Scala analysis: breetet2
doubled Breed tetrad
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: 25/24 70.672427 classic chromatic semitone, minor chroma 3: 7/6 266.870906 septimal minor third 4: 49/40 351.338099 larger approximation to neutral third 5: 5/4 386.313714 major third 6: 4/3 498.044999 perfect fourth 7: 10/7 617.487807 Euler's tritone 8: 35/24 653.184619 septimal semi-diminished fifth 9: 3/2 701.955001 perfect fifth 10: 49/30 849.383098 larger approximation to neutral sixth 11: 5/3 884.358713 major sixth, BP sixth 12: 7/4 968.825906 harmonic seventh 13: 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: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 3: 28/25 196.1985 middle second 4: 21/20 84.4672 minor semitone 5: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 6: 16/15 111.7313 minor diatonic semitone 7: 15/14 119.4428 major diatonic semitone 8: 49/48 35.6968 slendro diesis, septimal 1/6-tone 9: 36/35 48.7704 septimal diesis, 1/4-tone 10: 49/45 147.4281 BP minor semitone 11: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 12: 21/20 84.4672 minor semitone 13: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 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 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 49/45 147.428 cents BP minor semitone 1: 1 28/25 196.198 cents middle second 1: 1 8/7 231.174 cents septimal whole tone 2: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 1 21/20 84.467 cents minor semitone 2: 2 15/14 119.443 cents major diatonic semitone 2: 1 160/147 146.707 cents 2: 1 35/32 155.140 cents septimal neutral second 2: 1 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 2: 2 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 147/125 280.666 cents 2: 1 6/5 315.641 cents minor third 3: 1 9/8 203.910 cents major whole tone 3: 2 8/7 231.174 cents septimal whole tone 3: 1 343/300 231.895 cents 3: 1 400/343 266.150 cents 3: 3 7/6 266.871 cents septimal minor third 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 2 6/5 315.641 cents minor third 3: 1 60/49 350.617 cents smaller approximation to neutral third 3: 1 49/40 351.338 cents larger approximation to neutral third 4: 1 7/6 266.871 cents septimal minor third 4: 1 25/21 301.847 cents BP second, quasi-equal minor third 4: 2 6/5 315.641 cents minor third 4: 2 60/49 350.617 cents smaller approximation to neutral third 4: 2 49/40 351.338 cents larger approximation to neutral third 4: 2 5/4 386.314 cents major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 2 4/3 498.045 cents perfect fourth 5: 1 60/49 350.617 cents smaller approximation to neutral third 5: 1 49/40 351.338 cents larger approximation to neutral third 5: 3 5/4 386.314 cents major third 5: 1 125/98 421.289 cents 5: 1 64/49 462.348 cents 2 septatones or septatonic major third 5: 1 98/75 463.069 cents 5: 1 49/36 533.742 cents Arabic lute acute fourth 5: 2 48/35 546.815 cents septimal semi-augmented fourth 5: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 9/7 435.084 cents septimal major third, BP third 6: 1 21/16 470.781 cents narrow fourth 6: 3 4/3 498.045 cents perfect fourth 6: 1 25/18 568.717 cents classic augmented fourth 6: 1 480/343 581.791 cents 6: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 2 10/7 617.488 cents Euler's tritone 6: 1 147/100 666.979 cents 7: 1 200/147 533.021 cents 7: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 3 10/7 617.488 cents Euler's tritone 7: 1 343/240 618.209 cents 7: 1 36/25 631.283 cents classic diminished fifth 7: 3 3/2 701.955 cents perfect fifth 7: 1 32/21 729.219 cents wide fifth 7: 1 14/9 764.916 cents septimal minor sixth 8: 2 10/7 617.488 cents Euler's tritone 8: 2 35/24 653.185 cents septimal semi-diminished fifth 8: 1 72/49 666.258 cents Arabic lute grave fifth 8: 1 75/49 736.931 cents BP fifth 8: 1 49/32 737.652 cents 8: 1 196/125 778.711 cents 8: 3 8/5 813.686 cents minor sixth 8: 1 80/49 848.662 cents smaller approximation to neutral sixth 8: 1 49/30 849.383 cents larger approximation to neutral sixth 9: 2 3/2 701.955 cents perfect fifth 9: 1 25/16 772.627 cents classic augmented fifth 9: 2 8/5 813.686 cents minor sixth 9: 2 80/49 848.662 cents smaller approximation to neutral sixth 9: 2 49/30 849.383 cents larger approximation to neutral sixth 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 1 12/7 933.129 cents septimal major sixth 10: 1 80/49 848.662 cents smaller approximation to neutral sixth 10: 1 49/30 849.383 cents larger approximation to neutral sixth 10: 2 5/3 884.359 cents major sixth, BP sixth 10: 1 42/25 898.153 cents quasi-equal major sixth 10: 3 12/7 933.129 cents septimal major sixth 10: 1 343/200 933.850 cents 10: 1 600/343 968.105 cents 10: 2 7/4 968.826 cents harmonic seventh 10: 1 16/9 996.090 cents Pythagorean minor seventh 11: 1 5/3 884.359 cents major sixth, BP sixth 11: 1 250/147 919.334 cents 11: 1 12/7 933.129 cents septimal major sixth 11: 2 7/4 968.826 cents harmonic seventh 11: 1 25/14 1003.802 cents middle minor seventh 11: 1 9/5 1017.596 cents just minor seventh, BP seventh 11: 1 64/35 1044.860 cents septimal neutral seventh 11: 1 147/80 1053.293 cents 11: 2 28/15 1080.557 cents grave major seventh 11: 1 40/21 1115.533 cents acute major seventh 11: 1 48/25 1129.328 cents classic diminished octave 12: 1 7/4 968.826 cents harmonic seventh 12: 1 25/14 1003.802 cents middle minor seventh 12: 1 90/49 1052.572 cents 12: 1 28/15 1080.557 cents grave major seventh 12: 1 15/8 1088.269 cents classic major seventh 12: 2 40/21 1115.533 cents acute major seventh 12: 1 35/18 1151.230 cents septimal semi-diminished octave 12: 2 96/49 1164.303 cents 12: 3 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 11 Average number of different intervals per interval class: 9.00000 = 9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 0.0 : 35.7 70.7 266.9 351.3 386.3 498.0 617.5 653.2 702.0 849.4 884.4 968.8 1200.0 35.7 : 35.0 231.2 315.6 350.6 462.3 581.8 617.5 666.3 813.7 848.7 933.1 1164.3 1200.0 70.7 : 196.2 280.7 315.6 427.4 546.8 582.5 631.3 778.7 813.7 898.2 1129.3 1165.0 1200.0 266.9 : 84.5 119.4 231.2 350.6 386.3 435.1 582.5 617.5 702.0 933.1 968.8 1003.8 1200.0 351.3 : 35.0 146.7 266.1 301.8 350.6 498.0 533.0 617.5 848.7 884.4 919.3 1115.5 1200.0 386.3 : 111.7 231.2 266.9 315.6 463.1 498.0 582.5 813.7 849.4 884.4 1080.6 1165.0 1200.0 498.0 : 119.4 155.1 203.9 351.3 386.3 470.8 702.0 737.7 772.6 968.8 1053.3 1088.3 1200.0 617.5 : 35.7 84.5 231.9 266.9 351.3 582.5 618.2 653.2 849.4 933.9 968.8 1080.6 1200.0 653.2 : 48.8 196.2 231.2 315.6 546.8 582.5 617.5 813.7 898.2 933.1 1044.9 1164.3 1200.0 702.0 : 147.4 182.4 266.9 498.0 533.7 568.7 764.9 849.4 884.4 996.1 1115.5 1151.2 1200.0 849.4 : 35.0 119.4 350.6 386.3 421.3 617.5 702.0 736.9 848.7 968.1 1003.8 1052.6 1200.0 884.4 : 84.5 315.6 351.3 386.3 582.5 667.0 702.0 813.7 933.1 968.8 1017.6 1165.0 1200.0 968.8 : 231.2 266.9 301.8 498.0 582.5 617.5 729.2 848.7 884.4 933.1 1080.6 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 231.1741 cents 28/25, 196.1985 cents 50/49, 34.9756 cents 2: 70.6724 .. 315.6413 cents 144/125, 244.9689 cents 175/192,-160.5017 cents 3: 203.9100 .. 351.3381 cents 49/45, 147.4281 cents 15/16,-111.7313 cents 4: 266.8709 .. 498.0450 cents 8/7, 231.1741 cents 20/21,-84.4672 cents 5: 350.6169 .. 582.5122 cents 343/300, 231.8953 cents 45/49,-147.4281 cents 6: 435.0841 .. 666.9794 cents 343/300, 231.8953 cents 45/49,-147.4281 cents 7: 533.0206 .. 764.9159 cents 343/300, 231.8953 cents 20000/21609,-133.9588 cents 8: 617.4878 .. 849.3831 cents 343/300, 231.8953 cents 45/49,-147.4281 cents 9: 701.9550 .. 933.1291 cents 8/7, 231.1741 cents 45/49,-147.4281 cents 10: 848.6619 .. 996.0900 cents 49/45, 147.4281 cents 20/21,-84.4672 cents 11: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 15/16,-111.7313 cents 12: 968.8259 .. 1165.0244 cents 28/25, 196.1985 cents 175/192,-160.5017 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.639201 Largest / Average step : 2.504386 Largest / Smallest step : 6.609579 Median interval of one step : 21/20, 84.4672 cents, amount: 2 Most common interval of one step : 50/49, 34.9756 cents, amount: 3 Least squares average step : 83.78024 cents, oct.: 1089.14317 cents Scale is not proper Step pattern alph. order: ABCDBEFAGHBDI Step pattern size order : BAHDAEFBCGADI Scale is not a Constant Structure Scale diversity : 1.499467 Lumma stability : 0.058293 Lumma impropriety factor : 0.882213 Number of different interval sizes : 72 = 6.00000 / class Number of one step interval sizes : 9 Highest interval variety : 11 Mean interval variety : 9.00000 = 9 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 7 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 3 = 23.0769% Scale is n-1 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 classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 6 and 7 combined -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.016289 Average absolute harmonicity : 0.163659 Specific harmonicity : 0.106003 Fundamental : 1/1680, -10.7142 octaves, 0.1557 Hz. Guide tone : 14700, 13.8435 octaves, 3845895.810 Hz. Exponens Consonantiae : 2.469600E+07, 24.55777 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 223.0, average 17.15385 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.90007, average 0.99231 Sum of Tenney's harmonic distance : 25.08443, average 1.92957 Vogel's harmonic complexity : 22.23077 Wille's k value : 857 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 8 Triangular lattice diameter : 3 Lattice compactness : 271.67910, average 2.98548 Lattice compactness (without 2's) : 167.61891, average 1.84197 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.23077 24 1 3: -1 .. 1 -0.46154 8 2 5: -1 .. 2 0.30769 8 3 7: -1 .. 2 0.61538 10 7 Average exponent except 2's : 6 / 13 = 0.46154 Average absolute exponent except 2's: 26 / 13 = 2.00000
FIT/MODE
13: 0 1 2 1 0 1 2 0 1 1 1 1 2 N T3 SD: 27.7423 c. M:-46.5587 c. 14: 0 1 2 1 0 2 1 0 1 2 0 1 3 N SD: 25.8588 c. M: 53.1846 c. 15: 0 1 2 1 1 1 2 0 1 2 0 1 3 N SD: 20.7899 c. M: 35.6968 c. 17: 1 0 3 1 1 1 2 0 1 2 1 1 3 N SD: 19.6173 c. M:-37.2157 c. 19: 0 1 3 1 1 2 2 0 1 2 1 1 4 N SD: 19.3830 c. M: 35.6968 c. 20: 1 0 3 2 0 2 2 1 1 2 1 1 4 N SD: 16.6598 c. M: 26.8709 c. 21: 1 0 4 1 1 2 2 0 1 3 0 2 4 N SD: 15.9836 c. M: 27.2159 c. 22: 1 0 4 1 1 2 2 1 1 3 0 2 4 N SD: 13.8884 c. M: 24.0654 c. 24: 1 0 4 2 1 2 2 1 1 3 1 1 5 N SD: 12.4922 c. M: 20.6724 c. 27: 1 1 4 2 1 2 3 1 1 3 1 2 5 N SD: 9.2421 c. M:-18.2165 c. 30: 1 1 5 2 1 2 3 1 2 3 1 2 6 N SD: 11.9489 c. M:-18.0450 c. 31: 1 1 5 2 1 3 3 1 1 4 1 2 6 N SD: 3.9555 c. M:-6.7469 c. 68: 2 2 11 5 2 6 7 2 3 8 2 5 13 N SD: 2.0491 c. M:-3.9274 c. 72: 2 2 12 5 2 7 7 2 3 9 2 5 14 N SD: 2.0921 c. M: 4.0058 c. 99: 3 3 16 7 3 9 10 3 4 12 3 7 19 N SD: 1.0244 c. M:-2.0548 c. 140: 4 4 23 10 4 13 14 4 6 17 4 10 27 N SD: 1.1066 c. M: 2.1010 c. 171: 5 5 28 12 5 16 17 5 7 21 5 12 33 N SD: 0.3548 c. M: 0.6091 c. 270: 8 8 44 19 8 25 27 8 11 33 8 19 52 N SD: 0.2682 c. M: 0.4942 c. 441: 13 13 72 31 13 41 44 13 18 54 13 31 85 N SD: 0.1972 c. M: 0.4035 c. 612: 18 18 100 43 18 57 61 18 25 75 18 43 118 N SD: 0.2146 c. M: 0.4027 c. 711: 21 21 116 50 21 66 71 21 29 87 21 50 137 N SD: 0.2083 c. M: 0.4380 c. 836: 25 24 137 59 24 78 83 25 34 103 24 59 161 N SD: 0.2075 c. M:-0.3777 c. 935: 28 27 153 66 27 87 93 28 38 115 27 66 180 N SD: 0.1537 c. M:-0.3197 c. 966: 29 28 158 68 28 90 96 29 39 119 28 68 186 N SD: 0.1791 c. M:-0.3280 c. 1007: 30 29 165 71 29 94 100 30 41 124 29 71 194 N SD: 0.1751 c. M: 0.3646 c. 1034: 31 30 169 73 30 96 103 31 42 127 30 73 199 N SD: 0.1725 c. M:-0.3060 c. 1038: 31 30 170 73 30 97 103 31 42 128 30 73 200 N SD: 0.1645 c. M:-0.3279 c. 1106: 33 32 181 78 32 103 110 33 45 136 32 78 213 N SD: 0.1028 c. M:-0.1990 c. 1137: 34 33 186 80 33 106 113 34 46 140 33 80 219 N SD: 0.1143 c. M:-0.2211 c. 1205: 36 35 197 85 35 112 120 36 49 148 35 85 232 N SD: 0.1028 c. M:-0.1972 c. 1277: 38 37 209 90 37 119 127 38 52 157 37 90 246 N SD: 0.0877 c. M: 0.1947 c. 1308: 39 38 214 92 38 122 130 39 53 161 38 92 252 N SD: 0.0810 c. M:-0.1582 c. 1376: 41 40 225 97 40 128 137 41 56 169 40 97 265 N SD: 0.0574 c. M:-0.1154 c. 1547: 46 45 253 109 45 144 154 46 63 190 45 109 298 N SD: 0.0434 c. M: 0.0842 c. 1578: 47 46 258 111 46 147 157 47 64 194 46 111 304 N SD: 0.0391 c. M:-0.0539 c. 1749: 52 51 286 123 51 163 174 52 71 215 51 123 337 N SD: 0.0369 c. M:-0.0682 c.
FIT/HARMONIC
1 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 x 3 x x x 4 S SD: 0.0000 cents 3 x x x x x 4 x x x x 5 x 6 S SD: 0.0000 cents 4 x x x x 5 x x x 6 x x 7:8 S SD: 0.0000 cents 5 x x x 6 x x 7 x x 8 x 9:10 S SD: 15.6849 cents 6 x x 7 x x 8 x x 9 x 10:11:12 S SD: 13.4228 cents 7 x x 8 x 9 x 10 x x 11 x 12:14 S SD: 16.1602 cents 8 x x 9 x 10:11 x x 12:13 x 14:16 S SD: 11.8498 cents 9 x x x 11 x 12 x 13:14 x 15:16:18 SD: 10.0988 cents 10 x 11 x 12 x 13:14 x 15:16:17:18:20 S SD: 14.9672 cents 11 x 12:13 x 14:15 x 16:17:18 x 19:22 SD: 12.4692 cents 12 x 13:14 x 15:16:17 x 18 x 20:21:24 S SD: 7.7143 cents 13 x 14:15:16 x 17 x 19:20:21:22:23:26 SD: 9.0781 cents 14 x 15:16:17:18:19:20 x 21:23 x 25:28 SD: 9.2337 cents 15 x 16 x 18:19:20:21:22:23 x 25:26:30 SD: 8.0801 cents 16 x 17:19 x 20:21:23 x 24:26:27:28:32 SD: 5.9286 cents 17 x 18:20:21 x 23:24:25:26:28 x 30:34 SD: 6.3545 cents 18 x 19:21:22:23:24 x 26:27:29:30:32:36 SD: 5.4313 cents 19 x 20:22:23:24:25:27:28:29:31:32:33:38 SD: 4.9991 cents 20 x 21:23 x 25:27 x 29:30 x 33:35:40 SD: 4.5468 cents 21 x 22:25 x 26:28:30:31:32:34:35:37:42 SD: 5.1034 cents 22 x 23:26:27:28:29:31:32:33:36:37:39:44 SD: 4.7532 cents 23 x 24:27:28:29:31:33:34:35 x 38:40:46 SD: 4.4436 cents 24 x 25:28:29:30:32:34:35:36:39:40:42:48 SD: 2.4306 cents 25 x 26:29 x 31:33:36 x 38:41:42:44:50 SD: 4.0690 cents 26 x 27:30:32:33:35:37:38:39:42:43:46:52 SD: 4.0785 cents 27 x 28:32:33:34:36 x 39:41:44:45:47:54 SD: 3.8644 cents 28 x 29:33:34:35:37:40:41:42:46:47:49:56 SD: 2.8658 cents 29 x 30:34 x 36:39:41:42:44:47:48:51:58 SD: 3.8957 cents 30 x 31:35:37:38:40:43:44:45:49:50:53:60 SD: 2.9542 cents 31 x 32:36:38:39:41:44:45:47:51:52:54:62 SD: 3.2369 cents 32 x 33:37:39:40:43:46:47:48:52:53:56:64 SD: 2.9676 cents 33:34 x 39:40:41:44:47:48:50:54:55:58:66 SD: 3.3510 cents 34:35 x 40:42:43:45:49:50:51:56:57:60:68 SD: 3.8792 cents 35:36 x 41:43:44:47:50:51:53:57:58:61:70 SD: 2.5558 cents 40:41:42:47:49:50:53:57:58:60:65:67:70:80 SD: 2.1481 cents 44:45:46:51:54:55:59:63:64:66:72:73:77:88 SD: 1.5225 cents 48:49:50:56:59:60:64:69:70:72:78:80:84:96 SD: 1.1649 cents 72:74:75:84:88:90:96:103:105:108:118:120:126:144 SD: 1.0701 cents 84:86:88:98:103:105:112:120:123:126:137:140:147:168 SD: 1.0367 cents 88:90:92:103:108:110:117:126:128:132:144:147:154:176 SD: 1.0243 cents 90:92:94:105:110:113:120:129:131:135:147:150:158:180 SD: 1.0187 cents 92:94:96:107:113:115:123:131:134:138:150:153:161:184 SD: 0.9228 cents 96:98:100:112:118:120:128:137:140:144:157:160:168:192 SD: 0.5026 cents 144:147:150:168:176:180:192:206:210:216:235:240:252:288 SD: 0.3720 cents 192:196:200:224:235:240:256:274:280:288:314:320:336:384 SD: 0.2468 cents 240:245:250:280:294:300:320:343:350:360:392:400:420:480 SD: 0.0555 cents