Scala analysis: brect33
3x3 breed rectangle scale, <9 15 22 26| epimorphic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 6/5 315.641287 minor third 3: 49/40 351.338099 larger approximation to neutral third 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 8/5 813.686286 minor sixth 6: 49/30 849.383098 larger approximation to neutral sixth 7: 12/7 933.129094 septimal major sixth 8: 49/25 1165.024385 BP eighth 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 1: 8/7 231.1741 septimal whole tone 2: 21/20 84.4672 minor semitone 3: 49/48 35.6968 slendro diesis, septimal 1/6-tone 4: 8/7 231.1741 septimal whole tone 5: 8/7 231.1741 septimal whole tone 6: 49/48 35.6968 slendro diesis, septimal 1/6-tone 7: 360/343 83.7460 8: 343/300 231.8953 9: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 360/343 83.746 cents 1: 1 21/20 84.467 cents minor semitone 1: 3 8/7 231.174 cents septimal whole tone 1: 1 343/300 231.895 cents 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 343/320 120.164 cents 2: 1 400/343 266.150 cents 2: 3 7/6 266.871 cents septimal 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: 3 60/49 350.617 cents smaller approximation to neutral third 3: 3 49/40 351.338 cents larger approximation to neutral third 3: 3 4/3 498.045 cents perfect fourth 4: 2 5/4 386.314 cents major third 4: 1 49/36 533.742 cents Arabic lute acute fourth 4: 2 480/343 581.791 cents 4: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 4 10/7 617.488 cents Euler's tritone 5: 2 343/240 618.209 cents 5: 1 72/49 666.258 cents Arabic lute grave fifth 5: 2 8/5 813.686 cents minor sixth 6: 3 3/2 701.955 cents perfect fifth 6: 3 80/49 848.662 cents smaller approximation to neutral sixth 6: 3 49/30 849.383 cents larger approximation to neutral sixth 7: 1 49/32 737.652 cents 7: 2 5/3 884.359 cents major sixth, BP sixth 7: 3 12/7 933.129 cents septimal major sixth 7: 1 343/200 933.850 cents 7: 1 640/343 1079.836 cents 7: 1 28/15 1080.557 cents grave major seventh 8: 1 600/343 968.105 cents 8: 3 7/4 968.826 cents harmonic seventh 8: 1 40/21 1115.533 cents acute major seventh 8: 1 343/180 1116.254 cents 8: 2 96/49 1164.303 cents 8: 1 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.75000 = 19/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 231.2 315.6 351.3 582.5 813.7 849.4 933.1 1165.0 1200.0 231.2 : 84.5 120.2 351.3 582.5 618.2 702.0 933.9 968.8 1200.0 315.6 : 35.7 266.9 498.0 533.7 617.5 849.4 884.4 1115.5 1200.0 351.3 : 231.2 462.3 498.0 581.8 813.7 848.7 1079.8 1164.3 1200.0 582.5 : 231.2 266.9 350.6 582.5 617.5 848.7 933.1 968.8 1200.0 813.7 : 35.7 119.4 351.3 386.3 617.5 702.0 737.7 968.8 1200.0 849.4 : 83.7 315.6 350.6 581.8 666.3 702.0 933.1 1164.3 1200.0 933.1 : 231.9 266.9 498.0 582.5 618.2 849.4 1080.6 1116.3 1200.0 1165.0: 35.0 266.1 350.6 386.3 617.5 848.7 884.4 968.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 231.8953 cents 16807/15000, 196.9197 cents 50/49, 34.9756 cents 2: 119.4428 .. 462.3482 cents 128/105, 342.9054 cents 2250/2401,-112.4525 cents 3: 350.6169 .. 498.0450 cents 49/45, 147.4281 cents 15/16,-111.7313 cents 4: 386.3137 .. 582.5122 cents 28/25, 196.1985 cents 15/16,-111.7313 cents 5: 617.4878 .. 813.6863 cents 28/25, 196.1985 cents 50/49, 34.9756 cents 6: 701.9550 .. 849.3831 cents 49/45, 147.4281 cents 15/16,-111.7313 cents 7: 737.6518 .. 1080.5572 cents 128/105, 342.9054 cents 15/16,-111.7313 cents 8: 968.1047 .. 1165.0244 cents 16807/15000, 196.9197 cents 2250/2401,-112.4525 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 343/300, 231.8953 cents Average / Smallest step : 3.812180 Largest / Average step : 1.739215 Largest / Smallest step : 6.630199 Median interval of one step : 21/20, 84.4672 cents, amount: 1 Most common interval of one step : 8/7, 231.1741 cents, amount: 3 Least squares average step : 140.57315 cents, oct.: 1265.15837 cents Scale is not proper Step pattern alph. order: ABCAACDEF Step pattern size order : EDBEEBCFA Scale is a Constant Structure, by a margin of 34.25442 cents Scale diversity : 1.385023 Lumma stability : 0.087439 Lumma impropriety factor : 0.433134 Rothenberg efficiency : 0.331129 redundancy: 0.668871 Efficiency x scale size : 2.980159 Number of different interval sizes : 38 = 4.75000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.75000 = 19/4 Median interval variety : 3.5 Lowest interval variety : 3 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 4 Number of recognisable fifths : 3, average 701.9550 cents 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 classes 1 and 2 combined Limited inverse transpositions with margin 196.9197 cents: 8 -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.018185 Average absolute harmonicity : 0.167085 Specific harmonicity : 0.099870 Fundamental : 1/4200, -12.0362 octaves, 0.0623 Hz. Guide tone : 1176, 10.1997 octaves, 307671.665 Hz. Exponens Consonantiae : 4.939200E+06, 22.23585 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 157.5, average 17.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.00382, average 1.00042 Sum of Tenney's harmonic distance : 18.14446, average 2.01605 Vogel's harmonic complexity : 24.00000 Wille's k value : 2572 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 135.95954, average 3.02132 Lattice compactness (without 2's) : 85.01871, average 1.88930 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.66667 14 1 3: -1 .. 1 0.11111 3 5: -2 .. 0 -0.77778 7 2 7: -1 .. 2 0.55556 9 6 Average exponent except 2's :-1 / 9 =-0.11111 Average absolute exponent except 2's: 19 / 9 = 2.11111 Scale is weakly epimorphic with val: <9 13 23 26| Scale is weakly epimorphic with val: <9 15 20 25| Scale is JI-epimorphic with val: <9 15 22 26|
FIT/MODE
9: 1 1 0 2 2 0 1 1 1 N T3 S SD: 61.3364 c. M: 98.3577 c. 10: 2 1 0 2 2 0 1 2 0 N S SD: 23.9264 c. M:-44.3587 c. 14: 3 1 0 3 3 0 1 3 0 N S SD: 23.7099 c. M:-43.4566 c. 15: 3 1 0 3 3 1 1 3 0 N G SD: 22.7445 c. M:-34.9756 c. 17: 3 1 1 3 3 1 1 3 1 N D3 S SD: 22.8591 c. M: 37.2157 c. 18: 3 2 0 4 3 1 1 3 1 N SD: 19.4514 c. M: 31.6911 c. 21: 4 1 1 4 4 1 1 4 1 N D3 S SD: 15.6033 c. M: 29.9270 c. 22: 4 2 0 5 4 1 1 4 1 N SD: 15.5331 c. M: 24.0654 c. 23: 4 2 1 4 5 0 2 4 1 N SD: 14.0184 c. M: 22.4784 c. 24: 5 1 1 5 4 1 2 4 1 N SD: 13.3530 c. M:-18.8259 c. 27: 5 2 1 5 5 1 2 5 1 N S SD: 7.0100 c. M: 13.6863 c. 31: 6 2 1 6 6 1 2 6 1 N S SD: 3.0777 c. M: 5.9639 c. 68: 13 5 2 13 13 2 5 13 2 N S SD: 1.6196 c. M: 2.3243 c. 72: 14 5 2 14 14 2 5 14 2 N S SD: 1.4974 c. M:-2.9804 c. 99: 19 7 3 19 19 3 7 19 3 N S SD: 0.8651 c. M: 1.5651 c. 140: 27 10 4 27 27 4 10 27 4 N S SD: 0.7658 c. M:-1.5016 c. 171: 33 12 5 33 33 5 12 33 5 N S SD: 0.2677 c. M: 0.4609 c. 270: 52 19 8 52 52 8 19 52 8 N S SD: 0.3151 c. M: 0.5799 c. 441: 85 31 13 85 85 13 31 85 13 N S SD: 0.2414 c. M: 0.4035 c. 612: 118 43 18 118 118 18 43 118 18 N S SD: 0.2289 c. M: 0.3635 c. 783: 151 55 23 151 151 23 55 151 23 N S SD: 0.2288 c. M: 0.3802 c. 836: 161 59 25 161 161 25 58 162 24 N SD: 0.2745 c. M:-0.5259 c. 851: 164 60 25 164 164 25 60 164 25 N S SD: 0.2548 c. M: 0.4994 c. 863: 166 61 26 166 166 26 60 167 25 N SD: 0.2370 c. M:-0.4580 c. 894: 172 63 27 172 172 27 62 173 26 N SD: 0.2269 c. M:-0.3398 c. 904: 174 64 27 174 174 27 63 175 26 N SD: 0.2606 c. M:-0.4623 c. 923: 178 65 27 178 178 27 65 178 27 N S SD: 0.2542 c. M: 0.4124 c. 935: 180 66 28 180 180 28 65 181 27 N SD: 0.1914 c. M:-0.3232 c. 966: 186 68 29 186 186 29 67 187 28 N SD: 0.1693 c. M:-0.3063 c. 1034: 199 73 31 199 199 31 72 200 30 N SD: 0.1561 c. M:-0.3060 c. 1065: 205 75 32 205 205 32 74 206 31 N SD: 0.1487 c. M:-0.2112 c. 1106: 213 78 33 213 213 33 77 214 32 N SD: 0.1360 c. M:-0.2559 c. 1137: 219 80 34 219 219 34 79 220 33 N SD: 0.1148 c. M:-0.2211 c. 1205: 232 85 36 232 232 36 84 233 35 N SD: 0.0999 c. M:-0.1972 c. 1236: 238 87 37 238 238 37 86 239 36 N SD: 0.0930 c. M:-0.1315 c. 1277: 246 90 38 246 246 38 89 247 37 N SD: 0.1034 c. M:-0.2066 c. 1308: 252 92 39 252 252 39 91 253 38 N SD: 0.0822 c. M:-0.1582 c. 1376: 265 97 41 265 265 41 96 266 40 N SD: 0.0613 c. M:-0.1154 c. 1407: 271 99 42 271 271 42 98 272 41 N SD: 0.0529 c. M:-0.0839 c. 1547: 298 109 46 298 298 46 108 299 45 N SD: 0.0405 c. M:-0.0693 c. 1578: 304 111 47 304 304 47 110 305 46 N SD: 0.0287 c. M: 0.0519 c. 1749: 337 123 52 337 337 52 122 338 51 N SD: 0.0300 c. M: 0.0516 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: 55.8656 cents 3 x x x 4 x 5 x x 6 S SD: 30.4740 cents 4 x x 5 x 6 x 7 x 8 S SD: 30.5997 cents 5 x 6 x 7:8 x 9 x 10 S SD: 16.8934 cents 6:7 x x 8 x 10 x x 12 S SD: 24.5360 cents 7:8 x 9:10:11 x 12 x 14 S SD: 15.9946 cents 8:9 x 10:11 x 13:14 x 16 SD: 10.9194 cents 9:10 x 11:13:14:15 x x 18 SD: 15.7438 cents 10:11:12 x 14:16 x 17 x 20 SD: 11.2895 cents 11 x 13 x 15 x 18:19 x 22 SD: 10.8729 cents 12:14 x 15:17:19:20:21 x 24 SD: 10.8266 cents 13:15 x 16:18:21 x 22:25:26 SD: 7.2338 cents 14:16 x 17:20:22:23:24:27:28 SD: 7.1939 cents 15:17:18 x 21:24:25:26:29:30 SD: 6.0745 cents 16:18:19:20:22 x 26:27:31:32 SD: 8.3756 cents 17:19:20:21:24:27:28:29:33:34 SD: 6.8592 cents 18:21 x 22:25:29 x 31:35:36 SD: 6.1905 cents 19:22:23 x 27:30:31:33:37:38 SD: 6.3433 cents 20:23:24:25:28:32:33:34:39:40 SD: 4.8900 cents 21:24:25:26:29 x 34:36:41:42 SD: 4.6240 cents 22:25:26:27:31:35:36:38:43:44 SD: 3.9022 cents 23:26 x 28:32:37:38:39:45:46 SD: 4.7441 cents 24:27:29 x 34:38:39:41:47:48 SD: 5.2323 cents 25:29:30:31:35:40:41:43:49:50 SD: 3.8349 cents 26:30:31:32:36:42 x 45:51:52 SD: 4.6457 cents 27:31:32:33:38:43:44:46:53:54 SD: 3.1955 cents 28:32 x 34:39:45:46:48:55:56 SD: 2.7523 cents 30:34:36:37:42:48:49:51:59:60 SD: 2.7037 cents 33:38:40 x 46:53:54:57:65:66 SD: 3.5941 cents 35:40:42:43:49:56:57:60:69:70 SD: 1.3711 cents 50:57:60:61:70:80:82:86:98:100 SD: 1.3691 cents 70:80:84:86:98:112:114:120:137:140 SD: 0.8413 cents 85:97:102:104:119:136:139:146:167:170 SD: 0.7359 cents 120:137:144:147:168:192:196:206:235:240 SD: 0.3718 cents 155:177:186:190:217:248:253:266:304:310 SD: 0.3390 cents 210:240:252:257:294:336:343:360:412:420 SD: 0.2644 cents 245:280:294:300:343:392:400:420:480:490 SD: 0.1388 cents 475:543:570:582:665:760:776:814:931:950 SD: 0.1026 cents 560:640:672:686:784:896:915:960:1098:1120 SD: 0.0991 cents 595:680:714:729:833:952:972:1020:1166:1190 SD: 0.0571 cents