Scala analysis: cv5
Fifth 12/5 scale <12 19 28 34| epimorphic = inverse hen12
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: 9/8 203.910002 major whole tone 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major 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: 7/4 968.825906 harmonic 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: 15/14 119.4428 major diatonic semitone 2: 21/20 84.4672 minor semitone 3: 16/15 111.7313 minor diatonic semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 21/20 84.4672 minor semitone 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: 49/48 35.6968 slendro diesis, septimal 1/6-tone 11: 15/14 119.4428 major diatonic semitone 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: 3 35/32 155.140 cents septimal neutral second 2: 1 10/9 182.404 cents minor whole tone 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: 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: 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: 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: 1 16/9 996.090 cents Pythagorean minor seventh 10: 2 25/14 1003.802 cents middle minor seventh 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 10: 3 64/35 1044.860 cents septimal neutral seventh 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 : 119.4 203.9 315.6 386.3 470.8 582.5 702.0 813.7 933.1 968.8 1088.3 1200.0 119.4 : 84.5 196.2 266.9 351.3 463.1 582.5 694.2 813.7 849.4 968.8 1080.6 1200.0 203.9 : 111.7 182.4 266.9 378.6 498.0 609.8 729.2 764.9 884.4 996.1 1115.5 1200.0 315.6 : 70.7 155.1 266.9 386.3 498.0 617.5 653.2 772.6 884.4 1003.8 1088.3 1200.0 386.3 : 84.5 196.2 315.6 427.4 546.8 582.5 702.0 813.7 933.1 1017.6 1129.3 1200.0 470.8 : 111.7 231.2 342.9 462.3 498.0 617.5 729.2 848.7 933.1 1044.9 1115.5 1200.0 582.5 : 119.4 231.2 350.6 386.3 505.8 617.5 736.9 821.4 933.1 1003.8 1088.3 1200.0 702.0 : 111.7 231.2 266.9 386.3 498.0 617.5 702.0 813.7 884.4 968.8 1080.6 1200.0 813.7 : 119.4 155.1 274.6 386.3 505.8 590.2 702.0 772.6 857.1 968.8 1088.3 1200.0 933.1 : 35.7 155.1 266.9 386.3 470.8 582.5 653.2 737.7 849.4 968.8 1080.6 1200.0 968.8 : 119.4 231.2 350.6 435.1 546.8 617.5 702.0 813.7 933.1 1044.9 1164.3 1200.0 1088.3: 111.7 231.2 315.6 427.4 498.0 582.5 694.2 813.7 925.4 1044.9 1080.6 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: 155.1396 .. 231.1741 cents 256/245, 76.0345 cents 49/48, 35.6968 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 .. 1044.8604 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 11: 1080.5572 .. 1164.3032 cents 360/343, 83.7460 cents 49/48, 35.6968 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 : 99.61380 cents, oct.: 1195.36562 cents Scale is strictly proper Step pattern alph. order: ABCDBCACAEAC Step pattern size order : ECDBCDEDEAED Scale is a Constant Structure, by a margin of 0.72120 cents Scale diversity : 1.491525 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 : 5/4, 386.3137 cents & inv., amount: 6 Number of recognisable fifths : 7, average 699.7517 cents Scale contains a complete diamond : 1 5 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 3 = 25.0000% Scale is differentially coherent in interval class 1 Scale is 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 : 105 (O: 105 U: 105) Highest odd numerator or denominator: 21 Scale harmonicity : 0.021880 Average absolute harmonicity : 0.176391 Specific harmonicity : 0.134462 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 : 94.5, average 7.87500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.73797, average 0.81150 Sum of Tenney's harmonic distance : 19.15997, average 1.59666 Vogel's harmonic complexity : 17.83333 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 240.32148, average 3.08104 Lattice compactness (without 2's) : 120.87633, average 1.54970 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 3 -0.75000 23 1 3: 0 .. 2 0.66667 8 2 5: -1 .. 1 0.00000 6 4 7: -1 .. 1 0.08333 5 5 Average exponent except 2's : 9 / 12 = 0.75000 Average absolute exponent except 2's: 19 / 12 = 1.58333 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: 19.1115 c. M: 33.1291 c. Twelve-tone Chromatic (1/11-comma) 18: 2 1 2 1 1 2 2 1 2 1 1 2 P B D3 SD: 17.4206 c. M:-31.3783 c. 19: 2 1 2 1 1 2 2 2 2 0 2 2 N SD: 13.8836 c. M: 28.6756 c. 22: 2 2 2 1 2 2 2 2 2 1 2 2 SP B ME SD: 11.0246 c. M:-20.1282 c. Pajara-12 28: 3 2 2 2 2 3 2 3 3 1 2 3 P SD: 11.7962 c. M:-17.4878 c. 30: 3 2 3 2 2 3 3 2 3 1 3 3 P SD: 10.9708 c. M:-18.0450 c. 31: 3 2 3 2 2 3 3 3 3 1 3 3 P SD: 4.6727 c. M: 10.3616 c. 41: 4 3 4 2 3 4 4 4 4 1 4 4 P SD: 3.8529 c. M:-6.3099 c. 53: 5 4 5 3 4 5 5 5 5 2 5 5 SP SD: 3.5687 c. M: 6.2353 c. 68: 7 5 6 4 5 6 7 6 7 2 7 6 P SD: 3.8690 c. M:-7.8547 c. 72: 7 5 7 4 5 7 7 7 7 2 7 7 P SD: 2.7733 c. M: 4.9354 c. 87: 9 6 8 5 6 8 9 8 9 2 9 8 N SD: 2.6654 c. M:-4.8019 c. 94: 9 7 9 5 7 9 9 9 9 3 9 9 SP SD: 2.7916 c. M:-4.7218 c. 99: 10 7 9 6 7 9 10 9 10 3 10 9 P SD: 1.4746 c. M:-2.6404 c. 130: 13 9 12 8 9 12 13 12 13 4 13 12 P SD: 0.9537 c. M: 1.7951 c. 140: 14 10 13 8 10 13 14 13 14 4 14 13 P SD: 0.8844 c. M:-1.8043 c. 171: 17 12 16 10 12 16 17 16 17 5 17 16 P SD: 0.3372 c. M: 0.6055 c. 441: 44 31 41 26 31 41 44 41 44 13 44 41 P SD: 0.1459 c. M:-0.2851 c. 612: 61 43 57 36 43 57 61 57 61 18 61 57 P SD: 0.1215 c. M:-0.2042 c. 935: 93 66 87 55 66 87 93 87 93 28 93 87 SP SD: 0.1161 c. M:-0.2351 c. 1106: 110 78 103 65 78 103 110 103 110 33 110 103 SP SD: 0.0729 c. M:-0.1280 c. 1236: 123 87 115 73 87 115 123 115 123 37 123 115 SP SD: 0.0772 c. M: 0.1194 c. 1277: 127 90 119 75 90 119 127 119 127 38 127 119 SP SD: 0.0695 c. M:-0.1033 c. 1376: 137 97 128 81 97 128 137 128 137 41 137 128 SP SD: 0.0803 c. M:-0.1598 c. 1407: 140 99 131 83 99 131 140 131 140 42 140 131 SP SD: 0.0462 c. M: 0.0801 c. 1547: 154 109 144 91 109 144 154 144 154 46 154 144 SP SD: 0.0457 c. M:-0.0978 c. 1718: 171 121 160 101 121 160 171 160 171 51 171 160 SP SD: 0.0387 c. M:-0.0747 c. 1848: 184 130 172 109 130 172 184 172 184 55 184 172 SP SD: 0.0340 c. M: 0.0569 c. 2019: 201 142 188 119 142 188 201 188 201 60 201 188 SP SD: 0.0305 c. M: 0.0528 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 x 7 x 8 S SD: 0.0000 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.7541 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 13.9584 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 9.5708 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 5.1441 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 11.5502 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0017 cents 11:12 x 13:14 x 15:17:18:19 x 21:22 SD: 11.1384 cents 12:13 x 14:15:16:17:18:19 x 21:23:24 SD: 7.5393 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 7.5512 cents 14:15:16:17 x 18:20:21:22:24:25:26:28 S SD: 7.1185 cents 15:16:17:18:19:20:21:23:24 x 26:28:30 SD: 5.2014 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 4.5456 cents 19:20:21:23:24:25:27:29:30 x 33:36:38 SD: 6.4624 cents 20:21:23:24:25:26:28:30:32:34:35:38:40 SD: 5.0561 cents 23:25:26:28:29:30:32:35:37:39:40:43:46 SD: 4.5462 cents 24:26:27:29:30:32:34:36:38:41:42:45:48 SD: 3.7615 cents 25:27:28:30:31:33:35:38:40:43:44:47:50 SD: 2.9083 cents 32:34:36:38:40:42:45:48:51:55:56:60:64 SD: 2.1476 cents 40:43:45:48:50:53:56:60:64:69:70:75:80 SD: 1.7054 cents 55:59:62:66:69:72:77:83:88:94:96:103:110 SD: 1.2858 cents 70:75:79:84:88:92:98:105:112:120:123:131:140 SD: 1.1595 cents 80:86:90:96:100:105:112:120:128:137:140:150:160 SD: 0.5031 cents 112:120:126:134:140:147:157:168:179:192:196:210:224 SD: 0.4947 cents 160:171:180:192:200:210:224:240:256:274:280:300:320 SD: 0.3912 cents 192:206:216:230:240:252:269:288:307:329:336:360:384 SD: 0.3567 cents 200:214:225:240:250:263:280:300:320:343:350:375:400 SD: 0.3406 cents 208:223:234:250:260:273:291:312:333:357:364:390:416 SD: 0.3306 cents 224:240:252:269:280:294:314:336:358:384:392:420:448 SD: 0.2670 cents 240:257:270:288:300:315:336:360:384:411:420:450:480 SD: 0.1704 cents 320:343:360:384:400:420:448:480:512:549:560:600:640 SD: 0.1277 cents 448:480:504:538:560:588:627:672:717:768:784:840:896 SD: 0.1235 cents 480:514:540:576:600:630:672:720:768:823:840:900:960 SD: 0.0840 cents 560:600:630:672:700:735:784:840:896:960:980:1050:1120 S SD: 0.0000 cents