Scala analysis: julius22
Julius[22] hobbit (176/175&896/891) in POTE tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 59.003 cents 59.003340 2: 104.602 cents 104.601910 3: 163.605 cents 163.605240 4: 209.204 cents 209.203820 5: 286.194 cents 286.194280 6: 313.806 cents 313.805720 7: 390.796 cents 390.796180 8: 436.395 cents 436.394760 9: 495.398 cents 495.398090 10: 540.997 cents 540.996660 11: 600.000 cents 600.000000 12: 659.003 cents 659.003340 13: 704.602 cents 704.601910 14: 763.605 cents 763.605240 15: 809.204 cents 809.203820 16: 886.194 cents 886.194280 17: 913.806 cents 913.805720 18: 990.796 cents 990.796180 19: 1036.395 cents 1036.394760 20: 1095.398 cents 1095.398090 21: 1140.997 cents 1140.996660 22: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 59.0033 cents 59.0033 1: 59.0033 cents 59.0033 2: 45.5986 cents 45.5986 3: 59.0033 cents 59.0033 4: 45.5986 cents 45.5986 5: 76.9905 cents 76.9905 6: 27.6114 cents 27.6114 7: 76.9905 cents 76.9905 8: 45.5986 cents 45.5986 9: 59.0033 cents 59.0033 10: 45.5986 cents 45.5986 11: 59.0033 cents 59.0033 12: 59.0033 cents 59.0033 13: 45.5986 cents 45.5986 14: 59.0033 cents 59.0033 15: 45.5986 cents 45.5986 16: 76.9905 cents 76.9905 17: 27.6114 cents 27.6114 18: 76.9905 cents 76.9905 19: 45.5986 cents 45.5986 20: 59.0033 cents 59.0033 21: 45.5986 cents 45.5986 22: 59.0033 cents 59.0033
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 27.61144 cents 1: 8 45.59857 cents 1: 8 59.00334 cents 1: 4 76.99046 cents 2: 16 104.60191 cents 2: 2 118.00668 cents 2: 4 122.58904 cents 3: 8 150.20048 cents 3: 8 163.60524 cents 3: 6 181.59237 cents 4: 10 209.20382 cents 4: 4 222.60858 cents 4: 8 227.19094 cents 5: 4 254.80238 cents 5: 8 268.20716 cents 5: 2 272.78952 cents 5: 8 286.19428 cents 6: 8 313.80572 cents 6: 2 327.21048 cents 6: 8 331.79284 cents 6: 4 345.19762 cents 7: 8 372.80906 cents 7: 4 377.39142 cents 7: 10 390.79618 cents 8: 6 418.40763 cents 8: 8 436.39476 cents 8: 8 449.79952 cents 9: 4 477.41096 cents 9: 2 481.99332 cents 9: 16 495.39809 cents 10: 4 523.00954 cents 10: 8 540.99666 cents 10: 8 554.40143 cents 10: 2 572.38856 cents 11: 22 600.00000 cents 12: 2 627.61144 cents 12: 8 645.59857 cents 12: 8 659.00334 cents 12: 4 676.99046 cents 13: 16 704.60191 cents 13: 2 718.00668 cents 13: 4 722.58904 cents 14: 8 750.20048 cents 14: 8 763.60524 cents 14: 6 781.59237 cents 15: 10 809.20382 cents 15: 4 822.60858 cents 15: 8 827.19094 cents 16: 4 854.80238 cents 16: 8 868.20716 cents 16: 2 872.78952 cents 16: 8 886.19428 cents 17: 8 913.80572 cents 17: 2 927.21048 cents 17: 8 931.79284 cents 17: 4 945.19762 cents 18: 8 972.80906 cents 18: 4 977.39142 cents 18: 10 990.79618 cents 19: 6 1018.40763 cents 19: 8 1036.39476 cents 19: 8 1049.79952 cents 20: 4 1077.41096 cents 20: 2 1081.99332 cents 20: 16 1095.39809 cents 21: 4 1123.00954 cents 21: 8 1140.99666 cents 21: 8 1154.40143 cents 21: 2 1172.38856 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.28571 = 23/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0.0 : 59.0 104.6 163.6 209.2 286.2 313.8 390.8 436.4 495.4 541.0 600.0 659.0 704.6 763.6 809.2 886.2 913.8 990.8 1036.4 1095.4 1141.0 1200.0 59.0 : 45.6 104.6 150.2 227.2 254.8 331.8 377.4 436.4 482.0 541.0 600.0 645.6 704.6 750.2 827.2 854.8 931.8 977.4 1036.4 1082.0 1141.0 1200.0 104.6 : 59.0 104.6 181.6 209.2 286.2 331.8 390.8 436.4 495.4 554.4 600.0 659.0 704.6 781.6 809.2 886.2 931.8 990.8 1036.4 1095.4 1154.4 1200.0 163.6 : 45.6 122.6 150.2 227.2 272.8 331.8 377.4 436.4 495.4 541.0 600.0 645.6 722.6 750.2 827.2 872.8 931.8 977.4 1036.4 1095.4 1141.0 1200.0 209.2 : 77.0 104.6 181.6 227.2 286.2 331.8 390.8 449.8 495.4 554.4 600.0 677.0 704.6 781.6 827.2 886.2 931.8 990.8 1049.8 1095.4 1154.4 1200.0 286.2 : 27.6 104.6 150.2 209.2 254.8 313.8 372.8 418.4 477.4 523.0 600.0 627.6 704.6 750.2 809.2 854.8 913.8 972.8 1018.4 1077.4 1123.0 1200.0 313.8 : 77.0 122.6 181.6 227.2 286.2 345.2 390.8 449.8 495.4 572.4 600.0 677.0 722.6 781.6 827.2 886.2 945.2 990.8 1049.8 1095.4 1172.4 1200.0 390.8 : 45.6 104.6 150.2 209.2 268.2 313.8 372.8 418.4 495.4 523.0 600.0 645.6 704.6 750.2 809.2 868.2 913.8 972.8 1018.4 1095.4 1123.0 1200.0 436.4 : 59.0 104.6 163.6 222.6 268.2 327.2 372.8 449.8 477.4 554.4 600.0 659.0 704.6 763.6 822.6 868.2 927.2 972.8 1049.8 1077.4 1154.4 1200.0 495.4 : 45.6 104.6 163.6 209.2 268.2 313.8 390.8 418.4 495.4 541.0 600.0 645.6 704.6 763.6 809.2 868.2 913.8 990.8 1018.4 1095.4 1141.0 1200.0 541.0 : 59.0 118.0 163.6 222.6 268.2 345.2 372.8 449.8 495.4 554.4 600.0 659.0 718.0 763.6 822.6 868.2 945.2 972.8 1049.8 1095.4 1154.4 1200.0 600.0 : 59.0 104.6 163.6 209.2 286.2 313.8 390.8 436.4 495.4 541.0 600.0 659.0 704.6 763.6 809.2 886.2 913.8 990.8 1036.4 1095.4 1141.0 1200.0 659.0 : 45.6 104.6 150.2 227.2 254.8 331.8 377.4 436.4 482.0 541.0 600.0 645.6 704.6 750.2 827.2 854.8 931.8 977.4 1036.4 1082.0 1141.0 1200.0 704.6 : 59.0 104.6 181.6 209.2 286.2 331.8 390.8 436.4 495.4 554.4 600.0 659.0 704.6 781.6 809.2 886.2 931.8 990.8 1036.4 1095.4 1154.4 1200.0 763.6 : 45.6 122.6 150.2 227.2 272.8 331.8 377.4 436.4 495.4 541.0 600.0 645.6 722.6 750.2 827.2 872.8 931.8 977.4 1036.4 1095.4 1141.0 1200.0 809.2 : 77.0 104.6 181.6 227.2 286.2 331.8 390.8 449.8 495.4 554.4 600.0 677.0 704.6 781.6 827.2 886.2 931.8 990.8 1049.8 1095.4 1154.4 1200.0 886.2 : 27.6 104.6 150.2 209.2 254.8 313.8 372.8 418.4 477.4 523.0 600.0 627.6 704.6 750.2 809.2 854.8 913.8 972.8 1018.4 1077.4 1123.0 1200.0 913.8 : 77.0 122.6 181.6 227.2 286.2 345.2 390.8 449.8 495.4 572.4 600.0 677.0 722.6 781.6 827.2 886.2 945.2 990.8 1049.8 1095.4 1172.4 1200.0 990.8 : 45.6 104.6 150.2 209.2 268.2 313.8 372.8 418.4 495.4 523.0 600.0 645.6 704.6 750.2 809.2 868.2 913.8 972.8 1018.4 1095.4 1123.0 1200.0 1036.4: 59.0 104.6 163.6 222.6 268.2 327.2 372.8 449.8 477.4 554.4 600.0 659.0 704.6 763.6 822.6 868.2 927.2 972.8 1049.8 1077.4 1154.4 1200.0 1095.4: 45.6 104.6 163.6 209.2 268.2 313.8 390.8 418.4 495.4 541.0 600.0 645.6 704.6 763.6 809.2 868.2 913.8 990.8 1018.4 1095.4 1141.0 1200.0 1141.0: 59.0 118.0 163.6 222.6 268.2 345.2 372.8 449.8 495.4 554.4 600.0 659.0 718.0 763.6 822.6 868.2 945.2 972.8 1049.8 1095.4 1154.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.6114 .. 76.9905 cents 49.37902 cents 27.61144 cents 2: 104.6019 .. 122.5890 cents 17.98713 cents 27.61145 cents 3: 150.2005 .. 181.5924 cents 31.39189 cents 27.61144 cents 4: 209.2038 .. 227.1909 cents 17.98712 cents 27.61145 cents 5: 254.8024 .. 286.1943 cents 31.39190 cents 27.61144 cents 6: 313.8057 .. 345.1976 cents 31.39190 cents 27.61144 cents 7: 372.8091 .. 390.7962 cents 17.98712 cents 27.61144 cents 8: 418.4076 .. 449.7995 cents 31.39189 cents 27.61145 cents 9: 477.4110 .. 495.3981 cents 17.98713 cents 27.61144 cents 10: 523.0095 .. 572.3886 cents 49.37902 cents 27.61145 cents 11: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 27.61144 cents 12: 627.6114 .. 676.9905 cents 49.37902 cents 27.61144 cents 13: 704.6019 .. 722.5890 cents 17.98713 cents 27.61145 cents 14: 750.2005 .. 781.5924 cents 31.39189 cents 27.61144 cents 15: 809.2038 .. 827.1909 cents 17.98712 cents 27.61145 cents 16: 854.8024 .. 886.1943 cents 31.39190 cents 27.61144 cents 17: 913.8057 .. 945.1976 cents 31.39190 cents 27.61144 cents 18: 972.8091 .. 990.7962 cents 17.98712 cents 27.61144 cents 19: 1018.4076 .. 1049.7995 cents 31.39189 cents 27.61145 cents 20: 1077.4110 .. 1095.3981 cents 17.98713 cents 27.61144 cents 21: 1123.0095 .. 1172.3886 cents 49.37902 cents 27.61145 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 27.61144 cents, class 1 Average step (divided formal octave): 54.5455 cents Largest one step interval : 76.99046 cents Average / Smallest step : 1.975466 Largest / Average step : 1.411492 Largest / Smallest step : 2.788354 Median interval of one step : 59.00334 cents, amount: 8 Least squares average step : 54.54805 cents, oct.: 1200.05710 cents Scale is strictly proper Scale has 2 repeating blocks of 11 notes Step pattern alph. order: ABABCDCBABAABABCDCBABA Step pattern size order : CBCBDADBCBCCBCBDADBCBC Scale is a Constant Structure, by a margin of 27.61144 cents Scale diversity : 1.308549 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.506210 Number of different interval sizes : 69 = 3.28571 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.28571 = 23/7 Median interval variety : 3 Lowest interval variety : 1 Smallest interval difference : 4.58236 cents Most common intervals : 600.00000 cents & inv., amount: 22 Number of recognisable fifths : 18, average 706.0913 cents Number of appreciable fifths : 16, average 704.6019 cents Scale contains two identical disjunct "tetrachords" of 10 notes Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 22 = 100.0000% Limited transpositions : 11 Limited inverse transpositions : 11 Inversional symmetry on degrees : 0 11 Inversional symmetry on intervals : 5-6 16-17 -- Rational properties --
FIT/MODE
22: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.4099 c. M:-13.4670 c. 34: 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 P B ME I SD: 7.6596 c. M:-12.8653 c. 38: 2 1 2 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 2 1 2 P B ME I SD: 7.2804 c. M:-11.8488 c. 42: 2 2 2 1 3 1 3 1 2 2 2 2 2 2 1 3 1 3 1 2 2 2 P B D3 I SD: 6.6522 c. M:-9.6838 c. 46: 2 2 2 2 3 1 3 2 2 2 2 2 2 2 2 3 1 3 2 2 2 2 SP B D3 I SD: 4.2151 c. M:-7.0835 c. 58: 3 2 3 2 4 1 4 2 3 2 3 3 2 3 2 4 1 4 2 3 2 3 SP B I SD: 2.4002 c. M:-3.4609 c. 80: 4 3 4 3 5 2 5 3 4 3 4 4 3 4 3 5 2 5 3 4 3 4 SP B I SD: 0.9684 c. M:-1.3948 c. 184: 9 7 9 7 12 4 12 7 9 7 9 9 7 9 7 12 4 12 7 9 7 9 SP B I SD: 0.4888 c. M: 0.7622 c. 206: 10 8 10 8 13 5 13 8 10 8 10 10 8 10 8 13 5 13 8 10 8 10 SP B I SD: 0.5567 c. M: 0.7574 c. 264: 13 10 13 10 17 6 17 10 13 10 13 13 10 13 10 17 6 17 10 13 10 13 SP B I SD: 0.0984 c. M:-0.1694 c. 734: 36 28 36 28 47 17 47 28 36 28 36 36 28 36 28 47 17 47 28 36 28 36 SP B I SD: 0.0939 c. M: 0.1478 c. 998: 49 38 49 38 64 23 64 38 49 38 49 49 38 49 38 64 23 64 38 49 38 49 SP B I SD: 0.0508 c. M: 0.0855 c. 1262: 62 48 62 48 81 29 81 48 62 48 62 62 48 62 48 81 29 81 48 62 48 62 SP B I SD: 0.0330 c. M:-0.0553 c. 1342: 66 51 66 51 86 31 86 51 66 51 66 66 51 66 51 86 31 86 51 66 51 66 SP B I SD: 0.0322 c. M:-0.0542 c. 1526: 75 58 75 58 98 35 98 58 75 58 75 75 58 75 58 98 35 98 58 75 58 75 SP B I SD: 0.0311 c. M:-0.0443 c. 1606: 79 61 79 61 103 37 103 61 79 61 79 79 61 79 61 103 37 103 61 79 61 79 SP B I SD: 0.0195 c. M:-0.0311 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.3235 cents 3 .. 6 match: 3 H SD: 1.0737 cents 4 .. 8 match: 4 H SD: 5.6446 cents 5 .. 10 match: 5 H SD: 5.2256 cents 6 .. 12 match: 6 H SD: 3.9403 cents 7 .. 14 match: 7 H SD: 6.5182 cents 8 .. 16 match: 8 H SD: 5.1179 cents 9 .. 18 match: 9 H SD: 5.0377 cents 10 .. 20 match: 10 H SD: 3.5808 cents 11 .. 22 match: 11 H SD: 5.3009 cents 12 .. 24 match: 12 H SD: 3.8179 cents 13 .. 26 match: 13 H SD: 5.8569 cents 14 .. 28 match: 14 H SD: 4.4373 cents 15 .. 30 match: 14 SD: 3.1411 cents 16 .. 32 match: 16 H SD: 3.6536 cents 17 .. 34 match: 17 H SD: 3.2461 cents 18 .. 36 match: 18 H SD: 3.8331 cents 19 .. 38 match: 17 S SD: 4.0494 cents 20 .. 40 match: 19 S SD: 3.5677 cents 21 .. 42 match: 20 S SD: 3.6397 cents 22 .. 44 match: 18 SD: 2.7592 cents 23 .. 46 match: 20 SD: 3.5963 cents 24 .. 48 match: 21 SD: 2.5813 cents 25 .. 50 match: 20 SD: 3.3874 cents 26 .. 52 match: 19 SD: 3.2364 cents 27 .. 54 match: 20 SD: 2.3171 cents 28 .. 56 match: 21 SD: 2.5683 cents 29 .. 58 match: 22 SD: 2.4995 cents 30 .. 60 match: 22 SD: 2.1012 cents 31 .. 62 match: 21 SD: 2.0858 cents 32 .. 64 match: 21 SD: 1.7467 cents 37 .. 74 match: 21 SD: 2.4098 cents 38 .. 76 match: 22 SD: 2.1357 cents 39 .. 78 match: 22 SD: 1.6839 cents 42 .. 84 match: 21 SD: 2.0513 cents 43 .. 86 match: 22 SD: 1.9231 cents 44 .. 88 match: 22 SD: 1.8282 cents 45 .. 90 match: 22 SD: 1.6694 cents 46 .. 92 match: 22 SD: 1.6459 cents 48 .. 96 match: 22 SD: 1.5205 cents 49 .. 98 match: 22 SD: 1.2881 cents 52 .. 104 match: 22 SD: 1.2492 cents 60 .. 120 match: 22 SD: 0.8314 cents 79 .. 158 match: 22 SD: 0.7376 cents 84 .. 168 match: 22 SD: 0.7103 cents 94 .. 188 match: 22 SD: 0.6815 cents 109 .. 218 match: 22 SD: 0.6445 cents 111 .. 222 match: 22 SD: 0.4949 cents 139 .. 278 match: 22 SD: 0.4608 cents 145 .. 290 match: 22 SD: 0.4305 cents 150 .. 300 match: 22 SD: 0.4200 cents 161 .. 322 match: 22 SD: 0.3903 cents 171 .. 342 match: 22 SD: 0.3249 cents 193 .. 386 match: 22 SD: 0.2986 cents 205 .. 410 match: 22 SD: 0.2847 cents 233 .. 466 match: 22 SD: 0.2831 cents 241 .. 482 match: 22 SD: 0.2714 cents 251 .. 502 match: 22 SD: 0.2683 cents 256 .. 512 match: 22 SD: 0.2331 cents 272 .. 544 match: 22 SD: 0.1849 cents 341 .. 682 match: 22 SD: 0.1753 cents 352 .. 704 match: 22 SD: 0.1618 cents 374 .. 748 match: 22 SD: 0.1449 cents 384 .. 768 match: 22 SD: 0.1443 cents 404 .. 808 match: 22 SD: 0.1322 cents 434 .. 868 match: 22 SD: 0.1258 cents 483 .. 966 match: 22 SD: 0.1213 cents 512 .. 1024 match: 22 SD: 0.1191 cents 544 .. 1088 match: 22 SD: 0.1092 cents 545 .. 1090 match: 22 SD: 0.1070 cents 577 .. 1154 match: 22 SD: 0.1046 cents