Scala analysis: akj_temperament
temperament based on 5/4, 24/19, and 19/15 filling the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 89.644 cents 89.644000 2: 193.157 cents 193.157000 3: 293.065 cents 293.065000 4: 386.314 cents 386.314000 5: 497.687 cents 497.687000 6: 588.534 cents 588.534000 7: 696.578 cents 696.578000 8: 790.754 cents 790.754000 9: 889.735 cents 889.735000 10: 995.376 cents 995.376000 11: 1087.424 cents 1087.424000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 112.5760 cents 112.5760 1: 89.6440 cents 89.6440 2: 103.5130 cents 103.5130 3: 99.9080 cents 99.9080 4: 93.2490 cents 93.2490 5: 111.3730 cents 111.3730 6: 90.8470 cents 90.8470 7: 108.0440 cents 108.0440 8: 94.1760 cents 94.1760 9: 98.9810 cents 98.9810 10: 105.6410 cents 105.6410 11: 92.0480 cents 92.0480 12: 112.5760 cents 112.5760
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 89.64400 cents 1: 1 90.84700 cents 1: 1 92.04800 cents 1: 1 93.24900 cents 1: 1 94.17600 cents 1: 1 98.98100 cents 1: 1 99.90800 cents 1: 1 103.51300 cents 1: 1 105.64100 cents 1: 1 108.04400 cents 1: 1 111.37300 cents 1: 1 112.57600 cents 2: 3 193.15700 cents 2: 1 197.68900 cents 2: 1 198.89100 cents 2: 3 202.22000 cents 2: 1 203.42100 cents 2: 2 204.62200 cents 2: 1 204.62400 cents 3: 1 293.06500 cents 3: 1 293.06700 cents 3: 1 294.26800 cents 3: 1 295.46900 cents 3: 2 296.67000 cents 3: 1 298.79800 cents 3: 1 301.20100 cents 3: 1 304.53000 cents 3: 1 305.73300 cents 3: 1 310.26400 cents 3: 1 310.26500 cents 4: 1 386.31400 cents 4: 1 390.84600 cents 4: 1 392.04800 cents 4: 1 395.37700 cents 4: 1 397.78100 cents 4: 1 399.90900 cents 4: 1 403.51300 cents 4: 1 404.44000 cents 4: 1 405.64100 cents 4: 1 406.84200 cents 4: 1 408.04300 cents 4: 1 409.24600 cents 5: 1 497.68700 cents 5: 3 497.68900 cents 5: 4 498.89000 cents 5: 2 503.42100 cents 5: 2 503.42200 cents 6: 1 588.53400 cents 6: 1 589.73700 cents 6: 1 590.93800 cents 6: 1 593.06600 cents 6: 1 596.67000 cents 6: 1 597.59700 cents 6: 1 602.40300 cents 6: 1 603.33000 cents 6: 1 606.93400 cents 6: 1 609.06200 cents 6: 1 610.26300 cents 6: 1 611.46600 cents 7: 2 696.57800 cents 7: 2 696.57900 cents 7: 4 701.11000 cents 7: 3 702.31100 cents 7: 1 702.31300 cents 8: 1 790.75400 cents 8: 1 791.95700 cents 8: 1 793.15800 cents 8: 1 794.35900 cents 8: 1 795.56000 cents 8: 1 796.48700 cents 8: 1 800.09100 cents 8: 1 802.21900 cents 8: 1 804.62300 cents 8: 1 807.95200 cents 8: 1 809.15400 cents 8: 1 813.68600 cents 9: 1 889.73500 cents 9: 1 889.73600 cents 9: 1 894.26700 cents 9: 1 895.47000 cents 9: 1 898.79900 cents 9: 1 901.20200 cents 9: 2 903.33000 cents 9: 1 904.53100 cents 9: 1 905.73200 cents 9: 1 906.93300 cents 9: 1 906.93500 cents 10: 1 995.37600 cents 10: 2 995.37800 cents 10: 1 996.57900 cents 10: 3 997.78000 cents 10: 1 1001.10900 cents 10: 1 1002.31100 cents 10: 3 1006.84300 cents 11: 1 1087.42400 cents 11: 1 1088.62700 cents 11: 1 1091.95600 cents 11: 1 1094.35900 cents 11: 1 1096.48700 cents 11: 1 1100.09200 cents 11: 1 1101.01900 cents 11: 1 1105.82400 cents 11: 1 1106.75100 cents 11: 1 1107.95200 cents 11: 1 1109.15300 cents 11: 1 1110.35600 cents Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 9.63636 = 106/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 89.6 193.2 293.1 386.3 497.7 588.5 696.6 790.8 889.7 995.4 1087.4 1200.0 89.6 : 103.5 203.4 296.7 408.0 498.9 606.9 701.1 800.1 905.7 997.8 1110.4 1200.0 193.2 : 99.9 193.2 304.5 395.4 503.4 597.6 696.6 802.2 894.3 1006.8 1096.5 1200.0 293.1 : 93.2 204.6 295.5 403.5 497.7 596.7 702.3 794.4 906.9 996.6 1100.1 1200.0 386.3 : 111.4 202.2 310.3 404.4 503.4 609.1 701.1 813.7 903.3 1006.8 1106.8 1200.0 497.7 : 90.8 198.9 293.1 392.0 497.7 589.7 702.3 792.0 895.5 995.4 1088.6 1200.0 588.5 : 108.0 202.2 301.2 406.8 498.9 611.5 701.1 804.6 904.5 997.8 1109.2 1200.0 696.6 : 94.2 193.2 298.8 390.8 503.4 593.1 696.6 796.5 889.7 1001.1 1092.0 1200.0 790.8 : 99.0 204.6 296.7 409.2 498.9 602.4 702.3 795.6 906.9 997.8 1105.8 1200.0 889.7 : 105.6 197.7 310.3 399.9 503.4 603.3 696.6 808.0 898.8 1006.8 1101.0 1200.0 995.4 : 92.0 204.6 294.3 397.8 497.7 590.9 702.3 793.2 901.2 995.4 1094.4 1200.0 1087.4: 112.6 202.2 305.7 405.6 498.9 610.3 701.1 809.2 903.3 1002.3 1108.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.6440 .. 112.5760 cents 22.93200 cents 89.64400 cents 2: 193.1570 .. 204.6240 cents 11.46700 cents 80.58100 cents 3: 293.0650 .. 310.2650 cents 17.20000 cents 88.44100 cents 4: 386.3140 .. 409.2460 cents 22.93200 cents 76.04900 cents 5: 497.6870 .. 503.4220 cents 5.73500 cents 88.44100 cents 6: 588.5340 .. 611.4660 cents 22.93200 cents 85.11200 cents 7: 696.5780 .. 702.3130 cents 5.73500 cents 85.11200 cents 8: 790.7540 .. 813.6860 cents 22.93200 cents 88.44100 cents 9: 889.7350 .. 906.9350 cents 17.20000 cents 76.04900 cents 10: 995.3760 .. 1006.8430 cents 11.46700 cents 88.44100 cents 11: 1087.4240 .. 1110.3560 cents 22.93200 cents 80.58100 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 89.64400 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 112.57600 cents Average / Smallest step : 1.115524 Largest / Average step : 1.125760 Largest / Smallest step : 1.255812 Median interval of one step : 99.44450 cents, amount: 0 Least squares average step : 99.14641 cents, oct.: 1189.75689 cents Scale is strictly proper Step pattern alph. order: ABCDEFGHIJKL Step pattern size order : AHGDKBJEFICL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 76.04900 cents Scale diversity : 1.129721 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.847113 Rothenberg efficiency : 0.197685 redundancy: 0.802315 Efficiency x scale size : 2.372222 Number of different interval sizes : 106 = 9.63636 / class Number of one step interval sizes : 12 Highest interval variety : 12 Mean interval variety : 9.63636 = 106/11 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 0.00100 cents Most common intervals : 498.89000 cents & inv., amount: 4 Most common triad is 0.0 498.890 701.110 cents, amount: 3 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 22.9320 cents: 2 5 7 10 Limited inverse transpositions with margin 21.7290 cents: 1 2 4 6 9 11 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.7006 c. M:-13.6860 c. Twelve-tone Chromatic (1/11-comma) 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 5.6004 c. M:-11.7210 c. Schismic-12 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 4.0277 c. M:-10.6166 c. Schismic-12 55: 4 5 4 5 5 4 5 4 5 5 4 5 SP M ME SD: 4.9790 c. M: 9.4286 c. 57: 4 5 5 4 6 4 5 5 4 5 5 5 SP D3 SD: 5.5238 c. M:-9.2460 c. 61: 5 5 5 5 5 5 5 5 5 6 4 6 SP D3 SD: 5.5756 c. M:-8.7167 c. 62: 5 5 5 5 6 4 6 5 5 5 5 6 SP D3 SD: 4.4852 c. M: 8.2792 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.7752 c. M:-9.9199 c. 67: 5 6 5 6 6 5 6 5 6 6 5 6 SP M ME SD: 4.7077 c. M:-7.7159 c. 72: 5 7 6 5 7 5 7 5 6 7 5 7 SP D3 SD: 5.1793 c. M: 7.4207 c. 74: 6 6 6 6 7 5 7 6 6 6 6 7 SP D3 SD: 3.8414 c. M:-7.6533 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 4.0378 c. M:-9.4404 c. 78: 6 7 6 6 7 6 7 6 7 7 6 7 SP D3 S SD: 4.1777 c. M:-6.8430 c. 81: 6 7 7 6 8 6 7 6 7 7 6 8 SP SD: 3.4174 c. M:-6.0167 c. 86: 6 8 7 7 8 6 8 7 7 7 7 8 SP D3 S SD: 3.4487 c. M: 5.9231 c. 93: 7 8 8 7 9 7 8 7 8 8 7 9 SP SD: 2.8944 c. M:-5.5388 c. 94: 7 8 8 7 9 7 9 7 8 8 7 9 SP D3 SD: 2.3793 c. M:-5.5497 c. 98: 7 9 8 8 9 7 9 8 8 8 8 9 SP D3 S SD: 3.3873 c. M:-5.5227 c. 105: 8 9 9 8 10 8 9 8 9 9 8 10 SP SD: 2.8586 c. M:-5.7517 c. 106: 8 9 9 8 10 8 10 8 9 9 8 10 SP D3 SD: 2.2089 c. M:-5.3088 c. 108: 8 9 9 9 10 8 10 8 9 10 8 10 SP T3 SD: 2.7044 c. M:-4.6240 c. 112: 8 10 9 9 10 9 10 9 9 10 8 11 SP SD: 2.7036 c. M: 5.2811 c. 118: 9 10 10 9 11 9 10 10 9 11 9 11 SP D3 SD: 2.3731 c. M: 5.0526 c. 119: 9 10 10 9 11 9 11 9 10 11 9 11 SP SD: 2.5009 c. M: 4.1994 c. 124: 9 11 10 10 11 10 11 10 10 11 9 12 SP SD: 2.1961 c. M: 4.1386 c. 128: 10 11 10 10 12 10 11 10 11 11 10 12 SP SD: 2.3709 c. M:-4.1060 c. 130: 10 11 11 10 12 10 12 10 11 11 10 12 SP D3 SD: 2.7717 c. M:-5.6496 c. 131: 10 11 11 10 12 10 12 10 11 12 10 12 SP SD: 2.0067 c. M:-3.0973 c. 135: 10 12 11 10 13 10 12 11 11 12 10 13 SP SD: 1.9773 c. M: 4.0918 c. 143: 11 12 12 11 13 11 13 11 12 13 11 13 SP SD: 1.8691 c. M:-3.4851 c. 147: 11 13 12 11 14 11 13 12 12 13 11 14 SP SD: 1.5179 c. M:-2.7614 c. 159: 12 14 13 12 15 12 14 13 13 14 12 15 SP SD: 1.4081 c. M:-3.0694 c. 171: 13 15 14 13 16 13 15 14 14 15 13 16 SP SD: 1.5720 c. M:-3.3342 c. 181: 13 16 15 14 17 14 16 14 15 16 14 17 SP SD: 1.4814 c. M: 3.4562 c. 193: 14 17 16 15 18 15 17 15 16 17 15 18 SP SD: 1.1313 c. M: 2.5974 c. 200: 15 17 17 15 19 15 18 16 16 18 15 19 SP S SD: 1.1325 c. M: 2.3140 c. 205: 15 18 17 16 19 16 18 16 17 18 16 19 SP SD: 1.0377 c. M:-2.6855 c. 210: 16 18 17 17 19 16 19 16 18 18 16 20 SP SD: 1.4316 c. M:-2.2574 c. 212: 16 18 18 16 20 16 19 17 17 19 16 20 SP S SD: 0.9311 c. M:-1.6988 c. 224: 17 19 19 17 21 17 20 18 18 20 17 21 SP S SD: 0.9824 c. M:-2.1031 c. 255: 19 22 21 20 24 19 23 20 21 22 20 24 SP SD: 0.8927 c. M: 2.4348 c. 263: 20 22 22 21 24 20 24 20 22 23 20 25 SP SD: 1.1341 c. M:-1.6108 c. 267: 20 23 22 21 25 20 24 21 22 23 21 25 SP SD: 0.7674 c. M: 2.1176 c. 331: 25 28 28 26 30 25 30 26 27 30 25 31 SP SD: 1.0318 c. M:-1.6029 c. 332: 25 28 28 26 31 25 30 26 27 29 26 31 SP SD: 0.8753 c. M: 1.5907 c. 336: 25 29 28 26 31 26 30 26 28 30 25 32 SP SD: 0.8747 c. M: 1.7097 c. 340: 25 30 28 26 32 26 30 27 28 30 26 32 SP SD: 0.8267 c. M: 1.6081 c. 344: 26 29 29 27 32 26 31 27 28 30 27 32 SP SD: 0.9443 c. M: 1.2965 c. 347: 26 30 29 27 32 26 31 28 28 31 26 33 SP SD: 0.9065 c. M: 1.5450 c. 348: 26 30 29 27 32 27 31 27 29 31 26 33 SP SD: 0.7439 c. M: 1.2171 c. 352: 26 31 29 27 33 27 31 28 29 31 27 33 SP SD: 0.7300 c. M:-1.2387 c. 374: 28 32 31 29 35 28 34 29 31 33 29 35 SP SD: 0.8673 c. M: 1.4492 c. 375: 28 32 32 29 35 28 34 29 31 33 29 35 SP SD: 0.8072 c. M:-1.5130 c. 376: 28 33 31 29 35 28 34 30 31 33 29 35 SP SD: 0.7672 c. M:-1.5239 c. 386: 29 33 32 30 36 29 35 30 32 34 30 36 SP SD: 0.6605 c. M: 1.1167 c. 398: 30 34 33 31 37 30 36 31 33 35 31 37 SP SD: 0.5424 c. M:-1.0182 c. 429: 32 37 36 33 40 32 39 34 35 38 33 40 SP SD: 0.5234 c. M: 1.1214 c. 441: 33 38 37 34 41 33 40 35 36 39 34 41 SP SD: 0.5676 c. M:-1.0827 c. 467: 35 40 39 36 44 35 42 37 38 41 36 44 SP SD: 0.5627 c. M: 0.9435 c. 479: 36 41 40 37 45 36 43 38 39 42 37 45 SP SD: 0.5017 c. M:-0.8953 c. 499: 37 43 42 39 46 38 45 39 41 44 38 47 SP SD: 0.5332 c. M:-0.8603 c. 510: 38 44 42 40 47 39 46 40 42 45 39 48 SP SD: 0.5650 c. M: 1.3003 c. 522: 39 45 43 41 48 40 47 41 43 46 40 49 SP SD: 0.4613 c. M: 1.1353 c. 534: 40 46 44 42 49 41 48 42 44 47 41 50 SP SD: 0.4381 c. M: 1.0578 c. 553: 41 48 46 43 51 42 50 43 46 49 42 52 SP SD: 0.4597 c. M: 0.8806 c. 557: 42 48 46 43 52 42 50 44 46 49 43 52 SP SD: 0.4720 c. M:-0.8407 c. 565: 42 49 47 44 52 43 51 44 47 50 43 53 SP SD: 0.3879 c. M:-0.7302 c. 603: 45 52 50 47 56 46 54 47 50 53 46 57 SP SD: 0.4137 c. M: 0.8568 c. 615: 46 53 51 48 57 47 55 48 51 54 47 58 SP SD: 0.3408 c. M:-0.7343 c. 639: 48 55 53 50 59 48 58 50 53 56 49 60 SP SD: 0.3406 c. M: 0.7406 c. 692: 52 59 58 54 64 52 63 54 57 61 53 65 SP SD: 0.3718 c. M: 0.6727 c. 696: 52 60 58 54 65 52 63 55 57 61 54 65 SP SD: 0.3744 c. M:-0.6253 c. 734: 55 63 61 57 68 56 66 58 60 65 56 69 SP SD: 0.3605 c. M: 0.6843 c. 746: 56 64 62 58 69 57 67 59 61 66 57 70 SP SD: 0.3426 c. M:-0.6669 c. 765: 57 66 64 59 71 58 69 60 63 67 59 72 SP SD: 0.3721 c. M: 0.8662 c. 774: 58 67 64 60 72 59 69 61 64 68 59 73 SP SD: 0.3590 c. M:-0.6414 c. 777: 58 67 65 60 72 59 70 61 64 68 60 73 SP SD: 0.2932 c. M: 0.7814 c. 789: 59 68 66 61 73 60 71 62 65 69 61 74 SP SD: 0.2676 c. M: 0.6992 c. 801: 60 69 67 62 74 61 72 63 66 70 62 75 SP SD: 0.3034 c. M: 0.6194 c. 808: 60 70 67 63 75 61 73 63 67 71 62 76 SP SD: 0.3423 c. M: 0.6550 c. 819: 61 71 68 64 76 62 73 65 67 72 63 77 SP SD: 0.3937 c. M: 0.6073 c. 820: 61 71 68 64 76 62 74 64 68 72 63 77 SP SD: 0.2413 c. M: 0.5101 c. 832: 62 72 69 65 77 63 75 65 69 73 64 78 SP SD: 0.1847 c. M: 0.3694 c. 1032: 77 89 86 80 96 78 93 81 85 91 79 97 SP SD: 0.1366 c. M: 0.2675 c. 1044: 78 90 87 81 97 79 94 82 86 92 80 98 SP SD: 0.0515 c. M: 0.1071 c. 2100: 157 181 175 163 195 159 189 165 173 185 161 197 SP SD: 0.0483 c. M:-0.1031 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: 2.6885 cents 3 x x x x 4 x x x 5 x x 6 S SD: 1.7961 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.7723 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.9135 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.8044 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.8327 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.5299 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.7173 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.5351 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.9476 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.7567 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.2320 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.2067 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.4856 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.1384 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.7021 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.3802 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.3891 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.8032 cents 33:35:37:39:41:44:46:49:52:55:59:62:66 SD: 2.3599 cents 36:38:40:43:45:48:51:54:57:60:64:67:72 SD: 2.3248 cents 39:41:44:46:49:52:55:58:62:65:69:73:78 SD: 2.2839 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 1.9441 cents 49:52:55:58:61:65:69:73:77:82:87:92:98 SD: 1.8383 cents 52:55:58:62:65:69:73:78:82:87:92:97:104 SD: 1.7228 cents 54:57:60:64:68:72:76:81:85:90:96:101:108 SD: 1.6755 cents 57:60:64:68:71:76:80:85:90:95:101:107:114 SD: 1.5236 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.2964 cents 60:63:67:71:75:80:84:90:95:100:107:112:120 SD: 1.2797 cents 69:73:77:82:86:92:97:103:109:115:123:129:138 SD: 1.2319 cents 75:79:84:89:94:100:105:112:118:125:133:141:150 SD: 1.1567 cents 76:80:85:90:95:101:107:114:120:127:135:142:152 SD: 0.8380 cents 93:98:104:110:116:124:131:139:147:155:165:174:186 SD: 0.7958 cents 109:115:122:129:136:145:153:163:172:182:194:204:218 SD: 0.6428 cents 129:136:144:153:161:172:181:193:204:216:229:242:258 SD: 0.5874 cents 135:142:151:160:169:180:190:202:213:226:240:253:270 SD: 0.4660 cents 153:161:171:181:191:204:215:229:242:256:272:287:306 SD: 0.4484 cents 168:177:188:199:210:224:236:251:265:281:299:315:336 SD: 0.3403 cents 228:240:255:270:285:304:320:341:360:381:405:427:456 SD: 0.2181 cents 304:320:340:360:380:405:427:455:480:508:540:570:608 SD: 0.2178 cents 363:382:406:430:454:484:510:543:573:607:645:680:726 SD: 0.1776 cents 396:417:443:469:495:528:556:592:625:662:704:742:792 SD: 0.1592 cents 432:455:483:512:540:576:607:646:682:722:768:810:864 SD: 0.1442 cents 484:510:541:573:605:645:680:724:764:809:860:907:968 SD: 0.1400 cents 525:553:587:622:656:700:738:785:829:878:933:984:1050 SD: 0.1266 cents 543:572:607:643:679:724:763:812:857:908:965:1018:1086 SD: 0.1231 cents 585:616:654:693:731:780:822:875:924:978:1040:1096:1170 SD: 0.1195 cents