Scala analysis: brect35
3x5 breed rectangle scale, <15 25 36 43| epimorphic
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: 8/7 231.174094 septimal whole tone 3: 7/6 266.870906 septimal minor third 4: 6/5 315.641287 minor third 5: 49/40 351.338099 larger approximation to neutral third 6: 5/4 386.313714 major third 7: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 8: 10/7 617.487807 Euler's tritone 9: 8/5 813.686286 minor sixth 10: 49/30 849.383098 larger approximation to neutral sixth 11: 5/3 884.358713 major sixth, BP sixth 12: 12/7 933.129094 septimal major sixth 13: 7/4 968.825906 harmonic seventh 14: 49/25 1165.024385 BP eighth 15: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 384/343 195.4773 3: 49/48 35.6968 slendro diesis, septimal 1/6-tone 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 49/48 35.6968 slendro diesis, septimal 1/6-tone 6: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 7: 28/25 196.1985 middle second 8: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 9: 28/25 196.1985 middle second 10: 49/48 35.6968 slendro diesis, septimal 1/6-tone 11: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 12: 36/35 48.7704 septimal diesis, 1/4-tone 13: 49/48 35.6968 slendro diesis, septimal 1/6-tone 14: 28/25 196.1985 middle second 15: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 5 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 384/343 195.477 cents 1: 3 28/25 196.198 cents middle second 2: 3 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 1 360/343 83.746 cents 2: 3 21/20 84.467 cents minor semitone 2: 6 8/7 231.174 cents septimal whole tone 2: 2 343/300 231.895 cents 3: 3 15/14 119.443 cents major diatonic semitone 3: 1 343/320 120.164 cents 3: 2 400/343 266.150 cents 3: 6 7/6 266.871 cents septimal minor third 3: 1 288/245 279.944 cents 3: 1 147/125 280.666 cents 3: 1 32/25 427.373 cents classic diminished fourth 4: 2 35/32 155.140 cents septimal neutral second 4: 3 25/21 301.847 cents BP second, quasi-equal minor third 4: 1 343/288 302.568 cents 4: 6 6/5 315.641 cents minor third 4: 2 64/49 462.348 cents 2 septatones or septatonic major third 4: 1 98/75 463.069 cents 5: 5 60/49 350.617 cents smaller approximation to neutral third 5: 5 49/40 351.338 cents larger approximation to neutral third 5: 5 4/3 498.045 cents perfect fourth 6: 6 5/4 386.314 cents major third 6: 1 200/147 533.021 cents 6: 2 49/36 533.742 cents Arabic lute acute fourth 6: 5 48/35 546.815 cents septimal semi-augmented fourth 6: 1 343/250 547.537 cents 7: 1 125/98 421.289 cents 7: 1 245/192 422.011 cents 7: 1 25/18 568.717 cents classic augmented fourth 7: 3 480/343 581.791 cents 7: 9 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 8: 9 10/7 617.488 cents Euler's tritone 8: 3 343/240 618.209 cents 8: 1 36/25 631.283 cents classic diminished fifth 8: 1 384/245 777.989 cents 8: 1 196/125 778.711 cents 9: 1 500/343 652.463 cents 9: 5 35/24 653.185 cents septimal semi-diminished fifth 9: 2 72/49 666.258 cents Arabic lute grave fifth 9: 1 147/100 666.979 cents 9: 6 8/5 813.686 cents minor sixth 10: 5 3/2 701.955 cents perfect fifth 10: 5 80/49 848.662 cents smaller approximation to neutral sixth 10: 5 49/30 849.383 cents larger approximation to neutral sixth 11: 1 75/49 736.931 cents BP fifth 11: 2 49/32 737.652 cents 11: 6 5/3 884.359 cents major sixth, BP sixth 11: 1 576/343 897.432 cents 11: 3 42/25 898.153 cents quasi-equal major sixth 11: 2 64/35 1044.860 cents septimal neutral seventh 12: 1 25/16 772.627 cents classic augmented fifth 12: 1 250/147 919.334 cents 12: 1 245/144 920.056 cents 12: 6 12/7 933.129 cents septimal major sixth 12: 2 343/200 933.850 cents 12: 1 640/343 1079.836 cents 12: 3 28/15 1080.557 cents grave major seventh 13: 2 600/343 968.105 cents 13: 6 7/4 968.826 cents harmonic seventh 13: 3 40/21 1115.533 cents acute major seventh 13: 1 343/180 1116.254 cents 13: 3 48/25 1129.328 cents classic diminished octave 14: 3 25/14 1003.802 cents middle minor seventh 14: 1 343/192 1004.523 cents 14: 2 35/18 1151.230 cents septimal semi-diminished octave 14: 5 96/49 1164.303 cents 14: 4 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.14286 = 36/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 35.7 231.2 266.9 315.6 351.3 386.3 582.5 617.5 813.7 849.4 884.4 933.1 968.8 1165.0 1200.0 35.7 : 195.5 231.2 279.9 315.6 350.6 546.8 581.8 778.0 813.7 848.7 897.4 933.1 1129.3 1164.3 1200.0 231.2 : 35.7 84.5 120.2 155.1 351.3 386.3 582.5 618.2 653.2 702.0 737.7 933.9 968.8 1004.5 1200.0 266.9 : 48.8 84.5 119.4 315.6 350.6 546.8 582.5 617.5 666.3 702.0 898.2 933.1 968.8 1164.3 1200.0 315.6 : 35.7 70.7 266.9 301.8 498.0 533.7 568.7 617.5 653.2 849.4 884.4 920.1 1115.5 1151.2 1200.0 351.3 : 35.0 231.2 266.1 462.3 498.0 533.0 581.8 617.5 813.7 848.7 884.4 1079.8 1115.5 1164.3 1200.0 386.3 : 196.2 231.2 427.4 463.1 498.0 546.8 582.5 778.7 813.7 849.4 1044.9 1080.6 1129.3 1165.0 1200.0 582.5 : 35.0 231.2 266.9 301.8 350.6 386.3 582.5 617.5 653.2 848.7 884.4 933.1 968.8 1003.8 1200.0 617.5 : 196.2 231.9 266.9 315.6 351.3 547.5 582.5 618.2 813.7 849.4 898.2 933.9 968.8 1165.0 1200.0 813.7 : 35.7 70.7 119.4 155.1 351.3 386.3 422.0 617.5 653.2 702.0 737.7 772.6 968.8 1003.8 1200.0 849.4 : 35.0 83.7 119.4 315.6 350.6 386.3 581.8 617.5 666.3 702.0 736.9 933.1 968.1 1164.3 1200.0 884.4 : 48.8 84.5 280.7 315.6 351.3 546.8 582.5 631.3 667.0 702.0 898.2 933.1 1129.3 1165.0 1200.0 933.1 : 35.7 231.9 266.9 302.6 498.0 533.7 582.5 618.2 653.2 849.4 884.4 1080.6 1116.3 1151.2 1200.0 968.8 : 196.2 231.2 266.9 462.3 498.0 546.8 582.5 617.5 813.7 848.7 1044.9 1080.6 1115.5 1164.3 1200.0 1165.0: 35.0 70.7 266.1 301.8 350.6 386.3 421.3 617.5 652.5 848.7 884.4 919.3 968.1 1003.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 196.1985 cents 686/625, 161.2229 cents 50/49, 34.9756 cents 2: 70.6724 .. 231.8953 cents 686/625, 161.2229 cents 625/672,-125.5261 cents 3: 119.4428 .. 427.3726 cents 448/375, 307.9298 cents 2250/2401,-112.4525 cents 4: 155.1396 .. 463.0694 cents 448/375, 307.9298 cents 875/1024,-272.2330 cents 5: 350.6169 .. 498.0450 cents 49/45, 147.4281 cents 2250/2401,-112.4525 cents 6: 386.3137 .. 547.5366 cents 686/625, 161.2229 cents 15/16,-111.7313 cents 7: 421.2893 .. 582.5122 cents 686/625, 161.2229 cents 15625/16807,-126.2472 cents 8: 617.4878 .. 778.7107 cents 686/625, 161.2229 cents 50/49, 34.9756 cents 9: 652.4634 .. 813.6863 cents 686/625, 161.2229 cents 15625/16807,-126.2472 cents 10: 701.9550 .. 849.3831 cents 49/45, 147.4281 cents 15/16,-111.7313 cents 11: 736.9306 .. 1044.8604 cents 448/375, 307.9298 cents 2250/2401,-112.4525 cents 12: 772.6274 .. 1080.5572 cents 448/375, 307.9298 cents 875/1024,-272.2330 cents 13: 968.1047 .. 1129.3276 cents 686/625, 161.2229 cents 2250/2401,-112.4525 cents 14: 1003.8015 .. 1165.0244 cents 686/625, 161.2229 cents 625/672,-125.5261 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 28/25, 196.1985 cents Average / Smallest step : 2.287308 Largest / Average step : 2.452481 Largest / Smallest step : 5.609579 Median interval of one step : 49/48, 35.6968 cents, amount: 5 Most common interval of one step : 49/48, 35.6968 cents, amount: 5 Least squares average step : 80.08134 cents, oct.: 1201.22013 cents Scale is not proper Step pattern alph. order: ABACADEDEADCAED Step pattern size order : BDBCBAEAEBACBEA Scale is a Constant Structure, by a margin of 5.36205 cents Scale diversity : 1.360480 Lumma stability : 0.087439 Lumma impropriety factor : 0.794774 Number of different interval sizes : 72 = 5.14286 / class Number of one step interval sizes : 5 Highest interval variety : 7 Mean interval variety : 5.14286 = 36/7 Median interval variety : 4 Lowest interval variety : 3 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 9 Most common triad is 0.0 582.512 617.488 cents, amount: 4 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 5 7 Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 2 at degree 14 Formal octave complements present : 11 = 73.3333% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.016028 Average absolute harmonicity : 0.131962 Specific harmonicity : 0.092985 Fundamental : 1/8400, -13.0362 octaves, 0.0311 Hz. Guide tone : 5880, 12.5216 octaves, 1538358.324 Hz. Exponens Consonantiae : 4.939200E+07, 25.55777 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 235.0, average 15.66667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.62725, average 0.97515 Sum of Tenney's harmonic distance : 28.90852, average 1.92723 Vogel's harmonic complexity : 25.86667 Wille's k value : 4287 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 8 Triangular lattice diameter : 3 Lattice compactness : 389.08551, average 3.24238 Lattice compactness (without 2's) : 238.24117, average 1.98534 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 3 -0.13333 24 1 3: -1 .. 1 -0.13333 6 5: -2 .. 1 -0.26667 10 4 7: -1 .. 2 0.53333 14 10 Average exponent except 2's : 2 / 15 = 0.13333 Average absolute exponent except 2's: 30 / 15 = 2.00000 Scale is weakly epimorphic with val: <15 22 32 44| Scale is weakly epimorphic with val: <15 23 37 43| Scale is weakly epimorphic with val: <15 25 32 41| Scale is weakly epimorphic with val: <15 25 34 42| Scale is JI-epimorphic with val: <15 25 36 43| Scale is weakly epimorphic with val: <15 25 38 44| Scale is weakly epimorphic with val: <15 26 37 40|
FIT/MODE
15: 0 3 0 1 0 1 2 1 2 1 0 1 0 3 0 N I SD: 22.2757 c. M: 35.6968 c. 16: 0 3 1 0 1 0 3 0 3 0 1 0 1 3 0 N I SD: 22.0306 c. M: 35.6968 c. 18: 1 2 1 1 0 1 3 0 3 1 0 1 1 2 1 N I SD: 20.2359 c. M: 31.6911 c. 19: 1 3 0 1 1 0 3 1 3 0 1 1 0 3 1 N I SD: 18.1573 c. M: 28.3305 c. 20: 1 3 0 1 1 0 4 0 4 0 1 1 0 3 1 N I SD: 19.0885 c. M:-26.8709 c. 21: 1 3 1 1 0 1 3 1 3 1 0 1 1 3 1 N I SD: 16.1429 c. M: 27.2159 c. 22: 1 3 1 1 0 1 4 0 4 1 0 1 1 3 1 N I SD: 14.5858 c. M: 24.0654 c. 23: 1 3 1 1 1 0 4 1 4 0 1 1 1 3 1 N I SD: 14.3925 c. M:-22.4784 c. 24: 1 4 0 1 1 1 4 0 4 1 1 1 0 4 1 N I SD: 14.5743 c. M:-18.8259 c. 25: 1 4 1 1 0 1 4 1 4 1 0 1 1 4 1 N I SD: 13.5230 c. M: 21.1291 c. 26: 1 4 1 1 1 0 5 0 5 0 1 1 1 4 1 N I SD: 12.6734 c. M: 18.6139 c. 27: 1 4 1 1 1 1 4 1 4 1 1 1 1 4 1 N D3 I SD: 7.4351 c. M: 13.6863 c. 31: 1 5 1 1 1 1 5 1 5 1 1 1 1 5 1 N D3 I SD: 3.1828 c. M: 5.9639 c. 68: 2 11 2 3 2 2 11 2 11 2 2 3 2 11 2 N I SD: 1.6187 c. M: 2.3243 c. 99: 3 16 3 4 3 3 16 3 16 3 3 4 3 16 3 N I SD: 0.8623 c. M:-1.5651 c. 140: 4 23 4 6 4 4 23 4 23 4 4 6 4 23 4 N I SD: 0.8720 c. M: 1.5016 c. 171: 5 28 5 7 5 5 28 5 28 5 5 7 5 28 5 N I SD: 0.3021 c. M: 0.6091 c. 270: 8 44 8 11 8 8 44 8 44 8 8 11 8 44 8 N I SD: 0.2799 c. M: 0.5799 c. 441: 13 72 13 18 13 13 72 13 72 13 13 18 13 72 13 N I SD: 0.2207 c. M: 0.4035 c. 612: 18 100 18 25 18 18 100 18 100 18 18 25 18 100 18 N I SD: 0.2227 c. M: 0.4027 c. 867: 26 141 26 35 26 25 142 25 142 26 25 35 26 142 25 N SD: 0.2206 c. M:-0.4439 c. 935: 28 152 28 38 28 27 153 27 153 28 27 38 28 153 27 N SD: 0.1734 c. M:-0.3232 c. 966: 29 157 29 39 29 28 158 28 158 29 28 39 29 158 28 N SD: 0.1724 c. M:-0.3280 c. 1034: 31 168 31 42 31 30 169 30 169 31 30 42 31 169 30 N SD: 0.1593 c. M:-0.3060 c. 1106: 33 180 33 45 33 32 181 32 181 33 32 45 33 181 32 N SD: 0.1190 c. M:-0.2559 c. 1137: 34 185 34 46 34 33 186 33 186 34 33 46 34 186 33 N SD: 0.1123 c. M:-0.2211 c. 1205: 36 196 36 49 36 35 197 35 197 36 35 49 36 197 35 N SD: 0.0979 c. M:-0.1972 c. 1277: 38 208 38 52 38 37 209 37 209 38 37 52 38 209 37 N SD: 0.0917 c. M:-0.2066 c. 1304: 39 212 39 53 39 38 213 38 213 39 38 53 39 213 38 N SD: 0.1215 c. M:-0.1956 c. 1308: 39 213 39 53 39 38 214 38 214 39 38 53 39 214 38 N SD: 0.0771 c. M:-0.1582 c. 1376: 41 224 41 56 41 40 225 40 225 41 40 56 41 225 40 N SD: 0.0566 c. M:-0.1154 c. 1479: 44 241 44 60 44 43 242 43 242 44 43 60 44 242 43 N SD: 0.0656 c. M:-0.1098 c. 1547: 46 252 46 63 46 45 253 45 253 46 45 63 46 253 45 N SD: 0.0385 c. M:-0.0693 c. 1578: 47 257 47 64 47 46 258 46 258 47 46 64 47 258 46 N SD: 0.0311 c. M: 0.0519 c. 1749: 52 285 52 71 52 51 286 51 286 52 51 71 52 286 51 N SD: 0.0299 c. M: 0.0516 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x 3 x x x x x x 4 S SD: 42.2336 cents 3 x x x x x x 4 x x x 5 x x x 6 S SD: 28.1557 cents 4 x x x x x 5 x 6 x x x x 7 x 8 S SD: 21.1168 cents 5 x x x 6 x x 7 x 8 x x x 9 x 10 S SD: 9.7541 cents 6 x x 7 x x x 8:9 x x 10 x 11 x 12 S SD: 24.0114 cents 7 x 8 x x x 9 x 10:11 x x 12 x x 14 S SD: 9.6489 cents 8 x 9 x x x 10:11 x x 13 x x 14 x 16 SD: 7.0609 cents 9 x 10 x x 11 x x 13:14 x 15 x 16 x 18 SD: 10.9562 cents 10 x 11 x 12 x 13:14 x 16 x x 17:18 x 20 S SD: 13.4497 cents 11 x x 13 x x 14:15:16 x 18 x 19 x x 22 SD: 9.7959 cents 12 x x 14 x x 15 x 17:19 x 20 x 21 x 24 SD: 3.3151 cents 13:14:15 x x 16 x 18:19:21 x x 22:23:25:26 SD: 11.4268 cents 14:15:16 x x 17:18 x 20:22:23 x 24:25:27:28 SD: 10.2466 cents 15:16:17 x 18 x 19:21 x 24 x 25 x 26:29:30 SD: 8.5755 cents 16:17:18 x 19 x 20:22:23 x 26:27 x 28:31:32 SD: 8.0795 cents 17:18:19:20 x 21 x 24 x 27:28 x 29:30:33:34 S SD: 7.6369 cents 18:19 x 21 x 22:23:25:26:29 x 30:31:32:35:36 SD: 6.7257 cents 19:20 x 22:23 x 24 x 27:30:31:32 x 33:37:38 SD: 6.2888 cents 20:21:23 x 24 x 25:28:29:32 x 33:34:35:39:40 SD: 5.1033 cents 21:22:24 x 25 x 26:29:30 x 34:35:36:37:41:42 SD: 4.8964 cents 22:23:25:26 x 27:28:31 x 35:36:37:38:39:43:44 SD: 5.1336 cents 23:24:26:27 x 28:29:32:33:37 x 38:39:40:45:46 SD: 4.3717 cents 24:25:27:28:29 x 30 x 34:38:39:40:41:42:47:48 SD: 4.0453 cents 25:26 x 29:30 x 31:35:36:40:41:42:43:44:49:50 SD: 3.3439 cents 26:27:30 x 31:32:33:36:37:42 x 43:45:46:51:52 SD: 4.5766 cents 27:28:31 x 32:33:34:38:39:43:44:45:46:47:53:54 SD: 3.3381 cents 28:29:32:33 x 34:35:39:40:45:46:47:48:49:55:56 SD: 2.8332 cents 29:30:33:34:35 x 36:41 x 46:47:48:50:51:57:58 SD: 3.3801 cents 30:31:34:35:36:37:38:42:43:48:49:50:51:53:59:60 SD: 2.8785 cents 32:33 x 37:38:39:40:45:46:51:52:53:55:56:63:64 SD: 2.7244 cents 33:34:38:39:40 x 41:46:47:53:54:55:57:58:65:66 SD: 3.0098 cents 35:36:40:41:42:43:44:49:50:56:57:58:60:61:69:70 SD: 1.6584 cents 48:49:55:56:58:59:60:67:69:77:78:80:82:84:94:96 SD: 1.4583 cents 49:50:56:57:59:60:61:69:70:78:80:82:84:86:96:98 SD: 1.2775 cents 72:74:82:84:86:88:90:101:103:115:118:120:123:126:141:144 SD: 1.2536 cents 76:78:87:89:91:93:95:106:109:122:124:127:130:133:149:152 SD: 1.1820 cents 77:79:88:90:92:94:96:108:110:123:126:128:132:135:151:154 SD: 1.0713 cents 80:82:91:93:96:98:100:112:114:128:131:133:137:140:157:160 SD: 0.9875 cents 84:86:96:98:101:103:105:118:120:134:137:140:144:147:165:168 SD: 0.7360 cents 112:114:128:131:134:137:140:157:160:179:183:187:192:196:220:224 SD: 0.7019 cents 120:123:137:140:144:147:150:168:171:192:196:200:206:210:235:240 SD: 0.5952 cents 133:136:152:155:160:163:166:186:190:213:217:222:228:233:261:266 SD: 0.5270 cents 140:143:160:163:168:172:175:196:200:224:229:233:240:245:274:280 SD: 0.5068 cents 145:148:166:169:174:178:181:203:207:232:237:242:249:254:284:290 SD: 0.4844 cents 155:158:177:181:186:190:194:217:221:248:253:258:266:271:304:310 SD: 0.4317 cents 175:179:200:204:210:214:219:245:250:280:286:292:300:306:343:350 SD: 0.3875 cents 196:200:224:229:235:240:245:274:280:314:320:327:336:343:384:392 SD: 0.3332 cents 235:240:269:274:282:288:294:329:336:376:384:392:403:411:461:470 SD: 0.3031 cents 240:245:274:280:288:294:300:336:343:384:392:400:411:420:470:480 SD: 0.2022 cents 245:250:280:286:294:300:306:343:350:392:400:408:420:429:480:490 SD: 0.1899 cents 280:286:320:327:336:343:350:392:400:448:457:467:480:490:549:560 SD: 0.1845 cents 385:393:440:449:462:472:481:539:550:616:629:642:660:674:755:770 SD: 0.1549 cents 420:429:480:490:504:515:525:588:600:672:686:700:720:735:823:840 SD: 0.1337 cents 475:485:543:554:570:582:594:665:679:760:776:792:814:831:931:950 SD: 0.1298 cents 480:490:549:560:576:588:600:672:686:768:784:800:823:840:941:960 SD: 0.1070 cents 595:607:680:694:714:729:744:833:850:952:972:992:1020:1041:1166:1190 SD: 0.1067 cents