Scala analysis: urania24
Urania[24] hobbit (81/80, 121/120) in POTE tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36.657 cents 36.656670 2: 119.062 cents 119.061910 3: 155.719 cents 155.718570 4: 192.375 cents 192.375240 5: 229.032 cents 229.031900 6: 311.437 cents 311.437140 7: 348.094 cents 348.093810 8: 384.750 cents 384.750470 9: 467.156 cents 467.155720 10: 503.812 cents 503.812380 11: 540.469 cents 540.469050 12: 584.490 cents 584.489610 13: 659.531 cents 659.530950 14: 696.188 cents 696.187620 15: 732.844 cents 732.844280 16: 815.250 cents 815.249530 17: 851.906 cents 851.906190 18: 888.563 cents 888.562860 19: 963.604 cents 963.604200 20: 1007.625 cents 1007.624760 21: 1044.281 cents 1044.281430 22: 1080.938 cents 1080.938090 23: 1163.343 cents 1163.343330 24: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 36.6567 cents 36.6567 1: 36.6567 cents 36.6567 2: 82.4052 cents 82.4052 3: 36.6567 cents 36.6567 4: 36.6567 cents 36.6567 5: 36.6567 cents 36.6567 6: 82.4052 cents 82.4052 7: 36.6567 cents 36.6567 8: 36.6567 cents 36.6567 9: 82.4053 cents 82.4053 10: 36.6567 cents 36.6567 11: 36.6567 cents 36.6567 12: 44.0206 cents 44.0206 13: 75.0413 cents 75.0413 14: 36.6567 cents 36.6567 15: 36.6567 cents 36.6567 16: 82.4053 cents 82.4053 17: 36.6567 cents 36.6567 18: 36.6567 cents 36.6567 19: 75.0413 cents 75.0413 20: 44.0206 cents 44.0206 21: 36.6567 cents 36.6567 22: 36.6567 cents 36.6567 23: 82.4052 cents 82.4052 24: 36.6567 cents 36.6567
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 15 36.65667 cents 1: 2 44.02056 cents 1: 2 75.04134 cents 1: 5 82.40524 cents 2: 8 73.31333 cents 2: 2 80.67723 cents 2: 2 111.69801 cents 2: 12 119.06191 cents 3: 1 109.96999 cents 3: 2 117.33389 cents 3: 2 148.35467 cents 3: 19 155.71857 cents 4: 18 192.37524 cents 4: 2 199.73914 cents 4: 2 230.75992 cents 4: 2 238.12382 cents 5: 11 229.03190 cents 5: 2 236.39580 cents 5: 2 267.41658 cents 5: 9 274.78047 cents 6: 4 265.68856 cents 6: 2 273.05247 cents 6: 2 304.07325 cents 6: 16 311.43714 cents 7: 21 348.09381 cents 7: 2 355.45771 cents 7: 1 379.11459 cents 8: 14 384.75047 cents 8: 2 392.11437 cents 8: 2 423.13515 cents 8: 6 430.49905 cents 9: 7 421.40714 cents 9: 2 428.77104 cents 9: 2 459.79182 cents 9: 13 467.15572 cents 10: 2 465.42770 cents 10: 2 496.44848 cents 10: 20 503.81238 cents 11: 17 540.46905 cents 11: 2 547.83294 cents 11: 2 578.85373 cents 11: 3 586.21763 cents 12: 10 577.12571 cents 12: 2 584.48961 cents 12: 2 615.51039 cents 12: 10 622.87428 cents 13: 3 613.78237 cents 13: 2 621.14627 cents 13: 2 652.16706 cents 13: 17 659.53095 cents 14: 20 696.18762 cents 14: 2 703.55152 cents 14: 2 734.57230 cents 15: 13 732.84428 cents 15: 2 740.20818 cents 15: 2 771.22896 cents 15: 7 778.59286 cents 16: 6 769.50095 cents 16: 2 776.86485 cents 16: 2 807.88563 cents 16: 14 815.24953 cents 17: 1 820.88541 cents 17: 2 844.54229 cents 17: 21 851.90619 cents 18: 16 888.56286 cents 18: 2 895.92675 cents 18: 2 926.94753 cents 18: 4 934.31143 cents 19: 9 925.21952 cents 19: 2 932.58342 cents 19: 2 963.60420 cents 19: 11 970.96809 cents 20: 2 961.87618 cents 20: 2 969.24008 cents 20: 2 1000.26086 cents 20: 18 1007.62476 cents 21: 19 1044.28143 cents 21: 2 1051.64533 cents 21: 2 1082.66611 cents 21: 1 1090.03001 cents 22: 12 1080.93809 cents 22: 2 1088.30199 cents 22: 2 1119.32277 cents 22: 8 1126.68666 cents 23: 5 1117.59476 cents 23: 2 1124.95866 cents 23: 2 1155.97944 cents 23: 15 1163.34333 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.82609 = 88/23
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 : 36.7 119.1 155.7 192.4 229.0 311.4 348.1 384.8 467.2 503.8 540.5 584.5 659.5 696.2 732.8 815.2 851.9 888.6 963.6 1007.6 1044.3 1080.9 1163.3 1200.0 36.7 : 82.4 119.1 155.7 192.4 274.8 311.4 348.1 430.5 467.2 503.8 547.8 622.9 659.5 696.2 778.6 815.2 851.9 926.9 971.0 1007.6 1044.3 1126.7 1163.3 1200.0 119.1 : 36.7 73.3 110.0 192.4 229.0 265.7 348.1 384.8 421.4 465.4 540.5 577.1 613.8 696.2 732.8 769.5 844.5 888.6 925.2 961.9 1044.3 1080.9 1117.6 1200.0 155.7 : 36.7 73.3 155.7 192.4 229.0 311.4 348.1 384.8 428.8 503.8 540.5 577.1 659.5 696.2 732.8 807.9 851.9 888.6 925.2 1007.6 1044.3 1080.9 1163.3 1200.0 192.4 : 36.7 119.1 155.7 192.4 274.8 311.4 348.1 392.1 467.2 503.8 540.5 622.9 659.5 696.2 771.2 815.2 851.9 888.6 971.0 1007.6 1044.3 1126.7 1163.3 1200.0 229.0 : 82.4 119.1 155.7 238.1 274.8 311.4 355.5 430.5 467.2 503.8 586.2 622.9 659.5 734.6 778.6 815.2 851.9 934.3 971.0 1007.6 1090.0 1126.7 1163.3 1200.0 311.4 : 36.7 73.3 155.7 192.4 229.0 273.1 348.1 384.8 421.4 503.8 540.5 577.1 652.2 696.2 732.8 769.5 851.9 888.6 925.2 1007.6 1044.3 1080.9 1117.6 1200.0 348.1 : 36.7 119.1 155.7 192.4 236.4 311.4 348.1 384.8 467.2 503.8 540.5 615.5 659.5 696.2 732.8 815.2 851.9 888.6 971.0 1007.6 1044.3 1080.9 1163.3 1200.0 384.8 : 82.4 119.1 155.7 199.7 274.8 311.4 348.1 430.5 467.2 503.8 578.9 622.9 659.5 696.2 778.6 815.2 851.9 934.3 971.0 1007.6 1044.3 1126.7 1163.3 1200.0 467.2 : 36.7 73.3 117.3 192.4 229.0 265.7 348.1 384.8 421.4 496.4 540.5 577.1 613.8 696.2 732.8 769.5 851.9 888.6 925.2 961.9 1044.3 1080.9 1117.6 1200.0 503.8 : 36.7 80.7 155.7 192.4 229.0 311.4 348.1 384.8 459.8 503.8 540.5 577.1 659.5 696.2 732.8 815.2 851.9 888.6 925.2 1007.6 1044.3 1080.9 1163.3 1200.0 540.5 : 44.0 119.1 155.7 192.4 274.8 311.4 348.1 423.1 467.2 503.8 540.5 622.9 659.5 696.2 778.6 815.2 851.9 888.6 971.0 1007.6 1044.3 1126.7 1163.3 1200.0 584.5 : 75.0 111.7 148.4 230.8 267.4 304.1 379.1 423.1 459.8 496.4 578.9 615.5 652.2 734.6 771.2 807.9 844.5 926.9 963.6 1000.3 1082.7 1119.3 1156.0 1200.0 659.5 : 36.7 73.3 155.7 192.4 229.0 304.1 348.1 384.8 421.4 503.8 540.5 577.1 659.5 696.2 732.8 769.5 851.9 888.6 925.2 1007.6 1044.3 1080.9 1125.0 1200.0 696.2 : 36.7 119.1 155.7 192.4 267.4 311.4 348.1 384.8 467.2 503.8 540.5 622.9 659.5 696.2 732.8 815.2 851.9 888.6 971.0 1007.6 1044.3 1088.3 1163.3 1200.0 732.8 : 82.4 119.1 155.7 230.8 274.8 311.4 348.1 430.5 467.2 503.8 586.2 622.9 659.5 696.2 778.6 815.2 851.9 934.3 971.0 1007.6 1051.6 1126.7 1163.3 1200.0 815.2 : 36.7 73.3 148.4 192.4 229.0 265.7 348.1 384.8 421.4 503.8 540.5 577.1 613.8 696.2 732.8 769.5 851.9 888.6 925.2 969.2 1044.3 1080.9 1117.6 1200.0 851.9 : 36.7 111.7 155.7 192.4 229.0 311.4 348.1 384.8 467.2 503.8 540.5 577.1 659.5 696.2 732.8 815.2 851.9 888.6 932.6 1007.6 1044.3 1080.9 1163.3 1200.0 888.6 : 75.0 119.1 155.7 192.4 274.8 311.4 348.1 430.5 467.2 503.8 540.5 622.9 659.5 696.2 778.6 815.2 851.9 895.9 971.0 1007.6 1044.3 1126.7 1163.3 1200.0 963.6 : 44.0 80.7 117.3 199.7 236.4 273.1 355.5 392.1 428.8 465.4 547.8 584.5 621.1 703.6 740.2 776.9 820.9 895.9 932.6 969.2 1051.6 1088.3 1125.0 1200.0 1007.6: 36.7 73.3 155.7 192.4 229.0 311.4 348.1 384.8 421.4 503.8 540.5 577.1 659.5 696.2 732.8 776.9 851.9 888.6 925.2 1007.6 1044.3 1080.9 1156.0 1200.0 1044.3: 36.7 119.1 155.7 192.4 274.8 311.4 348.1 384.8 467.2 503.8 540.5 622.9 659.5 696.2 740.2 815.2 851.9 888.6 971.0 1007.6 1044.3 1119.3 1163.3 1200.0 1080.9: 82.4 119.1 155.7 238.1 274.8 311.4 348.1 430.5 467.2 503.8 586.2 622.9 659.5 703.6 778.6 815.2 851.9 934.3 971.0 1007.6 1082.7 1126.7 1163.3 1200.0 1163.3: 36.7 73.3 155.7 192.4 229.0 265.7 348.1 384.8 421.4 503.8 540.5 577.1 621.1 696.2 732.8 769.5 851.9 888.6 925.2 1000.3 1044.3 1080.9 1117.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.6567 .. 82.4052 cents 45.74857 cents 36.65667 cents 2: 73.3133 .. 119.0619 cents 45.74858 cents -9.09191 cents 3: 109.9700 .. 155.7186 cents 45.74858 cents -9.09192 cents 4: 192.3752 .. 238.1238 cents 45.74858 cents 36.65667 cents 5: 229.0319 .. 274.7805 cents 45.74857 cents -9.09192 cents 6: 265.6886 .. 311.4371 cents 45.74858 cents -9.09191 cents 7: 348.0938 .. 379.1146 cents 31.02078 cents 36.65667 cents 8: 384.7505 .. 430.4991 cents 45.74858 cents 5.63588 cents 9: 421.4071 .. 467.1557 cents 45.74858 cents -9.09191 cents 10: 465.4277 .. 503.8124 cents 38.38468 cents -1.72802 cents 11: 540.4691 .. 586.2176 cents 45.74858 cents 36.65667 cents 12: 577.1257 .. 622.8743 cents 45.74857 cents -9.09192 cents 13: 613.7824 .. 659.5309 cents 45.74858 cents -9.09191 cents 14: 696.1876 .. 734.5723 cents 38.38468 cents 36.65667 cents 15: 732.8443 .. 778.5929 cents 45.74858 cents -1.72802 cents 16: 769.5009 .. 815.2495 cents 45.74858 cents -9.09191 cents 17: 820.8854 .. 851.9062 cents 31.02078 cents 5.63588 cents 18: 888.5629 .. 934.3114 cents 45.74857 cents 36.65667 cents 19: 925.2195 .. 970.9681 cents 45.74857 cents -9.09191 cents 20: 961.8762 .. 1007.6248 cents 45.74858 cents -9.09191 cents 21: 1044.2814 .. 1090.0300 cents 45.74858 cents 36.65667 cents 22: 1080.9381 .. 1126.6867 cents 45.74857 cents -9.09192 cents 23: 1117.5948 .. 1163.3433 cents 45.74857 cents -9.09190 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 36.65666 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 82.40524 cents Average / Smallest step : 1.364009 Largest / Average step : 1.648105 Largest / Smallest step : 2.248029 Median interval of one step : 36.65667 cents, amount: 15 Most common interval of one step : 36.65667 cents, amount: 15 Least squares average step : 49.95991 cents, oct.: 1199.03795 cents Scale is not proper Step pattern alph. order: ABAAABAABAACDAABAADCAABA Step pattern size order : ADAAADAADAABCAADAACBAADA Scale is a Constant Structure, by a margin of 1.72800 cents Scale diversity : 1.209307 Lumma stability : 0.253771 Lumma impropriety factor : 0.093799 Number of different interval sizes : 88 = 3.82609 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.82609 = 88/23 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1.72800 cents Most common intervals : 348.09381 cents & inv., amount: 21 Most common triad is 0.0 348.094 851.906 cents, amount: 20 Number of recognisable fifths : 22, average 696.8571 cents Formal octave complements present : 21 = 87.5000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 15-16 -- 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: 12.3544 c. M:-20.9681 c. 28: 1 2 0 1 1 2 1 1 2 1 0 1 2 1 1 2 1 1 1 1 1 1 2 1 N D3 SD: 14.5686 c. M: 27.3468 c. 29: 1 2 1 1 1 2 0 1 2 1 1 1 2 1 1 2 1 0 2 1 1 1 2 1 N SD: 11.7407 c. M:-19.5973 c. 30: 1 2 1 1 1 2 1 1 2 1 1 1 2 0 1 2 1 1 2 1 1 1 2 1 N D3 SD: 11.3663 c. M:-20.4691 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: 2.1266 c. M:-4.1377 c. 100: 3 7 3 3 3 7 3 3 7 3 3 4 6 3 3 7 3 3 6 4 3 3 7 3 N SD: 1.1753 c. M: 3.6042 c. 131: 4 9 4 4 4 9 4 4 9 4 4 5 8 4 4 9 4 4 8 5 4 4 9 4 N SD: 0.5114 c. M: 1.7721 c. 162: 5 11 5 5 5 11 5 5 11 5 5 6 10 5 5 11 5 5 10 6 5 5 11 5 N SD: 0.3833 c. M:-0.6956 c. 293: 9 20 9 9 9 20 9 9 20 9 9 11 18 9 9 20 9 9 18 11 9 9 20 9 N SD: 0.3792 c. M:-1.1759 c. 362: 11 25 11 11 11 25 11 11 25 11 11 13 23 11 11 25 11 11 23 13 11 11 25 11 N SD: 0.3465 c. M: 1.0642 c. 462: 14 32 14 14 14 32 14 14 32 14 14 17 29 14 14 32 14 14 29 17 14 14 32 14 N SD: 0.2556 c. M: 0.4605 c. 493: 15 34 15 15 15 34 15 15 34 15 15 18 31 15 15 34 15 15 31 18 15 15 34 15 N SD: 0.1536 c. M: 0.3111 c. 524: 16 36 16 16 16 36 16 16 36 16 16 19 33 16 16 36 16 16 33 19 16 16 36 16 N SD: 0.1504 c. M: 0.5201 c. 624: 19 43 19 19 19 43 19 19 43 19 19 23 39 19 19 43 19 19 39 23 19 19 43 19 N SD: 0.1100 c. M: 0.1857 c. 655: 20 45 20 20 20 45 20 20 45 20 20 24 41 20 20 45 20 20 41 24 20 20 45 20 N SD: 0.0222 c. M: 0.0621 c. 1472: 45 101 45 45 45 101 45 45 101 45 45 54 92 45 45 101 45 45 92 54 45 45 101 45 N SD: 0.0251 c. M:-0.0442 c. 2096: 64 144 64 64 64 144 64 64 144 64 64 77 131 64 64 144 64 64 131 77 64 64 144 64 N SD: 0.0205 c. M: 0.0546 c. 2127: 65 146 65 65 65 146 65 65 146 65 65 78 133 65 65 146 65 65 133 78 65 65 146 65 N SD: 0.0129 c. M:-0.0231 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 2.8837 cents 3 .. 6 match: 3 H SD: 2.3790 cents 4 .. 8 match: 4 H SD: 1.9839 cents 5 .. 10 match: 5 H SD: 2.2223 cents 6 .. 12 match: 6 H SD: 6.5443 cents 7 .. 14 match: 7 H SD: 9.2683 cents 8 .. 16 match: 8 H SD: 2.7865 cents 9 .. 18 match: 9 H SD: 5.2609 cents 10 .. 20 match: 10 H SD: 4.7233 cents 11 .. 22 match: 11 H SD: 5.7706 cents 12 .. 24 match: 11 S SD: 4.6318 cents 13 .. 26 match: 13 H SD: 4.6001 cents 14 .. 28 match: 14 H SD: 5.1942 cents 15 .. 30 match: 15 H SD: 2.7150 cents 16 .. 32 match: 15 S SD: 3.4837 cents 17 .. 34 match: 16 S SD: 3.8323 cents 18 .. 36 match: 16 SD: 4.1276 cents 19 .. 38 match: 18 SD: 3.7050 cents 20 .. 40 match: 18 SD: 3.2948 cents 21 .. 42 match: 15 SD: 2.9534 cents 22 .. 44 match: 20 SD: 3.1592 cents 23 .. 46 match: 18 SD: 3.1787 cents 24 .. 48 match: 21 SD: 2.9793 cents 25 .. 50 match: 20 SD: 2.9489 cents 26 .. 52 match: 20 SD: 3.0891 cents 27 .. 54 match: 22 SD: 2.4339 cents 28 .. 56 match: 21 SD: 2.1142 cents 29 .. 58 match: 22 SD: 2.6276 cents 30 .. 60 match: 22 SD: 1.8058 cents 31 .. 62 match: 22 SD: 2.5164 cents 32 .. 64 match: 24 SD: 2.0946 cents 33 .. 66 match: 23 SD: 2.0794 cents 34 .. 68 match: 22 SD: 2.4520 cents 35 .. 70 match: 24 SD: 1.9496 cents 36 .. 72 match: 23 SD: 1.7044 cents 37 .. 74 match: 23 SD: 2.2850 cents 38 .. 76 match: 23 SD: 2.1904 cents 39 .. 78 match: 24 SD: 1.9466 cents 40 .. 80 match: 24 SD: 1.6854 cents 41 .. 82 match: 24 SD: 1.5220 cents 42 .. 84 match: 24 SD: 1.4548 cents 44 .. 88 match: 24 SD: 1.4126 cents 45 .. 90 match: 24 SD: 1.4015 cents 51 .. 102 match: 24 SD: 1.2955 cents 52 .. 104 match: 24 SD: 1.1341 cents 65 .. 130 match: 24 SD: 1.0823 cents 68 .. 136 match: 24 SD: 1.0616 cents 71 .. 142 match: 24 SD: 0.9486 cents 76 .. 152 match: 24 SD: 0.9004 cents 77 .. 154 match: 24 SD: 0.8287 cents 85 .. 170 match: 24 SD: 0.5914 cents 112 .. 224 match: 24 SD: 0.5700 cents 125 .. 250 match: 24 SD: 0.5225 cents 127 .. 254 match: 24 SD: 0.4613 cents 136 .. 272 match: 24 SD: 0.4511 cents 142 .. 284 match: 24 SD: 0.4051 cents 169 .. 338 match: 24 SD: 0.3890 cents 171 .. 342 match: 24 SD: 0.3815 cents 172 .. 344 match: 24 SD: 0.3722 cents 180 .. 360 match: 24 SD: 0.3639 cents 181 .. 362 match: 24 SD: 0.3427 cents 184 .. 368 match: 24 SD: 0.3281 cents 212 .. 424 match: 24 SD: 0.3183 cents 213 .. 426 match: 24 SD: 0.3030 cents 220 .. 440 match: 24 SD: 0.2955 cents 224 .. 448 match: 24 SD: 0.2672 cents 233 .. 466 match: 24 SD: 0.2630 cents 239 .. 478 match: 24 SD: 0.2600 cents 254 .. 508 match: 24 SD: 0.2567 cents 264 .. 528 match: 24 SD: 0.2403 cents 269 .. 538 match: 24 SD: 0.2342 cents 278 .. 556 match: 24 SD: 0.2290 cents 281 .. 562 match: 24 SD: 0.2217 cents 289 .. 578 match: 24 SD: 0.2164 cents 309 .. 618 match: 24 SD: 0.1888 cents 319 .. 638 match: 24 SD: 0.1854 cents 332 .. 664 match: 24 SD: 0.1849 cents 338 .. 676 match: 24 SD: 0.1724 cents 341 .. 682 match: 24 SD: 0.1603 cents 376 .. 752 match: 24 SD: 0.1601 cents 381 .. 762 match: 24 SD: 0.1524 cents 382 .. 764 match: 24 SD: 0.1395 cents 423 .. 846 match: 24 SD: 0.1260 cents 459 .. 918 match: 24 SD: 0.1241 cents 467 .. 934 match: 24 SD: 0.1176 cents 503 .. 1006 match: 24 SD: 0.1150 cents 522 .. 1044 match: 24 SD: 0.1108 cents 552 .. 1104 match: 24 SD: 0.0980 cents