Scala analysis: xen15-oconnell-golden-section-25
25 parts of the Golden Section
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33.324 cents 33.323612 2: 66.647 cents 66.647224 3: 99.971 cents 99.970836 4: 133.294 cents 133.294447 5: 166.618 cents 166.618059 6: 199.942 cents 199.941671 7: 233.265 cents 233.265283 8: 266.589 cents 266.588895 9: 299.913 cents 299.912507 10: 333.236 cents 333.236119 11: 366.560 cents 366.559730 12: 399.883 cents 399.883342 13: 433.207 cents 433.206954 14: 466.531 cents 466.530566 15: 499.854 cents 499.854178 16: 533.178 cents 533.177790 17: 566.501 cents 566.501402 18: 599.825 cents 599.825013 19: 633.149 cents 633.148625 20: 666.472 cents 666.472237 21: 699.796 cents 699.795849 22: 733.119 cents 733.119461 23: 766.443 cents 766.443073 24: 799.767 cents 799.766685 25: 833.090 cents 833.090296
SHOW/INTERVAL
0: 33.3236 cents 33.3236 1: 33.3236 cents 33.3236 2: 33.3236 cents 33.3236 3: 33.3236 cents 33.3236 4: 33.3236 cents 33.3236 5: 33.3236 cents 33.3236 6: 33.3236 cents 33.3236 7: 33.3236 cents 33.3236 8: 33.3236 cents 33.3236 9: 33.3236 cents 33.3236 10: 33.3236 cents 33.3236 11: 33.3236 cents 33.3236 12: 33.3236 cents 33.3236 13: 33.3236 cents 33.3236 14: 33.3236 cents 33.3236 15: 33.3236 cents 33.3236 16: 33.3236 cents 33.3236 17: 33.3236 cents 33.3236 18: 33.3236 cents 33.3236 19: 33.3236 cents 33.3236 20: 33.3236 cents 33.3236 21: 33.3236 cents 33.3236 22: 33.3236 cents 33.3236 23: 33.3236 cents 33.3236 24: 33.3236 cents 33.3236 25: 33.3236 cents 33.3236
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 25 33.32361 cents 2: 25 66.64722 cents 3: 25 99.97084 cents 4: 25 133.29445 cents 5: 25 166.61806 cents 6: 25 199.94167 cents 7: 25 233.26528 cents 8: 25 266.58890 cents 9: 25 299.91251 cents 10: 25 333.23612 cents 11: 25 366.55973 cents 12: 25 399.88334 cents 13: 25 433.20695 cents 14: 25 466.53057 cents 15: 25 499.85418 cents 16: 25 533.17779 cents 17: 25 566.50140 cents 18: 25 599.82501 cents 19: 25 633.14862 cents 20: 25 666.47224 cents 21: 25 699.79585 cents 22: 25 733.11946 cents 23: 25 766.44307 cents 24: 25 799.76668 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
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 25 0.0 : 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 33.3 : 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 66.6 : 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 100.0: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 133.3: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 166.6: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 199.9: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 233.3: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 266.6: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 299.9: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 333.2: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 366.6: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 399.9: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 433.2: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 466.5: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 499.9: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 533.2: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 566.5: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 599.8: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 633.1: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 666.5: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 699.8: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 733.1: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 766.4: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 799.8: 33.3 66.6 100.0 133.3 166.6 199.9 233.3 266.6 299.9 333.2 366.6 399.9 433.2 466.5 499.9 533.2 566.5 599.8 633.1 666.5 699.8 733.1 766.4 799.8 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3236 .. 33.3236 cents 1/1, 0.0000 cents 33.32361 cents 2: 66.6472 .. 66.6472 cents 1/1, 0.0000 cents 33.32361 cents 3: 99.9708 .. 99.9708 cents 1/1, 0.0000 cents 33.32361 cents 4: 133.2944 .. 133.2944 cents 1/1, 0.0000 cents 33.32361 cents 5: 166.6181 .. 166.6181 cents 1/1, 0.0000 cents 33.32361 cents 6: 199.9417 .. 199.9417 cents 1/1, 0.0000 cents 33.32361 cents 7: 233.2653 .. 233.2653 cents 1/1, 0.0000 cents 33.32361 cents 8: 266.5889 .. 266.5889 cents 1/1, 0.0000 cents 33.32361 cents 9: 299.9125 .. 299.9125 cents 1/1, 0.0000 cents 33.32361 cents 10: 333.2361 .. 333.2361 cents 1/1, 0.0000 cents 33.32361 cents 11: 366.5597 .. 366.5597 cents 1/1, 0.0000 cents 33.32361 cents 12: 399.8833 .. 399.8833 cents 1/1, 0.0000 cents 33.32361 cents 13: 433.2070 .. 433.2070 cents 1/1, 0.0000 cents 33.32361 cents 14: 466.5306 .. 466.5306 cents 1/1, 0.0000 cents 33.32361 cents 15: 499.8542 .. 499.8542 cents 1/1, 0.0000 cents 33.32361 cents 16: 533.1778 .. 533.1778 cents 1/1, 0.0000 cents 33.32361 cents 17: 566.5014 .. 566.5014 cents 1/1, 0.0000 cents 33.32361 cents 18: 599.8250 .. 599.8250 cents 1/1, 0.0000 cents 33.32361 cents 19: 633.1486 .. 633.1486 cents 1/1, 0.0000 cents 33.32361 cents 20: 666.4722 .. 666.4722 cents 1/1, 0.0000 cents 33.32361 cents 21: 699.7958 .. 699.7958 cents 1/1, 0.0000 cents 33.32361 cents 22: 733.1195 .. 733.1195 cents 1/1, 0.0000 cents 33.32361 cents 23: 766.4431 .. 766.4431 cents 1/1, 0.0000 cents 33.32361 cents 24: 799.7667 .. 799.7667 cents 1/1, 0.0000 cents 33.32361 cents
SHOW DATA
Number of notes : 25 -- Interval properties -- Smallest interval : 33.32361 cents, class 1 Average step (divided formal octave): 33.3236 cents Largest one step interval : 33.32361 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 33.32361 cents, amount: 25 Most common interval of one step : 33.32361 cents, amount: 25 Least squares average step : 33.32361 cents, oct.: 833.09030 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 33.32361 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.040000 redundancy: 0.960000 Efficiency x scale size : 1.000000 Number of different interval sizes : 24 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 25, average 699.7958 cents Number of recognisable fourths : 25, average 499.8542 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
25: 1 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: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 366.9097 cents 2 .. 3 match: 1 H SD: 2.1592 cents 3 .. 5 match: 2 H SD: 25.6502 cents 4 .. 6 match: 2 H SD: 6.8702 cents 5 .. 8 match: 3 H SD: 8.8034 cents 6 .. 10 match: 4 H SD: 12.8366 cents 7 .. 11 match: 4 H SD: 5.6498 cents 8 .. 13 match: 5 H SD: 4.4290 cents 9 .. 15 match: 6 H SD: 9.2738 cents 10 .. 16 match: 6 H SD: 4.8776 cents 11 .. 18 match: 7 H SD: 5.3761 cents 12 .. 19 match: 7 H SD: 2.2488 cents 13 .. 21 match: 8 H SD: 2.9511 cents 14 .. 23 match: 9 H SD: 4.2025 cents 15 .. 24 match: 9 H SD: 3.9451 cents 16 .. 26 match: 10 H SD: 2.4517 cents 17 .. 28 match: 11 H SD: 3.5310 cents 18 .. 29 match: 11 H SD: 2.3198 cents 19 .. 31 match: 12 H SD: 2.5228 cents 20 .. 32 match: 12 H SD: 3.4401 cents 21 .. 34 match: 13 H SD: 2.3589 cents 22 .. 36 match: 14 H SD: 3.1989 cents 23 .. 37 match: 14 H SD: 2.5093 cents 24 .. 39 match: 15 H SD: 2.2468 cents 25 .. 40 match: 15 H SD: 2.4102 cents 26 .. 42 match: 16 H SD: 2.2825 cents 27 .. 44 match: 17 H SD: 2.3526 cents 28 .. 45 match: 17 H SD: 2.5369 cents 29 .. 47 match: 18 H SD: 2.1379 cents 30 .. 49 match: 19 H SD: 2.3931 cents 31 .. 50 match: 19 H SD: 2.2462 cents 32 .. 52 match: 20 H SD: 1.9669 cents 33 .. 53 match: 20 H SD: 2.5099 cents 34 .. 55 match: 21 H SD: 1.7865 cents 35 .. 57 match: 21 S SD: 2.5954 cents 36 .. 58 match: 22 H SD: 1.6070 cents 37 .. 60 match: 22 SD: 2.3381 cents 38 .. 61 match: 23 H SD: 1.7348 cents 39 .. 63 match: 23 S SD: 1.7260 cents 40 .. 65 match: 23 SD: 2.3100 cents 41 .. 66 match: 24 SD: 1.7443 cents 42 .. 68 match: 24 SD: 1.4650 cents 43 .. 70 match: 24 SD: 1.8099 cents 44 .. 71 match: 24 SD: 2.0962 cents 45 .. 73 match: 24 SD: 2.1018 cents 46 .. 74 match: 25 SD: 1.6647 cents 47 .. 76 match: 25 SD: 1.3947 cents 48 .. 78 match: 25 SD: 1.3050 cents 49 .. 79 match: 25 SD: 1.2815 cents 63 .. 102 match: 25 SD: 1.2679 cents 65 .. 105 match: 25 SD: 1.2362 cents 66 .. 107 match: 25 SD: 1.1952 cents 68 .. 110 match: 25 SD: 1.0687 cents 70 .. 113 match: 25 SD: 1.0361 cents 72 .. 116 match: 25 SD: 1.0089 cents 77 .. 125 match: 25 SD: 0.9869 cents 80 .. 129 match: 25 SD: 0.9374 cents 84 .. 136 match: 25 SD: 0.8379 cents 89 .. 144 match: 25 SD: 0.7896 cents 96 .. 155 match: 25 SD: 0.7739 cents 97 .. 157 match: 25 SD: 0.6978 cents 99 .. 160 match: 25 SD: 0.6653 cents 113 .. 183 match: 25 SD: 0.6446 cents 116 .. 188 match: 25 SD: 0.6126 cents 122 .. 197 match: 25 SD: 0.6102 cents 123 .. 199 match: 25 SD: 0.5955 cents 131 .. 212 match: 25 SD: 0.5434 cents 138 .. 223 match: 25 SD: 0.4735 cents 147 .. 238 match: 25 SD: 0.4516 cents 150 .. 243 match: 25 SD: 0.4469 cents 152 .. 246 match: 25 SD: 0.4200 cents 174 .. 282 match: 25 SD: 0.4090 cents 179 .. 290 match: 25 SD: 0.4065 cents 186 .. 301 match: 25 SD: 0.3703 cents 188 .. 304 match: 25 SD: 0.3665 cents 197 .. 319 match: 25 SD: 0.3494 cents 201 .. 325 match: 25 SD: 0.3404 cents 203 .. 328 match: 25 SD: 0.3320 cents 222 .. 359 match: 25 SD: 0.3036 cents 235 .. 380 match: 25 SD: 0.2924 cents 249 .. 403 match: 25 SD: 0.2649 cents 254 .. 411 match: 25 SD: 0.2619 cents 269 .. 435 match: 25 SD: 0.2615 cents 277 .. 448 match: 25 SD: 0.2454 cents 285 .. 461 match: 25 SD: 0.2426 cents 300 .. 485 match: 25 SD: 0.2283 cents 305 .. 494 match: 25 SD: 0.2081 cents 335 .. 542 match: 25 SD: 0.2064 cents 349 .. 565 match: 25 SD: 0.1807 cents 353 .. 571 match: 25 SD: 0.1760 cents 377 .. 610 match: 25 SD: 0.1755 cents 385 .. 623 match: 25 SD: 0.1743 cents 401 .. 649 match: 25 SD: 0.1725 cents 408 .. 660 match: 25 SD: 0.1473 cents 457 .. 739 match: 25 SD: 0.1466 cents 458 .. 741 match: 25 SD: 0.1367 cents 485 .. 785 match: 25 SD: 0.1322 cents 514 .. 832 match: 25 SD: 0.1226 cents 555 .. 898 match: 25 SD: 0.1139 cents