Scala analysis: lazy
JI tuning for Lazy Summer Afternoon
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 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: 4/3 498.044999 perfect fourth 7: 3/2 701.955001 perfect fifth 8: 5/3 884.358713 major sixth, BP sixth 9: 7/4 968.825906 harmonic seventh 10: 16/9 996.089998 Pythagorean minor 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: 10/9 182.4037 minor whole tone 2: 81/80 21.5063 syntonic comma, Didymus comma 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: 64/63 27.2641 septimal comma, Archytas' comma 7: 9/8 203.9100 major whole tone 8: 10/9 182.4037 minor whole tone 9: 21/20 84.4672 minor semitone 10: 64/63 27.2641 septimal comma, Archytas' comma 11: 135/128 92.1787 major chroma, major limma 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 2 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 21/20 84.467 cents minor semitone 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 1 21/20 84.467 cents minor semitone 2: 2 16/15 111.731 cents minor diatonic semitone 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 10/9 182.404 cents minor whole tone 2: 3 9/8 203.910 cents major whole tone 2: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 5/4 386.314 cents major third 3: 2 9/8 203.910 cents major whole tone 3: 2 8/7 231.174 cents septimal whole tone 3: 2 7/6 266.871 cents septimal minor third 3: 1 32/27 294.135 cents Pythagorean minor third 3: 2 6/5 315.641 cents minor third 3: 1 5/4 386.314 cents major third 3: 1 80/63 413.578 cents wide major third 3: 1 21/16 470.781 cents narrow fourth 4: 1 189/160 288.377 cents 4: 1 32/27 294.135 cents Pythagorean minor third 4: 1 6/5 315.641 cents minor third 4: 1 56/45 378.602 cents septimal narrow major third 4: 2 5/4 386.314 cents major third 4: 1 81/64 407.820 cents Pythagorean major third 4: 1 80/63 413.578 cents wide major third 4: 1 9/7 435.084 cents septimal major third, BP third 4: 3 4/3 498.045 cents perfect fourth 5: 1 6/5 315.641 cents minor third 5: 1 9/7 435.084 cents septimal major third, BP third 5: 2 21/16 470.781 cents narrow fourth 5: 4 4/3 498.045 cents perfect fourth 5: 1 256/189 525.309 cents 5: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 1 45/32 590.224 cents diatonic tritone 5: 1 10/7 617.488 cents Euler's tritone 6: 2 4/3 498.045 cents perfect fourth 6: 2 27/20 519.551 cents acute fourth 6: 1 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: 1 10/7 617.488 cents Euler's tritone 6: 2 40/27 680.449 cents grave fifth 6: 2 3/2 701.955 cents perfect fifth 7: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 1 64/45 609.776 cents 2nd tritone 7: 1 10/7 617.488 cents Euler's tritone 7: 1 189/128 674.691 cents 7: 4 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 7: 1 14/9 764.916 cents septimal minor sixth 7: 1 5/3 884.359 cents major sixth, BP sixth 8: 3 3/2 701.955 cents perfect fifth 8: 1 14/9 764.916 cents septimal minor sixth 8: 1 63/40 786.422 cents narrow minor sixth 8: 1 128/81 792.180 cents Pythagorean minor sixth 8: 2 8/5 813.686 cents minor sixth 8: 1 45/28 821.398 cents septimale wide minor sixth 8: 1 5/3 884.359 cents major sixth, BP sixth 8: 1 27/16 905.865 cents Pythagorean major sixth 8: 1 320/189 911.623 cents 9: 1 32/21 729.219 cents wide fifth 9: 1 63/40 786.422 cents narrow minor sixth 9: 1 8/5 813.686 cents minor sixth 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 27/16 905.865 cents Pythagorean major sixth 9: 2 12/7 933.129 cents septimal major sixth 9: 2 7/4 968.826 cents harmonic seventh 9: 2 16/9 996.090 cents Pythagorean minor seventh 10: 1 8/5 813.686 cents minor sixth 10: 1 27/16 905.865 cents Pythagorean major sixth 10: 1 12/7 933.129 cents septimal major sixth 10: 1 7/4 968.826 cents harmonic seventh 10: 3 16/9 996.090 cents Pythagorean minor seventh 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 28/15 1080.557 cents grave major seventh 10: 2 15/8 1088.269 cents classic major seventh 10: 1 40/21 1115.533 cents acute major seventh 11: 1 16/9 996.090 cents Pythagorean minor seventh 11: 2 9/5 1017.596 cents just minor seventh, BP seventh 11: 1 28/15 1080.557 cents grave major seventh 11: 1 15/8 1088.269 cents classic major seventh 11: 1 256/135 1107.821 cents octave - major chroma 11: 2 40/21 1115.533 cents acute major seventh 11: 1 27/14 1137.039 cents septimal major seventh 11: 2 63/32 1172.736 cents octave - septimal comma 11: 1 160/81 1178.494 cents octave - syntonic comma Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 8.54545 = 94/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 182.4 203.9 266.9 386.3 470.8 498.0 702.0 884.4 968.8 996.1 1088.3 1200.0 182.4 : 21.5 84.5 203.9 288.4 315.6 519.6 702.0 786.4 813.7 905.9 1017.6 1200.0 203.9 : 63.0 182.4 266.9 294.1 498.0 680.4 764.9 792.2 884.4 996.1 1178.5 1200.0 266.9 : 119.4 203.9 231.2 435.1 617.5 702.0 729.2 821.4 933.1 1115.5 1137.0 1200.0 386.3 : 84.5 111.7 315.6 498.0 582.5 609.8 702.0 813.7 996.1 1017.6 1080.6 1200.0 470.8 : 27.3 231.2 413.6 498.0 525.3 617.5 729.2 911.6 933.1 996.1 1115.5 1200.0 498.0 : 203.9 386.3 470.8 498.0 590.2 702.0 884.4 905.9 968.8 1088.3 1172.7 1200.0 702.0 : 182.4 266.9 294.1 386.3 498.0 680.4 702.0 764.9 884.4 968.8 996.1 1200.0 884.4 : 84.5 111.7 203.9 315.6 498.0 519.6 582.5 702.0 786.4 813.7 1017.6 1200.0 968.8 : 27.3 119.4 231.2 413.6 435.1 498.0 617.5 702.0 729.2 933.1 1115.5 1200.0 996.1 : 92.2 203.9 386.3 407.8 470.8 590.2 674.7 702.0 905.9 1088.3 1172.7 1200.0 1088.3: 111.7 294.1 315.6 378.6 498.0 582.5 609.8 813.7 996.1 1080.6 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 203.9100 cents 10/9, 182.4037 cents 81/80, 21.5063 cents 2: 84.4672 .. 386.3137 cents 25/21, 301.8465 cents 14/15,-119.4428 cents 3: 203.9100 .. 470.7809 cents 7/6, 266.8709 cents 9/10,-182.4037 cents 4: 288.3772 .. 498.0450 cents 640/567, 209.6678 cents 9/10,-182.4037 cents 5: 315.6413 .. 617.4878 cents 25/21, 301.8465 cents 9/10,-182.4037 cents 6: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 14/15,-119.4428 cents 7: 582.5122 .. 884.3587 cents 25/21, 301.8465 cents 14/15,-119.4428 cents 8: 701.9550 .. 911.6228 cents 640/567, 209.6678 cents 9/10,-182.4037 cents 9: 729.2191 .. 996.0900 cents 7/6, 266.8709 cents 9/10,-182.4037 cents 10: 813.6863 .. 1115.5328 cents 25/21, 301.8465 cents 9/10,-182.4037 cents 11: 996.0900 .. 1178.4937 cents 10/9, 182.4037 cents 14/15,-119.4428 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 4.649803 Largest / Average step : 2.039100 Largest / Smallest step : 9.481412 Median interval of one step : 88.32295 cents, amount: 0 Least squares average step : 100.48940 cents, oct.: 1205.87279 cents Scale is not proper Step pattern alph. order: ABCDEFGAEFHI Step pattern size order : HACGDBIHDBEF Scale is not a Constant Structure Scale diversity : 1.419541 Lumma stability : 0.035844 Lumma impropriety factor : 0.859221 Rothenberg efficiency : 0.390735 redundancy: 0.609265 Efficiency x scale size : 4.688817 Number of different interval sizes : 50 = 4.54545 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 8.54545 = 94/11 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 5120/5103, 5.7578 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 9 Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 9, average 701.9550 cents Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 41.6667% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 Scale is differentially coherent in interval classes 4 and 5 combined Scale is differentially coherent in interval classes 5 and 6 combined Scale is n-1 differentially coherent in interval classes 6 and 7 combined Scale is differentially coherent in interval classes 8 and 9 combined -- Rational properties -- Prime limit : 7 Odd number limit : 189 (O: 189 U: 189) Highest odd numerator or denominator: 21 Scale harmonicity : 0.028287 Average absolute harmonicity : 0.193080 Specific harmonicity : 0.162765 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 5040, 12.2992 octaves, 1318592.849 Hz. Exponens Consonantiae : 7.257600E+05, 19.46913 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 88.5, average 7.37500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.40342, average 0.78362 Sum of Tenney's harmonic distance : 18.28135, average 1.52345 Vogel's harmonic complexity : 12.25000 Wille's k value : 94 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 259.50542, average 3.32699 Lattice compactness (without 2's) : 138.90479, average 1.78083 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 -0.66667 24 1 3: -2 .. 2 -0.16667 12 4 5: 0 .. 1 0.33333 4 4 7: 0 .. 1 0.25000 3 3 Average exponent except 2's : 5 / 12 = 0.41667 Average absolute exponent except 2's: 19 / 12 = 1.58333 Scale is weakly epimorphic with val: <12 17 28 32|
FIT/MODE
12: 2 0 1 1 1 0 2 2 1 0 1 1 N SD: 17.8898 c. M:-33.1291 c. 18: 3 0 1 2 1 0 4 2 2 0 1 2 N SD: 18.8529 c. M: 31.3783 c. 19: 3 0 1 2 1 1 3 3 1 1 1 2 N SD: 13.9148 c. M: 28.6756 c. 22: 3 1 1 2 2 0 4 3 2 0 2 2 N SD: 11.6624 c. M:-20.1282 c. 26: 4 0 2 2 2 1 4 4 2 1 2 2 N SD: 12.4050 c. M:-19.4236 c. 27: 4 1 1 3 2 0 5 4 2 1 2 2 N SD: 13.9791 c. M:-26.1322 c. 28: 4 1 1 3 2 1 4 5 2 0 2 3 N SD: 12.1524 c. M:-16.8884 c. 29: 4 1 1 3 2 1 5 4 2 1 2 3 N SD: 12.1566 c. M: 18.5950 c. 31: 5 0 2 3 2 1 5 5 2 1 2 3 N SD: 6.4893 c. M:-11.1447 c. 41: 6 1 2 4 3 1 7 6 3 1 3 4 N SD: 3.8489 c. M: 6.7940 c. 53: 8 1 3 5 4 1 9 8 4 1 4 5 N SD: 2.5096 c. M:-4.8272 c. 77: 12 1 4 8 5 2 13 12 5 2 6 7 N SD: 2.5826 c. M:-4.6093 c. 84: 13 1 5 8 6 2 14 13 6 2 6 8 N SD: 2.6750 c. M:-4.5577 c. 87: 13 2 4 9 6 2 15 13 6 2 7 8 N SD: 2.4776 c. M: 4.8019 c. 94: 14 2 5 9 7 2 16 14 7 2 7 9 N SD: 2.1035 c. M: 3.6803 c. 99: 15 2 5 10 7 2 17 15 7 2 8 9 N SD: 1.4764 c. M:-2.6404 c. 118: 18 2 6 12 8 3 20 18 8 3 9 11 N SD: 1.4047 c. M: 2.9843 c. 130: 20 2 7 13 9 3 22 20 9 3 10 12 N SD: 1.0612 c. M:-2.2117 c. 171: 26 3 9 17 12 4 29 26 12 4 13 16 N SD: 0.3443 c. M: 0.6055 c. 270: 41 5 14 27 19 6 46 41 19 6 21 25 N SD: 0.3438 c. M:-0.6202 c. 441: 67 8 23 44 31 10 75 67 31 10 34 41 N SD: 0.1201 c. M: 0.2042 c. 612: 93 11 32 61 43 14 104 93 43 14 47 57 N SD: 0.1024 c. M: 0.2042 c. 665: 101 12 35 66 47 15 113 101 47 15 51 62 N SD: 0.1304 c. M:-0.1968 c. 836: 127 15 44 83 59 19 142 127 59 19 64 78 N SD: 0.1151 c. M: 0.2304 c. 1053: 160 19 55 105 74 24 179 160 74 24 81 98 N SD: 0.0949 c. M: 0.2042 c. 1106: 168 20 58 110 78 25 188 168 78 25 85 103 N SD: 0.0688 c. M: 0.1252 c. 1236: 188 22 65 123 87 28 210 188 87 28 95 115 N SD: 0.0803 c. M:-0.1206 c. 1277: 194 23 67 127 90 29 217 194 90 29 98 119 N SD: 0.0564 c. M: 0.1014 c. 1677: 255 30 88 167 118 38 285 255 118 38 129 156 N SD: 0.0561 c. M:-0.1034 c. 1718: 261 31 90 171 121 39 292 261 121 39 132 160 N SD: 0.0478 c. M: 0.0987 c. 1848: 281 33 97 184 130 42 314 281 130 42 142 172 N SD: 0.0320 c. M:-0.0638 c. 2019: 307 36 106 201 142 46 343 307 142 46 155 188 N SD: 0.0353 c. M:-0.0629 c. 2289: 348 41 120 228 161 52 389 348 161 52 176 213 N SD: 0.0332 c. M:-0.0668 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 x 4 x 5 x x x 6 S SD: 0.0000 cents 4 x x x 5 x x 6 x 7 x x 8 S SD: 0.0000 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 24.4707 cents 6 x x 7 x x 8:9:10 x x 11:12 S SD: 6.4843 cents 7 x 8 x x 9 x 11 x 12 x 13:14 SD: 16.7104 cents 8 x 9 x 10 x 11:12:13:14 x 15:16 S SD: 8.6233 cents 9:10 x x 11 x 12:14:15 x 16:17:18 S SD: 9.3883 cents 10:11 x 12 x 13 x 15:17 x 18:19:20 SD: 8.9438 cents 11:12 x 13:14 x 15:17:18:19:20:21:22 SD: 10.3315 cents 12:13 x 14:15 x 16:18:20:21 x 23:24 SD: 6.4492 cents 13:14 x 15:16:17 x 20:22 x 23:24:26 SD: 9.5994 cents 14 x 16 x x 18:19:21:23 x 25:26:28 SD: 7.8172 cents 15 x 17:18:19 x 20:23:25:26:27:28:30 SD: 7.2883 cents 16 x 18:19:20:21 x 24:27:28 x 30:32 S SD: 4.1596 cents 17:19 x 20:21:22:23:26:28 x 30:32:34 SD: 6.1048 cents 18:20 x 21:23 x 24:27:30 x 32:34:36 SD: 4.4598 cents 19:21 x 22:24:25 x 29:32:33:34:36:38 SD: 4.9649 cents 20:22 x 23:25:26:27:30:33:35:36:38:40 SD: 4.9387 cents 21:23:24:25:26 x 28:32:35:37 x 39:42 SD: 6.3381 cents 22:24:25:26:28:29 x 33:37 x 39:41:44 SD: 5.6748 cents 23 x 26:27:29:30:31:35:38:40:41:43:46 SD: 3.9508 cents 24 x 27:28:30 x 32:36:40:42:43:45:48 SD: 1.3473 cents 25 x 28:29:31:33 x 38:42:44 x 47:50 SD: 3.9803 cents 26:29 x 30:33:34:35:39:43 x 46:49:52 SD: 4.1837 cents 27:30 x 32:34:35:36:41:45:47:48:51:54 SD: 4.1340 cents 28:31:32:33:35:37 x 42:47:49:50:53:56 SD: 3.7581 cents 29:32:33:34:36:38:39:44:48:51:52:54:58 SD: 3.6814 cents 30:33:34:35:38:39:40:45:50 x 53:56:60 SD: 3.4540 cents 31:34:35:36:39:41 x 47:52:54:55:58:62 SD: 3.4785 cents 32 x 36:37:40:42:43:48:53:56:57:60:64 SD: 2.1355 cents 33 x 37:39:41:43:44:50:55:58:59:62:66 SD: 3.2373 cents 34:38 x 40:43 x 45:51:57 x 60:64:68 SD: 3.8466 cents 35:39 x 41:44:46:47:53:58:61:62:66:70 SD: 2.7004 cents 36:40:41:42:45:47:48:54:60:63:64:68:72 SD: 2.2030 cents 37:41:42:43:46 x 49:56:62:65:66:69:74 SD: 2.9155 cents 39:43:44:46:49:51:52:59:65:68:69:73:78 SD: 2.6557 cents 40:44:45:47:50 x 53:60:67:70:71:75:80 SD: 2.3253 cents 41 x 46:48:51:54:55:62:68:72:73:77:82 SD: 2.2200 cents 42 x 47:49:53:55:56:63:70:74:75:79:84 SD: 2.2202 cents 43:48 x 50:54:56:57:65:72:75:76:81:86 SD: 2.7099 cents 44:49:50:51:55:58:59:66:73:77:78:83:88 SD: 2.3473 cents 45:50:51:53:56:59:60:68:75:79:80:84:90 SD: 2.2794 cents 47:52:53:55:59:62:63:71:78:82:84:88:94 SD: 2.1018 cents 48:53:54:56:60:63:64:72:80:84:85:90:96 SD: 1.0663 cents 50 x 56:58:63:66:67:75:83:88:89:94:100 SD: 2.3905 cents 51:57 x 60:64:67:68:77:85:89:91:96:102 SD: 2.2242 cents 52:58:59:61:65:68:69:78:87:91:92:98:104 SD: 2.1302 cents 53:59:60:62:66:70:71:80:88:93:94:99:106 SD: 2.0735 cents 54:60:61:63:68:71:72:81:90:95:96:101:108 SD: 1.5020 cents 59 x 66:69:74:77:79:89:98:103:105:111:118 SD: 1.9976 cents 60:67:68:70:75:79:80:90:100:105:107:113:120 SD: 1.5724 cents 63:70:71:74:79:83:84:95:105:110:112:118:126 SD: 1.4956 cents 64:71:72:75:80:84:85:96:107:112:114:120:128 SD: 1.0318 cents 72:80:81:84:90:95:96:108:120:126:128:135:144 SD: 0.7613 cents 96:107:108:112:120:126:128:144:160:168:171:180:192 SD: 0.5309 cents 144:160:162:168:180:189:192:216:240:252:256:270:288 SD: 0.0000 cents