Scala analysis: sctemp22
225/224-tempered Fokker block for <2048/2025, 3125/3072>
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68.463 cents 68.462758 2: 116.006 cents 116.006339 3: 184.469 cents 184.469097 4: 199.683 cents 199.683043 5: 268.146 cents 268.145800 6: 315.689 cents 315.689382 7: 384.152 cents 384.152140 8: 431.696 cents 431.695721 9: 500.158 cents 500.158479 10: 547.702 cents 547.702060 11: 616.165 cents 616.164818 12: 652.298 cents 652.297940 13: 699.842 cents 699.841521 14: 768.304 cents 768.304279 15: 815.848 cents 815.847861 16: 884.311 cents 884.310618 17: 931.854 cents 931.854200 18: 1000.317 cents 1000.316957 19: 1015.531 cents 1015.530903 20: 1083.994 cents 1083.993661 21: 1131.537 cents 1131.537242 22: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 68.4628 cents 68.4628 1: 68.4628 cents 68.4628 2: 47.5436 cents 47.5436 3: 68.4628 cents 68.4628 4: 15.2139 cents 15.2139 5: 68.4628 cents 68.4628 6: 47.5436 cents 47.5436 7: 68.4628 cents 68.4628 8: 47.5436 cents 47.5436 9: 68.4628 cents 68.4628 10: 47.5436 cents 47.5436 11: 68.4628 cents 68.4628 12: 36.1331 cents 36.1331 13: 47.5436 cents 47.5436 14: 68.4628 cents 68.4628 15: 47.5436 cents 47.5436 16: 68.4628 cents 68.4628 17: 47.5436 cents 47.5436 18: 68.4628 cents 68.4628 19: 15.2139 cents 15.2139 20: 68.4628 cents 68.4628 21: 47.5436 cents 47.5436 22: 68.4628 cents 68.4628
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 15.21395 cents 1: 1 36.13312 cents 1: 8 47.54358 cents 1: 11 68.46276 cents 2: 5 83.67670 cents 2: 1 104.59588 cents 2: 15 116.00634 cents 2: 1 136.92552 cents 3: 4 131.22029 cents 3: 5 152.13946 cents 3: 4 163.54992 cents 3: 9 184.46910 cents 4: 10 199.68304 cents 4: 2 220.60222 cents 4: 8 232.01268 cents 4: 2 252.93185 cents 5: 4 247.22662 cents 5: 11 268.14580 cents 5: 2 279.55626 cents 5: 5 300.47544 cents 6: 13 315.68938 cents 6: 5 336.60856 cents 6: 3 348.01902 cents 6: 1 368.93819 cents 7: 4 363.23296 cents 7: 17 384.15214 cents 7: 1 416.48177 cents 8: 2 399.36609 cents 8: 12 431.69572 cents 8: 8 452.61490 cents 9: 5 467.82884 cents 9: 2 479.23930 cents 9: 15 500.15848 cents 10: 5 515.37242 cents 10: 3 536.29160 cents 10: 7 547.70206 cents 10: 7 568.62124 cents 11: 11 583.83518 cents 11: 11 616.16482 cents 12: 7 631.37876 cents 12: 7 652.29794 cents 12: 3 663.70840 cents 12: 5 684.62758 cents 13: 15 699.84152 cents 13: 2 720.76070 cents 13: 5 732.17116 cents 14: 8 747.38510 cents 14: 12 768.30428 cents 14: 2 800.63391 cents 15: 1 783.51823 cents 15: 17 815.84786 cents 15: 4 836.76704 cents 16: 1 831.06181 cents 16: 3 851.98098 cents 16: 5 863.39144 cents 16: 13 884.31062 cents 17: 5 899.52456 cents 17: 2 920.44374 cents 17: 11 931.85420 cents 17: 4 952.77338 cents 18: 2 947.06815 cents 18: 8 967.98732 cents 18: 2 979.39778 cents 18: 10 1000.31696 cents 19: 9 1015.53090 cents 19: 4 1036.45008 cents 19: 5 1047.86054 cents 19: 4 1068.77971 cents 20: 1 1063.07448 cents 20: 15 1083.99366 cents 20: 1 1095.40412 cents 20: 5 1116.32330 cents 21: 11 1131.53724 cents 21: 8 1152.45642 cents 21: 1 1163.86688 cents 21: 2 1184.78605 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.61905 = 76/21
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 : 68.5 116.0 184.5 199.7 268.1 315.7 384.2 431.7 500.2 547.7 616.2 652.3 699.8 768.3 815.8 884.3 931.9 1000.3 1015.5 1084.0 1131.5 1200.0 68.5 : 47.5 116.0 131.2 199.7 247.2 315.7 363.2 431.7 479.2 547.7 583.8 631.4 699.8 747.4 815.8 863.4 931.9 947.1 1015.5 1063.1 1131.5 1200.0 116.0 : 68.5 83.7 152.1 199.7 268.1 315.7 384.2 431.7 500.2 536.3 583.8 652.3 699.8 768.3 815.8 884.3 899.5 968.0 1015.5 1084.0 1152.5 1200.0 184.5 : 15.2 83.7 131.2 199.7 247.2 315.7 363.2 431.7 467.8 515.4 583.8 631.4 699.8 747.4 815.8 831.1 899.5 947.1 1015.5 1084.0 1131.5 1200.0 199.7 : 68.5 116.0 184.5 232.0 300.5 348.0 416.5 452.6 500.2 568.6 616.2 684.6 732.2 800.6 815.8 884.3 931.9 1000.3 1068.8 1116.3 1184.8 1200.0 268.1 : 47.5 116.0 163.5 232.0 279.6 348.0 384.2 431.7 500.2 547.7 616.2 663.7 732.2 747.4 815.8 863.4 931.9 1000.3 1047.9 1116.3 1131.5 1200.0 315.7 : 68.5 116.0 184.5 232.0 300.5 336.6 384.2 452.6 500.2 568.6 616.2 684.6 699.8 768.3 815.8 884.3 952.8 1000.3 1068.8 1084.0 1152.5 1200.0 384.2 : 47.5 116.0 163.5 232.0 268.1 315.7 384.2 431.7 500.2 547.7 616.2 631.4 699.8 747.4 815.8 884.3 931.9 1000.3 1015.5 1084.0 1131.5 1200.0 431.7 : 68.5 116.0 184.5 220.6 268.1 336.6 384.2 452.6 500.2 568.6 583.8 652.3 699.8 768.3 836.8 884.3 952.8 968.0 1036.5 1084.0 1152.5 1200.0 500.2 : 47.5 116.0 152.1 199.7 268.1 315.7 384.2 431.7 500.2 515.4 583.8 631.4 699.8 768.3 815.8 884.3 899.5 968.0 1015.5 1084.0 1131.5 1200.0 547.7 : 68.5 104.6 152.1 220.6 268.1 336.6 384.2 452.6 467.8 536.3 583.8 652.3 720.8 768.3 836.8 852.0 920.4 968.0 1036.5 1084.0 1152.5 1200.0 616.2 : 36.1 83.7 152.1 199.7 268.1 315.7 384.2 399.4 467.8 515.4 583.8 652.3 699.8 768.3 783.5 852.0 899.5 968.0 1015.5 1084.0 1131.5 1200.0 652.3 : 47.5 116.0 163.5 232.0 279.6 348.0 363.2 431.7 479.2 547.7 616.2 663.7 732.2 747.4 815.8 863.4 931.9 979.4 1047.9 1095.4 1163.9 1200.0 699.8 : 68.5 116.0 184.5 232.0 300.5 315.7 384.2 431.7 500.2 568.6 616.2 684.6 699.8 768.3 815.8 884.3 931.9 1000.3 1047.9 1116.3 1152.5 1200.0 768.3 : 47.5 116.0 163.5 232.0 247.2 315.7 363.2 431.7 500.2 547.7 616.2 631.4 699.8 747.4 815.8 863.4 931.9 979.4 1047.9 1084.0 1131.5 1200.0 815.8 : 68.5 116.0 184.5 199.7 268.1 315.7 384.2 452.6 500.2 568.6 583.8 652.3 699.8 768.3 815.8 884.3 931.9 1000.3 1036.5 1084.0 1152.5 1200.0 884.3 : 47.5 116.0 131.2 199.7 247.2 315.7 384.2 431.7 500.2 515.4 583.8 631.4 699.8 747.4 815.8 863.4 931.9 968.0 1015.5 1084.0 1131.5 1200.0 931.9 : 68.5 83.7 152.1 199.7 268.1 336.6 384.2 452.6 467.8 536.3 583.8 652.3 699.8 768.3 815.8 884.3 920.4 968.0 1036.5 1084.0 1152.5 1200.0 1000.3: 15.2 83.7 131.2 199.7 268.1 315.7 384.2 399.4 467.8 515.4 583.8 631.4 699.8 747.4 815.8 852.0 899.5 968.0 1015.5 1084.0 1131.5 1200.0 1015.5: 68.5 116.0 184.5 252.9 300.5 368.9 384.2 452.6 500.2 568.6 616.2 684.6 732.2 800.6 836.8 884.3 952.8 1000.3 1068.8 1116.3 1184.8 1200.0 1084.0: 47.5 116.0 184.5 232.0 300.5 315.7 384.2 431.7 500.2 547.7 616.2 663.7 732.2 768.3 815.8 884.3 931.9 1000.3 1047.9 1116.3 1131.5 1200.0 1131.5: 68.5 136.9 184.5 252.9 268.1 336.6 384.2 452.6 500.2 568.6 616.2 684.6 720.8 768.3 836.8 884.3 952.8 1000.3 1068.8 1084.0 1152.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 15.2139 .. 68.4628 cents 53.24881 cents 15.21395 cents 2: 83.6767 .. 136.9255 cents 53.24881 cents 15.21395 cents 3: 131.2203 .. 184.4691 cents 53.24881 cents -5.70523 cents 4: 199.6830 .. 252.9319 cents 53.24881 cents 15.21395 cents 5: 247.2266 .. 300.4754 cents 53.24881 cents -5.70523 cents 6: 315.6894 .. 368.9382 cents 53.24881 cents 15.21395 cents 7: 363.2330 .. 416.4818 cents 53.24881 cents -5.70523 cents 8: 399.3661 .. 452.6149 cents 53.24881 cents -17.11569 cents 9: 467.8288 .. 500.1585 cents 32.32964 cents 15.21395 cents 10: 515.3724 .. 568.6212 cents 53.24881 cents 15.21395 cents 11: 583.8352 .. 616.1648 cents 32.32964 cents 15.21395 cents 12: 631.3788 .. 684.6276 cents 53.24881 cents 15.21395 cents 13: 699.8415 .. 732.1712 cents 32.32964 cents 15.21395 cents 14: 747.3851 .. 800.6339 cents 53.24881 cents 15.21395 cents 15: 783.5182 .. 836.7670 cents 53.24881 cents -17.11569 cents 16: 831.0618 .. 884.3106 cents 53.24881 cents -5.70523 cents 17: 899.5246 .. 952.7734 cents 53.24881 cents 15.21395 cents 18: 947.0681 .. 1000.3170 cents 53.24881 cents -5.70523 cents 19: 1015.5309 .. 1068.7797 cents 53.24881 cents 15.21395 cents 20: 1063.0745 .. 1116.3233 cents 53.24881 cents -5.70523 cents 21: 1131.5372 .. 1184.7861 cents 53.24881 cents 15.21395 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 15.21395 cents, class 1 Average step (divided formal octave): 54.5455 cents Largest one step interval : 68.46276 cents Average / Smallest step : 3.585227 Largest / Average step : 1.255151 Largest / Smallest step : 4.500000 Median interval of one step : 58.00317 cents, amount: 0 Most common interval of one step : 68.46276 cents, amount: 11 Least squares average step : 54.50311 cents, oct.: 1199.06842 cents Scale is not proper Scale is a mode of a 631-tone equal temperament with octave 2/1 degrees: 36 61 97 105 141 166 202 227 263 288 324 343 368 404 429 465 490 526 534 570 595 631 Least number of segments generator : 317 of 602.853 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 512 of 973.693 cents and inv. generated superset size: 86 = 64 more = 390.909% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABABABADBABABACABA Step pattern size order : DCDADCDCDCDBCDCDCDADCD Scale is a Constant Structure, by a margin of 5.70523 cents Scale diversity : 1.375880 Lumma stability : 0.177496 Lumma impropriety factor : 0.057052 Number of different interval sizes : 76 = 3.61905 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.61905 = 76/21 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 5.70523 cents Most common intervals : 384.15214 cents & inv., amount: 17 Most common triad is 0.0 384.152 815.848 cents, amount: 12 Number of recognisable fifths : 15, average 699.8415 cents Best major thirds form a closed circle Formal octave complements present : 21 = 95.4545% -- Rational properties -- Prime limit : 2 (not all pitches rational)
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: 11.3673 c. M:-20.8327 c. 24: 1 1 2 0 1 1 2 1 1 1 1 1 1 1 1 2 1 1 0 2 1 1 N D3 I SD: 13.9348 c. M:-18.4628 c. 28: 2 1 1 1 1 1 2 1 2 1 1 1 1 2 1 2 1 1 1 1 1 2 N D3 I SD: 12.2012 c. M:-17.2515 c. 30: 2 1 2 0 2 1 2 1 1 2 1 1 1 2 1 2 1 2 0 2 1 2 N SD: 11.8763 c. M: 20.1585 c. 31: 2 1 2 0 2 1 2 1 2 1 2 1 1 2 1 2 1 2 0 2 1 2 N D3 SD: 5.5228 c. M:-9.0793 c. 50: 3 2 3 0 3 2 3 2 3 2 3 1 2 3 2 3 2 3 0 3 2 3 N SD: 4.6617 c. M:-7.8352 c. 53: 3 2 3 1 3 2 3 2 3 2 3 2 2 3 2 3 2 3 1 3 2 3 P D3 SD: 2.8216 c. M: 4.8441 c. 72: 4 3 4 1 4 3 4 3 4 3 4 2 3 4 3 4 3 4 1 4 3 4 N SD: 1.2424 c. M: 2.2979 c. 103: 6 4 6 1 6 4 6 4 6 4 6 3 4 6 4 6 4 6 1 6 4 6 N SD: 1.0467 c. M:-1.9387 c. 156: 9 6 9 2 9 6 9 6 9 6 9 5 6 9 6 9 6 9 2 9 6 9 N SD: 0.7488 c. M: 1.5482 c. 175: 10 7 10 2 10 7 10 7 10 7 10 5 7 10 7 10 7 10 2 10 7 10 N SD: 0.5697 c. M:-0.9780 c. 228: 13 9 13 3 13 9 13 9 13 9 13 7 9 13 9 13 9 13 3 13 9 13 N SD: 0.2186 c. M: 0.3753 c. 403: 23 16 23 5 23 16 23 16 23 16 23 12 16 23 16 23 16 23 5 23 16 23 N SD: 0.1237 c. M:-0.2124 c. 631: 36 25 36 8 36 25 36 25 36 25 36 19 25 36 25 36 25 36 8 36 25 36 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: 0.7047 cents 4 .. 8 match: 4 H SD: 7.9090 cents 5 .. 10 match: 5 H SD: 6.7570 cents 6 .. 12 match: 6 H SD: 5.6646 cents 7 .. 14 match: 7 H SD: 5.2662 cents 8 .. 16 match: 8 H SD: 5.0916 cents 9 .. 18 match: 9 H SD: 4.4177 cents 10 .. 20 match: 10 H SD: 5.1187 cents 11 .. 22 match: 11 H SD: 5.6552 cents 12 .. 24 match: 12 H SD: 4.7675 cents 13 .. 26 match: 13 H SD: 5.0685 cents 14 .. 28 match: 14 H SD: 3.7898 cents 15 .. 30 match: 15 H SD: 3.8858 cents 16 .. 32 match: 15 SD: 3.6469 cents 17 .. 34 match: 16 SD: 4.0485 cents 18 .. 36 match: 17 S SD: 3.3037 cents 19 .. 38 match: 16 S SD: 4.3799 cents 20 .. 40 match: 17 SD: 3.5510 cents 21 .. 42 match: 19 SD: 3.4708 cents 22 .. 44 match: 20 SD: 3.8021 cents 23 .. 46 match: 19 SD: 3.7125 cents 24 .. 48 match: 20 SD: 2.1677 cents 25 .. 50 match: 19 SD: 2.4796 cents 26 .. 52 match: 21 SD: 2.9098 cents 27 .. 54 match: 19 SD: 2.6365 cents 28 .. 56 match: 20 SD: 2.3245 cents 29 .. 58 match: 21 SD: 2.5823 cents 30 .. 60 match: 22 SD: 2.3148 cents 32 .. 64 match: 21 SD: 2.1873 cents 33 .. 66 match: 20 SD: 2.5323 cents 34 .. 68 match: 20 SD: 2.7298 cents 35 .. 70 match: 21 SD: 2.0849 cents 36 .. 72 match: 21 SD: 2.1636 cents 38 .. 76 match: 21 SD: 2.2705 cents 39 .. 78 match: 21 SD: 2.1705 cents 40 .. 80 match: 21 SD: 1.7024 cents 41 .. 82 match: 21 SD: 1.7337 cents 42 .. 84 match: 21 SD: 1.6734 cents 43 .. 86 match: 20 SD: 1.7999 cents 44 .. 88 match: 21 SD: 1.7143 cents 45 .. 90 match: 22 SD: 1.5436 cents 46 .. 92 match: 22 SD: 1.4961 cents 48 .. 96 match: 21 SD: 1.4185 cents 49 .. 98 match: 21 SD: 1.4967 cents 50 .. 100 match: 21 SD: 1.4721 cents 51 .. 102 match: 21 SD: 1.6259 cents 52 .. 104 match: 20 SD: 1.4265 cents 53 .. 106 match: 21 SD: 1.3062 cents 54 .. 108 match: 22 SD: 1.2046 cents 56 .. 112 match: 22 SD: 1.1221 cents 57 .. 114 match: 21 SD: 1.3860 cents 58 .. 116 match: 21 SD: 1.5386 cents 59 .. 118 match: 21 SD: 1.1611 cents 60 .. 120 match: 21 SD: 1.1022 cents 61 .. 122 match: 21 SD: 1.2464 cents 64 .. 128 match: 22 SD: 1.1936 cents 65 .. 130 match: 22 SD: 1.1533 cents 66 .. 132 match: 22 SD: 1.1530 cents 67 .. 134 match: 21 SD: 1.2772 cents 68 .. 136 match: 21 SD: 1.0545 cents 69 .. 138 match: 21 SD: 1.1884 cents 70 .. 140 match: 22 SD: 0.9031 cents 72 .. 144 match: 22 SD: 0.8490 cents 76 .. 152 match: 21 SD: 1.0546 cents 77 .. 154 match: 21 SD: 0.8950 cents 80 .. 160 match: 22 SD: 0.8944 cents 81 .. 162 match: 22 SD: 0.8567 cents 84 .. 168 match: 22 SD: 0.8281 cents 85 .. 170 match: 21 SD: 0.9688 cents 86 .. 172 match: 22 SD: 0.9642 cents 88 .. 176 match: 22 SD: 0.8264 cents 89 .. 178 match: 22 SD: 0.7384 cents 94 .. 188 match: 21 SD: 0.9239 cents 95 .. 190 match: 22 SD: 0.8214 cents 96 .. 192 match: 22 SD: 0.6637 cents 100 .. 200 match: 22 SD: 0.6064 cents 105 .. 210 match: 22 SD: 0.5562 cents 116 .. 232 match: 22 SD: 0.5424 cents 124 .. 248 match: 22 SD: 0.5197 cents 129 .. 258 match: 22 SD: 0.5079 cents 131 .. 262 match: 22 SD: 0.4812 cents 145 .. 290 match: 22 SD: 0.4360 cents 156 .. 312 match: 22 SD: 0.4189 cents 169 .. 338 match: 22 SD: 0.3999 cents 170 .. 340 match: 22 SD: 0.3676 cents 197 .. 394 match: 22 SD: 0.3192 cents 201 .. 402 match: 22 SD: 0.3191 cents 204 .. 408 match: 22 SD: 0.3117 cents 215 .. 430 match: 22 SD: 0.2939 cents 221 .. 442 match: 22 SD: 0.2912 cents 229 .. 458 match: 22 SD: 0.2476 cents 269 .. 538 match: 22 SD: 0.1976 cents 293 .. 586 match: 22 SD: 0.1923 cents 321 .. 642 match: 22 SD: 0.1920 cents 345 .. 690 match: 22 SD: 0.1861 cents 346 .. 692 match: 22 SD: 0.1552 cents 400 .. 800 match: 22 SD: 0.1321 cents 435 .. 870 match: 22 SD: 0.1241 cents 490 .. 980 match: 22 SD: 0.1213 cents 516 .. 1032 match: 22 SD: 0.1158 cents 540 .. 1080 match: 22 SD: 0.1105 cents 550 .. 1100 match: 22 SD: 0.1055 cents 596 .. 1192 match: 22 SD: 0.0937 cents