Scala analysis: ch9_2
Four tetrads two <9 14 21 26| permutation epimorphic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 35/32 155.139620 septimal neutral second 3: 5/4 386.313714 major third 4: 21/16 470.780907 narrow fourth 5: 35/24 653.184619 septimal semi-diminished fifth 6: 3/2 701.955001 perfect fifth 7: 49/32 737.651813 8: 7/4 968.825906 harmonic seventh 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 21/20 84.4672 minor semitone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 8/7 231.1741 septimal whole tone 4: 21/20 84.4672 minor semitone 5: 10/9 182.4037 minor whole tone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 49/48 35.6968 slendro diesis, septimal 1/6-tone 8: 8/7 231.1741 septimal whole tone 9: 8/7 231.1741 septimal whole tone
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: 2 21/20 84.467 cents minor semitone 1: 1 10/9 182.404 cents minor whole tone 1: 3 8/7 231.174 cents septimal whole tone 2: 1 21/20 84.467 cents minor semitone 2: 1 35/32 155.140 cents septimal neutral second 2: 1 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 2 6/5 315.641 cents minor third 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 3: 1 7/6 266.871 cents septimal minor third 3: 2 6/5 315.641 cents minor third 3: 3 5/4 386.314 cents major third 3: 2 4/3 498.045 cents perfect fourth 3: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 49/40 351.338 cents larger approximation to neutral third 4: 1 21/16 470.781 cents narrow fourth 4: 1 4/3 498.045 cents perfect fourth 4: 2 48/35 546.815 cents septimal semi-augmented fourth 4: 1 25/18 568.717 cents classic augmented fourth 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 10/7 617.488 cents Euler's tritone 5: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 1 10/7 617.488 cents Euler's tritone 5: 1 36/25 631.283 cents classic diminished fifth 5: 2 35/24 653.185 cents septimal semi-diminished fifth 5: 1 3/2 701.955 cents perfect fifth 5: 1 32/21 729.219 cents wide fifth 5: 1 80/49 848.662 cents smaller approximation to neutral sixth 6: 1 35/24 653.185 cents septimal semi-diminished fifth 6: 2 3/2 701.955 cents perfect fifth 6: 3 8/5 813.686 cents minor sixth 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 12/7 933.129 cents septimal major sixth 7: 1 49/32 737.652 cents 7: 2 5/3 884.359 cents major sixth, BP sixth 7: 1 42/25 898.153 cents quasi-equal major sixth 7: 2 12/7 933.129 cents septimal major sixth 7: 1 7/4 968.826 cents harmonic seventh 7: 1 64/35 1044.860 cents septimal neutral seventh 7: 1 40/21 1115.533 cents acute major seventh 8: 3 7/4 968.826 cents harmonic seventh 8: 1 9/5 1017.596 cents just minor seventh, BP seventh 8: 2 40/21 1115.533 cents acute 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: 7 Average number of different intervals per interval class: 6.25000 = 25/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 84.5 155.1 386.3 470.8 653.2 702.0 737.7 968.8 1200.0 84.5 : 70.7 301.8 386.3 568.7 617.5 653.2 884.4 1115.5 1200.0 155.1 : 231.2 315.6 498.0 546.8 582.5 813.7 1044.9 1129.3 1200.0 386.3 : 84.5 266.9 315.6 351.3 582.5 813.7 898.2 968.8 1200.0 470.8 : 182.4 231.2 266.9 498.0 729.2 813.7 884.4 1115.5 1200.0 653.2 : 48.8 84.5 315.6 546.8 631.3 702.0 933.1 1017.6 1200.0 702.0 : 35.7 266.9 498.0 582.5 653.2 884.4 968.8 1151.2 1200.0 737.7 : 231.2 462.3 546.8 617.5 848.7 933.1 1115.5 1164.3 1200.0 968.8 : 231.2 315.6 386.3 617.5 702.0 884.4 933.1 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 231.1741 cents 384/343, 195.4773 cents 49/48, 35.6968 cents 2: 84.4672 .. 462.3482 cents 1280/1029, 377.8810 cents 147/160,-146.7069 cents 3: 266.8709 .. 546.8154 cents 288/245, 279.9445 cents 343/384,-195.4773 cents 4: 351.3381 .. 617.4878 cents 400/343, 266.1497 cents 343/384,-195.4773 cents 5: 582.5122 .. 848.6619 cents 400/343, 266.1497 cents 49/50,-34.9756 cents 6: 653.1846 .. 933.1291 cents 288/245, 279.9445 cents 343/384,-195.4773 cents 7: 737.6518 .. 1115.5328 cents 1280/1029, 377.8810 cents 343/384,-195.4773 cents 8: 968.8259 .. 1164.3032 cents 384/343, 195.4773 cents 147/160,-146.7069 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 : 8/7, 231.1741 cents Average / Smallest step : 3.735161 Largest / Average step : 1.733806 Largest / Smallest step : 6.476043 Median interval of one step : 21/20, 84.4672 cents, amount: 2 Most common interval of one step : 8/7, 231.1741 cents, amount: 3 Least squares average step : 121.50398 cents, oct.: 1093.53582 cents Scale is not proper Step pattern alph. order: ABCADEFCC Step pattern size order : DCFDEBAFF Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.517284 Lumma stability : 0.059495 Lumma impropriety factor : 0.740232 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 : 6 Highest interval variety : 7 Mean interval variety : 6.25000 = 25/4 Median interval variety : 5.5 Lowest interval variety : 5 Smallest interval difference : 1029/1024, 8.4327 cents Number of recognisable fifths : 3, average 701.9550 cents 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 : 1 = 11.1111% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 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: 49 Scale harmonicity : 0.022369 Average absolute harmonicity : 0.189883 Specific harmonicity : 0.139192 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 1470, 10.5216 octaves, 384589.581 Hz. Exponens Consonantiae : 7.056000E+05, 19.42849 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 156.5, average 17.38889 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.44396, average 1.04933 Sum of Tenney's harmonic distance : 18.14580, average 2.01620 Vogel's harmonic complexity : 17.66667 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 133.85487, average 2.97455 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 -2.55556 25 1 3: -1 .. 1 0.22222 4 1 5: -1 .. 1 0.22222 4 1 7: 0 .. 2 0.77778 7 6 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 21 25| Scale is weakly epimorphic with val: <9 14 21 26| Scale is weakly epimorphic with val: <9 15 19 25| Scale is weakly epimorphic with val: <9 15 20 26|
FIT/MODE
9: 1 0 2 1 1 0 1 1 2 N T3 SD: 38.7837 c. M:-62.5524 c. 10: 1 0 2 1 1 1 0 2 2 N SD: 27.5247 c. M: 53.1846 c. 11: 1 0 3 0 2 0 1 2 2 N SD: 32.5062 c. M:-50.0499 c. 12: 1 1 2 1 2 0 1 2 2 N SD: 33.9107 c. M:-62.3482 c. 13: 1 1 2 1 2 1 0 2 3 N SD: 23.0539 c. M: 45.7490 c. 15: 1 1 3 1 2 1 0 3 3 N SD: 11.5702 c. M:-18.0450 c. 26: 2 1 5 2 4 1 1 5 5 N SD: 9.7764 c. M: 17.0829 c. 28: 2 2 5 2 4 1 1 6 5 N SD: 10.5712 c. M:-16.8884 c. 29: 2 2 5 2 5 1 1 5 6 N SD: 10.3954 c. M: 17.1018 c. 31: 2 2 6 2 5 1 1 6 6 N SD: 4.0298 c. M: 7.0478 c. 46: 3 3 9 3 7 2 1 9 9 N SD: 3.9252 c. M: 7.2170 c. 53: 4 3 10 4 8 2 2 10 10 N SD: 4.6827 c. M:-9.5180 c. 68: 5 4 13 5 10 3 2 13 13 N SD: 3.2463 c. M:-5.6897 c. 72: 5 4 14 5 11 3 2 14 14 N SD: 3.1761 c. M: 5.1396 c. 84: 6 5 16 6 13 3 3 16 16 N SD: 2.5757 c. M:-5.2053 c. 90: 6 6 17 6 14 4 2 18 17 N SD: 3.6791 c. M:-4.8604 c. 92: 6 6 18 6 14 4 3 17 18 N SD: 3.6595 c. M: 6.2063 c. 94: 7 5 18 7 14 4 3 18 18 N SD: 2.4822 c. M:-4.8945 c. 99: 7 6 19 7 15 4 3 19 19 N SD: 1.4575 c. M:-2.4361 c. 125: 9 7 24 9 19 5 4 24 24 N SD: 1.3368 c. M: 2.3137 c. 130: 9 8 25 9 20 5 4 25 25 N SD: 1.1948 c. M:-2.2000 c. 140: 10 8 27 10 21 6 4 27 27 N SD: 0.8997 c. M: 1.7560 c. 171: 12 10 33 12 26 7 5 33 33 N SD: 0.5042 c. M: 0.8097 c. 270: 19 16 52 19 41 11 8 52 52 N SD: 0.2405 c. M:-0.4159 c. 441: 31 26 85 31 67 18 13 85 85 N SD: 0.1128 c. M: 0.2368 c. 711: 50 42 137 50 108 29 21 137 137 N SD: 0.1085 c. M:-0.1842 c. 1106: 78 65 213 78 168 45 33 213 213 N SD: 0.0866 c. M:-0.1621 c. 1137: 80 67 219 80 173 46 34 219 219 N SD: 0.0662 c. M:-0.1135 c. 1277: 90 75 246 90 194 52 38 246 246 N SD: 0.0642 c. M:-0.1060 c. 1407: 99 83 271 99 214 57 42 271 271 N SD: 0.0626 c. M:-0.1203 c. 1547: 109 91 298 109 235 63 46 298 298 N SD: 0.0446 c. M:-0.0835 c. 1578: 111 93 304 111 240 64 47 304 304 N SD: 0.0364 c. M: 0.0585 c. 2019: 142 119 389 142 307 82 60 389 389 N SD: 0.0380 c. M: 0.0690 c. 2289: 161 135 441 161 348 93 68 441 441 N SD: 0.0352 c. M: 0.0635 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x 4 S SD: 0.0000 cents 3 x x x 4 x x x 5:6 S SD: 29.5861 cents 4 x x 5 x x 6 x 7:8 S SD: 0.0000 cents 5 x x 6 x 7 x 8:9:10 S SD: 26.9436 cents 6 x 7 x 8 x 9 x 11:12 SD: 28.0809 cents 7 x 8 x 9:10 x 11:12:14 S SD: 17.9619 cents 8 x 9:10:11 x 12 x 14:16 S SD: 15.6921 cents 9 x 10:11:12:13 x 14:16:18 S SD: 9.8576 cents 10 x 11 x 13 x 15 x 18:20 SD: 10.4887 cents 11 x 12:14 x 16 x 17:19:22 SD: 7.0343 cents 12 x 13:15:16 x 18 x 21:24 SD: 5.3171 cents 13 x 14:16:17:19 x 20:23:26 SD: 6.2595 cents 14:15 x x 18:20:21 x 25:28 SD: 11.7794 cents 15:16 x 19:20:22 x 23:26:30 SD: 6.9836 cents 17:18:19:21:22:25 x 26:30:34 SD: 6.9035 cents 19:20:21:24:25:28 x 29:33:38 SD: 4.3757 cents 20:21:22:25:26:29:30:31:35:40 SD: 3.3594 cents 21:22:23:26:28:31 x 32:37:42 SD: 5.1411 cents 22:23:24:28:29:32:33:34:39:44 SD: 4.8183 cents 23:24:25:29:30:34 x 35:40:46 SD: 4.6072 cents 24:25:26:30:32:35:36:37:42:48 SD: 4.0762 cents 25:26:27:31:33:36 x 38:44:50 SD: 5.2809 cents 27:28:30:34:35:39 x 41:47:54 SD: 6.1229 cents 28:29:31:35:37:41:42:43:49:56 SD: 3.8798 cents 29:30:32:36:38:42 x 44:51:58 SD: 4.8713 cents 31:33:34:39:41:45 x 47:54:62 SD: 4.5248 cents 32:34:35:40:42:47:48:49:56:64 SD: 2.6565 cents 40:42:44:50:53:58:60:61:70:80 SD: 2.5219 cents 41:43:45:51:54:60:62:63:72:82 SD: 2.3662 cents 44:46:48:55:58:64:66:67:77:88 SD: 1.7436 cents 60:63:66:75:79:88:90:92:105:120 SD: 1.6861 cents 64:67:70:80:84:93:96:98:112:128 SD: 0.8958 cents 96:101:105:120:126:140:144:147:168:192 SD: 0.3813 cents 160:168:175:200:210:233:240:245:280:320 SD: 0.2750 cents 224:235:245:280:294:327:336:343:392:448 SD: 0.2555 cents 256:269:280:320:336:373:384:392:448:512 SD: 0.2236 cents 320:336:350:400:420:467:480:490:560:640 SD: 0.1374 cents 384:403:420:480:504:560:576:588:672:768 SD: 0.0954 cents 480:504:525:600:630:700:720:735:840:960 S SD: 0.0000 cents