Scala analysis: akj19_12
Fokker block from 81/80, 361/360 and 513/512
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/18 93.603014 undevicesimal semitone 2: 9/8 203.910002 major whole tone 3: 19/16 297.513016 19th harmonic 4: 19/15 409.244301 undevicesimal ditone 5: 4/3 498.044999 perfect fourth 6: 38/27 591.648014 7: 3/2 701.955001 perfect fifth 8: 19/12 795.558015 undevicesimal minor sixth 9: 27/16 905.865003 Pythagorean major sixth 10: 16/9 996.089998 Pythagorean minor seventh 11: 19/10 1111.199302 undevicesimal major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 20/19 88.8007 small undevicesimal semitone 1: 19/18 93.6030 undevicesimal semitone 2: 81/76 110.3070 3: 19/18 93.6030 undevicesimal semitone 4: 16/15 111.7313 minor diatonic semitone 5: 20/19 88.8007 small undevicesimal semitone 6: 19/18 93.6030 undevicesimal semitone 7: 81/76 110.3070 8: 19/18 93.6030 undevicesimal semitone 9: 81/76 110.3070 10: 256/243 90.2250 limma, Pythagorean minor second 11: 171/160 115.1093 12: 20/19 88.8007 small undevicesimal semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 20/19 88.801 cents small undevicesimal semitone 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 4 19/18 93.603 cents undevicesimal semitone 1: 3 81/76 110.307 cents 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 171/160 115.109 cents 2: 2 10/9 182.404 cents minor whole tone 2: 2 64/57 200.532 cents 2: 6 9/8 203.910 cents major whole tone 2: 2 152/135 205.334 cents 3: 2 45/38 292.711 cents 3: 4 32/27 294.135 cents Pythagorean minor third 3: 3 19/16 297.513 cents 19th harmonic 3: 1 729/608 314.217 cents 3: 2 6/5 315.641 cents minor third 4: 2 5/4 386.314 cents major third 4: 2 304/243 387.738 cents 4: 4 24/19 404.442 cents smaller undevicesimal major third 4: 2 81/64 407.820 cents Pythagorean major third 4: 2 19/15 409.244 cents undevicesimal ditone 5: 1 405/304 496.621 cents 5: 9 4/3 498.045 cents perfect fourth 5: 1 171/128 501.423 cents 5: 1 27/20 519.551 cents acute fourth 6: 2 80/57 586.846 cents 6: 4 38/27 591.648 cents 6: 4 27/19 608.352 cents 6: 2 57/40 613.154 cents 7: 1 40/27 680.449 cents grave fifth 7: 1 256/171 698.577 cents 7: 9 3/2 701.955 cents perfect fifth 7: 1 608/405 703.379 cents 8: 2 30/19 790.756 cents smaller undevicesimal minor sixth 8: 2 128/81 792.180 cents Pythagorean minor sixth 8: 4 19/12 795.558 cents undevicesimal minor sixth 8: 2 243/152 812.262 cents 8: 2 8/5 813.686 cents minor sixth 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 1216/729 885.783 cents 9: 3 32/19 902.487 cents 19th subharmonic 9: 4 27/16 905.865 cents Pythagorean major sixth 9: 2 76/45 907.289 cents 10: 2 135/76 994.666 cents 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 2 57/32 999.468 cents undevicesimal minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 11: 1 320/171 1084.891 cents 11: 1 15/8 1088.269 cents classic major seventh 11: 3 152/81 1089.693 cents 11: 4 36/19 1106.397 cents smaller undevicesimal major seventh 11: 1 243/128 1109.775 cents Pythagorean major seventh 11: 2 19/10 1111.199 cents undevicesimal major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.72727 = 52/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 93.6 203.9 297.5 409.2 498.0 591.6 702.0 795.6 905.9 996.1 1111.2 1200.0 93.6 : 110.3 203.9 315.6 404.4 498.0 608.4 702.0 812.3 902.5 1017.6 1106.4 1200.0 203.9 : 93.6 205.3 294.1 387.7 498.0 591.6 702.0 792.2 907.3 996.1 1089.7 1200.0 297.5 : 111.7 200.5 294.1 404.4 498.0 608.4 698.6 813.7 902.5 996.1 1106.4 1200.0 409.2 : 88.8 182.4 292.7 386.3 496.6 586.8 702.0 790.8 884.4 994.7 1088.3 1200.0 498.0 : 93.6 203.9 297.5 407.8 498.0 613.2 702.0 795.6 905.9 999.5 1111.2 1200.0 591.6 : 110.3 203.9 314.2 404.4 519.6 608.4 702.0 812.3 905.9 1017.6 1106.4 1200.0 702.0 : 93.6 203.9 294.1 409.2 498.0 591.6 702.0 795.6 907.3 996.1 1089.7 1200.0 795.6 : 110.3 200.5 315.6 404.4 498.0 608.4 702.0 813.7 902.5 996.1 1106.4 1200.0 905.9 : 90.2 205.3 294.1 387.7 498.0 591.6 703.4 792.2 885.8 996.1 1089.7 1200.0 996.1 : 115.1 203.9 297.5 407.8 501.4 613.2 702.0 795.6 905.9 999.5 1109.8 1200.0 1111.2: 88.8 182.4 292.7 386.3 498.0 586.8 680.4 790.8 884.4 994.7 1084.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8007 .. 115.1093 cents 3249/3200, 26.3086 cents 20/19, 88.8007 cents 2: 182.4037 .. 205.3343 cents 76/75, 22.9306 cents 1600/1539, 67.2944 cents 3: 292.7107 .. 315.6413 cents 76/75, 22.9306 cents 6075/5776, 87.3764 cents 4: 386.3137 .. 409.2443 cents 76/75, 22.9306 cents 25/24, 70.6724 cents 5: 496.6207 .. 519.5513 cents 76/75, 22.9306 cents 6075/5776, 87.3764 cents 6: 586.8457 .. 613.1543 cents 3249/3200, 26.3086 cents 1600/1539, 67.2944 cents 7: 680.4487 .. 703.3793 cents 76/75, 22.9306 cents 1600/1539, 67.2944 cents 8: 790.7557 .. 813.6863 cents 76/75, 22.9306 cents 6075/5776, 87.3764 cents 9: 884.3587 .. 907.2893 cents 76/75, 22.9306 cents 25/24, 70.6724 cents 10: 994.6657 .. 1017.5963 cents 76/75, 22.9306 cents 6075/5776, 87.3764 cents 11: 1084.8907 .. 1111.1993 cents 3249/3200, 26.3086 cents 1600/1539, 67.2944 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 20/19, 88.8007 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 171/160, 115.1093 cents Average / Smallest step : 1.126117 Largest / Average step : 1.151093 Largest / Smallest step : 1.296266 Median interval of one step : 19/18, 93.6030 cents, amount: 4 Most common interval of one step : 19/18, 93.6030 cents, amount: 4 Least squares average step : 100.13243 cents, oct.: 1201.58915 cents Scale is strictly proper Step pattern alph. order: ABACDABABEFD Step pattern size order : CDCEACDCDBFA Scale is a Constant Structure, by a margin of 67.29441 cents Scale diversity : 1.173896 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.781358 Rothenberg efficiency : 0.390356 redundancy: 0.609644 Efficiency x scale size : 4.684271 Number of different interval sizes : 52 = 4.72727 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.72727 = 52/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1216/1215, 1.4243 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 9 Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 11, average 701.7774 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 5 = 41.6667% Limited inverse transpositions with margin 26.3086 cents: 5 -- Rational properties -- Prime limit : 19 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.015503 Average absolute harmonicity : 0.162059 Specific harmonicity : 0.077526 Fundamental : 1/2160, -11.0768 octaves, 0.1211 Hz. Guide tone : 8208, 13.0028 octaves, 2147422.640 Hz. Exponens Consonantiae : 1.772928E+07, 24.07963 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 165.5, average 13.79167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.11922, average 1.00994 Sum of Tenney's harmonic distance : 23.92912, average 1.99409 Vogel's harmonic complexity : 25.00000 Wille's k value : 1822 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 290.42994, average 3.72346 Lattice compactness (without 2's) : 171.78172, average 2.20233 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 -0.66667 24 1 3: -3 .. 3 -0.33333 16 5 5: -1 .. 0 -0.16667 2 19: 0 .. 1 0.50000 6 6 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 24 / 12 = 2.00000 Scale is JI-epimorphic with val: <12 19 28 51| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.9167 c. M: 11.1993 c. Twelve-tone Chromatic (1/11-comma) 41: 3 4 3 4 3 3 4 3 4 3 4 3 SP M ME SD: 3.2959 c. M: 6.2822 c. 53: 4 5 4 5 4 4 5 4 5 4 5 4 SP M ME SD: 1.9112 c. M: 3.1734 c. 65: 5 6 5 6 5 5 6 5 6 5 6 5 SP M ME SD: 1.7092 c. M: 3.5070 c. 118: 9 11 9 11 9 9 11 9 11 9 11 9 SP M DE SD: 1.6984 c. M: 2.7247 c. 152: 12 14 12 14 11 12 14 12 14 11 15 11 SP SD: 1.4472 c. M:-2.4870 c. 164: 13 15 13 15 12 13 15 13 15 12 16 12 SP SD: 1.2675 c. M:-2.4870 c. 176: 14 16 14 16 13 14 16 14 16 13 17 13 SP SD: 1.2463 c. M:-2.4870 c. 193: 15 18 15 18 14 15 18 15 18 14 19 14 SP SD: 1.0812 c. M:-1.9070 c. 205: 16 19 16 19 15 16 19 16 19 15 20 15 SP SD: 0.7762 c. M:-1.4521 c. 217: 17 20 17 20 16 17 20 17 20 16 21 16 SP SD: 0.6041 c. M:-1.1045 c. 229: 18 21 18 21 17 18 21 18 21 17 22 17 SP SD: 0.6039 c. M:-1.1769 c. 258: 20 24 20 24 19 20 24 20 24 19 25 19 SP SD: 0.5849 c. M:-1.1117 c. 270: 21 25 21 25 20 21 25 21 25 20 26 20 SP SD: 0.4002 c. M:-0.8017 c. 282: 22 26 22 26 21 22 26 22 26 21 27 21 SP SD: 0.3661 c. M: 0.7337 c. 436: 34 40 34 41 32 34 40 34 40 33 42 32 SP SD: 0.3677 c. M:-0.8474 c. 448: 35 41 35 42 33 35 41 35 41 34 43 33 SP SD: 0.3166 c. M:-0.5771 c. 501: 39 46 39 47 37 39 46 39 46 38 48 37 SP SD: 0.2942 c. M: 0.5070 c. 653: 51 60 51 61 48 51 60 51 60 49 63 48 SP SD: 0.2526 c. M:-0.5924 c. 665: 52 61 52 62 49 52 61 52 61 50 64 49 SP SD: 0.2047 c. M:-0.3798 c. 677: 53 62 53 63 50 53 62 53 62 51 65 50 SP SD: 0.2085 c. M:-0.3756 c. 706: 55 65 55 66 52 55 65 55 65 53 68 52 SP SD: 0.1792 c. M:-0.4154 c. 718: 56 66 56 67 53 56 66 56 66 54 69 53 SP SD: 0.0920 c. M:-0.2265 c. 730: 57 67 57 68 54 57 67 57 67 55 70 54 SP SD: 0.0725 c. M:-0.1328 c. 1000: 78 92 78 93 74 78 92 78 92 75 96 74 SP SD: 0.0659 c. M:-0.1350 c. 1448: 113 133 113 135 107 113 133 113 133 109 139 107 SP SD: 0.0665 c. M:-0.1480 c. 1501: 117 138 117 140 111 117 138 117 138 113 144 111 SP SD: 0.0624 c. M: 0.1113 c. 1513: 118 139 118 141 112 118 139 118 139 114 145 112 SP SD: 0.0581 c. M: 0.1148 c. 1718: 134 158 134 160 127 134 158 134 158 129 165 127 SP SD: 0.0478 c. M:-0.0929 c. 1730: 135 159 135 161 128 135 159 135 159 130 166 128 SP SD: 0.0295 c. M:-0.0592 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: 7.1688 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.9063 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.9376 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.8519 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.6392 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.2227 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.9435 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.9292 cents 11 x 12:13:14:15 x x 17:19:20:21:22 SD: 10.8039 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.4605 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.6153 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.8808 cents 15:16:17:18:19:20:21:23:24:25:27:29:30 SD: 5.5977 cents 17:18:19:20:22:23:24:26:27:29:30:32:34 SD: 5.5267 cents 18:19:20:21:23:24:25:27:29:30:32:34:36 SD: 5.0195 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.0136 cents 32:34:36:38:41:43:45:48:51:54:57:61:64 SD: 2.4690 cents 38:40:43:45:48:51:53:57:60:64:68:72:76 SD: 2.2539 cents 41:43:46:49:52:55:58:62:65:69:73:78:82 SD: 2.2028 cents 42:44:47:50:53:56:59:63:67:71:75:80:84 SD: 2.0116 cents 48:51:54:57:61:64:68:72:76:81:85:91:96 SD: 1.5600 cents 54:57:61:64:68:72:76:81:86:91:96:103:108 SD: 1.4860 cents 64:68:72:76:81:85:90:96:101:108:114:122:128 SD: 1.3310 cents 70:74:79:83:89:93:99:105:111:118:124:133:140 SD: 1.3016 cents 71:75:80:84:90:95:100:107:112:120:126:135:142 SD: 1.2247 cents 72:76:81:86:91:96:101:108:114:122:128:137:144 SD: 1.1956 cents 74:78:83:88:94:99:104:111:117:125:132:141:148 SD: 1.0896 cents 86:91:97:102:109:115:121:129:136:145:153:163:172 SD: 0.8137 cents 90:95:101:107:114:120:127:135:143:152:160:171:180 SD: 0.7542 cents 108:114:122:128:137:144:152:162:171:182:192:205:216 SD: 0.7306 cents 112:118:126:133:142:149:158:168:177:189:199:213:224 SD: 0.6396 cents 128:135:144:152:162:171:180:192:203:216:228:243:256 SD: 0.5206 cents 144:152:162:171:182:192:203:216:228:243:256:274:288 SD: 0.4483 cents 176:186:198:209:223:235:248:264:279:297:313:334:352 SD: 0.4068 cents 192:203:216:228:243:256:270:288:304:324:341:365:384 SD: 0.3324 cents 240:253:270:285:304:320:338:360:380:405:427:456:480 SD: 0.2404 cents 288:304:324:342:365:384:405:432:456:486:512:547:576 SD: 0.1521 cents 432:456:486:513:547:576:608:648:684:729:768:821:864 SD: 0.0634 cents