Scala analysis: bala_ribbon
Parizekmic 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: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 9/8 203.910002 major whole tone 3: 6/5 315.641287 minor third 4: 13/10 454.213948 tridecimal semi-diminished fourth 5: 4/3 498.044999 perfect fourth 6: 83/60 561.778603 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 26/15 952.258947 tridecimal semi-augmented sixth 10: 9/5 1017.596288 just minor seventh, BP seventh 11: 39/20 1156.168949 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 40/39 43.8311 tridecimal minor diesis 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 16/15 111.7313 minor diatonic semitone 4: 13/12 138.5727 tridecimal 2/3-tone 5: 40/39 43.8311 tridecimal minor diesis 6: 83/80 63.7336 7: 90/83 140.1764 8: 16/15 111.7313 minor diatonic semitone 9: 13/12 138.5727 tridecimal 2/3-tone 10: 27/26 65.3373 tridecimal comma 11: 13/12 138.5727 tridecimal 2/3-tone 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 83/80 63.734 cents 1: 1 27/26 65.337 cents tridecimal comma 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 3 13/12 138.573 cents tridecimal 2/3-tone 1: 1 90/83 140.176 cents 2: 1 83/78 107.565 cents 2: 1 125/117 114.503 cents 2: 2 10/9 182.404 cents minor whole tone 2: 4 9/8 203.910 cents major whole tone 2: 1 144/125 244.969 cents classic diminished third 2: 2 52/45 250.304 cents 2: 1 96/83 251.908 cents 3: 1 83/72 246.137 cents 3: 3 15/13 247.741 cents tridecimal 5/4-tone 3: 1 125/108 253.076 cents semi-augmented whole tone 3: 1 32/27 294.135 cents Pythagorean minor third 3: 3 6/5 315.641 cents minor third 3: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 3: 1 156/125 383.542 cents 3: 1 104/83 390.480 cents 4: 1 125/104 318.413 cents 4: 1 166/135 357.869 cents 4: 2 16/13 359.472 cents tridecimal neutral third 4: 3 5/4 386.314 cents major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 3 13/10 454.214 cents tridecimal semi-diminished fourth 4: 1 108/83 455.818 cents 5: 1 135/104 451.651 cents 5: 1 125/96 456.986 cents classic augmented third 5: 1 166/125 491.106 cents 5: 7 4/3 498.045 cents perfect fourth 5: 1 27/20 519.551 cents acute fourth 5: 1 117/83 594.390 cents 6: 1 160/117 541.876 cents 6: 1 83/60 561.779 cents 6: 2 18/13 563.382 cents tridecimal augmented fourth 6: 1 25/18 568.717 cents classic augmented fourth 6: 1 45/32 590.224 cents diatonic tritone 6: 1 64/45 609.776 cents 2nd tritone 6: 1 36/25 631.283 cents classic diminished fifth 6: 2 13/9 636.618 cents tridecimal diminished fifth 6: 1 120/83 638.221 cents 6: 1 117/80 658.124 cents 7: 1 166/117 605.610 cents 7: 1 40/27 680.449 cents grave fifth 7: 7 3/2 701.955 cents perfect fifth 7: 1 125/83 708.894 cents 7: 1 192/125 743.014 cents classic diminished sixth 7: 1 208/135 748.349 cents 8: 1 83/54 744.182 cents 8: 3 20/13 745.786 cents tridecimal semi-augmented fifth 8: 1 25/16 772.627 cents classic augmented fifth 8: 3 8/5 813.686 cents minor sixth 8: 2 13/8 840.528 cents tridecimal neutral sixth 8: 1 135/83 842.131 cents 8: 1 208/125 881.587 cents 9: 1 83/52 809.520 cents 9: 1 125/78 816.458 cents 9: 1 64/39 857.517 cents 39th subharmonic 9: 3 5/3 884.359 cents major sixth, BP sixth 9: 1 27/16 905.865 cents Pythagorean major sixth 9: 1 216/125 946.924 cents semi-augmented sixth 9: 3 26/15 952.259 cents tridecimal semi-augmented sixth 9: 1 144/83 953.863 cents 10: 1 83/48 948.092 cents 10: 2 45/26 949.696 cents 10: 1 125/72 955.031 cents classic augmented sixth 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 234/125 1085.497 cents 10: 1 156/83 1092.435 cents 11: 1 83/45 1059.824 cents 11: 3 24/13 1061.427 cents tridecimal neutral seventh 11: 1 50/27 1066.762 cents grave major seventh 11: 2 15/8 1088.269 cents classic major seventh 11: 1 48/25 1129.328 cents classic diminished octave 11: 1 52/27 1134.663 cents 11: 1 160/83 1136.266 cents 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 : 70.7 203.9 315.6 454.2 498.0 561.8 702.0 813.7 952.3 1017.6 1156.2 1200.0 70.7 : 133.2 245.0 383.5 427.4 491.1 631.3 743.0 881.6 946.9 1085.5 1129.3 1200.0 203.9 : 111.7 250.3 294.1 357.9 498.0 609.8 748.3 813.7 952.3 996.1 1066.8 1200.0 315.6 : 138.6 182.4 246.1 386.3 498.0 636.6 702.0 840.5 884.4 955.0 1088.3 1200.0 454.2 : 43.8 107.6 247.7 359.5 498.0 563.4 702.0 745.8 816.5 949.7 1061.4 1200.0 498.0 : 63.7 203.9 315.6 454.2 519.6 658.1 702.0 772.6 905.9 1017.6 1156.2 1200.0 561.8 : 140.2 251.9 390.5 455.8 594.4 638.2 708.9 842.1 953.9 1092.4 1136.3 1200.0 702.0 : 111.7 250.3 315.6 454.2 498.0 568.7 702.0 813.7 952.3 996.1 1059.8 1200.0 813.7 : 138.6 203.9 342.5 386.3 457.0 590.2 702.0 840.5 884.4 948.1 1088.3 1200.0 952.3 : 65.3 203.9 247.7 318.4 451.7 563.4 702.0 745.8 809.5 949.7 1061.4 1200.0 1017.6: 138.6 182.4 253.1 386.3 498.0 636.6 680.4 744.2 884.4 996.1 1134.7 1200.0 1156.2: 43.8 114.5 247.7 359.5 498.0 541.9 605.6 745.8 857.5 996.1 1061.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 140.1764 cents 351/332, 96.3453 cents 40/39, 43.8311 cents 2: 107.5647 .. 251.9077 cents 7488/6889, 144.3430 cents 6889/7020,-32.6117 cents 3: 246.1373 .. 390.4803 cents 7488/6889, 144.3430 cents 6889/6912,-5.7704 cents 4: 318.4135 .. 455.8177 cents 11232/10375, 137.4042 cents 10375/10816,-72.0669 cents 5: 451.6511 .. 594.3903 cents 1352/1245, 142.7393 cents 415/416,-4.1666 cents 6: 541.8761 .. 658.1239 cents 13689/12800, 116.2479 cents 13280/13689,-52.5143 cents 7: 605.6097 .. 748.3489 cents 1352/1245, 142.7393 cents 13280/13689,-52.5143 cents 8: 744.1823 .. 881.5865 cents 11232/10375, 137.4042 cents 415/416,-4.1666 cents 9: 809.5197 .. 953.8627 cents 7488/6889, 144.3430 cents 10375/10816,-72.0669 cents 10: 948.0923 .. 1092.4353 cents 7488/6889, 144.3430 cents 6889/6912,-5.7704 cents 11: 1059.8236 .. 1156.1689 cents 351/332, 96.3453 cents 6889/7020,-32.6117 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 : 90/83, 140.1764 cents Average / Smallest step : 2.281488 Largest / Average step : 1.401764 Largest / Smallest step : 3.198107 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Most common interval of one step : 13/12, 138.5727 cents, amount: 3 Least squares average step : 102.13922 cents, oct.: 1225.67069 cents Scale is not proper Step pattern alph. order: ABCDEFGCDHDE Step pattern size order : DFEGABHEGCGA Scale is a Constant Structure, by a margin of 1.16846 cents Scale diversity : 1.513585 Lumma stability : 0.073052 Lumma impropriety factor : 0.278550 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 : 10375/10368, 1.1685 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 702.8224 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 class 1 -- Rational properties -- Prime limit : 83 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 83 Scale harmonicity : 0.018066 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 1942200, 20.8893 octaves, 508129172.928 Hz. Exponens Consonantiae : 2.330640E+08, 27.79615 octaves Euler's gradus suavitatis : 119 Sum of Mann's harmonic distance : 192.5, average 16.04167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.45878, average 0.95490 Sum of Tenney's harmonic distance : 22.82057, average 1.90171 Vogel's harmonic complexity : 19.50000 Wille's k value : 67 Wilson's harmonic complexity : 120 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 243.70748, average 3.12445 Lattice compactness (without 2's) : 147.34360, average 1.88902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 -0.33333 20 1 3: -1 .. 2 0.25000 11 3 5: -1 .. 2 -0.41667 9 4 13: 0 .. 1 0.25000 3 3 83: 0 .. 1 0.08333 1 1 Average exponent except 2's : 2 / 12 = 0.16667 Average absolute exponent except 2's: 24 / 12 = 2.00000 Scale is JI-epimorphic with val: <12 19 28 44 77| = patent
FIT/MODE
12: 1 1 1 2 0 1 1 1 2 0 2 0 N T3 SD: 27.9616 c. M:-47.7411 c. 13: 1 1 1 2 0 1 2 1 1 1 2 0 N SD: 26.1262 c. M:-43.8311 c. 15: 1 2 1 2 0 1 2 1 2 1 2 0 N SD: 21.2096 c. M:-43.8311 c. 17: 1 2 1 2 1 1 2 1 2 1 2 1 P M ME SD: 22.9343 c. M: 37.2157 c. Supra-12 18: 1 2 1 3 0 1 2 2 2 1 2 1 N SD: 24.1532 c. M: 48.9746 c. 19: 1 2 2 2 1 1 2 2 2 1 2 1 N D3 SD: 9.4054 c. M: 19.3268 c. 24: 1 3 2 3 1 1 3 2 3 1 3 1 N SD: 10.7685 c. M: 20.6724 c. 27: 2 3 2 3 1 2 3 2 3 2 3 1 N SD: 12.1589 c. M: 18.9256 c. 28: 2 3 2 4 1 1 3 3 3 2 3 1 N SD: 11.6693 c. M:-17.2146 c. 29: 2 3 3 3 1 2 3 3 3 2 3 1 N SD: 9.9555 c. M:-17.5317 c. 31: 2 3 3 4 1 2 3 3 4 1 4 1 N SD: 9.5524 c. M:-18.8666 c. 32: 2 3 3 4 1 2 4 3 3 2 4 1 N SD: 9.9382 c. M: 16.4100 c. 34: 2 4 3 4 1 2 4 3 4 2 4 1 N SD: 4.4594 c. M:-8.5369 c. 53: 3 6 5 6 2 3 6 5 6 3 6 2 N SD: 1.7528 c. M:-4.2591 c. 87: 5 10 8 10 3 5 10 8 10 5 10 3 N SD: 2.0336 c. M:-3.7386 c. 111: 7 12 10 13 4 6 13 10 13 6 13 4 N SD: 1.9242 c. M:-5.0032 c. 118: 7 13 11 14 4 6 14 11 14 6 14 4 N SD: 1.8791 c. M:-3.6733 c. 130: 8 14 12 15 5 7 15 12 15 7 15 5 N SD: 1.6848 c. M:-3.1737 c. 137: 8 15 13 16 5 7 16 13 16 7 16 5 N SD: 1.3495 c. M:-2.4856 c. 164: 10 18 15 19 6 9 19 15 19 9 19 6 N SD: 1.1265 c. M:-2.4983 c. 171: 10 19 16 20 6 9 20 16 20 9 20 6 N SD: 0.9995 c. M:-2.1270 c. 190: 11 21 18 22 7 10 22 18 22 10 22 7 N SD: 0.9386 c. M: 1.8047 c. 217: 13 24 20 25 8 12 25 20 25 12 25 8 N SD: 0.9206 c. M:-2.2767 c. 224: 13 25 21 26 8 12 26 21 26 12 26 8 N SD: 0.7270 c. M:-1.3125 c. 301: 18 33 28 35 11 16 35 28 35 16 35 11 N SD: 0.5644 c. M:-1.0884 c. 323: 19 36 30 37 12 17 38 30 37 18 37 12 N SD: 0.5721 c. M: 1.1754 c. 335: 20 37 31 39 12 18 39 31 39 18 39 12 N SD: 0.5426 c. M:-0.9694 c. 354: 21 39 33 41 13 19 41 33 41 19 41 13 N SD: 0.4342 c. M:-0.9333 c. 388: 23 43 36 45 14 21 45 36 45 21 45 14 N SD: 0.4274 c. M:-1.1080 c. 441: 26 49 41 51 16 23 52 41 51 24 51 16 N SD: 0.3800 c. M: 1.2344 c. 460: 27 51 43 53 17 24 54 43 53 25 53 17 N SD: 0.3675 c. M: 0.9090 c. 494: 29 55 46 57 18 26 58 46 57 27 57 18 N SD: 0.2209 c. M: 0.6450 c. 513: 30 57 48 59 19 27 60 48 59 28 59 19 N SD: 0.3375 c. M: 0.6134 c. 547: 32 61 51 63 20 29 64 51 63 30 63 20 N SD: 0.2084 c. M: 0.4713 c. 658: 39 73 61 76 24 35 77 61 76 36 76 24 N SD: 0.2243 c. M:-0.4522 c. 711: 42 79 66 82 26 38 83 66 82 39 82 26 N SD: 0.1990 c. M: 0.3602 c. 795: 47 88 74 92 29 42 93 74 92 43 92 29 N SD: 0.1648 c. M:-0.2710 c. 848: 50 94 79 98 31 45 99 79 98 46 98 31 N SD: 0.0782 c. M: 0.1435 c. 1342: 79 149 125 155 49 71 157 125 155 73 155 49 N SD: 0.0706 c. M: 0.2287 c. 1395: 82 155 130 161 51 74 163 130 161 76 161 51 N SD: 0.0552 c. M: 0.1348 c. 1730: 102 192 161 200 63 92 202 161 200 94 200 63 N SD: 0.0707 c. M:-0.1316 c. 1783: 105 198 166 206 65 95 208 166 206 97 206 65 N SD: 0.0687 c. M:-0.1956 c. 2053: 121 228 191 237 75 109 240 191 237 112 237 75 N SD: 0.0517 c. M: 0.0914 c. 2243: 132 249 209 259 82 119 262 209 259 122 259 82 N SD: 0.0390 c. M: 0.0759 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: 4.1467 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 14.9054 cents 7 x 8 x 9 x 10 x 11:12:13 x 14 S SD: 13.1547 cents 8 x 9 x 10 x 11:12:13:14 x x 16 S SD: 10.7995 cents 9 x 10:11 x 12 x x 14 x 16 x 18 S SD: 10.9452 cents 10 x 11:12:13 x 14:15:16:17:18 x 20 S SD: 6.1601 cents 11 x 12:13:14 x 15:17:18:19:20:21:22 SD: 10.6639 cents 12 x x 14 x 16:17:18:19:21:22:23:24 SD: 9.0137 cents 13:14:15:16:17 x 18:20:21 x 23:25:26 SD: 10.4575 cents 14:15:16:17:18:19 x 21:22:24:25:27:28 SD: 7.4644 cents 15:16:17:18 x 20:21:23:24:26:27:29:30 SD: 5.7118 cents 16:17:18:19:21 x 22:24:26:28:29:31:32 SD: 5.1025 cents 18:19:20:22:23:24:25:27:29:31:32:35:36 SD: 5.0628 cents 19:20:21:23:25 x 26:29:30:33:34:37:38 SD: 5.6322 cents 20:21:23:24:26:27:28:30:32:35:36:39:40 SD: 4.4135 cents 22:23:25:26 x 29:30:33:35:38:40:43:44 SD: 4.5471 cents 23:24:26:28:30:31:32:35:37:40:41:45:46 SD: 3.9438 cents 24:25:27:29:31:32:33:36:38:42:43:47:48 SD: 2.7627 cents 25:26:28:30 x 33:35:38:40:43:45:49:50 SD: 3.6167 cents 26:27:29:31:34:35:36:39:42:45:47:51:52 SD: 2.8801 cents 30:31:34:36:39:40:42:45:48:52:54:59:60 SD: 2.6399 cents 39:41:44:47:51:52:54:59:62:68:70:76:78 SD: 2.5135 cents 40:42:45:48:52:53:55:60:64:69:72:78:80 SD: 1.8393 cents 50:52:56:60:65:67:69:75:80:87:90:98:100 SD: 1.3988 cents 66:69:74:79:86:88:91:99:106:114:119:129:132 SD: 1.3065 cents 70:73:79:84:91:93:97:105:112:121:126:137:140 SD: 1.0000 cents 80:83:90:96:104:107:111:120:128:139:144:156:160 SD: 0.9194 cents 90:94:101:108:117:120:125:135:144:156:162:176:180 SD: 0.8818 cents 94:98:106:113:122:125:130:141:150:163:169:183:188 SD: 0.7983 cents 96:100:108:115:125:128:133:144:154:166:173:187:192 SD: 0.6902 cents 120:125:135:144:156:160:166:180:192:208:216:234:240 SD: 0.0000 cents