Scala analysis: ch9_1
Four tetrads one <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: 6/5 315.641287 minor third 3: 5/4 386.313714 major third 4: 21/16 470.780907 narrow fourth 5: 3/2 701.955001 perfect fifth 6: 12/7 933.129094 septimal major sixth 7: 7/4 968.825906 harmonic seventh 8: 9/5 1017.596288 just minor seventh, BP seventh 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 21/20 84.4672 minor semitone 2: 8/7 231.1741 septimal whole tone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 21/20 84.4672 minor semitone 5: 8/7 231.1741 septimal whole tone 6: 8/7 231.1741 septimal whole tone 7: 49/48 35.6968 slendro diesis, septimal 1/6-tone 8: 36/35 48.7704 septimal diesis, 1/4-tone 9: 10/9 182.4037 minor 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 : 84.5 315.6 386.3 470.8 702.0 933.1 968.8 1017.6 1200.0 84.5 : 231.2 301.8 386.3 617.5 848.7 884.4 933.1 1115.5 1200.0 315.6 : 70.7 155.1 386.3 617.5 653.2 702.0 884.4 968.8 1200.0 386.3 : 84.5 315.6 546.8 582.5 631.3 813.7 898.2 1129.3 1200.0 470.8 : 231.2 462.3 498.0 546.8 729.2 813.7 1044.9 1115.5 1200.0 702.0 : 231.2 266.9 315.6 498.0 582.5 813.7 884.4 968.8 1200.0 933.1 : 35.7 84.5 266.9 351.3 582.5 653.2 737.7 968.8 1200.0 968.8 : 48.8 231.2 315.6 546.8 617.5 702.0 933.1 1164.3 1200.0 1017.6: 182.4 266.9 498.0 568.7 653.2 884.4 1115.5 1151.2 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 : 135.39970 cents, oct.: 1218.59734 cents Scale is not proper Step pattern alph. order: ABCABBDEF Step pattern size order : DFCDFFABE 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 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 21 Scale harmonicity : 0.022369 Average absolute harmonicity : 0.203381 Specific harmonicity : 0.145863 Fundamental : 1/560, -9.1293 octaves, 0.4672 Hz. Guide tone : 1260, 10.2992 octaves, 329648.212 Hz. Exponens Consonantiae : 7.056000E+05, 19.42849 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 75.0, average 8.33333 Mersenne's string divisions : 199743390 Sum of van Prooijen's expressibility: 7.16394, average 0.79599 Sum of Tenney's harmonic distance : 14.03157, average 1.55906 Vogel's harmonic complexity : 18.00000 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 125.53319, average 2.78963 Lattice compactness (without 2's) : 67.24531, average 1.49434 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.77778 15 1 3: 0 .. 2 0.77778 7 1 5: -1 .. 1 -0.22222 4 3 7: -1 .. 1 0.22222 4 4 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 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: 0 2 0 1 2 2 0 0 2 N SD: 65.3740 c. M: 119.6470 c. 10: 1 2 0 1 2 2 0 1 1 N SD: 31.6710 c. M:-62.4037 c. 12: 1 2 1 1 2 2 1 0 2 N SD: 20.8428 c. M: 33.1291 c. 15: 1 3 1 1 3 3 0 1 2 N SD: 14.6771 c. M:-26.8709 c. 22: 2 4 1 2 4 4 1 1 3 N SD: 14.0365 c. M:-24.6237 c. 24: 2 4 2 1 5 5 0 1 4 N SD: 15.1202 c. M: 20.7809 c. 25: 2 5 1 2 5 4 1 1 4 N SD: 13.2492 c. M: 21.1291 c. 26: 2 5 1 2 5 5 1 1 4 N SD: 8.7761 c. M: 17.0829 c. 27: 2 5 2 2 5 5 1 1 4 N SD: 9.0719 c. M:-18.1080 c. 28: 2 5 2 2 5 6 1 1 4 N SD: 10.5990 c. M:-16.8884 c. 31: 2 6 2 2 6 6 1 1 5 N SD: 5.7165 c. M: 11.1447 c. 41: 3 8 2 3 8 8 1 2 6 N SD: 4.1934 c. M:-6.7940 c. 46: 3 9 3 3 9 9 1 2 7 N SD: 3.7484 c. M: 6.2063 c. 53: 4 10 3 4 10 10 2 2 8 N SD: 3.5047 c. M:-6.0988 c. 68: 5 13 4 5 13 13 2 3 10 N SD: 3.5388 c. M:-5.9331 c. 72: 5 14 4 5 14 14 2 3 11 N SD: 2.0422 c. M: 4.1142 c. 99: 7 19 6 7 19 19 3 4 15 N SD: 0.9957 c. M:-1.9464 c. 171: 12 33 10 12 33 33 5 7 26 N SD: 0.3027 c. M: 0.6055 c. 270: 19 52 16 19 52 52 8 11 41 N SD: 0.2086 c. M:-0.3530 c. 441: 31 85 26 31 85 85 13 18 67 N SD: 0.1010 c. M:-0.2042 c. 1106: 78 213 65 78 213 213 33 45 168 N SD: 0.0895 c. M:-0.1621 c. 1137: 80 219 67 80 219 219 34 46 173 N SD: 0.0947 c. M: 0.1820 c. 1236: 87 238 73 87 238 238 37 50 188 N SD: 0.0877 c. M: 0.1206 c. 1277: 90 246 75 90 246 246 38 52 194 N SD: 0.0672 c. M:-0.1060 c. 1407: 99 271 83 99 271 271 42 57 214 N SD: 0.0585 c. M: 0.1123 c. 1547: 109 298 91 109 298 298 46 63 235 N SD: 0.0606 c. M:-0.1154 c. 1578: 111 304 93 111 304 304 47 64 240 N SD: 0.0536 c. M: 0.1058 c. 1677: 118 323 99 118 323 323 50 68 255 N SD: 0.0543 c. M:-0.0906 c. 1718: 121 331 101 121 331 331 51 70 261 N SD: 0.0516 c. M:-0.0987 c. 1848: 130 356 109 130 356 356 55 75 281 N SD: 0.0376 c. M: 0.0638 c. 2019: 142 389 119 142 389 389 60 82 307 N SD: 0.0405 c. M: 0.0690 c. 2289: 161 441 135 161 441 441 68 93 348 N SD: 0.0361 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 3 x x x 4 S SD: 0.0000 cents 3 x x x 4 x 5 x x 6 S SD: 18.6246 cents 4 x x 5 x 6 x 7 x 8 S SD: 0.0000 cents 5 x 6 x 7:8 x x 9:10 S SD: 31.6024 cents 6 x 7 x 8:9:10 x 11:12 S SD: 13.4470 cents 7 x 8 x 9:11:12 x 13:14 SD: 22.2502 cents 8 x x 10:11:12 x 14 x 16 S SD: 16.1074 cents 9:10:11 x 12:14:15 x 16:18 S SD: 19.2455 cents 10:11:12 x 13:15:17 x 18:20 SD: 11.9271 cents 11:12:13:14 x 17:19 x 20:22 SD: 13.6984 cents 12:13:14:15:16:18 x 21:22:24 S SD: 10.5018 cents 13:14 x 16:17:20:22:23 x 26 SD: 10.5561 cents 14:15:17 x 18:21:24 x 25:28 SD: 7.9637 cents 15:16:18:19:20:23 x 26:27:30 SD: 7.6391 cents 16:17:19:20:21:24:27:28:29:32 SD: 4.4932 cents 18:19:22:23:24:27:31 x 32:36 SD: 7.7159 cents 19:20:23:24:25:29 x 33:34:38 SD: 5.2666 cents 20:21:24:25:26:30:34:35:36:40 SD: 2.4453 cents 36:38:43:45:47:54:62:63:65:72 SD: 2.0023 cents 44:46:53:55:58:66:75:77:79:88 SD: 1.8313 cents 56:59:67:70:74:84:96:98:101:112 SD: 1.6129 cents 60:63:72:75:79:90:103:105:108:120 SD: 0.6656 cents 80:84:96:100:105:120:137:140:144:160 SD: 0.2005 cents 220:231:264:275:289:330:377:385:396:440 SD: 0.1817 cents 300:315:360:375:394:450:514:525:540:600 SD: 0.1623 cents 320:336:384:400:420:480:549:560:576:640 SD: 0.1502 cents 340:357:408:425:446:510:583:595:612:680 SD: 0.1177 cents 400:420:480:500:525:600:686:700:720:800 SD: 0.0801 cents 480:504:576:600:630:720:823:840:864:960 SD: 0.0334 cents 560:588:672:700:735:840:960:980:1008:1120 S SD: 0.0000 cents