Scala analysis: mean2-5_19
2/5-comma meantone, Gb-B# (19)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 53.467 cents 53.467400 2: 133.238 cents 133.237570 3: 186.705 cents 186.704970 4: 240.172 cents 240.172370 5: 319.943 cents 319.942540 6: 373.410 cents 373.409940 7: 426.877 cents 426.877340 8: 506.648 cents 506.647510 9: 560.115 cents 560.114910 10: 639.885 cents 639.885090 11: 693.352 cents 693.352490 12: 746.820 cents 746.819880 13: 826.590 cents 826.590060 14: 880.057 cents 880.057460 15: 933.525 cents 933.524850 16: 1013.295 cents 1013.295030 17: 1066.762 cents 1066.762430 18: 1120.230 cents 1120.229820 19: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 79.7702 cents 79.7702 1: 53.4674 cents 53.4674 2: 79.7702 cents 79.7702 3: 53.4674 cents 53.4674 4: 53.4674 cents 53.4674 5: 79.7702 cents 79.7702 6: 53.4674 cents 53.4674 7: 53.4674 cents 53.4674 8: 79.7702 cents 79.7702 9: 53.4674 cents 53.4674 10: 79.7702 cents 79.7702 11: 53.4674 cents 53.4674 12: 53.4674 cents 53.4674 13: 79.7702 cents 79.7702 14: 53.4674 cents 53.4674 15: 53.4674 cents 53.4674 16: 79.7702 cents 79.7702 17: 53.4674 cents 53.4674 18: 53.4674 cents 53.4674 19: 79.7702 cents 79.7702
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 53.46740 cents 1: 7 79.77017 cents 2: 5 106.93480 cents 2: 14 133.23757 cents 3: 17 186.70497 cents 3: 2 213.00775 cents 4: 10 240.17237 cents 4: 9 266.47514 cents 5: 3 293.63977 cents 5: 16 319.94254 cents 6: 15 373.40994 cents 6: 4 399.71272 cents 7: 8 426.87734 cents 7: 11 453.18011 cents 8: 1 480.34473 cents 8: 18 506.64751 cents 9: 13 560.11491 cents 9: 6 586.41769 cents 10: 6 613.58231 cents 10: 13 639.88509 cents 11: 18 693.35249 cents 11: 1 719.65527 cents 12: 11 746.81988 cents 12: 8 773.12266 cents 13: 4 800.28728 cents 13: 15 826.59006 cents 14: 16 880.05746 cents 14: 3 906.36023 cents 15: 9 933.52485 cents 15: 10 959.82763 cents 16: 2 986.99225 cents 16: 17 1013.29503 cents 17: 14 1066.76243 cents 17: 5 1093.06520 cents 18: 7 1120.22982 cents 18: 12 1146.53260 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 53.5 133.2 186.7 240.2 319.9 373.4 426.9 506.6 560.1 639.9 693.4 746.8 826.6 880.1 933.5 1013.3 1066.8 1120.2 1200.0 53.5 : 79.8 133.2 186.7 266.5 319.9 373.4 453.2 506.6 586.4 639.9 693.4 773.1 826.6 880.1 959.8 1013.3 1066.8 1146.5 1200.0 133.2 : 53.5 106.9 186.7 240.2 293.6 373.4 426.9 506.6 560.1 613.6 693.4 746.8 800.3 880.1 933.5 987.0 1066.8 1120.2 1200.0 186.7 : 53.5 133.2 186.7 240.2 319.9 373.4 453.2 506.6 560.1 639.9 693.4 746.8 826.6 880.1 933.5 1013.3 1066.8 1146.5 1200.0 240.2 : 79.8 133.2 186.7 266.5 319.9 399.7 453.2 506.6 586.4 639.9 693.4 773.1 826.6 880.1 959.8 1013.3 1093.1 1146.5 1200.0 319.9 : 53.5 106.9 186.7 240.2 319.9 373.4 426.9 506.6 560.1 613.6 693.4 746.8 800.3 880.1 933.5 1013.3 1066.8 1120.2 1200.0 373.4 : 53.5 133.2 186.7 266.5 319.9 373.4 453.2 506.6 560.1 639.9 693.4 746.8 826.6 880.1 959.8 1013.3 1066.8 1146.5 1200.0 426.9 : 79.8 133.2 213.0 266.5 319.9 399.7 453.2 506.6 586.4 639.9 693.4 773.1 826.6 906.4 959.8 1013.3 1093.1 1146.5 1200.0 506.6 : 53.5 133.2 186.7 240.2 319.9 373.4 426.9 506.6 560.1 613.6 693.4 746.8 826.6 880.1 933.5 1013.3 1066.8 1120.2 1200.0 560.1 : 79.8 133.2 186.7 266.5 319.9 373.4 453.2 506.6 560.1 639.9 693.4 773.1 826.6 880.1 959.8 1013.3 1066.8 1146.5 1200.0 639.9 : 53.5 106.9 186.7 240.2 293.6 373.4 426.9 480.3 560.1 613.6 693.4 746.8 800.3 880.1 933.5 987.0 1066.8 1120.2 1200.0 693.4 : 53.5 133.2 186.7 240.2 319.9 373.4 426.9 506.6 560.1 639.9 693.4 746.8 826.6 880.1 933.5 1013.3 1066.8 1146.5 1200.0 746.8 : 79.8 133.2 186.7 266.5 319.9 373.4 453.2 506.6 586.4 639.9 693.4 773.1 826.6 880.1 959.8 1013.3 1093.1 1146.5 1200.0 826.6 : 53.5 106.9 186.7 240.2 293.6 373.4 426.9 506.6 560.1 613.6 693.4 746.8 800.3 880.1 933.5 1013.3 1066.8 1120.2 1200.0 880.1 : 53.5 133.2 186.7 240.2 319.9 373.4 453.2 506.6 560.1 639.9 693.4 746.8 826.6 880.1 959.8 1013.3 1066.8 1146.5 1200.0 933.5 : 79.8 133.2 186.7 266.5 319.9 399.7 453.2 506.6 586.4 639.9 693.4 773.1 826.6 906.4 959.8 1013.3 1093.1 1146.5 1200.0 1013.3: 53.5 106.9 186.7 240.2 319.9 373.4 426.9 506.6 560.1 613.6 693.4 746.8 826.6 880.1 933.5 1013.3 1066.8 1120.2 1200.0 1066.8: 53.5 133.2 186.7 266.5 319.9 373.4 453.2 506.6 560.1 639.9 693.4 773.1 826.6 880.1 959.8 1013.3 1066.8 1146.5 1200.0 1120.2: 79.8 133.2 213.0 266.5 319.9 399.7 453.2 506.6 586.4 639.9 719.7 773.1 826.6 906.4 959.8 1013.3 1093.1 1146.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.4674 .. 79.7702 cents 26.30277 cents 53.46740 cents 2: 106.9348 .. 133.2376 cents 26.30277 cents 27.16463 cents 3: 186.7050 .. 213.0078 cents 26.30278 cents 53.46740 cents 4: 240.1724 .. 266.4751 cents 26.30277 cents 27.16462 cents 5: 293.6398 .. 319.9425 cents 26.30277 cents 27.16463 cents 6: 373.4099 .. 399.7127 cents 26.30278 cents 53.46740 cents 7: 426.8773 .. 453.1801 cents 26.30277 cents 27.16462 cents 8: 480.3447 .. 506.6475 cents 26.30278 cents 27.16462 cents 9: 560.1149 .. 586.4177 cents 26.30278 cents 53.46740 cents 10: 613.5823 .. 639.8851 cents 26.30278 cents 27.16462 cents 11: 693.3525 .. 719.6553 cents 26.30278 cents 53.46740 cents 12: 746.8199 .. 773.1227 cents 26.30278 cents 27.16461 cents 13: 800.2873 .. 826.5901 cents 26.30278 cents 27.16462 cents 14: 880.0575 .. 906.3602 cents 26.30277 cents 53.46740 cents 15: 933.5248 .. 959.8276 cents 26.30278 cents 27.16462 cents 16: 986.9923 .. 1013.2950 cents 26.30278 cents 27.16462 cents 17: 1066.7624 .. 1093.0652 cents 26.30277 cents 53.46740 cents 18: 1120.2298 .. 1146.5326 cents 26.30278 cents 27.16462 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 53.46739 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 79.77017 cents Average / Smallest step : 1.181241 Largest / Average step : 1.263028 Largest / Smallest step : 1.491941 Median interval of one step : 53.46740 cents, amount: 12 Most common interval of one step : 53.46740 cents, amount: 12 Least squares average step : 62.80648 cents, oct.: 1193.32314 cents Scale is strictly proper Scale has Myhill's property chromas: 26.30277 cents and 27.16463 cents, ratio: 1.032767 generators: 8 of 506.64751 cents and 11 of 693.35249 cents ET pair of linear temperament : 19&45 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1369-tone equal temperament with octave 2/1 degrees: 61 152 213 274 365 426 487 578 639 730 791 852 943 1004 1065 1156 1217 1278 1369 generators: 578 and 791 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAABABAABAABAAB Step pattern size order : SLSSLSSLSLSSLSSLSSL Scale is a Constant Structure, by a margin of 27.16461 cents Ratio Whole / Half tone : 1.401294 Scale diversity : 1.189025 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.605458 Rothenberg efficiency : 0.701754 redundancy: 0.298246 Efficiency x scale size : 13.333333 Number of different interval sizes : 36 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 26.30277 cents Most common intervals : 506.64751 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 506.648 1013.295 cents Most common triad is 0.0 506.648 693.352 cents, amount: 17 Number of recognisable fifths : 19, average 694.7368 cents Number of appreciable fifths : 18, average 693.3525 cents Scale contains two identical disjunct "tetrachords" of 9 notes Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 13 = 68.4211% Limited inverse transpositions : 9 Inversional symmetry on degrees : 14 Inversional symmetry on intervals : 4-5 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.6453 c. M:-16.6123 c. 26: 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 1 2 P M ME S SD: 6.5247 c. M: 12.5375 c. 45: 2 3 2 2 3 2 2 3 2 3 2 2 3 2 2 3 2 2 3 SP M ME S SD: 0.1196 c. M: 0.2298 c. 739: 33 49 33 33 49 33 33 49 33 49 33 33 49 33 33 49 33 33 49 SP M DE S SD: 0.1057 c. M:-0.2032 c. 784: 35 52 35 35 52 35 35 52 35 52 35 35 52 35 35 52 35 35 52 SP M DE S SD: 0.0928 c. M:-0.1783 c. 829: 37 55 37 37 55 37 37 55 37 55 37 37 55 37 37 55 37 37 55 SP M DE S SD: 0.0813 c. M:-0.1562 c. 874: 39 58 39 39 58 39 39 58 39 58 39 39 58 39 39 58 39 39 58 SP M DE S SD: 0.0709 c. M:-0.1363 c. 919: 41 61 41 41 61 41 41 61 41 61 41 41 61 41 41 61 41 41 61 SP M DE S SD: 0.0616 c. M:-0.1184 c. 964: 43 64 43 43 64 43 43 64 43 64 43 43 64 43 43 64 43 43 64 SP M DE S SD: 0.0531 c. M:-0.1021 c. 1009: 45 67 45 45 67 45 45 67 45 67 45 45 67 45 45 67 45 45 67 SP M DE S SD: 0.0454 c. M:-0.0873 c. 1054: 47 70 47 47 70 47 47 70 47 70 47 47 70 47 47 70 47 47 70 SP M DE S SD: 0.0384 c. M:-0.0738 c. 1099: 49 73 49 49 73 49 49 73 49 73 49 49 73 49 49 73 49 49 73 SP M DE S SD: 0.0319 c. M:-0.0614 c. 1144: 51 76 51 51 76 51 51 76 51 76 51 51 76 51 51 76 51 51 76 SP M DE S SD: 0.0260 c. M:-0.0499 c. 1189: 53 79 53 53 79 53 53 79 53 79 53 53 79 53 53 79 53 53 79 SP M DE S SD: 0.0205 c. M:-0.0393 c. 1234: 55 82 55 55 82 55 55 82 55 82 55 55 82 55 55 82 55 55 82 SP M DE S SD: 0.0154 c. M:-0.0295 c. 1279: 57 85 57 57 85 57 57 85 57 85 57 57 85 57 57 85 57 57 85 SP M DE S SD: 0.0106 c. M:-0.0204 c. 1324: 59 88 59 59 88 59 59 88 59 88 59 59 88 59 59 88 59 59 88 SP M DE S SD: 0.0062 c. M:-0.0119 c. 1369: 61 91 61 61 91 61 61 91 61 91 61 61 91 61 61 91 61 61 91 SP M DE S SD: 0.0020 c. M:-0.0039 c. 1414: 63 94 63 63 94 63 63 94 63 94 63 63 94 63 63 94 63 63 94 SP M DE S SD: 0.0018 c. M: 0.0035 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 4.3013 cents 3 .. 6 match: 3 H SD: 3.2060 cents 4 .. 8 match: 4 H SD: 9.6394 cents 5 .. 10 match: 5 H SD: 5.3109 cents 6 .. 12 match: 6 H SD: 5.7302 cents 7 .. 14 match: 7 H SD: 6.3036 cents 8 .. 16 match: 8 H SD: 6.2710 cents 9 .. 18 match: 9 H SD: 4.7000 cents 10 .. 20 match: 10 H SD: 4.7963 cents 11 .. 22 match: 11 H SD: 5.2252 cents 12 .. 24 match: 12 H SD: 5.8830 cents 13 .. 26 match: 13 H SD: 4.4473 cents 14 .. 28 match: 14 H SD: 4.3779 cents 15 .. 30 match: 15 H SD: 4.0504 cents 16 .. 32 match: 15 SD: 5.2525 cents 17 .. 34 match: 14 SD: 5.7793 cents 18 .. 36 match: 17 S SD: 3.9847 cents 19 .. 38 match: 16 SD: 4.8292 cents 20 .. 40 match: 18 S SD: 3.4807 cents 21 .. 42 match: 18 S SD: 3.2229 cents 22 .. 44 match: 18 SD: 4.2341 cents 23 .. 46 match: 17 SD: 3.8739 cents 24 .. 48 match: 19 SD: 2.8038 cents 26 .. 52 match: 19 SD: 2.3330 cents 29 .. 58 match: 19 SD: 2.2290 cents 33 .. 66 match: 19 SD: 2.0393 cents 35 .. 70 match: 19 SD: 1.8460 cents 39 .. 78 match: 19 SD: 1.8311 cents 45 .. 90 match: 19 SD: 1.7914 cents 47 .. 94 match: 19 SD: 1.7307 cents 49 .. 98 match: 19 SD: 1.6996 cents 50 .. 100 match: 19 SD: 1.5949 cents 53 .. 106 match: 19 SD: 1.2486 cents 54 .. 108 match: 19 SD: 1.2120 cents 60 .. 120 match: 19 SD: 1.2079 cents 61 .. 122 match: 19 SD: 1.1744 cents 62 .. 124 match: 19 SD: 1.1695 cents 63 .. 126 match: 19 SD: 1.0759 cents 65 .. 130 match: 19 SD: 1.0493 cents 74 .. 148 match: 19 SD: 0.9161 cents 87 .. 174 match: 19 SD: 0.7227 cents 89 .. 178 match: 19 SD: 0.7004 cents 100 .. 200 match: 19 SD: 0.6381 cents 121 .. 242 match: 19 SD: 0.5748 cents 123 .. 246 match: 19 SD: 0.5712 cents 128 .. 256 match: 19 SD: 0.5580 cents 133 .. 266 match: 19 SD: 0.5319 cents 147 .. 294 match: 19 SD: 0.4897 cents 150 .. 300 match: 19 SD: 0.4587 cents 154 .. 308 match: 19 SD: 0.4443 cents 157 .. 314 match: 19 SD: 0.4364 cents 162 .. 324 match: 19 SD: 0.4136 cents 167 .. 334 match: 19 SD: 0.3979 cents 183 .. 366 match: 19 SD: 0.3583 cents 186 .. 372 match: 19 SD: 0.3400 cents 201 .. 402 match: 19 SD: 0.3197 cents 217 .. 434 match: 19 SD: 0.3151 cents 221 .. 442 match: 19 SD: 0.2778 cents 261 .. 522 match: 19 SD: 0.2764 cents 262 .. 524 match: 19 SD: 0.2302 cents 290 .. 580 match: 19 SD: 0.2224 cents 291 .. 582 match: 19 SD: 0.2088 cents 315 .. 630 match: 19 SD: 0.1750 cents 376 .. 752 match: 19 SD: 0.1738 cents 385 .. 770 match: 19 SD: 0.1724 cents 411 .. 822 match: 19 SD: 0.1642 cents 412 .. 824 match: 19 SD: 0.1490 cents 465 .. 930 match: 19 SD: 0.1450 cents 477 .. 954 match: 19 SD: 0.1302 cents 508 .. 1016 match: 19 SD: 0.1295 cents 512 .. 1024 match: 19 SD: 0.1113 cents 536 .. 1072 match: 19 SD: 0.1026 cents