Scala analysis: mohaj-bala_213
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: 71/60 291.427829 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: 16/9 996.089998 Pythagorean minor seventh 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: 213/208 41.1239 4: 78/71 162.7861 porcupine neutral second 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: 40/39 43.8311 tridecimal minor diesis 11: 351/320 160.0790 12: 40/39 43.8311 tridecimal minor diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 213/208 41.124 cents 1: 3 40/39 43.831 cents tridecimal minor diesis 1: 1 135/128 92.179 cents major chroma, major limma 1: 3 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 351/320 160.079 cents 1: 1 78/71 162.786 cents porcupine neutral second 2: 2 128/117 155.562 cents 2: 1 71/64 179.697 cents 2: 1 10/9 182.404 cents minor whole tone 2: 5 9/8 203.910 cents major whole tone 2: 1 80/71 206.617 cents 2: 2 52/45 250.304 cents 3: 3 15/13 247.741 cents tridecimal 5/4-tone 3: 1 71/60 291.428 cents 3: 2 32/27 294.135 cents Pythagorean minor third 3: 2 6/5 315.641 cents minor third 3: 1 256/213 318.348 cents 3: 3 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 4: 1 142/117 335.259 cents 4: 3 16/13 359.472 cents tridecimal neutral third 4: 3 5/4 386.314 cents major third 4: 1 90/71 410.527 cents 4: 4 13/10 454.214 cents tridecimal semi-diminished fourth 5: 1 135/104 451.651 cents 5: 1 213/160 495.338 cents 5: 8 4/3 498.045 cents perfect fourth 5: 1 96/71 522.258 cents 5: 1 351/256 546.393 cents 6: 1 71/52 539.169 cents 6: 2 160/117 541.876 cents 6: 1 18/13 563.382 cents tridecimal augmented fourth 6: 2 45/32 590.224 cents diatonic tritone 6: 2 64/45 609.776 cents 2nd tritone 6: 1 13/9 636.618 cents tridecimal diminished fifth 6: 2 117/80 658.124 cents 6: 1 104/71 660.831 cents 7: 1 512/351 653.607 cents 7: 1 71/48 677.742 cents 7: 8 3/2 701.955 cents perfect fifth 7: 1 320/213 704.662 cents 7: 1 208/135 748.349 cents 8: 4 20/13 745.786 cents tridecimal semi-augmented fifth 8: 1 71/45 789.473 cents 8: 3 8/5 813.686 cents minor sixth 8: 3 13/8 840.528 cents tridecimal neutral sixth 8: 1 117/71 864.741 cents 9: 3 64/39 857.517 cents 39th subharmonic 9: 1 213/128 881.652 cents 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 2 27/16 905.865 cents Pythagorean major sixth 9: 1 120/71 908.572 cents 9: 3 26/15 952.259 cents tridecimal semi-augmented sixth 10: 2 45/26 949.696 cents 10: 1 71/40 993.383 cents 10: 5 16/9 996.090 cents Pythagorean minor seventh 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 128/71 1020.303 cents 10: 2 117/64 1044.438 cents 11: 1 71/39 1037.214 cents 11: 1 640/351 1039.921 cents 11: 2 24/13 1061.427 cents tridecimal neutral seventh 11: 3 15/8 1088.269 cents classic major seventh 11: 1 256/135 1107.821 cents octave - major chroma 11: 3 39/20 1156.169 cents 11: 1 416/213 1158.876 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 250.3 291.4 454.2 498.0 609.8 702.0 813.7 952.3 996.1 1156.2 1200.0 111.7 : 138.6 179.7 342.5 386.3 498.0 590.2 702.0 840.5 884.4 1044.4 1088.3 1200.0 250.3 : 41.1 203.9 247.7 359.5 451.7 563.4 702.0 745.8 905.9 949.7 1061.4 1200.0 291.4 : 162.8 206.6 318.3 410.5 522.3 660.8 704.7 864.7 908.6 1020.3 1158.9 1200.0 454.2 : 43.8 155.6 247.7 359.5 498.0 541.9 702.0 745.8 857.5 996.1 1037.2 1200.0 498.0 : 111.7 203.9 315.6 454.2 498.0 658.1 702.0 813.7 952.3 993.4 1156.2 1200.0 609.8 : 92.2 203.9 342.5 386.3 546.4 590.2 702.0 840.5 881.7 1044.4 1088.3 1200.0 702.0 : 111.7 250.3 294.1 454.2 498.0 609.8 748.3 789.5 952.3 996.1 1107.8 1200.0 813.7 : 138.6 182.4 342.5 386.3 498.0 636.6 677.7 840.5 884.4 996.1 1088.3 1200.0 952.3 : 43.8 203.9 247.7 359.5 498.0 539.2 702.0 745.8 857.5 949.7 1061.4 1200.0 996.1 : 160.1 203.9 315.6 454.2 495.3 658.1 702.0 813.7 905.9 1017.6 1156.2 1200.0 1156.2: 43.8 155.6 294.1 335.3 498.0 541.9 653.6 745.8 857.5 996.1 1039.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.1239 .. 162.7861 cents 5408/5041, 121.6622 cents 213/208, 41.1239 cents 2: 155.5623 .. 250.3039 cents 169/160, 94.7416 cents 4544/4563,-7.2238 cents 3: 247.7411 .. 342.4827 cents 169/160, 94.7416 cents 675/676,-2.5629 cents 4: 335.2589 .. 454.2139 cents 1521/1420, 118.9551 cents 4544/4563,-7.2238 cents 5: 451.6511 .. 546.3927 cents 169/160, 94.7416 cents 675/676,-2.5629 cents 6: 539.1689 .. 660.8311 cents 5408/5041, 121.6622 cents 4544/4563,-7.2238 cents 7: 653.6073 .. 748.3489 cents 169/160, 94.7416 cents 4544/4563,-7.2238 cents 8: 745.7861 .. 864.7411 cents 1521/1420, 118.9551 cents 675/676,-2.5629 cents 9: 857.5173 .. 952.2589 cents 169/160, 94.7416 cents 4544/4563,-7.2238 cents 10: 949.6961 .. 1044.4377 cents 169/160, 94.7416 cents 675/676,-2.5629 cents 11: 1037.2139 .. 1158.8761 cents 5408/5041, 121.6622 cents 4544/4563,-7.2238 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 213/208, 41.1239 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 78/71, 162.7861 cents Average / Smallest step : 2.431677 Largest / Average step : 1.627861 Largest / Smallest step : 3.958433 Median interval of one step : 16/15, 111.7313 cents, amount: 3 Least squares average step : 102.34558 cents, oct.: 1228.14693 cents Scale is not proper Step pattern alph. order: ABCDEAFABEGE Step pattern size order : DEAGBDCDEBFB Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.495520 Lumma stability : 0.068540 Lumma impropriety factor : 0.044662 Rothenberg efficiency : 0.310880 redundancy: 0.689120 Efficiency x scale size : 3.730556 Number of different interval sizes : 66 = 6.00000 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 6.00000 = 6 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 676/675, 2.5629 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 8 Most common triad is 0.0 498.045 701.955 cents, amount: 5 Number of recognisable fifths : 9, average 702.2558 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 71 Odd number limit : 351 (O: 351 U: 351) Highest odd numerator or denominator: 71 Scale harmonicity : 0.022445 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 177216, 17.4351 octaves, 46364236.180 Hz. Exponens Consonantiae : 3.189888E+07, 24.92700 octaves Euler's gradus suavitatis : 101 Sum of Mann's harmonic distance : 272.0, average 22.66667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.82233, average 1.06853 Sum of Tenney's harmonic distance : 26.35412, average 2.19618 Vogel's harmonic complexity : 19.33333 Wille's k value : 175 Wilson's harmonic complexity : 98 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 275.75415, average 3.53531 Lattice compactness (without 2's) : 127.88476, average 1.63955 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 6 1.41667 29 1 3: -2 .. 1 -0.66667 12 3 5: -1 .. 0 -0.66667 8 3 13: 0 .. 1 0.33333 4 4 71: 0 .. 1 0.08333 1 1 Average exponent except 2's :-11 / 12 =-0.91667 Average absolute exponent except 2's: 25 / 12 = 2.08333 Scale is weakly epimorphic with val: <12 17 27 47 74| Scale is JI-epimorphic with val: <12 19 28 44 74| = patent
FIT/MODE
12: 1 2 0 2 0 1 1 1 2 0 2 0 N T3 SD: 27.8139 c. M:-49.6961 c. 14: 1 2 0 2 1 1 1 1 2 0 2 1 N D3 I SD: 28.3458 c. M: 53.2329 c. 15: 1 2 1 2 0 2 1 1 2 0 2 1 N SD: 24.1816 c. M: 36.1689 c. 16: 1 2 1 2 0 2 1 2 1 1 2 1 P D3 SD: 28.1165 c. M: 52.2589 c. 17: 1 2 1 2 1 1 2 1 2 1 2 1 P M ME SD: 28.3207 c. M: 45.0704 c. Supra-12 18: 1 2 1 3 0 2 1 2 2 1 2 1 N SD: 26.9833 c. M: 50.3039 c. 19: 2 2 1 2 1 2 1 2 2 1 2 1 P M ME SD: 13.5336 c. M:-24.3616 c. 22: 2 2 1 3 1 2 2 2 2 1 3 1 P D3 S SD: 15.4585 c. M: 32.1221 c. 24: 2 3 1 3 1 2 2 2 3 1 3 1 P T3 SD: 6.9398 c. M: 13.6863 c. 29: 3 3 1 4 1 3 2 3 3 1 4 1 P SD: 6.4167 c. M:-13.8999 c. 34: 3 4 1 5 1 3 3 3 4 1 5 1 N SD: 5.8701 c. M: 9.7763 c. 53: 5 6 2 7 2 5 4 5 6 2 7 2 P SD: 1.3651 c. M:-2.9118 c. 140: 13 16 5 19 5 13 11 13 16 5 19 5 N SD: 0.9760 c. M: 1.8043 c. 193: 18 22 7 26 7 18 15 18 22 7 26 7 N SD: 0.7992 c. M: 1.5993 c. 246: 23 28 9 33 9 23 19 23 28 9 33 9 N SD: 0.8067 c. M: 1.5235 c. 248: 23 29 8 34 9 23 19 23 29 9 33 9 N SD: 0.6988 c. M:-1.3090 c. 277: 26 32 9 38 10 26 21 26 32 10 37 10 N SD: 0.7237 c. M: 1.1751 c. 301: 28 35 10 41 11 28 23 28 35 11 40 11 N SD: 0.4095 c. M:-0.8588 c. 354: 33 41 12 48 13 33 27 33 41 13 47 13 N SD: 0.2938 c. M:-0.5435 c. 407: 38 47 14 55 15 38 31 38 47 15 54 15 N SD: 0.3196 c. M:-0.5431 c. 441: 41 51 15 60 16 41 34 41 51 16 59 16 N SD: 0.1736 c. M:-0.2936 c. 494: 46 57 17 67 18 46 38 46 57 18 66 18 N SD: 0.0751 c. M: 0.1386 c. 848: 79 98 29 115 31 79 65 79 98 31 113 31 N SD: 0.0892 c. M:-0.1678 c. 1289: 120 149 44 175 47 120 99 120 149 47 172 47 N SD: 0.0613 c. M:-0.1227 c. 1342: 125 155 46 182 49 125 103 125 155 49 179 49 N SD: 0.0433 c. M:-0.0774 c. 1783: 166 206 61 242 65 166 137 166 206 65 238 65 N SD: 0.0431 c. M:-0.0846 c. 1836: 171 212 63 249 67 171 141 171 212 67 245 67 N SD: 0.0335 c. M:-0.0754 c. 2330: 217 269 80 316 85 217 179 217 269 85 311 85 N SD: 0.0357 c. M:-0.0743 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 x 5 x x 6 x 7 x x 8 S SD: 17.4730 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 8.4667 cents 6 x 7 x x 8 x 9 x 10:11 x 12 S SD: 14.6467 cents 7 x 8 x 9 x 10 x 11:12 x x 14 S SD: 7.6927 cents 8 x 9 x 10:11 x 12:13:14 x x 16 S SD: 14.7051 cents 9 x 10:11 x 12:13 x 14 x 16 x 18 S SD: 14.8758 cents 10:11 x 12:13 x 14:15:16:17:18 x 20 S SD: 8.4329 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 10.3555 cents 12:13:14 x x 16:17:18:19:21 x 23:24 SD: 5.5942 cents 13:14:15 x 17 x 18:20:21 x 23:25:26 SD: 8.1516 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.2096 cents 15:16:17:18 x 20:21:23:24:26:27:29:30 SD: 6.1597 cents 16:17:18:19:21 x 23:24:26:28 x 31:32 SD: 6.3015 cents 17:18 x 20:22:23:24:26:27:29:30:33:34 SD: 5.3089 cents 18:19:21 x 23:24:26:27:29:31:32:35:36 SD: 4.5513 cents 19:20:22 x 25 x 27:29:30:33:34:37:38 SD: 5.0556 cents 20:21:23:24:26:27:28:30:32:35:36:39:40 SD: 4.8176 cents 22:23:25:26 x 29:31:33:35:38:39:43:44 SD: 4.8777 cents 23:25 x 27:30:31:33:35:37:40:41:45:46 SD: 4.6962 cents 24:26:28 x 31:32:34:36:38:42:43:47:48 SD: 4.0695 cents 25:27:29:30 x 33:36:38:40:43:44:49:50 SD: 4.9325 cents 26:28:30:31:34:35:37:39:42:45:46:51:52 SD: 2.9895 cents 29:31 x 34:38:39:41:44:46:50:52:57:58 SD: 3.9591 cents 30:32:35:36:39:40:43:45:48:52:53:59:60 SD: 3.0925 cents 32:34:37:38:42:43:46:48:51:55:57:62:64 SD: 2.9784 cents 33:35:38:39:43:44:47:50:53:57:59:64:66 SD: 2.2500 cents 40:43:46:47:52:53:57:60:64:69:71:78:80 SD: 2.0531 cents 44:47:51:52:57:59:63:66:70:76:78:86:88 SD: 1.8296 cents 45:48:52:53:59:60:64:68:72:78:80:88:90 SD: 1.8085 cents 50:53:58:59:65:67:71:75:80:87:89:98:100 SD: 1.6562 cents 57:61:66:67:74:76:81:86:91:99:101:111:114 SD: 1.5657 cents 59:63:68:70:77:79:84:89:94:102:105:115:118 SD: 1.4920 cents 60:64:69:71:78:80:85:90:96:104:107:117:120 SD: 1.0024 cents 76:81:88:90:99:101:108:114:122:132:135:148:152 SD: 0.8930 cents 90:96:104:107:117:120:128:135:144:156:160:176:180 SD: 0.7906 cents 102:109:118:121:133:136:145:153:163:177:181:199:204 SD: 0.7429 cents 104:111:120:123:135:139:148:156:166:180:185:203:208 SD: 0.6529 cents 120:128:139:142:156:160:171:180:192:208:213:234:240 SD: 0.5001 cents 168:179:194:199:218:224:239:252:269:291:299:328:336 SD: 0.4546 cents 180:192:208:213:234:240:256:270:288:312:320:351:360 SD: 0.0000 cents