Scala analysis: xen12-wilson-06d-diamond
1-3-5-7 diamond, Figure 6d
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 7/6 266.870906 septimal minor third 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 10/7 617.487807 Euler's tritone 8: 3/2 701.955001 perfect fifth 9: 8/5 813.686286 minor sixth 10: 5/3 884.358713 major sixth, BP sixth 11: 12/7 933.129094 septimal major sixth 12: 7/4 968.825906 harmonic seventh 13: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 8/7 231.1741 septimal whole tone 2: 49/48 35.6968 slendro diesis, septimal 1/6-tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 16/15 111.7313 minor diatonic semitone 6: 21/20 84.4672 minor semitone 7: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 8: 21/20 84.4672 minor semitone 9: 16/15 111.7313 minor diatonic semitone 10: 25/24 70.6724 classic chromatic semitone, minor chroma 11: 36/35 48.7704 septimal diesis, 1/4-tone 12: 49/48 35.6968 slendro diesis, septimal 1/6-tone 13: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 8/7 231.174 cents septimal whole tone 2: 2 21/20 84.467 cents minor semitone 2: 4 15/14 119.443 cents major diatonic semitone 2: 2 10/9 182.404 cents minor whole tone 2: 2 28/25 196.198 cents middle second 2: 2 7/6 266.871 cents septimal minor third 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 3: 2 35/32 155.140 cents septimal neutral second 3: 1 9/8 203.910 cents major whole tone 3: 4 8/7 231.174 cents septimal whole tone 3: 2 7/6 266.871 cents septimal minor third 3: 2 6/5 315.641 cents minor third 3: 2 4/3 498.045 cents perfect fourth 4: 2 7/6 266.871 cents septimal minor third 4: 2 25/21 301.847 cents BP second, quasi-equal minor third 4: 4 6/5 315.641 cents minor third 4: 2 5/4 386.314 cents major third 4: 1 49/36 533.742 cents Arabic lute acute fourth 4: 2 48/35 546.815 cents septimal semi-augmented fourth 5: 2 60/49 350.617 cents smaller approximation to neutral third 5: 2 49/40 351.338 cents larger approximation to neutral third 5: 2 5/4 386.314 cents major third 5: 1 32/25 427.373 cents classic diminished fourth 5: 2 4/3 498.045 cents perfect fourth 5: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 2 10/7 617.488 cents Euler's tritone 6: 2 5/4 386.314 cents major third 6: 2 9/7 435.084 cents septimal major third, BP third 6: 2 4/3 498.045 cents perfect fourth 6: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 36/25 631.283 cents classic diminished fifth 6: 2 35/24 653.185 cents septimal semi-diminished fifth 6: 2 32/21 729.219 cents wide fifth 7: 2 21/16 470.781 cents narrow fourth 7: 2 48/35 546.815 cents septimal semi-augmented fourth 7: 1 25/18 568.717 cents classic augmented fourth 7: 2 10/7 617.488 cents Euler's tritone 7: 2 3/2 701.955 cents perfect fifth 7: 2 14/9 764.916 cents septimal minor sixth 7: 2 8/5 813.686 cents minor sixth 8: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 8: 2 10/7 617.488 cents Euler's tritone 8: 2 3/2 701.955 cents perfect fifth 8: 1 25/16 772.627 cents classic augmented fifth 8: 2 8/5 813.686 cents minor sixth 8: 2 80/49 848.662 cents smaller approximation to neutral sixth 8: 2 49/30 849.383 cents larger approximation to neutral sixth 9: 2 35/24 653.185 cents septimal semi-diminished fifth 9: 1 72/49 666.258 cents Arabic lute grave fifth 9: 2 8/5 813.686 cents minor sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 2 42/25 898.153 cents quasi-equal major sixth 9: 2 12/7 933.129 cents septimal major sixth 10: 2 3/2 701.955 cents perfect fifth 10: 2 5/3 884.359 cents major sixth, BP sixth 10: 2 12/7 933.129 cents septimal major sixth 10: 4 7/4 968.826 cents harmonic seventh 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 2 64/35 1044.860 cents septimal neutral seventh 11: 1 49/32 737.652 cents 11: 2 12/7 933.129 cents septimal major sixth 11: 2 25/14 1003.802 cents middle minor seventh 11: 2 9/5 1017.596 cents just minor seventh, BP seventh 11: 4 28/15 1080.557 cents grave major seventh 11: 2 40/21 1115.533 cents acute major seventh 12: 2 7/4 968.826 cents harmonic seventh 12: 2 15/8 1088.269 cents classic major seventh 12: 2 40/21 1115.533 cents acute major seventh 12: 2 48/25 1129.328 cents classic diminished octave 12: 2 35/18 1151.230 cents septimal semi-diminished octave 12: 2 96/49 1164.303 cents 12: 1 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.50000 = 13/2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 0.0 : 231.2 266.9 315.6 386.3 498.0 582.5 617.5 702.0 813.7 884.4 933.1 968.8 1200.0 231.2 : 35.7 84.5 155.1 266.9 351.3 386.3 470.8 582.5 653.2 702.0 737.7 968.8 1200.0 266.9 : 48.8 119.4 231.2 315.6 350.6 435.1 546.8 617.5 666.3 702.0 933.1 1164.3 1200.0 315.6 : 70.7 182.4 266.9 301.8 386.3 498.0 568.7 617.5 653.2 884.4 1115.5 1151.2 1200.0 386.3 : 111.7 196.2 231.2 315.6 427.4 498.0 546.8 582.5 813.7 1044.9 1080.6 1129.3 1200.0 498.0 : 84.5 119.4 203.9 315.6 386.3 435.1 470.8 702.0 933.1 968.8 1017.6 1088.3 1200.0 582.5 : 35.0 119.4 231.2 301.8 350.6 386.3 617.5 848.7 884.4 933.1 1003.8 1115.5 1200.0 617.5 : 84.5 196.2 266.9 315.6 351.3 582.5 813.7 849.4 898.2 968.8 1080.6 1165.0 1200.0 702.0 : 111.7 182.4 231.2 266.9 498.0 729.2 764.9 813.7 884.4 996.1 1080.6 1115.5 1200.0 813.7 : 70.7 119.4 155.1 386.3 617.5 653.2 702.0 772.6 884.4 968.8 1003.8 1088.3 1200.0 884.4 : 48.8 84.5 315.6 546.8 582.5 631.3 702.0 813.7 898.2 933.1 1017.6 1129.3 1200.0 933.1 : 35.7 266.9 498.0 533.7 582.5 653.2 764.9 849.4 884.4 968.8 1080.6 1151.2 1200.0 968.8 : 231.2 462.3 498.0 546.8 617.5 729.2 813.7 848.7 933.1 1044.9 1115.5 1164.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 231.1741 cents 28/25, 196.1985 cents 50/49, 34.9756 cents 2: 84.4672 .. 462.3482 cents 1280/1029, 377.8810 cents 147/160,-146.7069 cents 3: 155.1396 .. 498.0450 cents 128/105, 342.9054 cents 1715/2048,-307.2086 cents 4: 266.8709 .. 546.8154 cents 288/245, 279.9445 cents 7/8,-231.1741 cents 5: 350.6169 .. 617.4878 cents 7/6, 266.8709 cents 25/28,-196.1985 cents 6: 386.3137 .. 729.2191 cents 128/105, 342.9054 cents 7/8,-231.1741 cents 7: 470.7809 .. 813.6863 cents 128/105, 342.9054 cents 441/512,-258.4382 cents 8: 582.5122 .. 849.3831 cents 7/6, 266.8709 cents 7/8,-231.1741 cents 9: 653.1846 .. 933.1291 cents 288/245, 279.9445 cents 25/28,-196.1985 cents 10: 701.9550 .. 1044.8604 cents 128/105, 342.9054 cents 7/8,-231.1741 cents 11: 737.6518 .. 1115.5328 cents 1280/1029, 377.8810 cents 1715/2048,-307.2086 cents 12: 968.8259 .. 1165.0244 cents 28/25, 196.1985 cents 147/160,-146.7069 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.639201 Largest / Average step : 2.504386 Largest / Smallest step : 6.609579 Median interval of one step : 25/24, 70.6724 cents, amount: 2 Least squares average step : 88.93473 cents, oct.: 1156.15146 cents Scale is not proper Step pattern alph. order: ABCDEFGFEDCBA Step pattern size order : GBCDFEAEFDCBG Scale is not a Constant Structure Scale diversity : 1.459486 Lumma stability : 0.058293 Lumma impropriety factor : 0.859221 Number of different interval sizes : 54 = 4.50000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.50000 = 13/2 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 2401/2400, 0.7212 cents Number of recognisable fifths : 6, average 701.9550 cents Scale is a complete diamond : 1 3 5 7 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 13 = 100.0000% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval class 3 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 6-7 -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 7 Scale harmonicity : 0.022881 Average absolute harmonicity : 0.179520 Specific harmonicity : 0.134776 Fundamental : 1/420, -8.7142 octaves, 0.6229 Hz. Guide tone : 840, 9.7142 octaves, 219765.475 Hz. Exponens Consonantiae : 3.528000E+05, 18.42849 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 71.5, average 5.50000 Mersenne's string divisions : 116396280 Sum of van Prooijen's expressibility: 8.82071, average 0.67852 Sum of Tenney's harmonic distance : 17.84671, average 1.37282 Vogel's harmonic complexity : 17.53846 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 243.02681, average 2.67062 Lattice compactness (without 2's) : 143.22605, average 1.57391 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.53846 19 1 3: -1 .. 1 0.00000 6 2 5: -1 .. 1 0.00000 6 4 7: -1 .. 1 0.00000 6 6 Average exponent except 2's : 0 / 13 = 0.00000 Average absolute exponent except 2's: 18 / 13 = 1.38462 Scale is weakly epimorphic with val: <13 21 27 36| Scale is weakly epimorphic with val: <13 21 28 38| Scale is weakly epimorphic with val: <13 21 32 35| Scale is weakly epimorphic with val: <13 21 33 37| Scale is weakly epimorphic with val: <13 22 28 36| Scale is weakly epimorphic with val: <13 22 32 34| Scale is weakly epimorphic with val: <13 22 33 38| Scale is weakly epimorphic with val: <13 23 27 34| Scale is weakly epimorphic with val: <13 23 28 35| Scale is weakly epimorphic with val: <13 23 30 38| Scale is weakly epimorphic with val: <13 23 32 37|
FIT/MODE
13: 2 0 1 1 1 1 0 1 1 1 1 0 3 N SD: 48.6492 c. M: 82.2555 c. 14: 3 0 1 1 1 1 0 1 1 1 1 0 3 N I SD: 24.3848 c. M: 42.2577 c. 15: 3 0 1 1 1 1 1 1 1 1 1 0 3 N I SD: 16.8188 c. M:-26.8709 c. 19: 4 0 1 1 2 1 1 1 2 1 1 0 4 N I SD: 12.2042 c. M:-21.4575 c. 22: 4 1 1 1 2 2 0 2 2 1 1 1 4 N I SD: 10.4906 c. M:-17.4878 c. 27: 5 1 1 2 2 2 1 2 2 2 1 1 5 N I SD: 7.7882 c. M: 13.6863 c. 31: 6 1 1 2 3 2 1 2 3 2 1 1 6 N I SD: 3.6048 c. M: 5.9639 c. 68: 13 2 3 4 6 5 2 5 6 4 3 2 13 N I SD: 2.1824 c. M:-3.9274 c. 72: 14 2 3 4 7 5 2 5 7 4 3 2 14 N I SD: 1.7157 c. M: 2.9804 c. 99: 19 3 4 6 9 7 3 7 9 6 4 3 19 N I SD: 0.8882 c. M:-1.5651 c. 140: 27 4 6 8 13 10 4 10 13 8 6 4 27 N I SD: 0.8726 c. M: 1.5016 c. 171: 33 5 7 10 16 12 5 12 16 10 7 5 33 N I SD: 0.2458 c. M:-0.4049 c. 270: 52 8 11 16 25 19 8 19 25 16 11 8 52 N I SD: 0.2264 c. M:-0.3530 c. 441: 85 13 18 26 41 31 13 31 41 26 18 13 85 N I SD: 0.1297 c. M: 0.2042 c. 935: 180 28 38 55 87 66 27 66 87 55 38 28 180 N I SD: 0.1039 c. M:-0.1616 c. 1106: 213 33 45 65 103 78 32 78 103 65 45 33 213 N I SD: 0.0739 c. M:-0.1280 c. 1236: 238 37 50 73 115 87 36 87 115 73 50 37 238 N I SD: 0.0843 c. M:-0.1194 c. 1277: 246 38 52 75 119 90 37 90 119 75 52 38 246 N I SD: 0.0676 c. M:-0.1033 c. 1376: 265 41 56 81 128 97 40 97 128 81 56 41 265 N I SD: 0.0514 c. M:-0.0799 c. 1407: 271 42 57 83 131 99 41 99 131 83 57 42 271 N I SD: 0.0513 c. M: 0.0801 c. 1547: 298 46 63 91 144 109 45 109 144 91 63 46 298 N I SD: 0.0385 c. M: 0.0665 c. 1578: 304 47 64 93 147 111 46 111 147 93 64 47 304 N I SD: 0.0352 c. M:-0.0539 c. 1848: 356 55 75 109 172 130 54 130 172 109 75 55 356 N I SD: 0.0350 c. M: 0.0569 c. 2019: 389 60 82 119 188 142 59 142 188 119 82 60 389 N I SD: 0.0287 c. M:-0.0456 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x 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 x 5 x x 6 S SD: 0.0000 cents 4 x x x 5 x x x 6 x x x 7:8 S SD: 0.0000 cents 5 x x 6 x x 7 x x 8 x x 9:10 S SD: 9.7541 cents 6 x 7 x x 8 x x 9 x 10 x 11:12 S SD: 13.4228 cents 7:8 x x 9 x x 10 x 11 x 12 x 14 S SD: 9.6489 cents 8:9 x x 10 x 11 x 12:13 x x 14:16 S SD: 7.0521 cents 9:10 x 11 x 12 x 13 x 14:15 x 16:18 S SD: 10.3648 cents 10:11 x 12 x 13:14 x 15:16 x 17:18:20 S SD: 10.4752 cents 11 x 13 x 14:15 x 16:17 x 18:19 x 22 SD: 11.0466 cents 12 x 14 x 15:16 x 17:18:19:20 x 21:24 S SD: 2.5784 cents 13:15 x x 16:17:18:19:20:21 x 22:23:26 SD: 8.4283 cents 14:16 x 17:18:19 x 20:21:22:23:24:25:28 SD: 7.3598 cents 15:17 x 18:19:20:21 x 23:24:25 x 26:30 SD: 4.9578 cents 16:18 x 19:20:21:22:23:24:26:27 x 28:32 S SD: 5.8123 cents 17:19:20 x 21:23:24 x 26:27:28:29:30:34 SD: 6.4057 cents 18 x 21:22:23:24:25:26:27:29:30:31:32:36 SD: 5.2467 cents 19 x 22:23:24:25 x 27:29:30:32 x 33:38 SD: 5.7175 cents 20:23 x 24:25:27:28:29:30:32:33:34:35:40 SD: 3.4919 cents 21:24 x 25:26:28:29:30:32:34:35:36:37:42 SD: 4.0208 cents 22:25:26 x 28:29:31 x 33:35:37:38:39:44 SD: 5.0608 cents 23:26:27:28:29:31:32:33:35:37:38:39:40:46 SD: 4.3871 cents 24:27:28:29:30:32 x 34:36:38:40:41:42:48 S SD: 3.1860 cents 25 x 29:30:31:33:35:36:38:40:42:43:44:50 SD: 3.3659 cents 26:30 x 31:33:35:36:37:39:42:43:45:46:52 SD: 4.4625 cents 27:31 x 32:34:36:38:39:41:43:45:46:47:54 SD: 3.5883 cents 28:32:33:34:35:37:39:40:42:45:47:48:49:56 SD: 2.7299 cents 29:33:34:35:36:39:41 x 44:46:48:50:51:58 SD: 3.5450 cents 30:34:35:36:38:40:42:43:45:48:50:51:53:60 SD: 2.7175 cents 32 x 37:38:40:43:45:46:48:51:53:55:56:64 SD: 2.7777 cents 35:40:41:42:44:47:49:50:53:56:58:60:61:70 SD: 2.0594 cents 36:41:42:43:45:48:50:51:54:58:60:62:63:72 SD: 2.0475 cents 40:46:47:48:50:53:56:57:60:64:67:69:70:80 SD: 1.8774 cents 48:55:56:58:60:64:67:69:72:77:80:82:84:96 SD: 1.4662 cents 56:64:65:67:70:75:78:80:84:90:93:96:98:112 SD: 1.4200 cents 60:69:70:72:75:80:84:86:90:96:100:103:105:120 SD: 0.9587 cents 84:96:98:101:105:112:118:120:126:134:140:144:147:168 SD: 0.6571 cents 120:137:140:144:150:160:168:171:180:192:200:206:210:240 SD: 0.4056 cents 168:192:196:202:210:224:235:240:252:269:280:288:294:336 SD: 0.3038 cents 180:206:210:216:225:240:252:257:270:288:300:309:315:360 SD: 0.2717 cents 240:274:280:288:300:320:336:343:360:384:400:411:420:480 SD: 0.2040 cents 252:288:294:302:315:336:353:360:378:403:420:432:441:504 SD: 0.2028 cents 300:343:350:360:375:400:420:429:450:480:500:514:525:600 SD: 0.1621 cents 360:411:420:432:450:480:504:514:540:576:600:617:630:720 SD: 0.1603 cents 420:480:490:504:525:560:588:600:630:672:700:720:735:840 S SD: 0.0000 cents