Scala analysis: mohaj-bala_443
Parizekmic Mohajira+Bala scale, based on a double Bala sequence
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 52/45 250.303946 3: 443/360 359.171751 4: 13/10 454.213948 tridecimal semi-diminished fourth 5: 4/3 498.044999 perfect fourth 6: 64/45 609.776284 2nd tritone 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 26/15 952.258947 tridecimal semi-augmented sixth 10: 83/45 1059.823602 11: 39/20 1156.168949 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 40/39 43.8311 tridecimal minor diesis 1: 16/15 111.7313 minor diatonic semitone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 443/416 108.8678 4: 468/443 95.0422 5: 40/39 43.8311 tridecimal minor diesis 6: 16/15 111.7313 minor diatonic semitone 7: 135/128 92.1787 major chroma, major limma 8: 16/15 111.7313 minor diatonic semitone 9: 13/12 138.5727 tridecimal 2/3-tone 10: 83/78 107.5647 11: 351/332 96.3453 12: 40/39 43.8311 tridecimal minor diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 40/39 43.831 cents tridecimal minor diesis 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 468/443 95.042 cents 1: 1 351/332 96.345 cents 1: 1 83/78 107.565 cents 1: 1 443/416 108.868 cents 1: 3 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 2: 1 480/443 138.873 cents 2: 1 90/83 140.176 cents 2: 2 128/117 155.562 cents 2: 4 9/8 203.910 cents major whole tone 2: 1 83/72 246.137 cents 2: 1 443/384 247.440 cents 2: 2 52/45 250.304 cents 3: 3 15/13 247.741 cents tridecimal 5/4-tone 3: 1 512/443 250.605 cents 3: 1 96/83 251.908 cents 3: 1 32/27 294.135 cents Pythagorean minor third 3: 1 6/5 315.641 cents minor third 3: 3 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 3: 1 166/135 357.869 cents 3: 1 443/360 359.172 cents 4: 1 540/443 342.783 cents 4: 3 16/13 359.472 cents tridecimal neutral third 4: 2 5/4 386.314 cents major third 4: 1 104/83 390.480 cents 4: 1 443/351 403.003 cents 4: 1 83/64 450.047 cents 4: 3 13/10 454.214 cents tridecimal semi-diminished fourth 5: 1 135/104 451.651 cents 5: 1 576/443 454.515 cents 5: 7 4/3 498.045 cents perfect fourth 5: 1 443/332 499.348 cents 5: 1 351/256 546.393 cents 5: 1 83/60 561.779 cents 6: 1 160/117 541.876 cents 6: 1 18/13 563.382 cents tridecimal augmented fourth 6: 2 45/32 590.224 cents diatonic tritone 6: 1 624/443 593.087 cents 6: 1 117/83 594.390 cents 6: 1 166/117 605.610 cents 6: 1 443/312 606.913 cents 6: 2 64/45 609.776 cents 2nd tritone 6: 1 13/9 636.618 cents tridecimal diminished fifth 6: 1 117/80 658.124 cents 7: 1 120/83 638.221 cents 7: 1 512/351 653.607 cents 7: 1 664/443 700.652 cents 7: 7 3/2 701.955 cents perfect fifth 7: 1 443/288 745.485 cents 7: 1 208/135 748.349 cents 8: 3 20/13 745.786 cents tridecimal semi-augmented fifth 8: 1 128/83 749.953 cents 8: 1 702/443 796.997 cents 8: 1 83/52 809.520 cents 8: 2 8/5 813.686 cents minor sixth 8: 3 13/8 840.528 cents tridecimal neutral sixth 8: 1 443/270 857.217 cents 9: 1 720/443 840.828 cents 9: 1 135/83 842.131 cents 9: 3 64/39 857.517 cents 39th subharmonic 9: 1 5/3 884.359 cents major sixth, BP sixth 9: 1 27/16 905.865 cents Pythagorean major sixth 9: 1 83/48 948.092 cents 9: 1 443/256 949.395 cents 9: 3 26/15 952.259 cents tridecimal semi-augmented sixth 10: 2 45/26 949.696 cents 10: 1 768/443 952.560 cents 10: 1 144/83 953.863 cents 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 2 117/64 1044.438 cents 10: 1 83/45 1059.824 cents 10: 1 443/240 1061.127 cents 11: 2 24/13 1061.427 cents tridecimal neutral seventh 11: 3 15/8 1088.269 cents classic major seventh 11: 1 832/443 1091.132 cents 11: 1 156/83 1092.435 cents 11: 1 664/351 1103.655 cents 11: 1 443/234 1104.958 cents 11: 1 256/135 1107.821 cents octave - major chroma 11: 2 39/20 1156.169 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 7.45455 = 82/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 250.3 359.2 454.2 498.0 609.8 702.0 813.7 952.3 1059.8 1156.2 1200.0 111.7 : 138.6 247.4 342.5 386.3 498.0 590.2 702.0 840.5 948.1 1044.4 1088.3 1200.0 250.3 : 108.9 203.9 247.7 359.5 451.7 563.4 702.0 809.5 905.9 949.7 1061.4 1200.0 359.2 : 95.0 138.9 250.6 342.8 454.5 593.1 700.7 797.0 840.8 952.6 1091.1 1200.0 454.2 : 43.8 155.6 247.7 359.5 498.0 605.6 702.0 745.8 857.5 996.1 1105.0 1200.0 498.0 : 111.7 203.9 315.6 454.2 561.8 658.1 702.0 813.7 952.3 1061.1 1156.2 1200.0 609.8 : 92.2 203.9 342.5 450.0 546.4 590.2 702.0 840.5 949.4 1044.4 1088.3 1200.0 702.0 : 111.7 250.3 357.9 454.2 498.0 609.8 748.3 857.2 952.3 996.1 1107.8 1200.0 813.7 : 138.6 246.1 342.5 386.3 498.0 636.6 745.5 840.5 884.4 996.1 1088.3 1200.0 952.3 : 107.6 203.9 247.7 359.5 498.0 606.9 702.0 745.8 857.5 949.7 1061.4 1200.0 1059.8: 96.3 140.2 251.9 390.5 499.3 594.4 638.2 750.0 842.1 953.9 1092.4 1200.0 1156.2: 43.8 155.6 294.1 403.0 498.0 541.9 653.6 745.8 857.5 996.1 1103.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 138.5727 cents 169/160, 94.7416 cents 40/39, 43.8311 cents 2: 138.8732 .. 250.3039 cents 5759/5400, 111.4307 cents 5760/5759, 0.3006 cents 3: 247.7411 .. 359.1718 cents 5759/5400, 111.4307 cents 675/676,-2.5629 cents 4: 342.7833 .. 454.2139 cents 5759/5400, 111.4307 cents 194400/196249,-16.3885 cents 5: 451.6511 .. 561.7786 cents 2158/2025, 110.1275 cents 675/676,-2.5629 cents 6: 541.8761 .. 658.1239 cents 13689/12800, 116.2479 cents 3200/3237,-19.9026 cents 7: 638.2214 .. 748.3489 cents 2158/2025, 110.1275 cents 3200/3237,-19.9026 cents 8: 745.7861 .. 857.2167 cents 5759/5400, 111.4307 cents 675/676,-2.5629 cents 9: 840.8282 .. 952.2589 cents 5759/5400, 111.4307 cents 194400/196249,-16.3885 cents 10: 949.6961 .. 1061.1268 cents 5759/5400, 111.4307 cents 675/676,-2.5629 cents 11: 1061.4273 .. 1156.1689 cents 169/160, 94.7416 cents 5760/5759, 0.3006 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 13/12, 138.5727 cents Average / Smallest step : 2.281488 Largest / Average step : 1.385727 Largest / Smallest step : 3.161518 Median interval of one step : 108.21623 cents, amount: 0 Most common interval of one step : 16/15, 111.7313 cents, amount: 3 Least squares average step : 103.63876 cents, oct.: 1243.66511 cents Scale is not proper Step pattern alph. order: ABCDEAFABGHE Step pattern size order : GHFCAGBGHEDA Scale is a Constant Structure, by a margin of 0.30059 cents Scale diversity : 1.430905 Lumma stability : 0.073553 Lumma impropriety factor : 0.069028 Rothenberg efficiency : 0.257912 redundancy: 0.742088 Efficiency x scale size : 3.094949 Number of different interval sizes : 82 = 7.45455 / class Number of one step interval sizes : 8 Highest interval variety : 10 Mean interval variety : 7.45455 = 82/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 5760/5759, 0.3006 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 8, average 701.7921 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 25.0000% -- Rational properties -- Prime limit : 443 Odd number limit : 443 (O: 443 U: 443) Highest odd numerator or denominator: 443 Scale harmonicity : 0.021952 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 91775424, 26.4516 octaves, 24010797184.739 Hz. Exponens Consonantiae : 3.303915E+10, 34.94346 octaves Euler's gradus suavitatis : 556 Sum of Mann's harmonic distance : 659.5, average 54.95833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.58231, average 1.21519 Sum of Tenney's harmonic distance : 29.34134, average 2.44511 Vogel's harmonic complexity : 57.16667 Wille's k value : 221 Wilson's harmonic complexity : 553 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 278.79076, average 3.57424 Lattice compactness (without 2's) : 130.50127, average 1.67309 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -3 .. 6 1.00000 26 1 3: -2 .. 1 -0.75000 13 2 5: -1 .. 0 -0.75000 9 3 13: 0 .. 1 0.33333 4 4 83: 0 .. 1 0.08333 1 1 443: 0 .. 1 0.08333 1 1 Average exponent except 2's :-12 / 12 =-1.00000 Average absolute exponent except 2's: 28 / 12 = 2.33333 Scale is JI-epimorphic with val: <12 19 28 44 76 105|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 39.6484 c. M: 59.8236 c. Twelve-tone Chromatic (1/11-comma) 14: 1 2 1 1 1 1 1 1 2 1 1 1 P D3 S SD: 23.9365 c. M: 42.2577 c. 18: 2 2 1 2 0 2 1 2 2 2 1 1 N SD: 20.4049 c. M: 35.2883 c. 19: 2 2 2 1 1 2 1 2 2 2 1 1 N D3 SD: 12.8427 c. M:-21.8027 c. 24: 2 3 2 2 1 2 2 2 3 2 2 1 P T3 SD: 7.4710 c. M: 13.6863 c. 34: 3 4 3 3 1 3 3 3 4 3 3 1 N SD: 5.0767 c. M: 9.7763 c. 43: 4 5 4 3 2 4 3 4 5 4 3 2 N SD: 5.0183 c. M: 11.9829 c. 53: 5 6 5 4 2 5 4 5 6 5 4 2 N SD: 1.8743 c. M:-4.3273 c. 77: 7 9 7 6 3 7 6 7 9 7 6 3 N SD: 1.8337 c. M: 3.2967 c. 87: 8 10 8 7 3 8 7 8 10 8 7 3 N SD: 1.6166 c. M: 2.8797 c. 130: 12 15 12 10 5 12 10 12 15 12 10 5 N SD: 1.2747 c. M: 2.3228 c. 140: 13 16 13 11 5 13 11 13 16 13 11 5 N SD: 1.2269 c. M:-3.0335 c. 164: 15 19 15 13 6 15 13 15 19 15 13 6 N SD: 1.2277 c. M: 2.4592 c. 193: 18 22 18 15 7 18 15 18 22 17 16 7 N SD: 1.1370 c. M: 2.8288 c. 195: 18 23 17 16 7 18 15 18 23 17 16 7 N SD: 1.2535 c. M: 2.2487 c. 214: 20 25 19 17 8 20 16 20 25 19 17 8 N SD: 0.9570 c. M:-2.0325 c. 217: 20 25 20 17 8 20 17 20 25 20 17 8 N SD: 1.0087 c. M:-1.9276 c. 224: 21 26 20 18 8 21 17 21 26 20 18 8 N SD: 0.8619 c. M:-1.4818 c. 248: 23 29 22 20 9 23 19 23 29 22 20 9 N SD: 0.6719 c. M:-1.3090 c. 277: 26 32 25 22 10 26 21 26 32 25 22 10 N SD: 0.7835 c. M:-1.5482 c. 301: 28 35 27 24 11 28 23 28 35 27 24 11 N SD: 0.4138 c. M:-0.8588 c. 354: 33 41 32 28 13 33 27 33 41 32 28 13 N SD: 0.4284 c. M:-1.1933 c. 417: 39 48 38 33 15 39 32 39 48 37 34 15 N SD: 0.4674 c. M: 0.8308 c. 431: 40 50 39 34 16 40 33 40 50 39 34 16 N SD: 0.4569 c. M:-0.9653 c. 441: 41 51 40 35 16 41 34 41 51 39 36 16 N SD: 0.4084 c. M: 1.3202 c. 460: 43 53 42 36 17 43 35 43 53 41 37 17 N SD: 0.4399 c. M:-0.8282 c. 465: 43 54 42 37 17 43 36 43 54 42 37 17 N SD: 0.4692 c. M:-0.8216 c. 470: 44 54 43 37 17 44 36 44 54 42 38 17 N SD: 0.4323 c. M:-0.8282 c. 494: 46 57 45 39 18 46 38 46 57 44 40 18 N SD: 0.2365 c. M: 0.7143 c. 547: 51 63 50 43 20 51 42 51 63 49 44 20 N SD: 0.2208 c. M:-0.6089 c. 581: 54 67 53 46 21 54 45 54 67 52 47 21 N SD: 0.2827 c. M: 0.4820 c. 624: 58 72 57 49 23 58 48 58 72 56 50 23 N SD: 0.2671 c. M:-0.4436 c. 634: 59 73 58 50 23 59 49 59 73 57 51 23 N SD: 0.2629 c. M: 0.4617 c. 718: 67 83 65 57 26 67 55 67 83 64 58 26 N SD: 0.2655 c. M:-0.3924 c. 742: 69 86 67 59 27 69 57 69 86 66 60 27 N SD: 0.2386 c. M: 0.5244 c. 771: 72 89 70 61 28 72 59 72 89 69 62 28 N SD: 0.2503 c. M:-0.3613 c. 795: 74 92 72 63 29 74 61 74 92 71 64 29 N SD: 0.1268 c. M:-0.2621 c. 848: 79 98 77 67 31 79 65 79 98 76 68 31 N SD: 0.1102 c. M:-0.2622 c. 1183: 110 137 107 94 43 110 91 110 137 106 95 43 N SD: 0.1643 c. M:-0.2455 c. 1236: 115 143 112 98 45 115 95 115 143 111 99 45 N SD: 0.1488 c. M:-0.3706 c. 1289: 120 149 117 102 47 120 99 120 149 115 104 47 N SD: 0.1390 c. M: 0.3977 c. 1342: 125 155 122 106 49 125 103 125 155 120 108 49 N SD: 0.1099 c. M:-0.2917 c. 1376: 128 159 125 109 50 128 106 128 159 123 111 50 N SD: 0.1307 c. M: 0.2306 c. 1395: 130 161 127 110 51 130 107 130 161 125 112 51 N SD: 0.1265 c. M:-0.3981 c. 1419: 132 164 129 112 52 132 109 132 164 127 114 52 N SD: 0.1194 c. M:-0.2363 c. 1429: 133 165 130 113 52 133 110 133 165 128 115 52 N SD: 0.1035 c. M:-0.2404 c. 1506: 140 174 137 119 55 140 116 140 174 135 121 55 N SD: 0.1143 c. M: 0.2145 c. 1643: 153 190 149 130 60 153 126 153 190 147 132 60 N SD: 0.1017 c. M:-0.2134 c. 1677: 156 194 152 133 61 156 129 156 194 150 135 61 N SD: 0.1104 c. M:-0.1817 c. 1720: 160 199 156 136 63 160 132 160 199 154 138 63 N SD: 0.1058 c. M: 0.1979 c. 1730: 161 200 157 137 63 161 133 161 200 155 139 63 N SD: 0.0846 c. M:-0.1346 c. 1942: 181 224 176 154 71 181 149 181 224 174 156 71 N SD: 0.0814 c. M: 0.1604 c. 2019: 188 233 183 160 74 188 155 188 233 181 162 74 N SD: 0.0915 c. M: 0.1822 c. 2029: 189 234 184 161 74 189 156 189 234 182 163 74 N SD: 0.0824 c. M: 0.1772 c. 2106: 196 243 191 167 77 196 162 196 243 189 169 77 N SD: 0.0925 c. M: 0.1974 c. 2224: 207 257 202 176 81 207 171 207 257 199 179 81 N SD: 0.0856 c. M:-0.1808 c. 2243: 209 259 203 178 82 209 172 209 259 201 180 82 N SD: 0.0767 c. M: 0.1882 c. 2330: 217 269 211 185 85 217 179 217 269 209 187 85 N SD: 0.0691 c. M: 0.2018 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 22.6334 cents 4 x x 5 x x x 6 x 7 x x 8 S SD: 7.9496 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.2987 cents 6 x 7 x x 8 x 9 x 10:11 x 12 S SD: 11.7784 cents 7 x 8 x 9 x 10 x 11:12:13 x 14 S SD: 6.8086 cents 8 x 9:10 x 11 x 12:13:14:15 x 16 S SD: 10.8478 cents 9 x 10:11 x 12:13 x 14:16:17 x 18 S SD: 13.3862 cents 10:11 x 12:13 x 14:15:16:17:18 x 20 S SD: 10.1771 cents 11:12:13 x 14:15:16:17:18:19:20:21:22 S SD: 10.5967 cents 12:13:14:15 x 16:17:18:19:21:22:23:24 SD: 5.2861 cents 13:14:15:16:17 x 18:20:21:23:24:25:26 SD: 7.3713 cents 14:15:16:17:18:19:20:21:22:24:26:27:28 S SD: 5.3792 cents 15:16:17:18 x 20:21:23:24:26:28:29:30 SD: 6.9633 cents 16:17:18:20:21 x 23:24:26:28:30:31:32 SD: 6.7295 cents 17:18:20:21:22:23:24:26:27:29:31:33:34 SD: 5.6175 cents 18:19:21:22:23:24:26:27:29:31:33:35:36 SD: 4.3734 cents 19:20:22:23:25 x 27:29:30:33:35:37:38 SD: 5.1738 cents 20:21:23:25:26:27:28:30:32:35:37:39:40 SD: 4.6076 cents 22:23:25:27 x 29:31:33:35:38:41:43:44 SD: 5.1363 cents 24:26:28:30:31:32:34:36:38:42:44:47:48 SD: 4.3048 cents 25:27:29:31 x 33:36:38:40:43:46:49:50 SD: 4.3098 cents 26:28:30:32:34:35:37:39:42:45:48:51:52 SD: 2.6989 cents 30:32:35:37:39:40:43:45:48:52:55:59:60 SD: 2.3537 cents 40:43:46:49:52:53:57:60:64:69:74:78:80 SD: 1.9337 cents 44:47:51:54:57:59:63:66:70:76:81:86:88 SD: 1.8357 cents 52:55:60:64:68:69:74:78:83:90:96:101:104 SD: 1.8046 cents 56:60:65:69:73:75:80:84:90:97:103:109:112 SD: 1.5809 cents 57:61:66:70:74:76:81:86:91:99:105:111:114 SD: 1.1880 cents 60:64:69:74:78:80:85:90:96:104:111:117:120 SD: 1.0471 cents 78:83:90:96:101:104:111:117:125:135:144:152:156 SD: 0.7908 cents 90:96:104:111:117:120:128:135:144:156:166:176:180 SD: 0.5237 cents 147:157:170:181:191:196:209:221:235:255:271:287:294 SD: 0.4823 cents 166:177:192:204:216:221:236:249:266:288:306:324:332 SD: 0.4645 cents 168:179:194:207:218:224:239:252:269:291:310:328:336 SD: 0.4451 cents 180:192:208:222:234:240:256:270:288:312:332:351:360 SD: 0.3253 cents 240:256:277:295:312:320:341:360:384:416:443:468:480 SD: 0.2972 cents 256:273:296:315:333:341:364:384:410:444:472:499:512 SD: 0.2667 cents 270:288:312:332:351:360:384:405:432:468:498:527:540 SD: 0.1748 cents 360:384:416:443:468:480:512:540:576:624:664:702:720 SD: 0.0000 cents