Scala analysis: euler20
3^5 5^4 Euler genus tempered by 225/224-planar
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.677 cents 83.676704 2: 152.139 cents 152.139461 3: 199.683 cents 199.683043 4: 268.146 cents 268.145800 5: 351.823 cents 351.822504 6: 384.152 cents 384.152140 7: 399.366 cents 399.366086 8: 467.829 cents 467.828843 9: 583.835 cents 583.835182 10: 652.298 cents 652.297940 11: 699.842 cents 699.841521 12: 768.304 cents 768.304279 13: 783.518 cents 783.518225 14: 851.981 cents 851.980983 15: 899.525 cents 899.524564 16: 967.987 cents 967.987322 17: 1083.994 cents 1083.993661 18: 1152.456 cents 1152.456418 19: 1167.670 cents 1167.670365 20: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 32.3296 cents 32.3296 1: 83.6767 cents 83.6767 2: 68.4628 cents 68.4628 3: 47.5436 cents 47.5436 4: 68.4628 cents 68.4628 5: 83.6767 cents 83.6767 6: 32.3296 cents 32.3296 7: 15.2139 cents 15.2139 8: 68.4628 cents 68.4628 9: 116.0063 cents 116.0063 10: 68.4628 cents 68.4628 11: 47.5436 cents 47.5436 12: 68.4628 cents 68.4628 13: 15.2139 cents 15.2139 14: 68.4628 cents 68.4628 15: 47.5436 cents 47.5436 16: 68.4628 cents 68.4628 17: 116.0063 cents 116.0063 18: 68.4628 cents 68.4628 19: 15.2139 cents 15.2139 20: 32.3296 cents 32.3296
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 15.21395 cents 1: 2 32.32964 cents 1: 3 47.54358 cents 1: 8 68.46276 cents 1: 2 83.67670 cents 1: 2 116.00634 cents 2: 2 47.54358 cents 2: 4 83.67670 cents 2: 8 116.00634 cents 2: 2 152.13946 cents 2: 4 184.46910 cents 3: 2 116.00634 cents 3: 4 131.22029 cents 3: 1 152.13946 cents 3: 5 184.46910 cents 3: 4 199.68304 cents 3: 2 232.01268 cents 3: 2 252.93185 cents 4: 8 199.68304 cents 4: 4 232.01268 cents 4: 4 268.14580 cents 4: 4 300.47544 cents 5: 3 247.22662 cents 5: 4 268.14580 cents 5: 4 300.47544 cents 5: 6 315.68938 cents 5: 1 351.82250 cents 5: 2 368.93819 cents 6: 6 315.68938 cents 6: 2 348.01902 cents 6: 12 384.15214 cents 7: 3 384.15214 cents 7: 4 399.36609 cents 7: 3 416.48177 cents 7: 6 431.69572 cents 7: 4 452.61490 cents 8: 4 431.69572 cents 8: 4 467.82884 cents 8: 12 500.15848 cents 9: 1 446.90967 cents 9: 4 500.15848 cents 9: 4 515.37242 cents 9: 2 547.70206 cents 9: 6 568.62124 cents 9: 2 583.83518 cents 9: 1 616.16482 cents 10: 2 515.37242 cents 10: 2 547.70206 cents 10: 6 583.83518 cents 10: 6 616.16482 cents 10: 2 652.29794 cents 10: 2 684.62758 cents 11: 1 583.83518 cents 11: 2 616.16482 cents 11: 6 631.37876 cents 11: 2 652.29794 cents 11: 4 684.62758 cents 11: 4 699.84152 cents 11: 1 753.09033 cents 12: 12 699.84152 cents 12: 4 732.17116 cents 12: 4 768.30428 cents 13: 4 747.38510 cents 13: 6 768.30428 cents 13: 3 783.51823 cents 13: 4 800.63391 cents 13: 3 815.84786 cents 14: 12 815.84786 cents 14: 2 851.98098 cents 14: 6 884.31062 cents 15: 2 831.06181 cents 15: 1 848.17750 cents 15: 6 884.31062 cents 15: 4 899.52456 cents 15: 4 931.85420 cents 15: 3 952.77338 cents 16: 4 899.52456 cents 16: 4 931.85420 cents 16: 4 967.98732 cents 16: 8 1000.31696 cents 17: 2 947.06815 cents 17: 2 967.98732 cents 17: 4 1000.31696 cents 17: 5 1015.53090 cents 17: 1 1047.86054 cents 17: 4 1068.77971 cents 17: 2 1083.99366 cents 18: 4 1015.53090 cents 18: 2 1047.86054 cents 18: 8 1083.99366 cents 18: 4 1116.32330 cents 18: 2 1152.45642 cents 19: 2 1083.99366 cents 19: 2 1116.32330 cents 19: 8 1131.53724 cents 19: 3 1152.45642 cents 19: 2 1167.67037 cents 19: 3 1184.78605 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.15789 = 98/19
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0.0 : 83.7 152.1 199.7 268.1 351.8 384.2 399.4 467.8 583.8 652.3 699.8 768.3 783.5 852.0 899.5 968.0 1084.0 1152.5 1167.7 1200.0 83.7 : 68.5 116.0 184.5 268.1 300.5 315.7 384.2 500.2 568.6 616.2 684.6 699.8 768.3 815.8 884.3 1000.3 1068.8 1084.0 1116.3 1200.0 152.1 : 47.5 116.0 199.7 232.0 247.2 315.7 431.7 500.2 547.7 616.2 631.4 699.8 747.4 815.8 931.9 1000.3 1015.5 1047.9 1131.5 1200.0 199.7 : 68.5 152.1 184.5 199.7 268.1 384.2 452.6 500.2 568.6 583.8 652.3 699.8 768.3 884.3 952.8 968.0 1000.3 1084.0 1152.5 1200.0 268.1 : 83.7 116.0 131.2 199.7 315.7 384.2 431.7 500.2 515.4 583.8 631.4 699.8 815.8 884.3 899.5 931.9 1015.5 1084.0 1131.5 1200.0 351.8 : 32.3 47.5 116.0 232.0 300.5 348.0 416.5 431.7 500.2 547.7 616.2 732.2 800.6 815.8 848.2 931.9 1000.3 1047.9 1116.3 1200.0 384.2 : 15.2 83.7 199.7 268.1 315.7 384.2 399.4 467.8 515.4 583.8 699.8 768.3 783.5 815.8 899.5 968.0 1015.5 1084.0 1167.7 1200.0 399.4 : 68.5 184.5 252.9 300.5 368.9 384.2 452.6 500.2 568.6 684.6 753.1 768.3 800.6 884.3 952.8 1000.3 1068.8 1152.5 1184.8 1200.0 467.8 : 116.0 184.5 232.0 300.5 315.7 384.2 431.7 500.2 616.2 684.6 699.8 732.2 815.8 884.3 931.9 1000.3 1084.0 1116.3 1131.5 1200.0 583.8 : 68.5 116.0 184.5 199.7 268.1 315.7 384.2 500.2 568.6 583.8 616.2 699.8 768.3 815.8 884.3 968.0 1000.3 1015.5 1084.0 1200.0 652.3 : 47.5 116.0 131.2 199.7 247.2 315.7 431.7 500.2 515.4 547.7 631.4 699.8 747.4 815.8 899.5 931.9 947.1 1015.5 1131.5 1200.0 699.8 : 68.5 83.7 152.1 199.7 268.1 384.2 452.6 467.8 500.2 583.8 652.3 699.8 768.3 852.0 884.3 899.5 968.0 1084.0 1152.5 1200.0 768.3 : 15.2 83.7 131.2 199.7 315.7 384.2 399.4 431.7 515.4 583.8 631.4 699.8 783.5 815.8 831.1 899.5 1015.5 1084.0 1131.5 1200.0 783.5 : 68.5 116.0 184.5 300.5 368.9 384.2 416.5 500.2 568.6 616.2 684.6 768.3 800.6 815.8 884.3 1000.3 1068.8 1116.3 1184.8 1200.0 852.0 : 47.5 116.0 232.0 300.5 315.7 348.0 431.7 500.2 547.7 616.2 699.8 732.2 747.4 815.8 931.9 1000.3 1047.9 1116.3 1131.5 1200.0 899.5 : 68.5 184.5 252.9 268.1 300.5 384.2 452.6 500.2 568.6 652.3 684.6 699.8 768.3 884.3 952.8 1000.3 1068.8 1084.0 1152.5 1200.0 968.0 : 116.0 184.5 199.7 232.0 315.7 384.2 431.7 500.2 583.8 616.2 631.4 699.8 815.8 884.3 931.9 1000.3 1015.5 1084.0 1131.5 1200.0 1084.0: 68.5 83.7 116.0 199.7 268.1 315.7 384.2 467.8 500.2 515.4 583.8 699.8 768.3 815.8 884.3 899.5 968.0 1015.5 1084.0 1200.0 1152.5: 15.2 47.5 131.2 199.7 247.2 315.7 399.4 431.7 446.9 515.4 631.4 699.8 747.4 815.8 831.1 899.5 947.1 1015.5 1131.5 1200.0 1167.7: 32.3 116.0 184.5 232.0 300.5 384.2 416.5 431.7 500.2 616.2 684.6 732.2 800.6 815.8 884.3 931.9 1000.3 1116.3 1184.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 15.2139 .. 116.0063 cents 100.79239 cents 15.21395 cents 2: 47.5436 .. 184.4691 cents 136.92552 cents -68.46276 cents 3: 116.0063 .. 252.9319 cents 136.92552 cents -68.46276 cents 4: 199.6830 .. 300.4754 cents 100.79239 cents -53.24881 cents 5: 247.2266 .. 368.9382 cents 121.71157 cents -53.24881 cents 6: 315.6894 .. 384.1521 cents 68.46276 cents -53.24881 cents 7: 384.1521 .. 452.6149 cents 68.46276 cents -0.00000 cents 8: 431.6957 .. 500.1585 cents 68.46276 cents -20.91918 cents 9: 446.9097 .. 616.1648 cents 169.25515 cents -53.24881 cents 10: 515.3724 .. 684.6276 cents 169.25515 cents -100.79239 cents 11: 583.8352 .. 753.0903 cents 169.25515 cents -100.79239 cents 12: 699.8415 .. 768.3043 cents 68.46276 cents -53.24881 cents 13: 747.3851 .. 815.8479 cents 68.46276 cents -20.91918 cents 14: 815.8479 .. 884.3106 cents 68.46276 cents -0.00000 cents 15: 831.0618 .. 952.7734 cents 121.71157 cents -53.24881 cents 16: 899.5246 .. 1000.3170 cents 100.79239 cents -53.24881 cents 17: 947.0681 .. 1083.9937 cents 136.92552 cents -53.24881 cents 18: 1015.5309 .. 1152.4564 cents 136.92551 cents -68.46276 cents 19: 1083.9937 .. 1184.7861 cents 100.79239 cents -68.46276 cents
SHOW DATA
Number of notes : 20 -- Interval properties -- Smallest interval : 15.21395 cents, class 1 Average step (divided formal octave): 60.0000 cents Largest one step interval : 116.00634 cents Average / Smallest step : 3.943750 Largest / Average step : 1.933439 Largest / Smallest step : 7.625000 Median interval of one step : 68.46276 cents, amount: 8 Most common interval of one step : 68.46276 cents, amount: 8 Least squares average step : 61.95442 cents, oct.: 1239.08844 cents Scale is not proper Scale is a mode of a 631-tone equal temperament with octave 2/1 degrees: 44 80 105 141 185 202 210 246 307 343 368 404 412 448 473 509 570 606 614 631 Least number of segments generator : 316 of 600.951 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 512 of 973.693 cents and inv. generated superset size: 98 = 78 more = 490.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBADEBFBCBEBCBFBED Step pattern size order : EDCDEBADFDCDADCDFDAB Scale is not a Constant Structure Scale diversity : 1.325381 Lumma stability : 0.025357 Lumma impropriety factor : 0.740095 Number of different interval sizes : 62 = 3.26316 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 5.15789 = 98/19 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 3.80349 cents Most common intervals : 500.15848 cents & inv., amount: 16 Most common triad is 0.0 500.158 699.842 cents, amount: 12 Number of recognisable fifths : 16, average 699.8415 cents Formal octave complements present : 1 = 5.0000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 12-13 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
20: 1 2 0 1 2 0 1 1 2 1 1 1 0 1 1 1 2 1 0 1 N T3 SD: 16.9720 c. M: 28.1458 c. 23: 2 1 1 1 2 0 1 1 2 2 0 2 0 1 1 2 2 1 0 1 N SD: 14.8977 c. M:-25.9629 c. 24: 2 1 1 1 2 1 0 1 3 1 1 1 1 1 1 1 3 1 0 1 N SD: 12.1421 c. M: 18.3043 c. 28: 2 2 1 1 2 1 0 2 3 1 1 2 0 2 1 2 2 2 0 1 N SD: 10.7944 c. M:-19.2891 c. 31: 2 2 1 2 2 1 0 2 3 2 1 2 0 2 1 2 3 2 0 1 N SD: 5.7102 c. M: 12.2693 c. 41: 3 2 2 2 3 1 1 2 4 2 2 2 1 2 2 2 4 2 1 1 N SD: 5.5108 c. M: 10.9930 c. 48: 3 3 2 3 3 1 1 3 4 3 2 3 0 3 2 3 4 3 1 1 N SD: 5.7471 c. M: 9.1521 c. 55: 4 3 2 3 4 2 0 3 6 3 2 3 1 3 2 3 6 3 0 2 N SD: 5.5862 c. M: 11.3067 c. 61: 4 4 2 4 4 2 0 4 6 3 3 3 1 3 3 3 6 4 0 2 N SD: 5.4501 c. M:-9.2905 c. 62: 4 4 2 4 4 2 1 3 6 4 2 4 0 4 2 4 6 4 0 2 N SD: 5.2526 c. M: 9.3247 c. 68: 5 4 2 4 5 2 1 4 6 4 3 4 0 4 3 4 6 4 1 2 N SD: 5.1212 c. M:-8.6417 c. 69: 5 4 2 4 5 2 1 4 7 3 3 4 1 4 3 4 6 4 1 2 N SD: 4.7702 c. M: 8.8197 c. 70: 5 4 3 4 5 1 1 4 7 4 3 4 1 4 2 4 7 4 1 2 N SD: 4.9311 c. M:-8.1775 c. 71: 5 4 3 4 5 2 1 4 7 4 2 4 1 4 3 4 7 4 1 2 N SD: 4.8263 c. M: 7.7409 c. 72: 5 4 3 4 5 2 1 4 7 4 3 4 1 4 3 4 7 4 1 2 N SD: 1.3110 c. M: 2.4564 c. 156: 11 9 6 9 11 4 2 9 15 9 6 9 2 9 6 9 15 9 2 4 N SD: 1.1586 c. M:-2.0236 c. 228: 16 13 9 13 16 6 3 13 22 13 9 13 3 13 9 13 22 13 3 6 N SD: 0.4671 c. M:-0.8091 c. 300: 21 17 12 17 21 8 4 17 29 17 12 17 4 17 12 17 29 17 4 8 N SD: 0.2950 c. M:-0.6339 c. 331: 23 19 13 19 23 9 4 19 32 19 13 19 4 19 13 19 32 19 4 9 N SD: 0.2674 c. M: 0.5745 c. 403: 28 23 16 23 28 11 5 23 39 23 16 23 5 23 16 23 39 23 5 11 N SD: 0.2642 c. M: 0.4577 c. 559: 39 32 22 32 39 15 7 32 54 32 22 32 7 32 22 32 54 32 7 15 N SD: 0.1689 c. M:-0.3164 c. 631: 44 36 25 36 44 17 8 36 61 36 25 36 8 36 25 36 61 36 8 17 N SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.0567 cents 3 .. 6 match: 3 H SD: 11.2695 cents 4 .. 8 match: 4 H SD: 0.7843 cents 5 .. 10 match: 5 H SD: 13.6850 cents 6 .. 12 match: 6 H SD: 8.0767 cents 7 .. 14 match: 7 H SD: 9.5595 cents 8 .. 16 match: 8 H SD: 4.3920 cents 9 .. 18 match: 9 H SD: 5.8784 cents 10 .. 20 match: 9 SD: 6.7421 cents 11 .. 22 match: 10 SD: 6.9031 cents 12 .. 24 match: 12 H SD: 5.0917 cents 13 .. 26 match: 13 H SD: 4.8132 cents 14 .. 28 match: 12 S SD: 6.5038 cents 15 .. 30 match: 14 S SD: 5.4574 cents 16 .. 32 match: 15 S SD: 3.8003 cents 17 .. 34 match: 14 SD: 3.8947 cents 18 .. 36 match: 16 SD: 4.1376 cents 19 .. 38 match: 15 SD: 3.5887 cents 20 .. 40 match: 15 SD: 3.1165 cents 21 .. 42 match: 15 SD: 4.8474 cents 22 .. 44 match: 18 SD: 2.8959 cents 23 .. 46 match: 16 SD: 2.7828 cents 24 .. 48 match: 18 SD: 2.9648 cents 25 .. 50 match: 16 SD: 2.9048 cents 26 .. 52 match: 17 SD: 3.3015 cents 27 .. 54 match: 17 SD: 3.6748 cents 28 .. 56 match: 17 SD: 2.9032 cents 29 .. 58 match: 19 SD: 3.2530 cents 30 .. 60 match: 18 SD: 2.7114 cents 31 .. 62 match: 19 SD: 2.4869 cents 32 .. 64 match: 18 SD: 2.0579 cents 34 .. 68 match: 18 SD: 2.4833 cents 35 .. 70 match: 18 SD: 1.7916 cents 36 .. 72 match: 19 SD: 2.1150 cents 37 .. 74 match: 19 SD: 2.4472 cents 38 .. 76 match: 19 SD: 2.2227 cents 39 .. 78 match: 18 SD: 2.0953 cents 40 .. 80 match: 19 SD: 1.6663 cents 41 .. 82 match: 18 SD: 1.7087 cents 42 .. 84 match: 19 SD: 1.7763 cents 43 .. 86 match: 18 SD: 1.7879 cents 44 .. 88 match: 17 SD: 1.5966 cents 45 .. 90 match: 19 SD: 1.8822 cents 46 .. 92 match: 18 SD: 1.9224 cents 47 .. 94 match: 19 SD: 1.7430 cents 48 .. 96 match: 18 SD: 1.4956 cents 51 .. 102 match: 19 SD: 1.9648 cents 52 .. 104 match: 19 SD: 1.3458 cents 53 .. 106 match: 19 SD: 1.5081 cents 54 .. 108 match: 20 SD: 1.2757 cents 55 .. 110 match: 18 SD: 1.2782 cents 57 .. 114 match: 20 SD: 1.1774 cents 59 .. 118 match: 19 SD: 1.2847 cents 60 .. 120 match: 19 SD: 1.4099 cents 61 .. 122 match: 20 SD: 1.2379 cents 62 .. 124 match: 19 SD: 1.3294 cents 63 .. 126 match: 19 SD: 1.2247 cents 64 .. 128 match: 20 SD: 1.1670 cents 65 .. 130 match: 20 SD: 1.0219 cents 67 .. 134 match: 19 SD: 1.2029 cents 68 .. 136 match: 20 SD: 1.0948 cents 69 .. 138 match: 19 SD: 1.4438 cents 70 .. 140 match: 20 SD: 1.2489 cents 71 .. 142 match: 19 SD: 1.3387 cents 72 .. 144 match: 20 SD: 0.9622 cents 75 .. 150 match: 19 SD: 0.9300 cents 77 .. 154 match: 20 SD: 0.7920 cents 79 .. 158 match: 19 SD: 0.9456 cents 80 .. 160 match: 20 SD: 0.8616 cents 84 .. 168 match: 20 SD: 0.7233 cents 97 .. 194 match: 20 SD: 0.6721 cents 100 .. 200 match: 20 SD: 0.6129 cents 107 .. 214 match: 20 SD: 0.5196 cents 120 .. 240 match: 20 SD: 0.4930 cents 138 .. 276 match: 20 SD: 0.4354 cents 142 .. 284 match: 20 SD: 0.4304 cents 161 .. 322 match: 20 SD: 0.3929 cents 173 .. 346 match: 20 SD: 0.3914 cents 181 .. 362 match: 20 SD: 0.3772 cents 185 .. 370 match: 20 SD: 0.3484 cents 197 .. 394 match: 20 SD: 0.2922 cents 222 .. 444 match: 20 SD: 0.2873 cents 238 .. 476 match: 20 SD: 0.2675 cents 239 .. 478 match: 20 SD: 0.2274 cents 262 .. 524 match: 20 SD: 0.2205 cents 297 .. 594 match: 20 SD: 0.2138 cents 319 .. 638 match: 20 SD: 0.2018 cents 327 .. 654 match: 20 SD: 0.1931 cents 346 .. 692 match: 20 SD: 0.1725 cents 351 .. 702 match: 20 SD: 0.1669 cents 402 .. 804 match: 20 SD: 0.1642 cents 423 .. 846 match: 20 SD: 0.1492 cents 426 .. 852 match: 20 SD: 0.1308 cents 458 .. 916 match: 20 SD: 0.1288 cents 467 .. 934 match: 20 SD: 0.1241 cents 524 .. 1048 match: 20 SD: 0.1064 cents 590 .. 1180 match: 20 SD: 0.1027 cents