Scala analysis: zeus22
Zeus[22] hobbit (121/120&176/175) in POTE tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 47.218 cents 47.217960 2: 109.870 cents 109.870100 3: 157.088 cents 157.088060 4: 230.889 cents 230.888830 5: 266.958 cents 266.958160 6: 314.176 cents 314.176120 7: 387.977 cents 387.976890 8: 424.046 cents 424.046220 9: 497.847 cents 497.846990 10: 545.065 cents 545.064950 11: 592.283 cents 592.282910 12: 654.935 cents 654.935050 13: 702.153 cents 702.153010 14: 775.954 cents 775.953780 15: 812.023 cents 812.023110 16: 885.824 cents 885.823880 17: 933.042 cents 933.041840 18: 969.111 cents 969.111170 19: 1042.912 cents 1042.911940 20: 1090.130 cents 1090.129900 21: 1152.782 cents 1152.782040 22: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 47.2180 cents 47.2180 1: 47.2180 cents 47.2180 2: 62.6521 cents 62.6521 3: 47.2180 cents 47.2180 4: 73.8008 cents 73.8008 5: 36.0693 cents 36.0693 6: 47.2180 cents 47.2180 7: 73.8008 cents 73.8008 8: 36.0693 cents 36.0693 9: 73.8008 cents 73.8008 10: 47.2180 cents 47.2180 11: 47.2180 cents 47.2180 12: 62.6521 cents 62.6521 13: 47.2180 cents 47.2180 14: 73.8008 cents 73.8008 15: 36.0693 cents 36.0693 16: 73.8008 cents 73.8008 17: 47.2180 cents 47.2180 18: 36.0693 cents 36.0693 19: 73.8008 cents 73.8008 20: 47.2180 cents 47.2180 21: 62.6521 cents 62.6521 22: 47.2180 cents 47.2180
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 36.06933 cents 1: 9 47.21796 cents 1: 3 62.65214 cents 1: 6 73.80077 cents 2: 2 83.28729 cents 2: 2 94.43592 cents 2: 12 109.87010 cents 2: 6 121.01873 cents 3: 16 157.08806 cents 3: 1 168.23669 cents 3: 5 183.67087 cents 4: 2 193.15739 cents 4: 6 204.30602 cents 4: 4 219.74020 cents 4: 10 230.88883 cents 5: 12 266.95816 cents 5: 9 278.10679 cents 5: 1 293.54097 cents 6: 11 314.17612 cents 6: 1 325.32475 cents 6: 9 340.75893 cents 6: 1 351.90756 cents 7: 3 361.39408 cents 7: 5 376.82826 cents 7: 14 387.97689 cents 8: 9 424.04622 cents 8: 7 435.19485 cents 8: 3 450.62903 cents 8: 3 461.77766 cents 9: 6 471.26418 cents 9: 1 482.41281 cents 9: 13 497.84699 cents 9: 2 508.99562 cents 10: 3 533.91632 cents 10: 17 545.06495 cents 10: 1 560.49913 cents 10: 1 571.64776 cents 11: 6 581.13428 cents 11: 5 592.28291 cents 11: 5 607.71709 cents 11: 6 618.86572 cents 12: 1 628.35224 cents 12: 1 639.50087 cents 12: 17 654.93505 cents 12: 3 666.08368 cents 13: 2 691.00438 cents 13: 13 702.15301 cents 13: 1 717.58719 cents 13: 6 728.73582 cents 14: 3 738.22234 cents 14: 3 749.37097 cents 14: 7 764.80515 cents 14: 9 775.95378 cents 15: 14 812.02311 cents 15: 5 823.17174 cents 15: 3 838.60592 cents 16: 1 848.09244 cents 16: 9 859.24107 cents 16: 1 874.67525 cents 16: 11 885.82388 cents 17: 1 906.45903 cents 17: 9 921.89321 cents 17: 12 933.04184 cents 18: 10 969.11117 cents 18: 4 980.25980 cents 18: 6 995.69398 cents 18: 2 1006.84261 cents 19: 5 1016.32913 cents 19: 1 1031.76331 cents 19: 16 1042.91194 cents 20: 6 1078.98127 cents 20: 12 1090.12990 cents 20: 2 1105.56408 cents 20: 2 1116.71271 cents 21: 6 1126.19923 cents 21: 3 1137.34786 cents 21: 9 1152.78204 cents 21: 4 1163.93067 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.71429 = 26/7
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 : 47.2 109.9 157.1 230.9 267.0 314.2 388.0 424.0 497.8 545.1 592.3 654.9 702.2 776.0 812.0 885.8 933.0 969.1 1042.9 1090.1 1152.8 1200.0 47.2 : 62.7 109.9 183.7 219.7 267.0 340.8 376.8 450.6 497.8 545.1 607.7 654.9 728.7 764.8 838.6 885.8 921.9 995.7 1042.9 1105.6 1152.8 1200.0 109.9 : 47.2 121.0 157.1 204.3 278.1 314.2 388.0 435.2 482.4 545.1 592.3 666.1 702.2 776.0 823.2 859.2 933.0 980.3 1042.9 1090.1 1137.3 1200.0 157.1 : 73.8 109.9 157.1 230.9 267.0 340.8 388.0 435.2 497.8 545.1 618.9 654.9 728.7 776.0 812.0 885.8 933.0 995.7 1042.9 1090.1 1152.8 1200.0 230.9 : 36.1 83.3 157.1 193.2 267.0 314.2 361.4 424.0 471.3 545.1 581.1 654.9 702.2 738.2 812.0 859.2 921.9 969.1 1016.3 1079.0 1126.2 1200.0 267.0 : 47.2 121.0 157.1 230.9 278.1 325.3 388.0 435.2 509.0 545.1 618.9 666.1 702.2 776.0 823.2 885.8 933.0 980.3 1042.9 1090.1 1163.9 1200.0 314.2 : 73.8 109.9 183.7 230.9 278.1 340.8 388.0 461.8 497.8 571.6 618.9 654.9 728.7 776.0 838.6 885.8 933.0 995.7 1042.9 1116.7 1152.8 1200.0 388.0 : 36.1 109.9 157.1 204.3 267.0 314.2 388.0 424.0 497.8 545.1 581.1 654.9 702.2 764.8 812.0 859.2 921.9 969.1 1042.9 1079.0 1126.2 1200.0 424.0 : 73.8 121.0 168.2 230.9 278.1 351.9 388.0 461.8 509.0 545.1 618.9 666.1 728.7 776.0 823.2 885.8 933.0 1006.8 1042.9 1090.1 1163.9 1200.0 497.8 : 47.2 94.4 157.1 204.3 278.1 314.2 388.0 435.2 471.3 545.1 592.3 654.9 702.2 749.4 812.0 859.2 933.0 969.1 1016.3 1090.1 1126.2 1200.0 545.1 : 47.2 109.9 157.1 230.9 267.0 340.8 388.0 424.0 497.8 545.1 607.7 654.9 702.2 764.8 812.0 885.8 921.9 969.1 1042.9 1079.0 1152.8 1200.0 592.3 : 62.7 109.9 183.7 219.7 293.5 340.8 376.8 450.6 497.8 560.5 607.7 654.9 717.6 764.8 838.6 874.7 921.9 995.7 1031.8 1105.6 1152.8 1200.0 654.9 : 47.2 121.0 157.1 230.9 278.1 314.2 388.0 435.2 497.8 545.1 592.3 654.9 702.2 776.0 812.0 859.2 933.0 969.1 1042.9 1090.1 1137.3 1200.0 702.2 : 73.8 109.9 183.7 230.9 267.0 340.8 388.0 450.6 497.8 545.1 607.7 654.9 728.7 764.8 812.0 885.8 921.9 995.7 1042.9 1090.1 1152.8 1200.0 776.0 : 36.1 109.9 157.1 193.2 267.0 314.2 376.8 424.0 471.3 533.9 581.1 654.9 691.0 738.2 812.0 848.1 921.9 969.1 1016.3 1079.0 1126.2 1200.0 812.0 : 73.8 121.0 157.1 230.9 278.1 340.8 388.0 435.2 497.8 545.1 618.9 654.9 702.2 776.0 812.0 885.8 933.0 980.3 1042.9 1090.1 1163.9 1200.0 885.8 : 47.2 83.3 157.1 204.3 267.0 314.2 361.4 424.0 471.3 545.1 581.1 628.4 702.2 738.2 812.0 859.2 906.5 969.1 1016.3 1090.1 1126.2 1200.0 933.0 : 36.1 109.9 157.1 219.7 267.0 314.2 376.8 424.0 497.8 533.9 581.1 654.9 691.0 764.8 812.0 859.2 921.9 969.1 1042.9 1079.0 1152.8 1200.0 969.1 : 73.8 121.0 183.7 230.9 278.1 340.8 388.0 461.8 497.8 545.1 618.9 654.9 728.7 776.0 823.2 885.8 933.0 1006.8 1042.9 1116.7 1163.9 1200.0 1042.9: 47.2 109.9 157.1 204.3 267.0 314.2 388.0 424.0 471.3 545.1 581.1 654.9 702.2 749.4 812.0 859.2 933.0 969.1 1042.9 1090.1 1126.2 1200.0 1090.1: 62.7 109.9 157.1 219.7 267.0 340.8 376.8 424.0 497.8 533.9 607.7 654.9 702.2 764.8 812.0 885.8 921.9 995.7 1042.9 1079.0 1152.8 1200.0 1152.8: 47.2 94.4 157.1 204.3 278.1 314.2 361.4 435.2 471.3 545.1 592.3 639.5 702.2 749.4 823.2 859.2 933.0 980.3 1016.3 1090.1 1137.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.0693 .. 73.8008 cents 37.73144 cents 36.06933 cents 2: 83.2873 .. 121.0187 cents 37.73144 cents 9.48652 cents 3: 157.0881 .. 183.6709 cents 26.58281 cents 36.06933 cents 4: 193.1574 .. 230.8888 cents 37.73144 cents 9.48652 cents 5: 266.9582 .. 293.5410 cents 26.58281 cents 36.06933 cents 6: 314.1761 .. 351.9076 cents 37.73144 cents 20.63515 cents 7: 361.3941 .. 387.9769 cents 26.58281 cents 9.48652 cents 8: 424.0462 .. 461.7777 cents 37.73144 cents 36.06933 cents 9: 471.2642 .. 508.9956 cents 37.73144 cents 9.48652 cents 10: 533.9163 .. 571.6478 cents 37.73144 cents 24.92070 cents 11: 581.1343 .. 618.8657 cents 37.73144 cents 9.48652 cents 12: 628.3522 .. 666.0837 cents 37.73144 cents 9.48652 cents 13: 691.0044 .. 728.7358 cents 37.73144 cents 24.92070 cents 14: 738.2223 .. 775.9538 cents 37.73144 cents 9.48652 cents 15: 812.0231 .. 838.6059 cents 26.58281 cents 36.06933 cents 16: 848.0924 .. 885.8239 cents 37.73144 cents 9.48652 cents 17: 906.4590 .. 933.0418 cents 26.58281 cents 20.63515 cents 18: 969.1112 .. 1006.8426 cents 37.73144 cents 36.06933 cents 19: 1016.3291 .. 1042.9119 cents 26.58281 cents 9.48652 cents 20: 1078.9813 .. 1116.7127 cents 37.73144 cents 36.06933 cents 21: 1126.1992 .. 1163.9307 cents 37.73144 cents 9.48652 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 36.06933 cents, class 1 Average step (divided formal octave): 54.5455 cents Largest one step interval : 73.80077 cents Average / Smallest step : 1.512239 Largest / Average step : 1.353014 Largest / Smallest step : 2.046081 Median interval of one step : 47.21796 cents, amount: 9 Most common interval of one step : 47.21796 cents, amount: 9 Least squares average step : 54.59087 cents, oct.: 1200.99924 cents Scale is strictly proper Step pattern alph. order: ABACDACDCAABACDCADCABA Step pattern size order : BCBDABDADBBCBDADBADBCB Scale is a Constant Structure, by a margin of 9.48652 cents Scale diversity : 1.340064 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.395443 Number of different interval sizes : 78 = 3.71429 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.71429 = 26/7 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 9.48652 cents Most common intervals : 545.06495 cents & inv., amount: 17 Most common triad is 0.0 545.065 654.935 cents, amount: 12 Number of recognisable fifths : 16, average 701.7241 cents Number of appreciable fifths : 15, average 700.6665 cents Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 21 = 95.4545% -- 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: 8.1529 c. M: 13.0966 c. 31: 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 1 P M ME SD: 4.9095 c. M: 11.6377 c. 46: 2 2 2 3 1 2 3 1 3 2 2 2 2 3 1 3 2 1 3 2 2 2 P D3 I SD: 4.3324 c. M:-7.7171 c. 53: 2 3 2 3 2 2 3 2 3 2 2 3 2 3 2 3 2 2 3 2 3 2 SP M ME SD: 3.3536 c. M: 6.1425 c. 68: 3 3 3 4 2 3 4 2 4 3 3 3 3 4 2 4 3 2 4 3 3 3 SP D3 I SD: 3.2886 c. M:-7.7171 c. 77: 3 4 3 5 2 3 5 2 5 3 3 4 3 5 2 5 3 2 5 3 4 3 P SD: 1.7878 c. M: 3.2670 c. 99: 4 5 4 6 3 4 6 3 6 4 4 5 4 6 3 6 4 3 6 4 5 4 SP SD: 0.7490 c. M:-1.6565 c. 130: 5 7 5 8 4 5 8 4 8 5 5 7 5 8 4 8 5 4 8 5 7 5 SP SD: 0.6579 c. M: 1.5137 c. 176: 7 9 7 11 5 7 11 5 11 7 7 9 7 11 5 11 7 5 11 7 9 7 SP SD: 0.7348 c. M: 1.3189 c. 207: 8 11 8 13 6 8 13 6 13 8 8 11 8 13 6 13 8 6 13 8 11 8 SP SD: 0.6990 c. M: 1.1326 c. 229: 9 12 9 14 7 9 14 7 14 9 9 12 9 14 7 14 9 7 14 9 12 9 SP SD: 0.2167 c. M: 0.4079 c. 405: 16 21 16 25 12 16 25 12 25 16 16 21 16 25 12 25 16 12 25 16 21 16 SP SD: 0.2034 c. M: 0.3425 c. 535: 21 28 21 33 16 21 33 16 33 21 21 28 21 33 16 33 21 16 33 21 28 21 SP SD: 0.0971 c. M: 0.1574 c. 634: 25 33 25 39 19 25 39 19 39 25 25 33 25 39 19 39 25 19 39 25 33 25 SP SD: 0.0663 c. M:-0.1461 c. 764: 30 40 30 47 23 30 47 23 47 30 30 40 30 47 23 47 30 23 47 30 40 30 SP SD: 0.0579 c. M: 0.1363 c. 863: 34 45 34 53 26 34 53 26 53 34 34 45 34 53 26 53 34 26 53 34 45 34 SP SD: 0.0473 c. M: 0.0765 c. 1398: 55 73 55 86 42 55 86 42 86 55 55 73 55 86 42 86 55 42 86 55 73 55 SP SD: 0.0081 c. M: 0.0130 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.0990 cents 3 .. 6 match: 3 H SD: 0.4928 cents 4 .. 8 match: 4 H SD: 0.4248 cents 5 .. 10 match: 5 H SD: 5.4452 cents 6 .. 12 match: 6 H SD: 1.1036 cents 7 .. 14 match: 7 H SD: 4.8225 cents 8 .. 16 match: 8 H SD: 4.9778 cents 9 .. 18 match: 9 H SD: 6.1381 cents 10 .. 20 match: 10 H SD: 4.8635 cents 11 .. 22 match: 11 H SD: 5.2875 cents 12 .. 24 match: 12 H SD: 3.2013 cents 13 .. 26 match: 13 H SD: 5.8320 cents 14 .. 28 match: 14 H SD: 4.5894 cents 15 .. 30 match: 15 H SD: 3.6716 cents 16 .. 32 match: 16 H SD: 3.9437 cents 17 .. 34 match: 17 H SD: 4.2734 cents 18 .. 36 match: 18 H SD: 3.5864 cents 19 .. 38 match: 17 SD: 3.9566 cents 20 .. 40 match: 19 SD: 3.4336 cents 21 .. 42 match: 20 SD: 3.4260 cents 22 .. 44 match: 19 SD: 3.2203 cents 23 .. 46 match: 19 SD: 3.7461 cents 24 .. 48 match: 20 SD: 2.6426 cents 25 .. 50 match: 20 SD: 2.9987 cents 26 .. 52 match: 19 SD: 3.3404 cents 27 .. 54 match: 20 SD: 2.8653 cents 28 .. 56 match: 22 SD: 2.5562 cents 29 .. 58 match: 22 SD: 2.4510 cents 30 .. 60 match: 21 SD: 1.8435 cents 32 .. 64 match: 21 SD: 1.7865 cents 34 .. 68 match: 21 SD: 2.1609 cents 35 .. 70 match: 22 SD: 1.7485 cents 40 .. 80 match: 22 SD: 1.6328 cents 42 .. 84 match: 22 SD: 1.5616 cents 44 .. 88 match: 22 SD: 1.5198 cents 48 .. 96 match: 22 SD: 1.4405 cents 56 .. 112 match: 22 SD: 1.3879 cents 57 .. 114 match: 22 SD: 1.3660 cents 59 .. 118 match: 22 SD: 1.3377 cents 60 .. 120 match: 22 SD: 1.1368 cents 64 .. 128 match: 22 SD: 0.9783 cents 72 .. 144 match: 22 SD: 0.8132 cents 76 .. 152 match: 22 SD: 0.6716 cents 104 .. 208 match: 22 SD: 0.6558 cents 105 .. 210 match: 22 SD: 0.5892 cents 108 .. 216 match: 22 SD: 0.5389 cents 120 .. 240 match: 22 SD: 0.5012 cents 140 .. 280 match: 22 SD: 0.4408 cents 154 .. 308 match: 22 SD: 0.4203 cents 156 .. 312 match: 22 SD: 0.4013 cents 168 .. 336 match: 22 SD: 0.3802 cents 180 .. 360 match: 22 SD: 0.3284 cents 210 .. 420 match: 22 SD: 0.3026 cents 211 .. 422 match: 22 SD: 0.2822 cents 216 .. 432 match: 22 SD: 0.2821 cents 244 .. 488 match: 22 SD: 0.2729 cents 246 .. 492 match: 22 SD: 0.2345 cents 276 .. 552 match: 22 SD: 0.2285 cents 287 .. 574 match: 22 SD: 0.2133 cents 292 .. 584 match: 22 SD: 0.2056 cents 294 .. 588 match: 22 SD: 0.2030 cents 316 .. 632 match: 22 SD: 0.1880 cents 336 .. 672 match: 22 SD: 0.1769 cents 367 .. 734 match: 22 SD: 0.1757 cents 378 .. 756 match: 22 SD: 0.1695 cents 392 .. 784 match: 22 SD: 0.1650 cents 398 .. 796 match: 22 SD: 0.1602 cents 414 .. 828 match: 22 SD: 0.1587 cents 426 .. 852 match: 22 SD: 0.1460 cents 433 .. 866 match: 22 SD: 0.1417 cents 461 .. 922 match: 22 SD: 0.1357 cents 462 .. 924 match: 22 SD: 0.1319 cents 498 .. 996 match: 22 SD: 0.1217 cents 504 .. 1008 match: 22 SD: 0.1208 cents 518 .. 1036 match: 22 SD: 0.1157 cents 546 .. 1092 match: 22 SD: 0.1050 cents 576 .. 1152 match: 22 SD: 0.0972 cents