Scala analysis: ch9_4
Four tetrads four
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 49/48 35.696812 slendro diesis, septimal 1/6-tone 2: 35/32 155.139620 septimal neutral second 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 35/24 653.184619 septimal semi-diminished fifth 7: 3/2 701.955001 perfect fifth 8: 7/4 968.825906 harmonic seventh 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 15/14 119.4428 major diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 15/14 119.4428 major diatonic semitone 5: 28/25 196.1985 middle second 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 36/35 48.7704 septimal diesis, 1/4-tone 8: 7/6 266.8709 septimal minor third 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: 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 : 35.7 155.1 266.9 386.3 582.5 653.2 702.0 968.8 1200.0 35.7 : 119.4 231.2 350.6 546.8 617.5 666.3 933.1 1164.3 1200.0 155.1 : 111.7 231.2 427.4 498.0 546.8 813.7 1044.9 1080.6 1200.0 266.9 : 119.4 315.6 386.3 435.1 702.0 933.1 968.8 1088.3 1200.0 386.3 : 196.2 266.9 315.6 582.5 813.7 849.4 968.8 1080.6 1200.0 582.5 : 70.7 119.4 386.3 617.5 653.2 772.6 884.4 1003.8 1200.0 653.2 : 48.8 315.6 546.8 582.5 702.0 813.7 933.1 1129.3 1200.0 702.0 : 266.9 498.0 533.7 653.2 764.9 884.4 1080.6 1151.2 1200.0 968.8 : 231.2 266.9 386.3 498.0 617.5 813.7 884.4 933.1 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 : 115.74668 cents, oct.: 1041.72014 cents Scale is not proper Step pattern alph. order: ABCBDEFGH Step pattern size order : AEDEFCBHG 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 1 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 1 = 11.1111% Scale is n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 -- 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 : 0.192482 Specific harmonicity : 0.140364 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 : 138.0, average 15.33333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.48972, average 0.94330 Sum of Tenney's harmonic distance : 16.33962, average 1.81551 Vogel's harmonic complexity : 17.00000 Wille's k value : 262 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 127.65439, average 2.83676 Lattice compactness (without 2's) : 67.24531, average 1.49434 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.88889 19 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 : 7 / 9 = 0.77778 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: 0 1 1 1 1 1 0 2 2 N T3 S SD: 27.9731 c. M: 49.1789 c. 15: 0 2 1 2 2 1 1 3 3 N SD: 19.1236 c. M: 35.6968 c. 19: 0 2 2 2 3 1 1 4 4 N SD: 19.8326 c. M: 35.6968 c. 21: 1 2 2 2 3 1 1 5 4 N SD: 15.8705 c. M: 24.6132 c. 22: 1 2 2 2 4 1 1 5 4 N SD: 10.5902 c. M:-18.8486 c. 24: 1 2 2 3 4 1 1 5 5 N SD: 12.3699 c. M: 18.8259 c. 26: 1 2 3 2 5 1 1 6 5 N SD: 11.6851 c. M:-17.4878 c. 27: 1 3 2 3 4 2 1 6 5 N SD: 11.2769 c. M:-22.6382 c. 29: 1 3 2 3 5 2 1 6 6 N SD: 10.8671 c. M: 18.5950 c. 31: 1 3 3 3 5 2 1 7 6 N SD: 3.0163 c. M: 5.1808 c. 68: 2 7 6 7 11 4 3 15 13 N SD: 2.1273 c. M:-3.9274 c. 99: 3 10 9 10 16 6 4 22 19 N SD: 1.2073 c. M:-2.4361 c. 130: 4 13 12 13 21 8 5 29 25 N SD: 1.2195 c. M:-2.2000 c. 140: 4 14 13 14 23 8 6 31 27 N SD: 0.9718 c. M: 1.7560 c. 171: 5 17 16 17 28 10 7 38 33 N SD: 0.4237 c. M: 0.7537 c. 270: 8 27 25 27 44 16 11 60 52 N SD: 0.2451 c. M:-0.4159 c. 441: 13 44 41 44 72 26 18 98 85 N SD: 0.1599 c. M: 0.3227 c. 472: 14 47 44 47 77 28 19 105 91 N SD: 0.1745 c. M: 0.3088 c. 612: 18 61 57 61 100 36 25 136 118 N SD: 0.2071 c. M: 0.4027 c. 643: 19 64 60 64 105 38 26 143 124 N SD: 0.1798 c. M: 0.2443 c. 711: 21 71 66 71 116 42 29 158 137 N SD: 0.1632 c. M: 0.2538 c. 742: 22 74 69 74 121 44 30 165 143 N SD: 0.1528 c. M: 0.3020 c. 836: 25 83 78 83 137 49 34 186 161 N SD: 0.1413 c. M:-0.2629 c. 913: 27 91 85 91 149 54 37 203 176 N SD: 0.1331 c. M: 0.2559 c. 935: 28 93 87 93 153 55 38 208 180 N SD: 0.1294 c. M:-0.2390 c. 1007: 30 100 94 100 165 59 41 224 194 N SD: 0.1399 c. M: 0.2240 c. 1075: 32 107 100 107 176 63 44 239 207 N SD: 0.1152 c. M:-0.1855 c. 1106: 33 110 103 110 181 65 45 246 213 N SD: 0.0662 c. M:-0.1280 c. 1277: 38 127 119 127 209 75 52 284 246 N SD: 0.0635 c. M:-0.1033 c. 1376: 41 137 128 137 225 81 56 306 265 N SD: 0.0540 c. M:-0.0929 c. 1547: 46 154 144 154 253 91 63 344 298 N SD: 0.0296 c. M: 0.0495 c. 2019: 60 201 188 201 330 119 82 449 389 N SD: 0.0244 c. M: 0.0456 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x 4 S SD: 0.0000 cents 3 x x x x 4 x x 5:6 S SD: 39.8182 cents 4 x x x 5 x x 6:7:8 S SD: 0.0000 cents 5 x x 6 x 7 x 8:9:10 S SD: 26.2610 cents 6 x x 7 x 8 x 9:11:12 SD: 23.3417 cents 7 x x 8:9:10 x 11:12:14 S SD: 18.7354 cents 8 x 9 x 10:11 x 12:14:16 S SD: 9.6489 cents 9 x 10 x 11 x 13:14:16:18 SD: 14.1802 cents 10 x 11:12:13:14 x 15:18:20 S SD: 13.8982 cents 11 x 12:13:14:15:16:17:19:22 SD: 10.2863 cents 12 x 13:14:15:17 x 18:21:24 SD: 3.7640 cents 13 x 14:15:16:18:19:20:23:26 SD: 8.3539 cents 14 x 15:16:18:20 x 21:25:28 SD: 12.2671 cents 15 x 16:18:19:21:22:23:26:30 SD: 10.1614 cents 16 x 18:19:20:22:23:24:28:32 S SD: 8.7599 cents 17 x 19:20:21:24:25:26:30:34 SD: 7.6949 cents 20:21:22:23:25:28:29:30:35:40 SD: 6.2803 cents 24:25:26:28:30:34:35:36:42:48 SD: 4.8655 cents 28:29:31:33:35:39:41:42:49:56 SD: 4.3158 cents 30:31:33:35:38:42:44:45:53:60 SD: 4.2071 cents 31:32:34:36:39:43:45:47:54:62 SD: 4.0211 cents 32:33:35:37:40:45:47:48:56:64 SD: 3.0657 cents 40:41:44:47:50:56:58:60:70:80 SD: 2.2147 cents 44:45:48:51:55:62:64:66:77:88 SD: 1.9360 cents 48:49:53:56:60:67:70:72:84:96 SD: 1.9113 cents 52:53:57:61:65:73:76:78:91:104 SD: 1.3555 cents 83:85:91:97:104:116:121:125:145:166 SD: 1.3166 cents 84:86:92:98:105:118:123:126:147:168 SD: 1.1927 cents 85:87:93:99:106:119:124:128:149:170 SD: 1.1167 cents 88:90:96:103:110:123:128:132:154:176 SD: 1.0555 cents 92:94:101:107:115:129:134:138:161:184 SD: 1.0224 cents 96:98:105:112:120:134:140:144:168:192 SD: 0.5734 cents 140:143:153:163:175:196:204:210:245:280 SD: 0.4651 cents 192:196:210:224:240:269:280:288:336:384 SD: 0.1431 cents 288:294:315:336:360:403:420:432:504:576 SD: 0.0954 cents 480:490:525:560:600:672:700:720:840:960 SD: 0.0000 cents