Scala analysis: sctemp19
225/224-tempered Fokker block for <81/80, 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: 268.146 cents 268.145800 5: 315.689 cents 315.689382 6: 384.152 cents 384.152140 7: 431.696 cents 431.695721 8: 500.158 cents 500.158479 9: 568.621 cents 568.621236 10: 631.379 cents 631.378764 11: 699.842 cents 699.841521 12: 768.304 cents 768.304279 13: 815.848 cents 815.847861 14: 884.311 cents 884.310618 15: 931.854 cents 931.854200 16: 1015.531 cents 1015.530903 17: 1083.994 cents 1083.993661 18: 1131.537 cents 1131.537242 19: 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: 83.6767 cents 83.6767 5: 47.5436 cents 47.5436 6: 68.4628 cents 68.4628 7: 47.5436 cents 47.5436 8: 68.4628 cents 68.4628 9: 68.4628 cents 68.4628 10: 62.7575 cents 62.7575 11: 68.4628 cents 68.4628 12: 68.4628 cents 68.4628 13: 47.5436 cents 47.5436 14: 68.4628 cents 68.4628 15: 47.5436 cents 47.5436 16: 83.6767 cents 83.6767 17: 68.4628 cents 68.4628 18: 47.5436 cents 47.5436 19: 68.4628 cents 68.4628
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 47.54358 cents 1: 1 62.75753 cents 1: 10 68.46276 cents 1: 2 83.67670 cents 2: 10 116.00634 cents 2: 4 131.22029 cents 2: 3 136.92551 cents 2: 2 152.13946 cents 3: 2 163.54992 cents 3: 8 184.46910 cents 3: 9 199.68304 cents 4: 3 232.01268 cents 4: 6 247.22662 cents 4: 4 252.93185 cents 4: 6 268.14580 cents 5: 4 300.47544 cents 5: 12 315.68938 cents 5: 3 336.60856 cents 6: 4 363.23296 cents 6: 1 368.93819 cents 6: 14 384.15214 cents 7: 9 431.69572 cents 7: 2 446.90967 cents 7: 8 452.61490 cents 8: 14 500.15848 cents 8: 4 515.37242 cents 8: 1 536.29160 cents 9: 4 547.70206 cents 9: 2 562.91601 cents 9: 7 568.62124 cents 9: 6 583.83518 cents 10: 6 616.16482 cents 10: 7 631.37876 cents 10: 2 637.08399 cents 10: 4 652.29794 cents 11: 1 663.70840 cents 11: 4 684.62758 cents 11: 14 699.84152 cents 12: 8 747.38510 cents 12: 2 753.09033 cents 12: 9 768.30428 cents 13: 14 815.84786 cents 13: 1 831.06181 cents 13: 4 836.76704 cents 14: 3 863.39144 cents 14: 12 884.31062 cents 14: 4 899.52456 cents 15: 6 931.85420 cents 15: 4 947.06815 cents 15: 6 952.77338 cents 15: 3 967.98732 cents 16: 9 1000.31696 cents 16: 8 1015.53090 cents 16: 2 1036.45008 cents 17: 2 1047.86054 cents 17: 3 1063.07448 cents 17: 4 1068.77971 cents 17: 10 1083.99366 cents 18: 2 1116.32330 cents 18: 10 1131.53724 cents 18: 1 1137.24247 cents 18: 6 1152.45642 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.44444 = 31/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 68.5 116.0 184.5 268.1 315.7 384.2 431.7 500.2 568.6 631.4 699.8 768.3 815.8 884.3 931.9 1015.5 1084.0 1131.5 1200.0 68.5 : 47.5 116.0 199.7 247.2 315.7 363.2 431.7 500.2 562.9 631.4 699.8 747.4 815.8 863.4 947.1 1015.5 1063.1 1131.5 1200.0 116.0 : 68.5 152.1 199.7 268.1 315.7 384.2 452.6 515.4 583.8 652.3 699.8 768.3 815.8 899.5 968.0 1015.5 1084.0 1152.5 1200.0 184.5 : 83.7 131.2 199.7 247.2 315.7 384.2 446.9 515.4 583.8 631.4 699.8 747.4 831.1 899.5 947.1 1015.5 1084.0 1131.5 1200.0 268.1 : 47.5 116.0 163.5 232.0 300.5 363.2 431.7 500.2 547.7 616.2 663.7 747.4 815.8 863.4 931.9 1000.3 1047.9 1116.3 1200.0 315.7 : 68.5 116.0 184.5 252.9 315.7 384.2 452.6 500.2 568.6 616.2 699.8 768.3 815.8 884.3 952.8 1000.3 1068.8 1152.5 1200.0 384.2 : 47.5 116.0 184.5 247.2 315.7 384.2 431.7 500.2 547.7 631.4 699.8 747.4 815.8 884.3 931.9 1000.3 1084.0 1131.5 1200.0 431.7 : 68.5 136.9 199.7 268.1 336.6 384.2 452.6 500.2 583.8 652.3 699.8 768.3 836.8 884.3 952.8 1036.5 1084.0 1152.5 1200.0 500.2 : 68.5 131.2 199.7 268.1 315.7 384.2 431.7 515.4 583.8 631.4 699.8 768.3 815.8 884.3 968.0 1015.5 1084.0 1131.5 1200.0 568.6 : 62.8 131.2 199.7 247.2 315.7 363.2 446.9 515.4 562.9 631.4 699.8 747.4 815.8 899.5 947.1 1015.5 1063.1 1131.5 1200.0 631.4 : 68.5 136.9 184.5 252.9 300.5 384.2 452.6 500.2 568.6 637.1 684.6 753.1 836.8 884.3 952.8 1000.3 1068.8 1137.2 1200.0 699.8 : 68.5 116.0 184.5 232.0 315.7 384.2 431.7 500.2 568.6 616.2 684.6 768.3 815.8 884.3 931.9 1000.3 1068.8 1131.5 1200.0 768.3 : 47.5 116.0 163.5 247.2 315.7 363.2 431.7 500.2 547.7 616.2 699.8 747.4 815.8 863.4 931.9 1000.3 1063.1 1131.5 1200.0 815.8 : 68.5 116.0 199.7 268.1 315.7 384.2 452.6 500.2 568.6 652.3 699.8 768.3 815.8 884.3 952.8 1015.5 1084.0 1152.5 1200.0 884.3 : 47.5 131.2 199.7 247.2 315.7 384.2 431.7 500.2 583.8 631.4 699.8 747.4 815.8 884.3 947.1 1015.5 1084.0 1131.5 1200.0 931.9 : 83.7 152.1 199.7 268.1 336.6 384.2 452.6 536.3 583.8 652.3 699.8 768.3 836.8 899.5 968.0 1036.5 1084.0 1152.5 1200.0 1015.5: 68.5 116.0 184.5 252.9 300.5 368.9 452.6 500.2 568.6 616.2 684.6 753.1 815.8 884.3 952.8 1000.3 1068.8 1116.3 1200.0 1084.0: 47.5 116.0 184.5 232.0 300.5 384.2 431.7 500.2 547.7 616.2 684.6 747.4 815.8 884.3 931.9 1000.3 1047.9 1131.5 1200.0 1131.5: 68.5 136.9 184.5 252.9 336.6 384.2 452.6 500.2 568.6 637.1 699.8 768.3 836.8 884.3 952.8 1000.3 1084.0 1152.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 47.5436 .. 83.6767 cents 36.13312 cents 47.54358 cents 2: 116.0063 .. 152.1395 cents 36.13312 cents 32.32964 cents 3: 163.5499 .. 199.6830 cents 36.13312 cents 11.41046 cents 4: 232.0127 .. 268.1458 cents 36.13312 cents 32.32964 cents 5: 300.4754 .. 336.6086 cents 36.13312 cents 32.32964 cents 6: 363.2330 .. 384.1521 cents 20.91918 cents 26.62441 cents 7: 431.6957 .. 452.6149 cents 20.91918 cents 47.54358 cents 8: 500.1585 .. 536.2916 cents 36.13312 cents 47.54358 cents 9: 547.7021 .. 583.8352 cents 36.13312 cents 11.41046 cents 10: 616.1648 .. 652.2979 cents 36.13312 cents 32.32964 cents 11: 663.7084 .. 699.8415 cents 36.13312 cents 11.41046 cents 12: 747.3851 .. 768.3043 cents 20.91918 cents 47.54358 cents 13: 815.8479 .. 836.7670 cents 20.91918 cents 47.54358 cents 14: 863.3914 .. 899.5246 cents 36.13312 cents 26.62441 cents 15: 931.8542 .. 967.9873 cents 36.13312 cents 32.32964 cents 16: 1000.3170 .. 1036.4501 cents 36.13312 cents 32.32964 cents 17: 1047.8605 .. 1083.9937 cents 36.13312 cents 11.41046 cents 18: 1116.3233 .. 1152.4564 cents 36.13312 cents 32.32964 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 47.54358 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 83.67670 cents Average / Smallest step : 1.328421 Largest / Average step : 1.324881 Largest / Smallest step : 1.760000 Median interval of one step : 68.46276 cents, amount: 10 Most common interval of one step : 68.46276 cents, amount: 10 Least squares average step : 63.15405 cents, oct.: 1199.92686 cents Scale is strictly proper Scale is a mode of a 631-tone equal temperament with octave 2/1 degrees: 36 61 97 141 166 202 227 263 299 332 368 404 429 465 490 534 570 595 631 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: 67 = 48 more = 352.632% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACBABAADAABABCABA Step pattern size order : CACDACACCBCCACADCAC Scale is a Constant Structure, by a margin of 11.41046 cents Scale diversity : 1.294409 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.508716 Number of different interval sizes : 62 = 3.44444 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.44444 = 31/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 5.70523 cents Number of recognisable fifths : 14, average 699.8415 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 19 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.6895 c. M:-15.5142 c. 31: 2 1 2 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 2 P M ME I SD: 6.5221 c. M:-12.0239 c. 45: 3 1 3 3 2 2 2 3 2 3 2 3 2 2 2 3 3 1 3 P D3 I SD: 7.2906 c. M:-11.5372 c. 50: 3 2 3 3 2 3 2 3 3 2 3 3 2 3 2 3 3 2 3 SP M ME I SD: 4.4164 c. M:-7.5309 c. 53: 3 2 3 4 2 3 2 3 3 3 3 3 2 3 2 4 3 2 3 P D3 I SD: 2.2300 c. M:-3.5523 c. 72: 4 3 4 5 3 4 3 4 4 4 4 4 3 4 3 5 4 3 4 SP D3 I SD: 1.2688 c. M: 1.9546 c. 103: 6 4 6 7 4 6 4 6 6 5 6 6 4 6 4 7 6 4 6 SP I SD: 1.1969 c. M: 2.2526 c. 156: 9 6 9 11 6 9 6 9 9 8 9 9 6 9 6 11 9 6 9 SP I SD: 0.6272 c. M:-1.0850 c. 175: 10 7 10 12 7 10 7 10 10 9 10 10 7 10 7 12 10 7 10 SP I SD: 0.4502 c. M:-0.7172 c. 228: 13 9 13 16 9 13 9 13 13 12 13 13 9 13 9 16 13 9 13 SP I SD: 0.1728 c. M:-0.2753 c. 403: 23 16 23 28 16 23 16 23 23 21 23 23 16 23 16 28 23 16 23 SP I SD: 0.0978 c. M:-0.1557 c. 631: 36 25 36 44 25 36 25 36 36 33 36 36 25 36 25 44 36 25 36 SP I 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: 9.2738 cents 5 .. 10 match: 5 H SD: 2.8418 cents 6 .. 12 match: 6 H SD: 5.6646 cents 7 .. 14 match: 7 H SD: 6.2684 cents 8 .. 16 match: 8 H SD: 6.4720 cents 9 .. 18 match: 9 H SD: 4.6114 cents 10 .. 20 match: 10 H SD: 4.0994 cents 11 .. 22 match: 11 H SD: 6.4562 cents 12 .. 24 match: 12 H SD: 5.4520 cents 13 .. 26 match: 13 H SD: 5.6374 cents 14 .. 28 match: 14 H SD: 4.4945 cents 15 .. 30 match: 15 H SD: 4.2657 cents 16 .. 32 match: 15 SD: 3.9451 cents 17 .. 34 match: 15 SD: 4.7879 cents 18 .. 36 match: 17 S SD: 3.1427 cents 19 .. 38 match: 16 S SD: 5.0315 cents 20 .. 40 match: 18 S SD: 3.4680 cents 21 .. 42 match: 17 SD: 3.3813 cents 22 .. 44 match: 17 SD: 4.3734 cents 23 .. 46 match: 19 SD: 3.7960 cents 24 .. 48 match: 19 SD: 2.7986 cents 25 .. 50 match: 19 SD: 2.3964 cents 27 .. 54 match: 18 SD: 2.9388 cents 28 .. 56 match: 19 SD: 2.3997 cents 36 .. 72 match: 19 SD: 2.0110 cents 41 .. 82 match: 19 SD: 1.8532 cents 43 .. 86 match: 19 SD: 1.8006 cents 44 .. 88 match: 19 SD: 1.7960 cents 45 .. 90 match: 19 SD: 1.5411 cents 48 .. 96 match: 19 SD: 1.4838 cents 52 .. 104 match: 19 SD: 1.4601 cents 53 .. 106 match: 19 SD: 1.3782 cents 54 .. 108 match: 19 SD: 1.2165 cents 60 .. 120 match: 19 SD: 1.1383 cents 70 .. 140 match: 19 SD: 0.9289 cents 77 .. 154 match: 19 SD: 0.9155 cents 80 .. 160 match: 19 SD: 0.9091 cents 84 .. 168 match: 19 SD: 0.8576 cents 89 .. 178 match: 19 SD: 0.8495 cents 90 .. 180 match: 19 SD: 0.7941 cents 95 .. 190 match: 19 SD: 0.7503 cents 98 .. 196 match: 19 SD: 0.7127 cents 100 .. 200 match: 19 SD: 0.6206 cents 114 .. 228 match: 19 SD: 0.6119 cents 116 .. 232 match: 19 SD: 0.5526 cents 125 .. 250 match: 19 SD: 0.4999 cents 141 .. 282 match: 19 SD: 0.4858 cents 144 .. 288 match: 19 SD: 0.4419 cents 149 .. 298 match: 19 SD: 0.4385 cents 168 .. 336 match: 19 SD: 0.4302 cents 170 .. 340 match: 19 SD: 0.3808 cents 177 .. 354 match: 19 SD: 0.3709 cents 198 .. 396 match: 19 SD: 0.3448 cents 204 .. 408 match: 19 SD: 0.3409 cents 216 .. 432 match: 19 SD: 0.3071 cents 221 .. 442 match: 19 SD: 0.3051 cents 229 .. 458 match: 19 SD: 0.2779 cents 247 .. 494 match: 19 SD: 0.2711 cents 257 .. 514 match: 19 SD: 0.2599 cents 269 .. 538 match: 19 SD: 0.2502 cents 275 .. 550 match: 19 SD: 0.2097 cents 293 .. 586 match: 19 SD: 0.2085 cents 321 .. 642 match: 19 SD: 0.1963 cents 345 .. 690 match: 19 SD: 0.1782 cents 346 .. 692 match: 19 SD: 0.1689 cents 347 .. 694 match: 19 SD: 0.1679 cents 375 .. 750 match: 19 SD: 0.1626 cents 419 .. 838 match: 19 SD: 0.1578 cents 430 .. 860 match: 19 SD: 0.1552 cents 435 .. 870 match: 19 SD: 0.1509 cents 471 .. 942 match: 19 SD: 0.1434 cents 480 .. 960 match: 19 SD: 0.1396 cents 490 .. 980 match: 19 SD: 0.1363 cents 516 .. 1032 match: 19 SD: 0.1245 cents 519 .. 1038 match: 19 SD: 0.1187 cents 550 .. 1100 match: 19 SD: 0.1031 cents