Scala analysis: xen13-grady-sophia
Sophia, 1.3.5.7.9 Double Dexany
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 35/32 155.139620 septimal neutral second 2: 9/8 203.910002 major whole tone 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 21/16 470.780907 narrow fourth 6: 45/32 590.223716 diatonic tritone 7: 35/24 653.184619 septimal semi-diminished fifth 8: 3/2 701.955001 perfect fifth 9: 105/64 857.094621 septimal neutral sixth 10: 5/3 884.358713 major sixth, BP sixth 11: 7/4 968.825906 harmonic seventh 12: 15/8 1088.268715 classic major seventh 13: 63/32 1172.735908 octave - septimal comma 14: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 64/63 27.2641 septimal comma, Archytas' comma 1: 35/32 155.1396 septimal neutral second 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 15/14 119.4428 major diatonic semitone 5: 21/20 84.4672 minor semitone 6: 15/14 119.4428 major diatonic semitone 7: 28/27 62.9609 Archytas' 1/3-tone 8: 36/35 48.7704 septimal diesis, 1/4-tone 9: 35/32 155.1396 septimal neutral second 10: 64/63 27.2641 septimal comma, Archytas' comma 11: 21/20 84.4672 minor semitone 12: 15/14 119.4428 major diatonic semitone 13: 21/20 84.4672 minor semitone 14: 64/63 27.2641 septimal comma, Archytas' comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 64/63 27.264 cents septimal comma, Archytas' comma 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 3 21/20 84.467 cents minor semitone 1: 3 15/14 119.443 cents major diatonic semitone 1: 2 35/32 155.140 cents septimal neutral second 2: 4 16/15 111.731 cents minor diatonic semitone 2: 4 10/9 182.404 cents minor whole tone 2: 6 9/8 203.910 cents major whole tone 3: 6 8/7 231.174 cents septimal whole tone 3: 6 7/6 266.871 cents septimal minor third 3: 1 189/160 288.377 cents 3: 1 135/112 323.353 cents septimal wide minor third 4: 2 32/27 294.135 cents Pythagorean minor third 4: 6 6/5 315.641 cents minor third 4: 6 5/4 386.314 cents major third 5: 1 128/105 342.905 cents septimal neutral third 5: 2 56/45 378.602 cents septimal narrow major third 5: 2 80/63 413.578 cents wide major third 5: 4 9/7 435.084 cents septimal major third, BP third 5: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 5: 4 21/16 470.781 cents narrow fourth 6: 10 4/3 498.045 cents perfect fourth 6: 2 27/20 519.551 cents acute fourth 6: 2 45/32 590.224 cents diatonic tritone 7: 3 48/35 546.815 cents septimal semi-augmented fourth 7: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 4 10/7 617.488 cents Euler's tritone 7: 3 35/24 653.185 cents septimal semi-diminished fifth 8: 2 64/45 609.776 cents 2nd tritone 8: 2 40/27 680.449 cents grave fifth 8: 10 3/2 701.955 cents perfect fifth 9: 4 32/21 729.219 cents wide fifth 9: 1 54/35 750.725 cents septimal semi-augmented fifth 9: 4 14/9 764.916 cents septimal minor sixth 9: 2 63/40 786.422 cents narrow minor sixth 9: 2 45/28 821.398 cents septimale wide minor sixth 9: 1 105/64 857.095 cents septimal neutral sixth 10: 6 8/5 813.686 cents minor sixth 10: 6 5/3 884.359 cents major sixth, BP sixth 10: 2 27/16 905.865 cents Pythagorean major sixth 11: 1 224/135 876.647 cents narrow septimal major sixth 11: 1 320/189 911.623 cents 11: 6 12/7 933.129 cents septimal major sixth 11: 6 7/4 968.826 cents harmonic seventh 12: 6 16/9 996.090 cents Pythagorean minor seventh 12: 4 9/5 1017.596 cents just minor seventh, BP seventh 12: 4 15/8 1088.269 cents classic major seventh 13: 2 64/35 1044.860 cents septimal neutral seventh 13: 3 28/15 1080.557 cents grave major seventh 13: 3 40/21 1115.533 cents acute major seventh 13: 2 27/14 1137.039 cents septimal major seventh 13: 2 35/18 1151.230 cents septimal semi-diminished octave 13: 2 63/32 1172.736 cents octave - septimal comma Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.15385 = 54/13
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 155.1 203.9 266.9 386.3 470.8 590.2 653.2 702.0 857.1 884.4 968.8 1088.3 1172.7 1200.0 155.1 : 48.8 111.7 231.2 315.6 435.1 498.0 546.8 702.0 729.2 813.7 933.1 1017.6 1044.9 1200.0 203.9 : 63.0 182.4 266.9 386.3 449.3 498.0 653.2 680.4 764.9 884.4 968.8 996.1 1151.2 1200.0 266.9 : 119.4 203.9 323.4 386.3 435.1 590.2 617.5 702.0 821.4 905.9 933.1 1088.3 1137.0 1200.0 386.3 : 84.5 203.9 266.9 315.6 470.8 498.0 582.5 702.0 786.4 813.7 968.8 1017.6 1080.6 1200.0 470.8 : 119.4 182.4 231.2 386.3 413.6 498.0 617.5 702.0 729.2 884.4 933.1 996.1 1115.5 1200.0 590.2 : 63.0 111.7 266.9 294.1 378.6 498.0 582.5 609.8 764.9 813.7 876.6 996.1 1080.6 1200.0 653.2 : 48.8 203.9 231.2 315.6 435.1 519.6 546.8 702.0 750.7 813.7 933.1 1017.6 1137.0 1200.0 702.0 : 155.1 182.4 266.9 386.3 470.8 498.0 653.2 702.0 764.9 884.4 968.8 1088.3 1151.2 1200.0 857.1 : 27.3 111.7 231.2 315.6 342.9 498.0 546.8 609.8 729.2 813.7 933.1 996.1 1044.9 1200.0 884.4 : 84.5 203.9 288.4 315.6 470.8 519.6 582.5 702.0 786.4 905.9 968.8 1017.6 1172.7 1200.0 968.8 : 119.4 203.9 231.2 386.3 435.1 498.0 617.5 702.0 821.4 884.4 933.1 1088.3 1115.5 1200.0 1088.3: 84.5 111.7 266.9 315.6 378.6 498.0 582.5 702.0 764.9 813.7 968.8 996.1 1080.6 1200.0 1172.7: 27.3 182.4 231.2 294.1 413.6 498.0 617.5 680.4 729.2 884.4 911.6 996.1 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 155.1396 cents 2205/2048, 127.8755 cents 64/63, 27.2641 cents 2: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 512/525,-43.4083 cents 3: 231.1741 .. 323.3528 cents 135/128, 92.1787 cents 64/63, 27.2641 cents 4: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 3584/3645,-29.2178 cents 5: 342.9054 .. 470.7809 cents 2205/2048, 127.8755 cents 512/525,-43.4083 cents 6: 498.0450 .. 590.2237 cents 135/128, 92.1787 cents 64/63, 27.2641 cents 7: 546.8154 .. 653.1846 cents 1225/1152, 106.3692 cents 512/525,-43.4083 cents 8: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 512/525,-43.4083 cents 9: 729.2191 .. 857.0946 cents 2205/2048, 127.8755 cents 64/63, 27.2641 cents 10: 813.6863 .. 905.8650 cents 135/128, 92.1787 cents 512/525,-43.4083 cents 11: 876.6472 .. 968.8259 cents 135/128, 92.1787 cents 3584/3645,-29.2178 cents 12: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 64/63, 27.2641 cents 13: 1044.8604 .. 1172.7359 cents 2205/2048, 127.8755 cents 512/525,-43.4083 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 85.7143 cents Largest one step interval : 35/32, 155.1396 cents Average / Smallest step : 3.143853 Largest / Average step : 1.809962 Largest / Smallest step : 5.690254 Median interval of one step : 21/20, 84.4672 cents, amount: 3 Least squares average step : 89.96189 cents, oct.: 1259.46650 cents Scale is not proper Step pattern alph. order: ABCDEDCBAFEDEF Step pattern size order : FBCEDECBFADEDA Scale is a Constant Structure, by a margin of 5.75780 cents Scale diversity : 1.460680 Lumma stability : 0.136320 Lumma impropriety factor : 0.265738 Number of different interval sizes : 54 = 4.15385 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.15385 = 54/13 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 5120/5103, 5.7578 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 10 Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 10, average 701.9550 cents Formal octave complements present : 1 = 7.1429% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval class 4 Scale is n-1 differentially coherent in interval classes 5 and 6 combined Scale is n-1 differentially coherent in interval classes 10 and 11 combined Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 11-12 -- Rational properties -- Prime limit : 7 Odd number limit : 189 (O: 189 U: 189) Highest odd numerator or denominator: 105 Scale harmonicity : 0.031560 Average absolute harmonicity : 0.153968 Specific harmonicity : 0.146129 Fundamental : 1/192, -7.5850 octaves, 1.3626 Hz. Guide tone : 630, 9.2992 octaves, 164824.106 Hz. Exponens Consonantiae : 1.209600E+05, 16.88417 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 296.5, average 21.17857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 15.57969, average 1.11283 Sum of Tenney's harmonic distance : 29.35328, average 2.09666 Vogel's harmonic complexity : 13.71429 Wille's k value : 157 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 336.95937, average 3.20914 Lattice compactness (without 2's) : 178.22611, average 1.69739 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 1 -2.78571 41 1 3: -1 .. 2 0.50000 13 2 5: 0 .. 1 0.50000 7 4 7: 0 .. 1 0.50000 7 7 Average exponent except 2's : 21 / 14 = 1.50000 Average absolute exponent except 2's: 27 / 14 = 1.92857 Scale is weakly epimorphic with val: <14 20 31 38| Scale is weakly epimorphic with val: <14 20 33 38| Scale is weakly epimorphic with val: <14 20 35 38| Scale is weakly epimorphic with val: <14 22 32 37| Scale is JI-epimorphic with val: <14 22 32 39| Scale is weakly epimorphic with val: <14 22 32 41| Scale is weakly epimorphic with val: <14 23 30 36| Scale is weakly epimorphic with val: <14 24 31 40| Scale is weakly epimorphic with val: <14 24 33 40| Scale is weakly epimorphic with val: <14 24 35 40|
FIT/MODE
14: 1 1 1 1 1 1 1 1 2 0 1 1 1 1 N T3 SD: 43.8291 c. M: 75.9380 c. 15: 2 1 0 2 1 1 1 1 2 0 1 2 1 0 N D3 SD: 20.8826 c. M:-36.0900 c. 18: 2 1 1 2 1 2 1 1 2 0 2 1 2 0 N D3 SD: 18.0148 c. M:-31.3783 c. 19: 2 1 1 2 1 2 1 1 2 1 1 2 1 1 P M ME SD: 21.3363 c. M: 36.0420 c. 22: 3 1 1 2 2 2 1 1 3 0 2 2 2 0 N SD: 12.4861 c. M:-27.2641 c. 24: 3 1 1 3 1 3 1 1 3 1 1 3 1 1 N M DE SD: 12.9807 c. M: 22.7359 c. 28: 4 1 1 3 2 3 1 1 4 1 2 2 2 1 N SD: 11.9253 c. M:-16.8884 c. 30: 4 1 2 3 2 3 1 2 3 1 2 3 2 1 N SD: 11.0140 c. M:-18.0450 c. 31: 4 1 2 3 2 3 2 1 4 1 2 3 2 1 N SD: 6.1158 c. M: 11.4456 c. 41: 5 2 2 4 3 4 2 2 5 1 3 4 3 1 N SD: 5.2830 c. M: 9.2822 c. 46: 6 2 2 5 3 5 2 2 6 1 3 5 3 1 N SD: 4.4678 c. M:-9.7763 c. 53: 7 2 3 5 4 5 3 2 7 1 4 5 4 1 N SD: 3.0634 c. M:-4.8272 c. 77: 10 3 4 8 5 8 4 3 10 2 5 8 5 2 N SD: 2.3630 c. M:-3.9530 c. 94: 12 4 5 9 7 9 5 4 12 2 7 9 7 2 N SD: 2.1178 c. M: 3.5076 c. 99: 13 4 5 10 7 10 5 4 13 2 7 10 7 2 N SD: 2.1227 c. M:-3.7157 c. 118: 15 5 6 12 8 12 6 5 15 3 8 12 8 3 N SD: 1.9635 c. M: 3.2444 c. 130: 17 5 7 13 9 13 7 5 17 3 9 13 9 3 N SD: 1.1378 c. M:-2.2000 c. 140: 18 6 7 14 10 14 7 6 18 3 10 14 10 3 N SD: 1.0779 c. M:-1.8043 c. 171: 22 7 9 17 12 17 9 7 22 4 12 17 12 4 N SD: 0.5487 c. M: 0.9543 c. 270: 35 11 14 27 19 27 14 11 35 6 19 27 19 6 N SD: 0.4500 c. M:-0.8874 c. 301: 39 12 16 30 21 30 16 12 39 7 21 30 21 7 N SD: 0.3994 c. M:-0.6911 c. 395: 51 16 21 39 28 39 21 16 51 9 28 39 28 9 N SD: 0.3967 c. M: 0.8566 c. 441: 57 18 23 44 31 44 23 18 57 10 31 44 31 10 N SD: 0.1235 c. M:-0.2525 c. 612: 79 25 32 61 43 61 32 25 79 14 43 61 43 14 N SD: 0.1531 c. M: 0.2434 c. 665: 86 27 35 66 47 66 35 27 86 15 47 66 47 15 N SD: 0.1335 c. M:-0.1968 c. 966: 125 39 51 96 68 96 51 39 125 22 68 96 68 22 N SD: 0.1267 c. M:-0.2315 c. 1053: 136 43 55 105 74 105 55 43 136 24 74 105 74 24 N SD: 0.1151 c. M: 0.2042 c. 1106: 143 45 58 110 78 110 58 45 143 25 78 110 78 25 N SD: 0.0643 c. M:-0.1393 c. 1277: 165 52 67 127 90 127 67 52 165 29 90 127 90 29 N SD: 0.0654 c. M: 0.0987 c. 1407: 182 57 74 140 99 140 74 57 182 32 99 140 99 32 N SD: 0.0586 c. M:-0.1203 c. 1547: 200 63 81 154 109 154 81 63 200 35 109 154 109 35 N SD: 0.0584 c. M:-0.1148 c. 1718: 222 70 90 171 121 171 90 70 222 39 121 171 121 39 N SD: 0.0490 c. M: 0.0996 c. 1848: 239 75 97 184 130 184 97 75 239 42 130 184 130 42 N SD: 0.0364 c. M:-0.0621 c. 2019: 261 82 106 201 142 201 106 82 261 46 142 201 142 46 N SD: 0.0345 c. M: 0.0762 c.
FIT/HARMONIC
1 x 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 x 4 S SD: 0.0000 cents 3 x x x x 4 x x x x 5 x x x 6 S SD: 9.0880 cents 4 x x x 5 x x x 6 x x 7 x x 8 S SD: 0.0000 cents 5 x x 6 x x 7 x x 8 x 9 x x 10 S SD: 16.3717 cents 6 x x 7 x 8 x x 9 x 10 x 11 x 12 S SD: 7.9180 cents 7 x 8 x x 9:10 x x 11 x 12:13 x 14 S SD: 14.1963 cents 8 x 9 x 10 x 11 x 12:13 x 14:15 x 16 S SD: 5.2858 cents 9 x 10 x 11:12 x 13:14 x 15:16:17 x 18 S SD: 9.8536 cents 10:11 x 12 x 13:14 x 15:16:17:18:19 x 20 S SD: 9.3668 cents 11:12 x 13:14 x 15:16:17:18 x 19:21 x 22 SD: 9.2343 cents 12:13 x 14:15:16:17 x 18 x 20:21:23 x 24 SD: 5.1273 cents 13:14 x 15:16:17:18:19:20:21:22:23:24 x 26 S SD: 6.9726 cents 14:15:16 x x 18:20 x 21:23 x 25:26 x 28 SD: 8.2690 cents 15:16:17:18:19:20:21:22:23 x 25:26:28 x 30 SD: 7.2810 cents 16 x 18:19:20:21 x 23:24:26:27:28:30 x 32 SD: 4.3565 cents 17 x 19:20:21:22:24:25:26:28 x 30:32:33:34 SD: 5.0268 cents 18 x 20:21:23:24:25:26:27 x 30:32:34:35:36 SD: 5.7493 cents 19:21 x 22:24:25:27:28:29:31:32:33:36:37:38 SD: 4.6712 cents 20:22 x 23:25:26:28:29:30:33 x 35:38:39:40 SD: 3.7710 cents 23:25:26:27:29:30:32:34:35:38 x 40:43:45:46 SD: 3.8936 cents 24:26:27:28:30:32:34:35:36:39:40:42:45:47:48 SD: 2.8029 cents 26:28:29:30:33:34:37:38:39 x 43:46:49:51:52 SD: 4.3106 cents 27 x 30:32:34:35:38:39:41:44:45:47:51:53:54 SD: 4.1910 cents 28:31:32:33:35:37:39:41:42:46:47:49:53:55:56 SD: 3.4995 cents 29:32:33:34:36:38:41:42:44 x 48:51:54:57:58 SD: 3.2973 cents 30:33:34:35:38:39:42:44:45:49:50:53:56:59:60 SD: 2.8653 cents 31:34:35:36:39:41:44:45:47:51:52:54:58:61:62 SD: 2.5899 cents 32:35:36:37:40:42:45:47:48 x 53:56:60:63:64 SD: 1.7384 cents 48:53:54:56:60:63:68:70:72:79:80:84:90:95:96 SD: 1.6692 cents 54:59:61:63:68:71:76:79:81:89:90:95:101:106:108 SD: 1.5137 cents 55:60:62:64:69:72:77:80:83:90:92:96:103:108:110 SD: 1.4400 cents 56:61:63:65:70:74:79:82:84:92:93:98:105:110:112 SD: 1.4384 cents 61:67:69:71:76:80:86:89:92:100:102:107:114:120:122 SD: 1.4039 cents 64:70:72:75:80:84:90:93:96:105:107:112:120:126:128 SD: 0.8050 cents 96:105:108:112:120:126:135:140:144:158:160:168:180:189:192 SD: 0.3919 cents 192:210:216:224:240:252:270:280:288:315:320:336:360:378:384 SD: 0.0000 cents