024, 8.4327 cents 6: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 49/48, 35.6968 cents 7: 653.1846 .. 729.2191 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 8: 737.6518 .. 848.6619 cents 2560/2401, 111.0101 cents 1029/1024, 8.4327 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 : 100.61043 cents, oct.: 1207.32519 cents Scale is strictly proper Step pattern alph. order: ABCBDCBCBAEC Step pattern size order : CEDEADEDECBD Scale is a Constant Structure, by a margin of 0.72120 cents Scale diversity : 1.501207 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.240383 Rothenberg efficiency : 0.284187 redundancy: 0.715813 Efficiency x scale size : 3.410245 Number of different interval sizes : 56 = 5.09091 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.09091 = 56/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Number of recognisable fifths : 7, average 700.8534 cents Best fifths form a closed circle All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 1 = 8.3333% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 7 Odd number limit : 105 (O: 105 U: 105) Highest odd numerator or denominator: 21 Scale harmonicity : 0.021880 Average absolute harmonicity : 0.171933 Specific harmonicity : 0.137213 Fundamental : 1/560, -9.1293 octaves, 0.4672 Hz. Guide tone : 2520, 11.2992 octaves, 659296.425 Hz. Exponens Consonantiae : 1.411200E+06, 20.42849 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 105.5, average 8.79167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.24851, average 0.85404 Sum of Tenney's harmonic distance : 20.16537, average 1.68045 Vogel's harmonic complexity : 17.41667 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 239.45879, average 3.06998 Lattice compactness (without 2's) : 123.34847, average 1.58139 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 3 -0.50000 20 1 3: 0 .. 2 1.00000 12 2 5: -1 .. 1 -0.33333 6 4 7: -1 .. 1 0.08333 5 5 Average exponent except 2's : 9 / 12 = 0.75000 Average absolute exponent except 2's: 23 / 12 = 1.91667 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: 19.6376 c. M: 35.0841 c. Twelve-tone Chromatic (1/11-comma) 18: 1 2 2 2 0 2 2 1 2 1 1 2 N T3 SD: 18.0592 c. M:-31.5826 c. 19: 1 2 2 2 0 2 2 2 2 1 1 2 N SD: 13.8579 c. M: 28.6756 c. 22: 2 2 2 2 1 2 2 2 2 2 1 2 SP B ME SD: 13.2995 c. M:-24.6237 c. 25: 2 2 3 2 1 2 3 2 2 2 2 2 P D3 SD: 12.7254 c. M: 21.1291 c. 26: 2 2 3 2 1 3 2 3 2 2 2 2 P T3 SD: 13.3431 c. M: 19.6995 c. 27: 2 3 2 3 1 2 3 2 3 2 2 2 P D3 SD: 11.6466 c. M:-22.8424 c. 28: 2 3 2 3 1 3 2 3 3 2 1 3 P SD: 11.0503 c. M:-17.4878 c. 31: 2 3 3 3 1 3 3 3 3 2 2 3 P SD: 6.5140 c. M: 11.1447 c. 41: 3 4 4 4 1 4 4 4 4 3 2 4 P SD: 4.1086 c. M:-6.7940 c. 53: 4 5 5 5 2 5 5 5 5 4 3 5 SP SD: 3.5602 c. M:-6.1671 c. 72: 5 7 7 7 2 7 7 7 7 5 4 7 P SD: 2.5209 c. M: 4.9354 c. 94: 7 9 9 9 3 9 9 9 9 7 5 9 SP SD: 2.8630 c. M:-4.8945 c. 99: 7 10 9 10 3 9 10 9 10 7 6 9 P SD: 1.3503 c. M:-2.6404 c. 130: 9 13 12 13 4 12 13 12 13 9 8 12 P SD: 1.1866 c. M: 2.2117 c. 140: 10 14 13 14 4 13 14 13 14 10 8 13 P SD: 1.2982 c. M:-2.4037 c. 171: 12 17 16 17 5 16 17 16 17 12 10 16 P SD: 0.3064 c. M: 0.6055 c. 441: 31 44 41 44 13 41 44 41 44 31 26 41 P SD: 0.1469 c. M:-0.2901 c. 612: 43 61 57 61 18 57 61 57 61 43 36 57 P SD: 0.1222 c. M:-0.2100 c. 935: 66 93 87 93 28 87 93 87 93 66 55 87 SP SD: 0.1327 c. M:-0.2387 c. 1053: 74 105 98 105 31 98 105 98 105 74 62 98 P SD: 0.1232 c. M:-0.2435 c. 1065: 75 106 99 106 32 99 106 99 106 75 63 99 SP SD: 0.1286 c. M:-0.2050 c. 1106: 78 110 103 110 33 103 110 103 110 78 65 103 SP SD: 0.0859 c. M:-0.1621 c. 1236: 87 123 115 123 37 115 123 115 123 87 73 115 SP SD: 0.0831 c. M: 0.1326 c. 1277: 90 127 119 127 38 119 127 119 127 90 75 119 SP SD: 0.0707 c. M:-0.1060 c. 1407: 99 140 131 140 42 131 140 131 140 99 83 131 SP SD: 0.0629 c. M: 0.1161 c. 1547: 109 154 144 154 46 144 154 144 154 109 91 144 SP SD: 0.0652 c. M:-0.1154 c. 1677: 118 167 156 167 50 156 167 156 167 118 99 156 SP SD: 0.0563 c. M:-0.1034 c. 1718: 121 171 160 171 51 160 171 160 171 121 101 160 SP SD: 0.0519 c. M:-0.0987 c. 1848: 130 184 172 184 55 172 184 172 184 130 109 172 SP SD: 0.0377 c. M: 0.0638 c. 2019: 142 201 188 201 60 188 201 188 201 142 119 188 SP SD: 0.0393 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: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 18.6246 cents 4 x x x 5 x x 6 x 7 x x 8 S SD: 15.1096 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 0.0000 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 13.4470 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 8.0991 cents 8 x 9 x 10 x 11:12:13:14 x 15:16 S SD: 9.1398 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 11.3992 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 5.0238 cents 11 x 12:13:14 x 15:17:18:19:20:21:22 SD: 10.7483 cents 12:13 x 14:15:16:17:18:19:21:22:23:24 SD: 10.3283 cents 13:14:15:16 x 17:18:20:21:22:23:24:26 S SD: 9.3047 cents 14:15:16:17:18 x 20:21:22:24:25:26:28 S SD: 6.4587 cents 15:16:17:18:19:20:21:23:24:26:27:28:30 SD: 5.3947 cents 16:17:18:19 x 21:22:24:26:27:29:30:32 SD: 5.2451 cents 17:18:19:20:22 x 24:26:27:29:31:32:34 SD: 5.5806 cents 18:19:20:22:23:24:25:27:29:31:32:34:36 SD: 4.8854 cents 20:21:23:24 x 26:28:30:32:34:36:38:40 SD: 4.5071 cents 22:23:25:26:28:29:31:33:35:38:40:41:44 SD: 3.9350 cents 23:24:26:28 x 30:32:35:37:39:41:43:46 SD: 4.4661 cents 24:25:27:29:31:32:34:36:38:41:43:45:48 SD: 3.7177 cents 25:26:28:30:32:33:35:38:40:43:45:47:50 SD: 2.7271 cents 27:28:30:32:35 x 38:41:43:46:49:51:54 SD: 4.6954 cents 28:29:32:34:36:37:39:42:45:48:50:53:56 SD: 4.1338 cents 30:32:34:36 x 39:42:45:48:51:54:56:60 S SD: 3.4622 cents 32:34:36:38:41:42:45:48:51:55:58:60:64 SD: 2.7053 cents 35:37:39:42:45:46:49:53:56:60:63:66:70 SD: 2.3339 cents 38:40:43:46:49:50:53:57:61:65:68:71:76 SD: 2.0801 cents 40:42:45:48:51:53:56:60:64:69:72:75:80 SD: 2.0336 cents 42:44:47:50:54:55:59:63:67:72:76:79:84 SD: 1.8263 cents 55:58:62:66:71:72:77:83:88:94:99:103:110 SD: 1.3909 cents 60:63:68:72:77:79:84:90:96:103:108:113:120 SD: 1.3652 cents 64:67:72:77:82:84:90:96:102:110:115:120:128 SD: 1.2300 cents 70:74:79:84:90:92:98:105:112:120:126:131:140 SD: 1.1313 cents 80:84:90:96:103:105:112:120:128:137:144:150:160 SD: 0.2504 cents 280:294:315:336:360:368:392:420:448:480:504:525:560 SD: 0.1962 cents 320:336:360:384:411:420:448:480:512:549:576:600:640 SD: 0.1879 cents 360:378:405:432:463:473:504:540:576:617:648:675:720 SD: 0.1624 cents 400:420:450:480:514:525:560:600:640:686:720:750:800 SD: 0.1002 cents 480:504:540:576:617:630:672:720:768:823:864:900:960 SD: 0.0417 cents 560:588:630:672:720:735:784:840:896:960:1008:1050:1120 S SD: 0.0000 cents