Scala analysis: zeus24
Zeus[24] 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: 204.306 cents 204.306020 5: 230.889 cents 230.888830 6: 314.176 cents 314.176120 7: 340.759 cents 340.758930 8: 387.977 cents 387.976890 9: 471.264 cents 471.264180 10: 497.847 cents 497.846990 11: 545.065 cents 545.064950 12: 592.283 cents 592.282910 13: 654.935 cents 654.935050 14: 702.153 cents 702.153010 15: 728.736 cents 728.735820 16: 812.023 cents 812.023110 17: 859.241 cents 859.241070 18: 885.824 cents 885.823880 19: 969.111 cents 969.111170 20: 995.694 cents 995.693980 21: 1042.912 cents 1042.911940 22: 1090.130 cents 1090.129900 23: 1152.782 cents 1152.782040 24: 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: 47.2180 cents 47.2180 5: 26.5828 cents 26.5828 6: 83.2873 cents 83.2873 7: 26.5828 cents 26.5828 8: 47.2180 cents 47.2180 9: 83.2873 cents 83.2873 10: 26.5828 cents 26.5828 11: 47.2180 cents 47.2180 12: 47.2180 cents 47.2180 13: 62.6521 cents 62.6521 14: 47.2180 cents 47.2180 15: 26.5828 cents 26.5828 16: 83.2873 cents 83.2873 17: 47.2180 cents 47.2180 18: 26.5828 cents 26.5828 19: 83.2873 cents 83.2873 20: 26.5828 cents 26.5828 21: 47.2180 cents 47.2180 22: 47.2180 cents 47.2180 23: 62.6521 cents 62.6521 24: 47.2180 cents 47.2180
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 26.58281 cents 1: 11 47.21796 cents 1: 3 62.65214 cents 1: 4 83.28729 cents 2: 6 73.80077 cents 2: 4 94.43592 cents 2: 12 109.87010 cents 2: 2 130.50525 cents 3: 3 121.01873 cents 3: 3 136.45291 cents 3: 18 157.08806 cents 4: 10 183.67087 cents 4: 10 204.30602 cents 4: 2 219.74020 cents 4: 2 240.37535 cents 5: 10 230.88883 cents 5: 3 251.52398 cents 5: 11 266.95816 cents 6: 1 257.47164 cents 6: 5 278.10679 cents 6: 5 293.54097 cents 6: 13 314.17612 cents 7: 14 340.75893 cents 7: 9 361.39408 cents 7: 1 376.82826 cents 8: 15 387.97689 cents 8: 1 403.41107 cents 8: 1 408.61204 cents 8: 7 424.04622 cents 9: 2 414.55970 cents 9: 7 435.19485 cents 9: 7 450.62903 cents 9: 8 471.26418 cents 10: 1 461.77766 cents 10: 1 482.41281 cents 10: 17 497.84699 cents 10: 5 518.48214 cents 11: 2 524.42980 cents 11: 17 545.06495 cents 11: 1 560.49913 cents 11: 4 581.13428 cents 12: 5 571.64776 cents 12: 7 592.28291 cents 12: 7 607.71709 cents 12: 5 628.35224 cents 13: 4 618.86572 cents 13: 1 639.50087 cents 13: 17 654.93505 cents 13: 2 675.57020 cents 14: 5 681.51786 cents 14: 17 702.15301 cents 14: 1 717.58719 cents 14: 1 738.22234 cents 15: 8 728.73582 cents 15: 7 749.37097 cents 15: 7 764.80515 cents 15: 2 785.44030 cents 16: 7 775.95378 cents 16: 1 791.38796 cents 16: 1 796.58893 cents 16: 15 812.02311 cents 17: 1 823.17174 cents 17: 9 838.60592 cents 17: 14 859.24107 cents 18: 13 885.82388 cents 18: 5 906.45903 cents 18: 5 921.89321 cents 18: 1 942.52836 cents 19: 11 933.04184 cents 19: 3 948.47602 cents 19: 10 969.11117 cents 20: 2 959.62465 cents 20: 2 980.25980 cents 20: 10 995.69398 cents 20: 10 1016.32913 cents 21: 18 1042.91194 cents 21: 3 1063.54709 cents 21: 3 1078.98127 cents 22: 2 1069.49475 cents 22: 12 1090.12990 cents 22: 4 1105.56408 cents 22: 6 1126.19923 cents 23: 4 1116.71271 cents 23: 3 1137.34786 cents 23: 11 1152.78204 cents 23: 6 1173.41719 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.73913 = 86/23
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 23 24 0.0 : 47.2 109.9 157.1 204.3 230.9 314.2 340.8 388.0 471.3 497.8 545.1 592.3 654.9 702.2 728.7 812.0 859.2 885.8 969.1 995.7 1042.9 1090.1 1152.8 1200.0 47.2 : 62.7 109.9 157.1 183.7 267.0 293.5 340.8 424.0 450.6 497.8 545.1 607.7 654.9 681.5 764.8 812.0 838.6 921.9 948.5 995.7 1042.9 1105.6 1152.8 1200.0 109.9 : 47.2 94.4 121.0 204.3 230.9 278.1 361.4 388.0 435.2 482.4 545.1 592.3 618.9 702.2 749.4 776.0 859.2 885.8 933.0 980.3 1042.9 1090.1 1137.3 1200.0 157.1 : 47.2 73.8 157.1 183.7 230.9 314.2 340.8 388.0 435.2 497.8 545.1 571.6 654.9 702.2 728.7 812.0 838.6 885.8 933.0 995.7 1042.9 1090.1 1152.8 1200.0 204.3 : 26.6 109.9 136.5 183.7 267.0 293.5 340.8 388.0 450.6 497.8 524.4 607.7 654.9 681.5 764.8 791.4 838.6 885.8 948.5 995.7 1042.9 1105.6 1152.8 1200.0 230.9 : 83.3 109.9 157.1 240.4 267.0 314.2 361.4 424.0 471.3 497.8 581.1 628.4 654.9 738.2 764.8 812.0 859.2 921.9 969.1 1016.3 1079.0 1126.2 1173.4 1200.0 314.2 : 26.6 73.8 157.1 183.7 230.9 278.1 340.8 388.0 414.6 497.8 545.1 571.6 654.9 681.5 728.7 776.0 838.6 885.8 933.0 995.7 1042.9 1090.1 1116.7 1200.0 340.8 : 47.2 130.5 157.1 204.3 251.5 314.2 361.4 388.0 471.3 518.5 545.1 628.4 654.9 702.2 749.4 812.0 859.2 906.5 969.1 1016.3 1063.5 1090.1 1173.4 1200.0 388.0 : 83.3 109.9 157.1 204.3 267.0 314.2 340.8 424.0 471.3 497.8 581.1 607.7 654.9 702.2 764.8 812.0 859.2 921.9 969.1 1016.3 1042.9 1126.2 1152.8 1200.0 471.3 : 26.6 73.8 121.0 183.7 230.9 257.5 340.8 388.0 414.6 497.8 524.4 571.6 618.9 681.5 728.7 776.0 838.6 885.8 933.0 959.6 1042.9 1069.5 1116.7 1200.0 497.8 : 47.2 94.4 157.1 204.3 230.9 314.2 361.4 388.0 471.3 497.8 545.1 592.3 654.9 702.2 749.4 812.0 859.2 906.5 933.0 1016.3 1042.9 1090.1 1173.4 1200.0 545.1 : 47.2 109.9 157.1 183.7 267.0 314.2 340.8 424.0 450.6 497.8 545.1 607.7 654.9 702.2 764.8 812.0 859.2 885.8 969.1 995.7 1042.9 1126.2 1152.8 1200.0 592.3 : 62.7 109.9 136.5 219.7 267.0 293.5 376.8 403.4 450.6 497.8 560.5 607.7 654.9 717.6 764.8 812.0 838.6 921.9 948.5 995.7 1079.0 1105.6 1152.8 1200.0 654.9 : 47.2 73.8 157.1 204.3 230.9 314.2 340.8 388.0 435.2 497.8 545.1 592.3 654.9 702.2 749.4 776.0 859.2 885.8 933.0 1016.3 1042.9 1090.1 1137.3 1200.0 702.2 : 26.6 109.9 157.1 183.7 267.0 293.5 340.8 388.0 450.6 497.8 545.1 607.7 654.9 702.2 728.7 812.0 838.6 885.8 969.1 995.7 1042.9 1090.1 1152.8 1200.0 728.7 : 83.3 130.5 157.1 240.4 267.0 314.2 361.4 424.0 471.3 518.5 581.1 628.4 675.6 702.2 785.4 812.0 859.2 942.5 969.1 1016.3 1063.5 1126.2 1173.4 1200.0 812.0 : 47.2 73.8 157.1 183.7 230.9 278.1 340.8 388.0 435.2 497.8 545.1 592.3 618.9 702.2 728.7 776.0 859.2 885.8 933.0 980.3 1042.9 1090.1 1116.7 1200.0 859.2 : 26.6 109.9 136.5 183.7 230.9 293.5 340.8 388.0 450.6 497.8 545.1 571.6 654.9 681.5 728.7 812.0 838.6 885.8 933.0 995.7 1042.9 1069.5 1152.8 1200.0 885.8 : 83.3 109.9 157.1 204.3 267.0 314.2 361.4 424.0 471.3 518.5 545.1 628.4 654.9 702.2 785.4 812.0 859.2 906.5 969.1 1016.3 1042.9 1126.2 1173.4 1200.0 969.1 : 26.6 73.8 121.0 183.7 230.9 278.1 340.8 388.0 435.2 461.8 545.1 571.6 618.9 702.2 728.7 776.0 823.2 885.8 933.0 959.6 1042.9 1090.1 1116.7 1200.0 995.7 : 47.2 94.4 157.1 204.3 251.5 314.2 361.4 408.6 435.2 518.5 545.1 592.3 675.6 702.2 749.4 796.6 859.2 906.5 933.0 1016.3 1063.5 1090.1 1173.4 1200.0 1042.9: 47.2 109.9 157.1 204.3 267.0 314.2 361.4 388.0 471.3 497.8 545.1 628.4 654.9 702.2 749.4 812.0 859.2 885.8 969.1 1016.3 1042.9 1126.2 1152.8 1200.0 1090.1: 62.7 109.9 157.1 219.7 267.0 314.2 340.8 424.0 450.6 497.8 581.1 607.7 654.9 702.2 764.8 812.0 838.6 921.9 969.1 995.7 1079.0 1105.6 1152.8 1200.0 1152.8: 47.2 94.4 157.1 204.3 251.5 278.1 361.4 388.0 435.2 518.5 545.1 592.3 639.5 702.2 749.4 776.0 859.2 906.5 933.0 1016.3 1042.9 1090.1 1137.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.5828 .. 83.2873 cents 56.70448 cents 26.58281 cents 2: 73.8008 .. 130.5052 cents 56.70448 cents -9.48652 cents 3: 121.0187 .. 157.0881 cents 36.06933 cents -9.48652 cents 4: 183.6709 .. 240.3753 cents 56.70448 cents 26.58281 cents 5: 230.8888 .. 266.9582 cents 36.06933 cents -9.48652 cents 6: 257.4716 .. 314.1761 cents 56.70448 cents -9.48652 cents 7: 340.7589 .. 376.8283 cents 36.06933 cents 26.58281 cents 8: 387.9769 .. 424.0462 cents 36.06933 cents 11.14863 cents 9: 414.5597 .. 471.2642 cents 56.70448 cents -9.48652 cents 10: 461.7777 .. 518.4821 cents 56.70448 cents -9.48652 cents 11: 524.4298 .. 581.1343 cents 56.70448 cents 5.94766 cents 12: 571.6478 .. 628.3522 cents 56.70448 cents -9.48652 cents 13: 618.8657 .. 675.5702 cents 56.70448 cents -9.48652 cents 14: 681.5179 .. 738.2223 cents 56.70448 cents 5.94766 cents 15: 728.7358 .. 785.4403 cents 56.70448 cents -9.48652 cents 16: 775.9538 .. 812.0231 cents 36.06933 cents -9.48652 cents 17: 823.1717 .. 859.2411 cents 36.06933 cents 11.14863 cents 18: 885.8239 .. 942.5284 cents 56.70448 cents 26.58281 cents 19: 933.0418 .. 969.1112 cents 36.06933 cents -9.48652 cents 20: 959.6247 .. 1016.3291 cents 56.70448 cents -9.48652 cents 21: 1042.9119 .. 1078.9813 cents 36.06933 cents 26.58281 cents 22: 1069.4948 .. 1126.1992 cents 56.70448 cents -9.48652 cents 23: 1116.7127 .. 1173.4172 cents 56.70448 cents -9.48652 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 26.58281 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 83.28729 cents Average / Smallest step : 1.880915 Largest / Average step : 1.665746 Largest / Smallest step : 3.133126 Median interval of one step : 47.21796 cents, amount: 11 Most common interval of one step : 47.21796 cents, amount: 11 Least squares average step : 49.94932 cents, oct.: 1198.78360 cents Scale is not proper Step pattern alph. order: ABAACDCADCAABACDACDCAABA Step pattern size order : BCBBADABDABBCBADBADABBCB Scale is a Constant Structure, by a margin of 5.94766 cents Scale diversity : 1.356779 Lumma stability : 0.161408 Lumma impropriety factor : 0.110676 Number of different interval sizes : 86 = 3.73913 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.73913 = 86/23 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 5.20097 cents Most common intervals : 157.08806 cents & inv., amount: 18 Most common triad is 0.0 157.088 1042.912 cents, amount: 13 Number of recognisable fifths : 18, average 703.0105 cents Number of appreciable fifths : 17, average 702.1530 cents Formal octave complements present : 23 = 95.8333% -- Rational properties --
FIT/MODE
24: 1 1 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: 11.1094 c. M:-21.2642 c. 26: 1 1 1 1 1 2 0 1 2 1 1 1 1 1 1 2 1 0 2 1 1 1 1 1 N D3 I SD: 13.1844 c. M:-19.6906 c. 28: 1 2 1 1 0 2 1 1 2 1 1 1 1 1 1 2 1 1 2 0 1 1 2 1 N D3 I SD: 11.5689 c. M:-18.7013 c. 30: 1 2 1 1 1 2 1 1 2 0 2 1 1 2 0 2 1 1 2 1 1 1 2 1 N D3 I SD: 11.0344 c. M: 19.2411 c. 31: 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 2 1 P M ME SD: 6.2277 c. M: 11.6377 c. 41: 2 2 1 2 1 3 1 1 3 1 2 1 2 2 1 3 1 1 3 1 2 1 2 2 N SD: 7.5660 c. M:-11.3186 c. 43: 2 2 2 1 1 3 1 2 3 1 2 1 2 2 1 3 2 1 3 1 1 2 2 2 N SD: 7.2848 c. M:-13.0746 c. 46: 2 2 2 2 1 3 1 2 3 1 2 2 2 2 1 3 2 1 3 1 2 2 2 2 P D3 I SD: 3.5346 c. M:-7.7171 c. 53: 2 3 2 2 1 4 1 2 4 1 2 2 3 2 1 4 2 1 4 1 2 2 3 2 N SD: 2.6266 c. M: 4.4737 c. 77: 3 4 3 3 2 5 2 3 5 2 3 3 4 3 2 5 3 2 5 2 3 3 4 3 P SD: 1.8628 c. M:-3.7317 c. 99: 4 5 4 4 2 7 2 4 7 2 4 4 5 4 2 7 4 2 7 2 4 4 5 4 N SD: 1.0460 c. M:-1.7546 c. 130: 5 7 5 5 3 9 3 5 9 3 5 5 7 5 3 9 5 3 9 3 5 5 7 5 N SD: 0.7223 c. M: 1.5137 c. 176: 7 9 7 7 4 12 4 7 12 4 7 7 9 7 4 12 7 4 12 4 7 7 9 7 N SD: 0.5653 c. M: 0.9294 c. 229: 9 12 9 9 5 16 5 9 16 5 9 9 12 9 5 16 9 5 16 5 9 9 12 9 N SD: 0.1858 c. M:-0.3515 c. 405: 16 21 16 16 9 28 9 16 28 9 16 16 21 16 9 28 16 9 28 9 16 16 21 16 N SD: 0.1569 c. M:-0.3097 c. 535: 21 28 21 21 12 37 12 21 37 12 21 21 28 21 12 37 21 12 37 12 21 21 28 21 N SD: 0.1327 c. M:-0.2361 c. 634: 25 33 25 25 14 44 14 25 44 14 25 25 33 25 14 44 25 14 44 14 25 25 33 25 N SD: 0.0670 c. M:-0.1461 c. 764: 30 40 30 30 17 53 17 30 53 17 30 30 40 30 17 53 30 17 53 17 30 30 40 30 N SD: 0.0682 c. M: 0.1363 c. 863: 34 45 34 34 19 60 19 34 60 19 34 34 45 34 19 60 34 19 60 19 34 34 45 34 N SD: 0.0655 c. M:-0.1147 c. 993: 39 52 39 39 22 69 22 39 69 22 39 39 52 39 22 69 39 22 69 22 39 39 52 39 N SD: 0.0637 c. M: 0.1379 c. 1169: 46 61 46 46 26 81 26 46 81 26 46 46 61 46 26 81 46 26 81 26 46 46 61 46 N SD: 0.0466 c. M: 0.0922 c. 1398: 55 73 55 55 31 97 31 55 97 31 55 55 73 55 31 97 55 31 97 31 55 55 73 55 N SD: 0.0105 c. M:-0.0195 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: 4.8170 cents 6 .. 12 match: 6 H SD: 6.0977 cents 7 .. 14 match: 7 H SD: 9.5306 cents 8 .. 16 match: 8 H SD: 2.4868 cents 9 .. 18 match: 9 H SD: 5.3170 cents 10 .. 20 match: 10 H SD: 4.9542 cents 11 .. 22 match: 11 H SD: 5.5704 cents 12 .. 24 match: 12 H SD: 4.3863 cents 13 .. 26 match: 13 H SD: 4.5119 cents 14 .. 28 match: 13 SD: 4.7736 cents 15 .. 30 match: 15 H SD: 2.8994 cents 16 .. 32 match: 15 S SD: 3.0171 cents 17 .. 34 match: 16 S SD: 3.6972 cents 18 .. 36 match: 16 SD: 4.2619 cents 19 .. 38 match: 19 H SD: 3.2548 cents 20 .. 40 match: 18 SD: 3.1990 cents 21 .. 42 match: 17 SD: 3.6252 cents 22 .. 44 match: 20 SD: 3.1954 cents 23 .. 46 match: 18 SD: 3.0374 cents 24 .. 48 match: 20 SD: 2.5637 cents 25 .. 50 match: 19 SD: 3.0946 cents 26 .. 52 match: 21 SD: 3.2411 cents 27 .. 54 match: 22 SD: 2.5688 cents 28 .. 56 match: 21 SD: 2.3250 cents 29 .. 58 match: 20 SD: 2.4484 cents 30 .. 60 match: 22 SD: 2.1973 cents 31 .. 62 match: 21 SD: 2.1107 cents 32 .. 64 match: 23 SD: 1.7510 cents 33 .. 66 match: 22 SD: 1.8088 cents 34 .. 68 match: 21 SD: 2.0886 cents 35 .. 70 match: 23 SD: 1.8964 cents 36 .. 72 match: 23 SD: 1.7791 cents 37 .. 74 match: 21 SD: 2.1590 cents 38 .. 76 match: 22 SD: 2.3124 cents 39 .. 78 match: 22 SD: 1.8140 cents 40 .. 80 match: 23 SD: 1.4297 cents 41 .. 82 match: 23 SD: 1.5182 cents 42 .. 84 match: 24 SD: 1.4520 cents 43 .. 86 match: 23 SD: 1.8647 cents 44 .. 88 match: 23 SD: 1.4719 cents 45 .. 90 match: 23 SD: 1.5238 cents 48 .. 96 match: 23 SD: 1.3241 cents 52 .. 104 match: 23 SD: 1.4536 cents 54 .. 108 match: 24 SD: 1.3569 cents 55 .. 110 match: 24 SD: 1.3457 cents 56 .. 112 match: 24 SD: 1.2784 cents 57 .. 114 match: 24 SD: 1.2405 cents 61 .. 122 match: 24 SD: 1.2132 cents 63 .. 126 match: 24 SD: 1.0083 cents 64 .. 128 match: 24 SD: 0.8821 cents 72 .. 144 match: 24 SD: 0.8599 cents 76 .. 152 match: 24 SD: 0.7932 cents 92 .. 184 match: 24 SD: 0.7703 cents 95 .. 190 match: 24 SD: 0.7560 cents 96 .. 192 match: 24 SD: 0.6211 cents 105 .. 210 match: 24 SD: 0.5084 cents 120 .. 240 match: 24 SD: 0.4901 cents 135 .. 270 match: 24 SD: 0.4370 cents 156 .. 312 match: 24 SD: 0.4115 cents 166 .. 332 match: 24 SD: 0.4037 cents 167 .. 334 match: 24 SD: 0.3941 cents 170 .. 340 match: 24 SD: 0.3690 cents 176 .. 352 match: 24 SD: 0.3588 cents 180 .. 360 match: 24 SD: 0.3525 cents 184 .. 368 match: 24 SD: 0.3374 cents 202 .. 404 match: 24 SD: 0.3054 cents 211 .. 422 match: 24 SD: 0.2758 cents 224 .. 448 match: 24 SD: 0.2728 cents 230 .. 460 match: 24 SD: 0.2632 cents 243 .. 486 match: 24 SD: 0.2568 cents 246 .. 492 match: 24 SD: 0.2431 cents 252 .. 504 match: 24 SD: 0.2367 cents 262 .. 524 match: 24 SD: 0.2258 cents 287 .. 574 match: 24 SD: 0.2145 cents 294 .. 588 match: 24 SD: 0.1814 cents 336 .. 672 match: 24 SD: 0.1626 cents 367 .. 734 match: 24 SD: 0.1545 cents 392 .. 784 match: 24 SD: 0.1522 cents 400 .. 800 match: 24 SD: 0.1448 cents 422 .. 844 match: 24 SD: 0.1323 cents 441 .. 882 match: 24 SD: 0.1234 cents 502 .. 1004 match: 24 SD: 0.1180 cents 518 .. 1036 match: 24 SD: 0.1051 cents 537 .. 1074 match: 24 SD: 0.0997 cents