Scala analysis: 19berger
Tom dent's 19berger scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 151/135 193.906971 3: 19/16 297.513016 19th harmonic 4: 304/243 387.738012 5: 4864/3645 499.469297 6: 2215/1576 589.246997 7: 2423/1620 696.960710 8: 271/162 890.758846 9: 8417/4728 998.491298 10: 15/8 1088.268715 classic major seventh 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 256/243 90.2250 limma, Pythagorean minor second 2: 1359/1280 103.6820 3: 2565/2416 103.6060 4: 256/243 90.2250 limma, Pythagorean minor second 5: 16/15 111.7313 minor diatonic semitone 6: 8073675/7665664 89.7777 7: 954662/897075 107.7137 8: 2710/2423 193.7981 9: 227259/213548 107.7325 10: 8865/8417 89.7774 11: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 8865/8417 89.777 cents 1: 1 8073675/7665664 89.778 cents 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 1 2565/2416 103.606 cents 1: 1 1359/1280 103.682 cents 1: 1 954662/897075 107.714 cents 1: 1 227259/213548 107.732 cents 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 2710/2423 193.798 cents 2: 1 1520/1359 193.831 cents 2: 1 151/135 193.907 cents 2: 1 21807/19456 197.491 cents 2: 1 1215/1084 197.510 cents 2: 1 9456/8417 201.509 cents 2: 1 538245/479104 201.509 cents 2: 2 4096/3645 201.956 cents narrow diminished third 2: 1 4617/4096 207.288 cents 2: 1 213548/179415 301.512 cents 2: 1 1136295/954662 301.531 cents 3: 1 806912/681777 291.734 cents 3: 1 4430/3743 291.734 cents 3: 2 19/16 297.513 cents 19th harmonic 3: 1 4864/4077 305.562 cents 3: 1 2416/2025 305.638 cents 3: 1 7269/6080 309.223 cents 3: 1 324/271 309.241 cents 3: 1 12195/9728 391.290 cents 3: 1 6075/4846 391.308 cents 3: 1 19/15 409.244 cents undevicesimal ditone 4: 1 304/243 387.738 cents 4: 1 299025/237976 395.340 cents 4: 1 475952/378765 395.416 cents 4: 1 9692/7695 399.448 cents 4: 1 1024/813 399.466 cents 4: 2 19/15 409.244 cents undevicesimal ditone 4: 1 591/443 499.022 cents 4: 1 538245/403456 499.022 cents 4: 1 813/608 503.021 cents 4: 1 3240/2423 503.039 cents 5: 1 591/443 499.022 cents 5: 1 538245/403456 499.022 cents 5: 2 4864/3645 499.469 cents 5: 1 2423/1812 503.054 cents 5: 1 1812/1355 503.148 cents 5: 1 54675/38912 588.799 cents 5: 1 2168/1539 593.246 cents 5: 1 10240/7269 593.264 cents 5: 1 3152/2215 610.753 cents 5: 1 35883/25216 610.753 cents 6: 1 50432/35883 589.247 cents 6: 1 2215/1576 589.247 cents 6: 1 7269/5120 606.736 cents 6: 1 1539/1084 606.754 cents 6: 1 77824/54675 611.201 cents 6: 1 1355/906 696.852 cents 6: 1 3624/2423 696.946 cents 6: 2 3645/2432 700.531 cents 6: 1 806912/538245 700.978 cents 6: 1 886/591 700.978 cents 7: 1 2423/1620 696.961 cents 7: 1 1216/813 696.979 cents 7: 1 806912/538245 700.978 cents 7: 1 886/591 700.978 cents 7: 2 30/19 790.756 cents smaller undevicesimal minor sixth 7: 1 813/512 800.534 cents 7: 1 7695/4846 800.552 cents 7: 1 378765/237976 804.584 cents 7: 1 475952/299025 804.660 cents 7: 1 243/152 812.262 cents 8: 1 30/19 790.756 cents smaller undevicesimal minor sixth 8: 1 9692/6075 808.692 cents 8: 1 19456/12195 808.710 cents 8: 1 271/162 890.759 cents 8: 1 12160/7269 890.777 cents 8: 1 2025/1208 894.362 cents 8: 1 4077/2432 894.438 cents 8: 2 32/19 902.487 cents 19th subharmonic 8: 1 3743/2215 908.266 cents 8: 1 681777/403456 908.266 cents 9: 1 1909324/1136295 898.469 cents 9: 1 179415/106774 898.488 cents 9: 1 8192/4617 992.712 cents 9: 2 3645/2048 998.044 cents wide augmented sixth 9: 1 958208/538245 998.491 cents 9: 1 8417/4728 998.491 cents 9: 1 2168/1215 1002.490 cents 9: 1 38912/21807 1002.509 cents 9: 1 270/151 1006.093 cents 9: 1 1359/760 1006.169 cents 10: 1 2423/1355 1006.202 cents 10: 2 15/8 1088.269 cents classic major seventh 10: 1 427096/227259 1092.268 cents 10: 1 897075/477331 1092.286 cents 10: 1 2560/1359 1096.318 cents 10: 1 4832/2565 1096.394 cents 10: 2 243/128 1109.775 cents Pythagorean major seventh 10: 1 15331328/8073675 1110.222 cents 10: 1 16834/8865 1110.223 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 9.80000 = 49/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 90.2 193.9 297.5 387.7 499.5 589.2 697.0 890.8 998.5 1088.3 1200.0 90.2 : 103.7 207.3 297.5 409.2 499.0 606.7 800.5 908.3 998.0 1109.8 1200.0 193.9 : 103.6 193.8 305.6 395.3 503.1 696.9 804.6 894.4 1006.1 1096.3 1200.0 297.5 : 90.2 202.0 291.7 399.4 593.2 701.0 790.8 902.5 992.7 1096.4 1200.0 387.7 : 111.7 201.5 309.2 503.0 610.8 700.5 812.3 902.5 1006.2 1109.8 1200.0 499.5 : 89.8 197.5 391.3 499.0 588.8 700.5 790.8 894.4 998.0 1088.3 1200.0 589.2 : 107.7 301.5 409.2 499.0 610.8 701.0 804.7 908.3 998.5 1110.2 1200.0 697.0 : 193.8 301.5 391.3 503.0 593.3 696.9 800.6 890.8 1002.5 1092.3 1200.0 890.8 : 107.7 197.5 309.2 399.5 503.1 606.8 697.0 808.7 898.5 1006.2 1200.0 998.5 : 89.8 201.5 291.7 395.4 499.0 589.2 701.0 790.8 898.5 1092.3 1200.0 1088.3: 111.7 202.0 305.6 409.2 499.5 611.2 701.0 808.7 1002.5 1110.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.7774 .. 193.7981 cents 4562014/4295979, 104.0207 cents 8865/8417, 89.7774 cents 2: 193.8310 .. 301.5306 cents 16254999/15274592, 107.6995 cents 368296/368289, 0.0329 cents 3: 291.7337 .. 409.2443 cents 4317921/4034560, 117.5106 cents -9.79689 cents 4: 387.7380 .. 503.0393 cents 98415/92074, 115.3013 cents 80/81,-21.5063 cents 5: 499.0217 .. 610.7533 cents 5298723/4967552, 111.7316 cents 477331/478440,-4.0176 cents 6: 589.2467 .. 700.9783 cents 5298723/4967552, 111.7316 cents 1271693312/1287589689,-21.5066 cents 7: 696.9607 .. 812.2620 cents 98415/92074, 115.3013 cents 477331/478440,-4.0176 cents 8: 790.7557 .. 908.2663 cents 4317921/4034560, 117.5106 cents 80/81,-21.5063 cents 9: 898.4694 .. 1006.1690 cents 16254999/15274592, 107.6995 cents -9.79689 cents 10: 1006.2019 .. 1110.2226 cents 4562014/4295979, 104.0207 cents 368296/368289, 0.0329 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 8865/8417, 89.7774 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 2710/2423, 193.7981 cents Average / Smallest step : 1.215126 Largest / Average step : 1.776483 Largest / Smallest step : 2.158651 Median interval of one step : 1359/1280, 103.6820 cents, amount: 1 Least squares average step : 106.77522 cents, oct.: 1174.52746 cents Scale is not proper Step pattern alph. order: ABCADEFGHID Step pattern size order : BDCBGAEHFAG Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.164761 Lumma stability : 0.149684 Lumma impropriety factor : 0.076790 Rothenberg efficiency : 0.211019 redundancy: 0.788981 Efficiency x scale size : 2.321212 Number of different interval sizes : 92 = 9.20000 / class Number of one step interval sizes : 9 Highest interval variety : 10 Mean interval variety : 9.80000 = 49/5 Median interval variety : 9.5 Lowest interval variety : 9 Smallest interval difference : 79480845/79480832, 0.0003 cents Most common intervals : 19/15, 409.2443 cents & inv., amount: 3 Most common triad is 0.0 409.244 1110.223 cents, amount: 1 Number of recognisable fifths : 10, average 699.2712 cents Formal octave complements present : 1 = 9.0909% Limited inverse transpositions : 4 Inversional symmetry on degrees : 2 Inversional symmetry on intervals : 7-8 -- Rational properties -- Prime limit : 2423 Odd number limit : 8073675 (O: 8073675 U: 8073675) Highest odd numerator or denominator: 8417 Harmonicity values : limit above prime count Fundamental : 1/11489040, -23.4538 octaves, 0.0000 Hz. Guide tone : too high to compute Sum of Mann's harmonic distance : 15657.0, average 1423.36364 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 26.05459, average 2.36860 Sum of Tenney's harmonic distance : 51.46253, average 4.67841 Vogel's harmonic complexity : 526.90909 Wille's k value : 6821617 Lattice compactness : 397.63495, average 6.02477 Lattice compactness (without 2's) : 213.20237, average 3.23034 Number of different primes : 9 Prime exponents' range, average, count, tones@limit: 2: -4 .. 8 0.45455 37 1 3: -6 .. 1 -2.45455 29 1 5: -1 .. 1 -0.09091 5 1 19: 0 .. 1 0.36364 4 3 151: 0 .. 1 0.09091 1 1 197: -1 .. 0 -0.18182 2 271: 0 .. 1 0.09091 1 1 443: 0 .. 1 0.18182 2 2 2423: 0 .. 1 0.09091 1 1 Average exponent except 2's :-21 / 11 =-1.90909 Average absolute exponent except 2's: 45 / 11 = 4.09091
FIT/MODE
11: 1 1 1 1 1 0 1 2 1 1 1 N T3 SD: 31.0964 c. M:-48.6256 c. 12: 1 1 1 1 1 1 1 2 1 1 1 P M ME S SD: 7.6257 c. M:-12.2620 c. 31: 2 3 3 2 3 2 3 5 3 2 3 N G S SD: 6.6300 c. M: 12.8056 c. 43: 3 4 4 3 4 3 4 7 4 3 4 N G S SD: 4.3138 c. M:-9.4637 c. 55: 4 5 5 4 5 4 5 9 5 4 5 N G S SD: 3.7843 c. M:-7.9415 c. 65: 5 6 5 5 6 5 6 10 6 5 6 N SD: 3.5909 c. M:-9.1700 c. 67: 5 6 6 5 6 5 6 11 6 5 6 N G S SD: 3.9200 c. M:-6.9646 c. 77: 6 6 7 6 7 6 7 12 7 6 7 N SD: 3.1058 c. M: 6.8940 c. 81: 6 7 7 6 8 6 7 13 7 6 8 N S SD: 3.3768 c. M: 6.7872 c. 84: 6 8 7 6 8 6 8 13 8 6 8 N SD: 3.3575 c. M:-6.0930 c. 89: 7 7 8 7 8 7 8 14 8 7 8 N SD: 3.0932 c. M: 5.1429 c. 93: 7 8 8 7 9 7 8 15 8 7 9 N S SD: 2.6579 c. M: 4.9429 c. 96: 7 9 8 7 9 7 9 15 9 7 9 N SD: 2.6432 c. M:-6.0930 c. 97: 7 9 8 7 9 8 8 16 9 7 9 N SD: 3.3068 c. M: 4.6239 c. 98: 7 9 8 8 9 7 9 16 9 7 9 N SD: 3.1269 c. M:-5.5903 c. 105: 8 9 9 8 10 8 9 17 9 8 10 N S SD: 2.4118 c. M:-5.0387 c. 108: 8 9 10 8 10 8 10 17 10 8 10 N SD: 2.1380 c. M: 5.0181 c. 112: 8 10 10 8 11 8 10 18 10 9 10 N SD: 2.6340 c. M:-4.5884 c. 117: 9 10 10 9 11 8 11 19 10 9 11 N SD: 2.2811 c. M: 4.6316 c. 118: 9 10 10 9 11 9 11 19 10 9 11 N SD: 2.2469 c. M:-4.7342 c. 120: 9 10 11 9 11 9 11 19 11 9 11 N SD: 1.9668 c. M: 3.9070 c. 129: 10 11 11 10 12 9 12 21 11 10 12 N SD: 2.1871 c. M: 3.2005 c. 132: 10 11 12 10 12 10 12 21 12 10 12 N SD: 2.0725 c. M:-3.1711 c. 136: 10 12 12 10 13 10 12 22 12 10 13 N S SD: 1.8414 c. M:-3.4719 c. 148: 11 13 13 11 14 11 13 24 13 11 14 N S SD: 1.7395 c. M:-3.2334 c. 149: 11 13 13 11 14 11 14 24 13 11 14 N SD: 1.6919 c. M:-3.7104 c. 160: 12 14 14 12 15 12 14 26 14 12 15 N S SD: 1.8392 c. M:-3.2530 c. 161: 12 14 14 12 15 12 15 26 14 12 15 N SD: 1.5966 c. M:-3.6604 c. 163: 12 14 14 13 15 12 15 26 15 12 15 N SD: 1.9404 c. M: 3.0345 c. 171: 13 15 14 13 16 13 15 28 15 13 16 N SD: 1.6391 c. M: 2.7762 c. 173: 13 15 15 13 16 13 15 28 16 13 16 N SD: 1.3941 c. M: 3.3191 c. 185: 14 16 16 14 17 14 16 30 17 14 17 N SD: 1.3463 c. M: 2.9067 c. 186: 14 16 16 14 17 14 17 30 17 14 17 N S SD: 1.3383 c. M: 2.6951 c. 190: 14 17 16 14 18 14 17 31 17 14 18 N SD: 1.5475 c. M: 2.4749 c. 197: 15 17 17 15 18 15 17 32 18 15 18 N SD: 1.4592 c. M: 2.5445 c. 198: 15 17 17 15 18 15 18 32 18 15 18 N S SD: 1.2854 c. M:-2.6404 c. 202: 15 17 18 15 19 15 18 33 18 15 19 N SD: 1.5167 c. M: 3.8080 c. 205: 15 18 18 15 19 16 18 33 19 15 19 N SD: 1.4927 c. M:-2.4843 c. 210: 16 18 18 16 19 16 19 34 19 15 20 N SD: 1.2640 c. M: 2.5544 c. 213: 16 18 19 16 20 16 19 34 19 16 20 N SD: 1.4278 c. M: 2.3577 c. 214: 16 19 18 16 20 16 19 35 19 16 20 N SD: 0.9824 c. M:-2.3547 c. 222: 17 19 19 17 20 17 20 36 20 16 21 N SD: 1.2422 c. M: 2.1720 c. 226: 17 20 19 17 21 17 20 37 20 17 21 N SD: 0.9713 c. M:-2.5532 c. 230: 17 20 20 17 22 17 21 37 20 18 21 N SD: 1.4513 c. M:-2.1697 c. 236: 18 20 20 18 22 18 21 38 21 18 22 N S SD: 1.2370 c. M: 2.5978 c. 237: 18 20 21 18 22 17 22 38 21 18 22 N SD: 1.3635 c. M:-2.1354 c. 238: 18 20 21 18 22 18 21 39 21 18 22 N SD: 1.0117 c. M: 2.3103 c. 245: 18 22 21 18 23 18 22 40 22 18 23 N SD: 1.2304 c. M: 2.0617 c. 248: 19 21 21 19 23 19 22 40 22 19 23 N S SD: 1.1557 c. M: 2.3517 c. 250: 19 21 22 19 23 19 22 41 22 19 23 N SD: 1.1279 c. M:-2.0412 c. 255: 19 22 22 19 24 19 23 41 23 19 24 N S SD: 1.0356 c. M: 1.8557 c. 267: 20 23 23 20 25 20 24 43 24 20 25 N S SD: 0.6876 c. M: 1.2212 c. 279: 21 24 24 21 26 21 25 45 25 21 26 N S SD: 0.4304 c. M: 0.7388 c. 291: 22 25 25 22 27 22 26 47 26 22 27 N S SD: 0.3747 c. M: 0.6058 c. 322: 24 28 28 24 30 24 29 52 29 24 30 N S SD: 0.3464 c. M: 0.7840 c. 334: 25 29 29 25 31 25 30 54 30 25 31 N S SD: 0.3060 c. M:-0.6906 c. 601: 45 52 52 45 56 45 54 97 54 45 56 N S SD: 0.2313 c. M: 0.3836 c. 613: 46 53 53 46 57 46 55 99 55 46 57 N S SD: 0.1307 c. M: 0.2850 c. 947: 71 82 82 71 88 71 85 153 85 71 88 N S SD: 0.1467 c. M:-0.2695 c. 1214: 91 105 105 91 113 91 109 196 109 91 113 N S SD: 0.1710 c. M: 0.2930 c. 1238: 93 107 107 93 115 93 111 200 111 93 115 N S SD: 0.1277 c. M: 0.2771 c. 1436: 108 124 124 108 134 107 129 232 129 107 134 N S SD: 0.1188 c. M:-0.2522 c. 1448: 109 125 125 109 135 108 130 234 130 108 135 N S SD: 0.1136 c. M:-0.2545 c. 1560: 117 135 135 117 145 117 140 252 140 117 145 N S SD: 0.1298 c. M: 0.2385 c. 1715: 129 148 148 129 160 128 154 277 154 128 160 N S SD: 0.1019 c. M: 0.2221 c. 1727: 130 149 149 130 161 129 155 279 155 129 161 N S SD: 0.0767 c. M: 0.1390 c. 2049: 154 177 177 154 191 153 184 331 184 153 191 N S SD: 0.0608 c. M: 0.1282 c. 2061: 155 178 178 155 192 154 185 333 185 154 192 N S SD: 0.0458 c. M:-0.0940 c. 2340: 176 202 202 176 218 175 210 378 210 175 218 N S SD: 0.0424 c. M: 0.0771 c. 2352: 177 203 203 177 219 176 211 380 211 176 219 N S SD: 0.0405 c. M:-0.0811 c.
FIT/HARMONIC
1 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 4 S SD: 2.4971 cents 3 x x x x 4 x x 5 x x 6 S SD: 2.1856 cents 4 x x x 5 x x 6 x 7 x 8 S SD: 7.5291 cents 5 x x 6 x x 7 x 8:9 x 10 S SD: 16.3452 cents 6 x x 7 x 8 x 9:10 x 11:12 S SD: 8.3675 cents 7 x 8 x 9 x 10 x 12 x 13:14 S SD: 13.4348 cents 8 x 9 x 10 x 11:12:13:14:15:16 S SD: 8.8113 cents 9 x 10 x 11:12:13 x 15:16:17:18 SD: 8.1152 cents 10 x 11:12 x 13:14:15:17:18:19:20 SD: 7.8178 cents 11 x 12:13:14:15 x 16:18:20:21:22 S SD: 11.2905 cents 12:13 x 14:15:16:17:18:20:21:23:24 SD: 7.6573 cents 13:14 x 15:16:17:18:19:22:23:24:26 SD: 9.7251 cents 14:15:16:17:18:19:20:21:23:25:26:28 SD: 8.5930 cents 15:16:17:18:19:20:21:22:25:27:28:30 SD: 5.3284 cents 17:18:19:20:21:23:24:25:28:30:32:34 SD: 5.2264 cents 18:19:20:21:23:24:25:27:30:32:34:36 SD: 5.0474 cents 22:23:25:26:28:29:31:33:37:39:41:44 SD: 4.6597 cents 24:25:27:29:30:32:34:36:40:43:45:48 SD: 3.8253 cents 27:28:30:32:34:36:38:40:45:48:51:54 S SD: 3.5283 cents 32:34:36:38:40:43:45:48:54:57:60:64 SD: 2.4381 cents 36:38:40:43:45:48:51:54:60:64:68:72 SD: 2.3597 cents 42:44:47:50:53:56:59:63:70:75:79:84 SD: 1.9600 cents 52:55:58:62:65:69:73:78:87:93:98:104 SD: 1.7911 cents 54:57:60:64:68:72:76:81:90:96:101:108 SD: 1.7764 cents 57:60:64:68:71:76:80:85:95:101:107:114 SD: 1.6034 cents 59:62:66:70:74:79:83:88:99:105:111:118 SD: 1.1657 cents 87:92:97:103:109:116:122:130:146:155:163:174 SD: 1.1531 cents 91:96:102:108:114:121:128:136:152:162:171:182 SD: 0.8572 cents 95:100:106:113:119:127:134:142:159:169:178:190 SD: 0.8467 cents 111:117:124:132:139:148:156:166:186:198:208:222 SD: 0.5607 cents 128:135:143:152:160:171:180:191:214:228:240:256 SD: 0.5237 cents 150:158:168:178:188:200:211:224:251:267:281:300 SD: 0.5084 cents 167:176:187:198:209:223:235:250:279:297:313:334 SD: 0.4886 cents 168:177:188:200:210:224:236:251:281:299:315:336 SD: 0.4819 cents 170:179:190:202:213:227:239:254:284:303:319:340 SD: 0.4730 cents 183:193:205:217:229:244:257:274:306:326:343:366 SD: 0.4664 cents 186:196:208:221:233:248:261:278:311:331:349:372 SD: 0.4095 cents 192:202:215:228:240:256:270:287:321:342:360:384 SD: 0.3782 cents 224:236:251:266:280:299:315:335:375:399:420:448 SD: 0.3600 cents 242:255:271:287:303:323:340:362:405:431:454:484 SD: 0.3400 cents 246:259:275:292:308:328:346:368:412:438:461:492 SD: 0.3328 cents 260:274:291:309:325:347:365:389:435:463:488:520 SD: 0.3316 cents 262:276:293:311:328:350:368:392:438:466:491:524 SD: 0.3098 cents 263:277:294:312:329:351:370:393:440:468:493:526 SD: 0.2951 cents 278:293:311:330:348:371:391:416:465:495:521:556 SD: 0.2099 cents 373:393:417:443:467:498:524:558:624:664:699:746 SD: 0.2050 cents 395:416:442:469:494:527:555:591:661:703:741:790 SD: 0.1639 cents 431:454:482:512:539:575:606:645:721:767:808:862 SD: 0.1584 cents 446:470:499:530:558:595:627:667:746:794:836:892 SD: 0.1517 cents 490:516:548:582:613:654:689:733:820:872:919:980 SD: 0.1473 cents 506:533:566:601:633:675:711:757:846:901:949:1012 SD: 0.1310 cents 523:551:585:621:654:698:735:782:875:931:981:1046 SD: 0.1101 cents 565:595:632:671:707:754:794:845:945:1006:1059:1130 SD: 0.1009 cents