Scala analysis: ch9_3
Four tetrads three
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: 35/32 155.139620 septimal neutral second 3: 5/4 386.313714 major third 4: 35/24 653.184619 septimal semi-diminished fifth 5: 3/2 701.955001 perfect fifth 6: 25/16 772.627428 classic augmented fifth 7: 7/4 968.825906 harmonic seventh 8: 15/8 1088.268715 classic major seventh 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 15/14 119.4428 major diatonic semitone 2: 49/48 35.6968 slendro diesis, septimal 1/6-tone 3: 8/7 231.1741 septimal whole tone 4: 7/6 266.8709 septimal minor third 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 28/25 196.1985 middle second 8: 15/14 119.4428 major diatonic semitone 9: 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 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 28/25 196.198 cents middle second 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 35/32 155.140 cents septimal neutral second 2: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 2 6/5 315.641 cents minor third 2: 1 4/3 498.045 cents perfect fourth 3: 1 7/6 266.871 cents septimal minor third 3: 1 6/5 315.641 cents minor third 3: 1 60/49 350.617 cents smaller approximation to neutral third 3: 3 5/4 386.314 cents major third 3: 1 32/25 427.373 cents classic diminished fourth 3: 1 49/36 533.742 cents Arabic lute acute fourth 3: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 5/4 386.314 cents major third 4: 1 9/7 435.084 cents septimal major third, BP third 4: 2 4/3 498.045 cents perfect fourth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 10/7 617.488 cents Euler's tritone 4: 1 35/24 653.185 cents septimal semi-diminished fifth 5: 1 48/35 546.815 cents septimal semi-augmented fourth 5: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 2 10/7 617.488 cents Euler's tritone 5: 1 35/24 653.185 cents septimal semi-diminished fifth 5: 2 3/2 701.955 cents perfect fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 8/5 813.686 cents minor sixth 6: 1 35/24 653.185 cents septimal semi-diminished fifth 6: 1 72/49 666.258 cents Arabic lute grave fifth 6: 1 25/16 772.627 cents classic augmented fifth 6: 3 8/5 813.686 cents minor sixth 6: 1 49/30 849.383 cents larger approximation to neutral sixth 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 12/7 933.129 cents septimal major sixth 7: 1 3/2 701.955 cents perfect fifth 7: 2 5/3 884.359 cents major sixth, BP sixth 7: 2 12/7 933.129 cents septimal major sixth 7: 2 7/4 968.826 cents harmonic seventh 7: 1 64/35 1044.860 cents septimal neutral seventh 7: 1 28/15 1080.557 cents grave major seventh 8: 1 12/7 933.129 cents septimal major sixth 8: 1 7/4 968.826 cents harmonic seventh 8: 1 25/14 1003.802 cents middle minor seventh 8: 2 28/15 1080.557 cents grave major seventh 8: 1 15/8 1088.269 cents classic major seventh 8: 1 48/25 1129.328 cents classic diminished octave 8: 1 35/18 1151.230 cents septimal semi-diminished octave 8: 1 96/49 1164.303 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 119.4 155.1 386.3 653.2 702.0 772.6 968.8 1088.3 1200.0 119.4 : 35.7 266.9 533.7 582.5 653.2 849.4 968.8 1080.6 1200.0 155.1 : 231.2 498.0 546.8 617.5 813.7 933.1 1044.9 1164.3 1200.0 386.3 : 266.9 315.6 386.3 582.5 702.0 813.7 933.1 968.8 1200.0 653.2 : 48.8 119.4 315.6 435.1 546.8 666.3 702.0 933.1 1200.0 702.0 : 70.7 266.9 386.3 498.0 617.5 653.2 884.4 1151.2 1200.0 772.6 : 196.2 315.6 427.4 546.8 582.5 813.7 1080.6 1129.3 1200.0 968.8 : 119.4 231.2 350.6 386.3 617.5 884.4 933.1 1003.8 1200.0 1088.3: 111.7 231.2 266.9 498.0 764.9 813.7 884.4 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 266.8709 cents 8/7, 231.1741 cents 49/48, 35.6968 cents 2: 119.4428 .. 498.0450 cents 56/45, 378.6022 cents 45/49,-147.4281 cents 3: 266.8709 .. 546.8154 cents 288/245, 279.9445 cents 7/8,-231.1741 cents 4: 386.3137 .. 653.1846 cents 7/6, 266.8709 cents 175/192,-160.5017 cents 5: 546.8154 .. 813.6863 cents 7/6, 266.8709 cents 1152/1225,-106.3692 cents 6: 653.1846 .. 933.1291 cents 288/245, 279.9445 cents 175/192,-160.5017 cents 7: 701.9550 .. 1080.5572 cents 56/45, 378.6022 cents 7/8,-231.1741 cents 8: 933.1291 .. 1164.3032 cents 8/7, 231.1741 cents 45/49,-147.4281 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 3.735161 Largest / Average step : 2.001532 Largest / Smallest step : 7.476043 Median interval of one step : 15/14, 119.4428 cents, amount: 2 Most common interval of one step : 15/14, 119.4428 cents, amount: 2 Least squares average step : 135.56096 cents, oct.: 1220.04860 cents Scale is not proper Step pattern alph. order: ABCDEFGAH Step pattern size order : EAGHBCFED Scale is not a Constant Structure Scale diversity : 1.566444 Lumma stability : 0.059495 Lumma impropriety factor : 0.800929 Rothenberg efficiency : 0.343034 redundancy: 0.656966 Efficiency x scale size : 3.087302 Number of different interval sizes : 36 = 4.50000 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 7.00000 = 7 Median interval variety : 6.5 Lowest interval variety : 6 Smallest interval difference : 225/224, 7.7115 cents Number of recognisable fifths : 3, average 701.9550 cents Length of longest harmonic part : 2 at degree 7 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 1 = 11.1111% Scale is differentially coherent in interval class 1 Scale is 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 6 and 7 combined -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 35 Scale harmonicity : 0.022369 Average absolute harmonicity : 0.195061 Specific harmonicity : 0.143313 Fundamental : 1/672, -9.3923 octaves, 0.3893 Hz. Guide tone : 1050, 10.0362 octaves, 274706.844 Hz. Exponens Consonantiae : 7.056000E+05, 19.42849 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 123.5, average 13.72222 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.85945, average 0.98438 Sum of Tenney's harmonic distance : 16.80433, average 1.86715 Vogel's harmonic complexity : 18.88889 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 125.43360, average 2.78741 Lattice compactness (without 2's) : 67.32707, average 1.49616 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.22222 22 1 3: -1 .. 1 0.22222 4 1 5: 0 .. 2 0.77778 7 3 7: -1 .. 1 0.22222 4 4 Average exponent except 2's : 11 / 9 = 1.22222 Average absolute exponent except 2's: 15 / 9 = 1.66667 Scale is weakly epimorphic with val: <9 13 19 24| Scale is weakly epimorphic with val: <9 14 20 24| Scale is weakly epimorphic with val: <9 15 20 23| Scale is weakly epimorphic with val: <9 15 22 25| Scale is weakly epimorphic with val: <9 15 23 26|
FIT/MODE
9: 1 0 2 2 0 1 1 1 1 N T3 S SD: 22.9938 c. M: 35.4926 c. 12: 1 1 2 3 0 1 2 1 1 N SD: 27.1457 c. M:-46.8154 c. 15: 2 0 3 3 1 1 2 2 1 N SD: 21.5750 c. M:-40.5572 c. 17: 2 0 3 4 1 1 3 1 2 N SD: 19.3651 c. M: 33.3725 c. 19: 2 0 4 4 1 1 3 2 2 N SD: 16.1294 c. M: 28.8238 c. 20: 2 1 3 5 1 1 3 2 2 N SD: 14.4663 c. M: 26.3137 c. 22: 2 1 4 5 1 1 4 2 2 N SD: 7.5200 c. M:-12.9923 c. 31: 3 1 6 7 1 2 5 3 3 N SD: 3.0787 c. M: 5.1808 c. 68: 7 2 13 15 3 4 11 7 6 N SD: 3.3588 c. M:-5.8489 c. 72: 7 2 14 16 3 4 12 7 7 N SD: 3.6745 c. M: 5.9608 c. 77: 8 2 15 17 3 5 12 8 7 N SD: 3.3030 c. M:-6.5934 c. 84: 8 3 16 19 3 5 14 8 8 N SD: 2.6914 c. M: 5.1571 c. 87: 9 2 17 19 4 5 14 9 8 N SD: 2.8473 c. M: 4.9088 c. 99: 10 3 19 22 4 6 16 10 9 N SD: 1.8871 c. M:-3.1301 c. 109: 11 3 21 24 5 6 18 11 10 N SD: 1.8735 c. M: 3.6433 c. 118: 12 3 23 26 5 7 19 12 11 N SD: 1.7162 c. M: 2.7242 c. 130: 13 4 25 29 5 8 21 13 12 N SD: 1.4567 c. M:-2.7572 c. 140: 14 4 27 31 6 8 23 14 13 N SD: 0.8750 c. M: 1.7560 c. 171: 17 5 33 38 7 10 28 17 16 N SD: 0.4725 c. M: 0.7537 c. 270: 27 8 52 60 11 16 44 27 25 N SD: 0.4201 c. M:-0.7059 c. 301: 30 9 58 67 12 18 49 30 28 N SD: 0.3994 c. M:-0.7945 c. 410: 41 12 79 91 17 24 67 41 38 N SD: 0.3439 c. M:-0.5572 c. 441: 44 13 85 98 18 26 72 44 41 N SD: 0.1413 c. M:-0.2851 c. 472: 47 14 91 105 19 28 77 47 44 N SD: 0.1655 c. M: 0.2601 c. 612: 61 18 118 136 25 36 100 61 57 N SD: 0.1458 c. M: 0.2434 c. 643: 64 19 124 143 26 38 105 64 60 N SD: 0.1617 c. M: 0.2443 c. 904: 90 27 174 201 37 53 148 90 84 N SD: 0.1490 c. M:-0.2574 c. 913: 91 27 176 203 37 54 149 91 85 N SD: 0.1142 c. M:-0.2094 c. 935: 93 28 180 208 38 55 153 93 87 N SD: 0.0903 c. M:-0.1581 c. 1106: 110 33 213 246 45 65 181 110 103 N SD: 0.0599 c. M: 0.1139 c. 1376: 137 41 265 306 56 81 225 137 128 N SD: 0.0620 c. M:-0.1034 c. 1407: 140 42 271 313 57 83 230 140 131 N SD: 0.0619 c. M:-0.1203 c. 1547: 154 46 298 344 63 91 253 154 144 N SD: 0.0296 c. M: 0.0495 c. 2019: 201 60 389 449 82 119 330 201 188 N SD: 0.0198 c. M:-0.0323 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x 4 x x x 5 x 6 S SD: 46.6888 cents 4 x x 5 x 6 x 7 x 8 S SD: 0.0000 cents 5 x x 6:7 x 8:9 x 10 S SD: 23.7095 cents 6 x 7:8 x 9 x x 11:12 SD: 32.5462 cents 7 x 8:9:10 x 11:12:13:14 S SD: 15.0374 cents 8 x 9:10 x 12:13:14:15:16 S SD: 11.9429 cents 9 x 10:11:13 x 14:16:17:18 SD: 8.4485 cents 10 x 11:13 x 15:16:18:19:20 SD: 13.7751 cents 11 x 12:14:16 x 17:19:21:22 SD: 7.6392 cents 12 x 13:15 x 18:19:21:23:24 SD: 6.7735 cents 13:14 x 16:19 x 20:23:24:26 SD: 7.3014 cents 14:15 x 18:20:21:22:25:26:28 SD: 9.0553 cents 15:16 x 19:22 x 23:26:28:30 SD: 6.5164 cents 16:17:18:20:23:24:25:28:30:32 SD: 6.2942 cents 20:21:22:25:29:30:31:35:38:40 SD: 5.1379 cents 21 x 23:26:31:32:33:37:39:42 SD: 5.5577 cents 22 x 24:28:32:33:34:39:41:44 SD: 5.5678 cents 23 x 25:29:34:35:36:40:43:46 SD: 5.0995 cents 24 x 26:30:35:36:38:42:45:48 SD: 3.5361 cents 25:27 x 31:36:38:39:44:47:50 SD: 4.8661 cents 26:28 x 33:38:39:41:46:49:52 SD: 4.8104 cents 28:30:31:35:41:42:44:49:53:56 SD: 3.2589 cents 32:34:35:40:47:48:50:56:60:64 SD: 2.1132 cents 35 x 38:44:51:53:55:61:66:70 SD: 3.4828 cents 36 x 39:45:53:54:56:63:68:72 SD: 3.4606 cents 37:40 x 46:54:56:58:65:69:74 SD: 3.3911 cents 39:42:43:49:57:59:61:68:73:78 SD: 2.7971 cents 40:43:44:50:58:60:63:70:75:80 SD: 2.2750 cents 41:44:45:51:60:62:64:72:77:82 SD: 2.2101 cents 44:47:48:55:64:66:69:77:83:88 SD: 1.6370 cents 52:56:57:65:76:78:81:91:98:104 SD: 1.6261 cents 56:60:61:70:82:84:88:98:105:112 SD: 1.5602 cents 64:69:70:80:93:96:100:112:120:128 SD: 1.3821 cents 72:77:79:90:105:108:113:126:135:144 SD: 1.1075 cents 84:90:92:105:123:126:131:147:158:168 SD: 1.0902 cents 85:91:93:106:124:128:133:149:159:170 SD: 1.0893 cents 96:103:105:120:140:144:150:168:180:192 SD: 0.2670 cents 224:240:245:280:327:336:350:392:420:448 SD: 0.1962 cents 320:343:350:400:467:480:500:560:600:640 SD: 0.1590 cents 352:377:385:440:513:528:550:616:660:704 SD: 0.1446 cents 448:480:490:560:653:672:700:784:840:896 SD: 0.0982 cents 544:583:595:680:793:816:850:952:1020:1088 SD: 0.0936 cents 576:617:630:720:840:864:900:1008:1080:1152 SD: 0.0445 cents