Scala analysis: xen15-oconnell-golden-section-18
18 parts of the Golden Section
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46.283 cents 46.282794 2: 92.566 cents 92.565588 3: 138.848 cents 138.848383 4: 185.131 cents 185.131177 5: 231.414 cents 231.413971 6: 277.697 cents 277.696765 7: 323.980 cents 323.979560 8: 370.262 cents 370.262354 9: 416.545 cents 416.545148 10: 462.828 cents 462.827942 11: 509.111 cents 509.110737 12: 555.394 cents 555.393531 13: 601.676 cents 601.676325 14: 647.959 cents 647.959119 15: 694.242 cents 694.241914 16: 740.525 cents 740.524708 17: 786.808 cents 786.807502 18: 833.090 cents 833.090296
SHOW/INTERVAL
0: 46.2828 cents 46.2828 1: 46.2828 cents 46.2828 2: 46.2828 cents 46.2828 3: 46.2828 cents 46.2828 4: 46.2828 cents 46.2828 5: 46.2828 cents 46.2828 6: 46.2828 cents 46.2828 7: 46.2828 cents 46.2828 8: 46.2828 cents 46.2828 9: 46.2828 cents 46.2828 10: 46.2828 cents 46.2828 11: 46.2828 cents 46.2828 12: 46.2828 cents 46.2828 13: 46.2828 cents 46.2828 14: 46.2828 cents 46.2828 15: 46.2828 cents 46.2828 16: 46.2828 cents 46.2828 17: 46.2828 cents 46.2828 18: 46.2828 cents 46.2828
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 18 46.28279 cents 2: 18 92.56559 cents 3: 18 138.84838 cents 4: 18 185.13118 cents 5: 18 231.41397 cents 6: 18 277.69676 cents 7: 18 323.97956 cents 8: 18 370.26235 cents 9: 18 416.54515 cents 10: 18 462.82794 cents 11: 18 509.11074 cents 12: 18 555.39353 cents 13: 18 601.67632 cents 14: 18 647.95912 cents 15: 18 694.24191 cents 16: 18 740.52471 cents 17: 18 786.80750 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 0.0 : 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 46.3 : 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 92.6 : 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 138.8: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 185.1: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 231.4: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 277.7: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 324.0: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 370.3: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 416.5: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 462.8: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 509.1: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 555.4: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 601.7: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 648.0: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 694.2: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 740.5: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 786.8: 46.3 92.6 138.8 185.1 231.4 277.7 324.0 370.3 416.5 462.8 509.1 555.4 601.7 648.0 694.2 740.5 786.8 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 46.2828 .. 46.2828 cents 1/1, 0.0000 cents 46.28279 cents 2: 92.5656 .. 92.5656 cents 1/1, 0.0000 cents 46.28279 cents 3: 138.8484 .. 138.8484 cents 1/1, 0.0000 cents 46.28280 cents 4: 185.1312 .. 185.1312 cents 1/1, 0.0000 cents 46.28279 cents 5: 231.4140 .. 231.4140 cents 1/1, 0.0000 cents 46.28279 cents 6: 277.6968 .. 277.6968 cents 1/1, 0.0000 cents 46.28279 cents 7: 323.9796 .. 323.9796 cents 1/1, 0.0000 cents 46.28280 cents 8: 370.2624 .. 370.2624 cents 1/1, 0.0000 cents 46.28279 cents 9: 416.5451 .. 416.5451 cents 1/1, 0.0000 cents 46.28279 cents 10: 462.8279 .. 462.8279 cents 1/1, 0.0000 cents 46.28279 cents 11: 509.1107 .. 509.1107 cents 1/1, 0.0000 cents 46.28279 cents 12: 555.3935 .. 555.3935 cents 1/1, 0.0000 cents 46.28279 cents 13: 601.6763 .. 601.6763 cents 1/1, 0.0000 cents 46.28279 cents 14: 647.9591 .. 647.9591 cents 1/1, 0.0000 cents 46.28279 cents 15: 694.2419 .. 694.2419 cents 1/1, 0.0000 cents 46.28279 cents 16: 740.5247 .. 740.5247 cents 1/1, 0.0000 cents 46.28279 cents 17: 786.8075 .. 786.8075 cents 1/1, 0.0000 cents 46.28279 cents
SHOW DATA
Number of notes : 18 -- Interval properties -- Smallest interval : 46.28279 cents, class 1 Average step (divided formal octave): 46.2828 cents Largest one step interval : 46.28279 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 46.28279 cents, amount: 18 Most common interval of one step : 46.28279 cents, amount: 18 Least squares average step : 46.28279 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 46.28279 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.055556 redundancy: 0.944444 Efficiency x scale size : 1.000000 Number of different interval sizes : 17 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 18, average 694.2419 cents Number of recognisable fourths : 18, average 509.1107 cents Best minor thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
18: 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: 7.7131 cents 3 .. 5 match: 2 H SD: 26.2245 cents 4 .. 6 match: 2 H SD: 8.9042 cents 5 .. 8 match: 3 H SD: 9.5062 cents 6 .. 10 match: 4 H SD: 13.5268 cents 7 .. 11 match: 4 H SD: 6.1866 cents 8 .. 13 match: 5 H SD: 5.4469 cents 9 .. 15 match: 6 H SD: 10.3930 cents 10 .. 16 match: 6 H SD: 6.1285 cents 11 .. 18 match: 7 H SD: 4.8768 cents 12 .. 19 match: 7 H SD: 3.6004 cents 13 .. 21 match: 8 H SD: 3.2545 cents 14 .. 23 match: 9 H SD: 5.2986 cents 15 .. 24 match: 9 H SD: 4.7157 cents 16 .. 26 match: 10 H SD: 4.4042 cents 17 .. 28 match: 11 H SD: 4.2478 cents 18 .. 29 match: 11 H SD: 3.7830 cents 19 .. 31 match: 12 H SD: 3.7442 cents 20 .. 32 match: 12 H SD: 3.9517 cents 21 .. 34 match: 13 H SD: 3.6547 cents 22 .. 36 match: 14 H SD: 3.5055 cents 23 .. 37 match: 14 H SD: 3.8077 cents 24 .. 39 match: 15 H SD: 3.0171 cents 25 .. 40 match: 15 H SD: 4.1566 cents 26 .. 42 match: 16 H SD: 2.5204 cents 27 .. 44 match: 16 SD: 3.5926 cents 28 .. 45 match: 17 H SD: 3.3197 cents 29 .. 47 match: 17 S SD: 2.4622 cents 30 .. 49 match: 17 SD: 3.1196 cents 31 .. 50 match: 17 SD: 3.6728 cents 32 .. 52 match: 18 SD: 3.1505 cents 33 .. 53 match: 18 SD: 2.3980 cents 34 .. 55 match: 18 SD: 2.0605 cents 45 .. 73 match: 18 SD: 2.0004 cents 47 .. 76 match: 18 SD: 1.8611 cents 50 .. 81 match: 18 SD: 1.7235 cents 55 .. 89 match: 18 SD: 1.5746 cents 58 .. 94 match: 18 SD: 1.4370 cents 62 .. 100 match: 18 SD: 1.3235 cents 63 .. 102 match: 18 SD: 1.2986 cents 68 .. 110 match: 18 SD: 1.2571 cents 69 .. 112 match: 18 SD: 1.1312 cents 71 .. 115 match: 18 SD: 1.0017 cents 88 .. 142 match: 18 SD: 0.9865 cents 92 .. 149 match: 18 SD: 0.9100 cents 97 .. 157 match: 18 SD: 0.7484 cents 108 .. 175 match: 18 SD: 0.6504 cents 132 .. 214 match: 18 SD: 0.6235 cents 140 .. 227 match: 18 SD: 0.6098 cents 143 .. 231 match: 18 SD: 0.5656 cents 144 .. 233 match: 18 SD: 0.5300 cents 146 .. 236 match: 18 SD: 0.5102 cents 167 .. 270 match: 18 SD: 0.4933 cents 176 .. 285 match: 18 SD: 0.4253 cents 180 .. 291 match: 18 SD: 0.3979 cents 202 .. 327 match: 18 SD: 0.3910 cents 214 .. 346 match: 18 SD: 0.3418 cents 219 .. 354 match: 18 SD: 0.3225 cents 231 .. 374 match: 18 SD: 0.3210 cents 238 .. 385 match: 18 SD: 0.3111 cents 251 .. 406 match: 18 SD: 0.2871 cents 257 .. 416 match: 18 SD: 0.2793 cents 264 .. 427 match: 18 SD: 0.2767 cents 286 .. 463 match: 18 SD: 0.2646 cents 301 .. 487 match: 18 SD: 0.2614 cents 310 .. 502 match: 18 SD: 0.2501 cents 322 .. 521 match: 18 SD: 0.2328 cents 327 .. 529 match: 18 SD: 0.2205 cents 363 .. 587 match: 18 SD: 0.1997 cents 397 .. 642 match: 18 SD: 0.1853 cents 407 .. 659 match: 18 SD: 0.1673 cents 442 .. 715 match: 18 SD: 0.1659 cents 453 .. 733 match: 18 SD: 0.1651 cents 471 .. 762 match: 18 SD: 0.1628 cents 476 .. 770 match: 18 SD: 0.1536 cents 489 .. 791 match: 18 SD: 0.1357 cents 515 .. 833 match: 18 SD: 0.1270 cents 558 .. 903 match: 18 SD: 0.1193 cents