Scala analysis: xen15-oconnell-golden-section-25-pure
25 pure octaves reduced by phi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 38.923 cents 38.923184 2: 69.097 cents 69.097036 3: 108.020 cents 108.020220 4: 138.194 cents 138.194073 5: 168.368 cents 168.367926 6: 207.291 cents 207.291109 7: 237.465 cents 237.464962 8: 267.639 cents 267.638815 9: 306.562 cents 306.561998 10: 336.736 cents 336.735851 11: 366.910 cents 366.909704 12: 405.833 cents 405.832887 13: 436.007 cents 436.006740 14: 474.930 cents 474.929924 15: 505.104 cents 505.103777 16: 535.278 cents 535.277629 17: 574.201 cents 574.200813 18: 604.375 cents 604.374666 19: 634.549 cents 634.548518 20: 673.472 cents 673.471702 21: 703.646 cents 703.645555 22: 733.819 cents 733.819407 23: 772.743 cents 772.742591 24: 802.916 cents 802.916444 25: 833.090 cents 833.090296
SHOW/INTERVAL
0: 30.1739 cents 30.1739 1: 38.9232 cents 38.9232 2: 30.1739 cents 30.1739 3: 38.9232 cents 38.9232 4: 30.1739 cents 30.1739 5: 30.1739 cents 30.1739 6: 38.9232 cents 38.9232 7: 30.1739 cents 30.1739 8: 30.1739 cents 30.1739 9: 38.9232 cents 38.9232 10: 30.1739 cents 30.1739 11: 30.1739 cents 30.1739 12: 38.9232 cents 38.9232 13: 30.1739 cents 30.1739 14: 38.9232 cents 38.9232 15: 30.1739 cents 30.1739 16: 30.1739 cents 30.1739 17: 38.9232 cents 38.9232 18: 30.1739 cents 30.1739 19: 30.1739 cents 30.1739 20: 38.9232 cents 38.9232 21: 30.1739 cents 30.1739 22: 30.1739 cents 30.1739 23: 38.9232 cents 38.9232 24: 30.1739 cents 30.1739 25: 30.1739 cents 30.1739
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 16 30.17385 cents 1: 9 38.92318 cents 2: 7 60.34771 cents 2: 18 69.09704 cents 3: 23 99.27089 cents 3: 2 108.02022 cents 4: 14 129.44474 cents 4: 11 138.19407 cents 5: 5 159.61860 cents 5: 20 168.36793 cents 6: 21 198.54178 cents 6: 4 207.29111 cents 7: 12 228.71563 cents 7: 13 237.46496 cents 8: 3 258.88948 cents 8: 22 267.63882 cents 9: 19 297.81267 cents 9: 6 306.56200 cents 10: 10 327.98652 cents 10: 15 336.73585 cents 11: 1 358.16037 cents 11: 24 366.90970 cents 12: 17 397.08356 cents 12: 8 405.83289 cents 13: 8 427.25741 cents 13: 17 436.00674 cents 14: 24 466.18059 cents 14: 1 474.92992 cents 15: 15 496.35445 cents 15: 10 505.10378 cents 16: 6 526.52830 cents 16: 19 535.27763 cents 17: 22 565.45148 cents 17: 3 574.20081 cents 18: 13 595.62533 cents 18: 12 604.37467 cents 19: 4 625.79919 cents 19: 21 634.54852 cents 20: 20 664.72237 cents 20: 5 673.47170 cents 21: 11 694.89622 cents 21: 14 703.64555 cents 22: 2 725.07008 cents 22: 23 733.81941 cents 23: 18 763.99326 cents 23: 7 772.74259 cents 24: 9 794.16711 cents 24: 16 802.91644 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
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 : 38.9 69.1 108.0 138.2 168.4 207.3 237.5 267.6 306.6 336.7 366.9 405.8 436.0 474.9 505.1 535.3 574.2 604.4 634.5 673.5 703.6 733.8 772.7 802.9 833.1 38.9 : 30.2 69.1 99.3 129.4 168.4 198.5 228.7 267.6 297.8 328.0 366.9 397.1 436.0 466.2 496.4 535.3 565.5 595.6 634.5 664.7 694.9 733.8 764.0 794.2 833.1 69.1 : 38.9 69.1 99.3 138.2 168.4 198.5 237.5 267.6 297.8 336.7 366.9 405.8 436.0 466.2 505.1 535.3 565.5 604.4 634.5 664.7 703.6 733.8 764.0 802.9 833.1 108.0: 30.2 60.3 99.3 129.4 159.6 198.5 228.7 258.9 297.8 328.0 366.9 397.1 427.3 466.2 496.4 526.5 565.5 595.6 625.8 664.7 694.9 725.1 764.0 794.2 833.1 138.2: 30.2 69.1 99.3 129.4 168.4 198.5 228.7 267.6 297.8 336.7 366.9 397.1 436.0 466.2 496.4 535.3 565.5 595.6 634.5 664.7 694.9 733.8 764.0 802.9 833.1 168.4: 38.9 69.1 99.3 138.2 168.4 198.5 237.5 267.6 306.6 336.7 366.9 405.8 436.0 466.2 505.1 535.3 565.5 604.4 634.5 664.7 703.6 733.8 772.7 802.9 833.1 207.3: 30.2 60.3 99.3 129.4 159.6 198.5 228.7 267.6 297.8 328.0 366.9 397.1 427.3 466.2 496.4 526.5 565.5 595.6 625.8 664.7 694.9 733.8 764.0 794.2 833.1 237.5: 30.2 69.1 99.3 129.4 168.4 198.5 237.5 267.6 297.8 336.7 366.9 397.1 436.0 466.2 496.4 535.3 565.5 595.6 634.5 664.7 703.6 733.8 764.0 802.9 833.1 267.6: 38.9 69.1 99.3 138.2 168.4 207.3 237.5 267.6 306.6 336.7 366.9 405.8 436.0 466.2 505.1 535.3 565.5 604.4 634.5 673.5 703.6 733.8 772.7 802.9 833.1 306.6: 30.2 60.3 99.3 129.4 168.4 198.5 228.7 267.6 297.8 328.0 366.9 397.1 427.3 466.2 496.4 526.5 565.5 595.6 634.5 664.7 694.9 733.8 764.0 794.2 833.1 336.7: 30.2 69.1 99.3 138.2 168.4 198.5 237.5 267.6 297.8 336.7 366.9 397.1 436.0 466.2 496.4 535.3 565.5 604.4 634.5 664.7 703.6 733.8 764.0 802.9 833.1 366.9: 38.9 69.1 108.0 138.2 168.4 207.3 237.5 267.6 306.6 336.7 366.9 405.8 436.0 466.2 505.1 535.3 574.2 604.4 634.5 673.5 703.6 733.8 772.7 802.9 833.1 405.8: 30.2 69.1 99.3 129.4 168.4 198.5 228.7 267.6 297.8 328.0 366.9 397.1 427.3 466.2 496.4 535.3 565.5 595.6 634.5 664.7 694.9 733.8 764.0 794.2 833.1 436.0: 38.9 69.1 99.3 138.2 168.4 198.5 237.5 267.6 297.8 336.7 366.9 397.1 436.0 466.2 505.1 535.3 565.5 604.4 634.5 664.7 703.6 733.8 764.0 802.9 833.1 474.9: 30.2 60.3 99.3 129.4 159.6 198.5 228.7 258.9 297.8 328.0 358.2 397.1 427.3 466.2 496.4 526.5 565.5 595.6 625.8 664.7 694.9 725.1 764.0 794.2 833.1 505.1: 30.2 69.1 99.3 129.4 168.4 198.5 228.7 267.6 297.8 328.0 366.9 397.1 436.0 466.2 496.4 535.3 565.5 595.6 634.5 664.7 694.9 733.8 764.0 802.9 833.1 535.3: 38.9 69.1 99.3 138.2 168.4 198.5 237.5 267.6 297.8 336.7 366.9 405.8 436.0 466.2 505.1 535.3 565.5 604.4 634.5 664.7 703.6 733.8 772.7 802.9 833.1 574.2: 30.2 60.3 99.3 129.4 159.6 198.5 228.7 258.9 297.8 328.0 366.9 397.1 427.3 466.2 496.4 526.5 565.5 595.6 625.8 664.7 694.9 733.8 764.0 794.2 833.1 604.4: 30.2 69.1 99.3 129.4 168.4 198.5 228.7 267.6 297.8 336.7 366.9 397.1 436.0 466.2 496.4 535.3 565.5 595.6 634.5 664.7 703.6 733.8 764.0 802.9 833.1 634.5: 38.9 69.1 99.3 138.2 168.4 198.5 237.5 267.6 306.6 336.7 366.9 405.8 436.0 466.2 505.1 535.3 565.5 604.4 634.5 673.5 703.6 733.8 772.7 802.9 833.1 673.5: 30.2 60.3 99.3 129.4 159.6 198.5 228.7 267.6 297.8 328.0 366.9 397.1 427.3 466.2 496.4 526.5 565.5 595.6 634.5 664.7 694.9 733.8 764.0 794.2 833.1 703.6: 30.2 69.1 99.3 129.4 168.4 198.5 237.5 267.6 297.8 336.7 366.9 397.1 436.0 466.2 496.4 535.3 565.5 604.4 634.5 664.7 703.6 733.8 764.0 802.9 833.1 733.8: 38.9 69.1 99.3 138.2 168.4 207.3 237.5 267.6 306.6 336.7 366.9 405.8 436.0 466.2 505.1 535.3 574.2 604.4 634.5 673.5 703.6 733.8 772.7 802.9 833.1 772.7: 30.2 60.3 99.3 129.4 168.4 198.5 228.7 267.6 297.8 328.0 366.9 397.1 427.3 466.2 496.4 535.3 565.5 595.6 634.5 664.7 694.9 733.8 764.0 794.2 833.1 802.9: 30.2 69.1 99.3 138.2 168.4 198.5 237.5 267.6 297.8 336.7 366.9 397.1 436.0 466.2 505.1 535.3 565.5 604.4 634.5 664.7 703.6 733.8 764.0 802.9 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 30.1739 .. 38.9232 cents 8.74933 cents 30.17385 cents 2: 60.3477 .. 69.0970 cents 8.74933 cents 21.42452 cents 3: 99.2709 .. 108.0202 cents 8.74933 cents 30.17385 cents 4: 129.4447 .. 138.1941 cents 8.74933 cents 21.42452 cents 5: 159.6186 .. 168.3679 cents 8.74933 cents 21.42452 cents 6: 198.5418 .. 207.2911 cents 8.74933 cents 30.17385 cents 7: 228.7156 .. 237.4650 cents 8.74933 cents 21.42452 cents 8: 258.8895 .. 267.6388 cents 8.74933 cents 21.42452 cents 9: 297.8127 .. 306.5620 cents 8.74933 cents 30.17385 cents 10: 327.9865 .. 336.7359 cents 8.74933 cents 21.42452 cents 11: 358.1604 .. 366.9097 cents 8.74933 cents 21.42452 cents 12: 397.0836 .. 405.8329 cents 8.74933 cents 30.17385 cents 13: 427.2574 .. 436.0067 cents 8.74933 cents 21.42452 cents 14: 466.1806 .. 474.9299 cents 8.74933 cents 30.17385 cents 15: 496.3544 .. 505.1038 cents 8.74933 cents 21.42452 cents 16: 526.5283 .. 535.2776 cents 8.74933 cents 21.42452 cents 17: 565.4515 .. 574.2008 cents 8.74933 cents 30.17385 cents 18: 595.6253 .. 604.3747 cents 8.74933 cents 21.42452 cents 19: 625.7992 .. 634.5485 cents 8.74933 cents 21.42452 cents 20: 664.7224 .. 673.4717 cents 8.74933 cents 30.17385 cents 21: 694.8962 .. 703.6456 cents 8.74933 cents 21.42452 cents 22: 725.0701 .. 733.8194 cents 8.74933 cents 21.42452 cents 23: 763.9933 .. 772.7426 cents 8.74933 cents 30.17385 cents 24: 794.1671 .. 802.9164 cents 8.74933 cents 21.42452 cents
SHOW DATA
Number of notes : 25 -- Interval properties -- Smallest interval : 30.17385 cents, class 1 Average step (divided formal octave): 33.3236 cents Largest one step interval : 38.92318 cents Average / Smallest step : 1.104387 Largest / Average step : 1.168036 Largest / Smallest step : 1.289964 Median interval of one step : 30.17385 cents, amount: 16 Most common interval of one step : 30.17385 cents, amount: 16 Least squares average step : 33.55482 cents, oct.: 838.87040 cents Scale is strictly proper Scale has Myhill's property chromas: 8.74933 cents and 21.42452 cents, ratio: 2.448704 generators: 11 of 366.90970 cents and 466.18059 cents ET pair of linear temperament : 25&84 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1905-tone equal temperament with octave 833.090 cents degrees: 89 158 247 316 385 474 543 612 701 770 839 928 997 1086 1155 1224 1313 1382 1451 1540 1609 1678 1767 1836 1905 generators: 839 and 1066 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABBABBABBABABBABBABBABB Step pattern size order : LSLSSLSSLSSLSLSSLSSLSSLSS Scale is a Constant Structure, by a margin of 21.42452 cents Scale diversity : 0.724720 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.747946 Rothenberg efficiency : 0.693333 redundancy: 0.306667 Efficiency x scale size : 17.333333 Number of different interval sizes : 48 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 8.74933 cents Most common intervals : 366.90970 cents & inv., amount: 24 Scale is a chain of 12 triads 0.0 366.910 733.819 cents Most common triad is 0.0 366.910 466.181 cents, amount: 23 Number of recognisable fifths : 25, average 699.7958 cents Number of recognisable fourths : 25, average 499.8542 cents Best fifths form a closed circle Formal octave complements present : 1 = 4.0000% 2/1 octave complements present : 1 = 4.0000% Scale is n-1 differentially coherent in interval classes 10 and 11 combined Scale is n-1 differentially coherent in interval class 11 Scale is n-1 differentially coherent in interval classes 13 and 14 combined Scale is n-1 differentially coherent in interval class 14 Limited inverse transpositions : 14 Inversional symmetry on degrees : 7 Inversional symmetry on intervals : 19-20 -- 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: 4.8996 c. M: 8.3994 c. 48: 2 2 2 2 2 2 2 1 3 1 2 2 2 2 2 2 2 2 2 2 2 1 3 1 2 P D3 S SD: 4.8599 c. M:-8.2796 c. 49: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 3 2 1 3 1 2 2 2 2 P D3 SD: 4.7654 c. M: 8.2205 c. 51: 2 2 3 1 2 3 2 1 3 2 1 3 2 2 2 2 2 2 2 2 2 2 2 2 2 P D3 SD: 4.5521 c. M:-7.5616 c. 52: 2 2 3 2 2 2 2 2 2 2 2 2 2 3 2 1 3 2 2 2 2 2 2 2 2 P D3 SD: 4.4450 c. M:-7.8627 c. 54: 3 1 3 2 2 2 2 2 3 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 P D3 SD: 4.3199 c. M: 7.3866 c. 56: 3 2 2 2 2 3 2 2 3 2 2 2 2 3 2 2 3 2 2 2 2 2 3 2 2 P D3 S SD: 4.0022 c. M:-5.9871 c. 59: 3 2 3 2 2 3 2 2 3 2 2 3 2 3 2 2 3 2 2 3 2 2 3 2 2 SP M ME S SD: 3.0077 c. M:-5.1560 c. 77: 4 2 4 3 3 3 3 3 3 3 3 4 2 4 3 2 4 3 3 3 3 3 3 3 3 SP D3 SD: 2.9942 c. M:-5.3026 c. 79: 4 3 3 3 3 4 3 2 4 3 3 3 3 4 3 3 3 3 3 4 3 3 3 3 3 SP D3 SD: 3.0034 c. M: 5.1059 c. 81: 4 3 3 3 3 4 3 3 4 3 3 3 3 4 3 3 4 3 3 3 3 3 4 3 3 SP D3 S SD: 2.9685 c. M: 5.1696 c. 82: 4 3 4 3 3 3 3 3 4 3 3 4 3 4 3 3 4 2 3 4 3 3 4 3 3 SP D3 SD: 2.9925 c. M: 4.9560 c. 83: 4 3 4 3 3 4 3 3 4 3 3 3 3 4 3 3 4 3 3 4 3 3 4 3 3 SP D3 SD: 2.8482 c. M:-4.5922 c. 84: 4 3 4 3 3 4 3 3 4 3 3 4 3 4 3 3 4 3 3 4 3 3 4 3 3 SP M ME S SD: 0.6543 c. M:-1.1217 c. 109: 5 4 5 4 4 5 4 4 5 4 4 5 4 5 4 4 5 4 4 5 4 4 5 4 4 SP M ME S SD: 0.6195 c. M: 1.0620 c. 193: 9 7 9 7 7 9 7 7 9 7 7 9 7 9 7 7 9 7 7 9 7 7 9 7 7 SP M DE S SD: 0.0651 c. M: 0.1116 c. 470: 22 17 22 17 17 22 17 17 22 17 17 22 17 22 17 17 22 17 17 22 17 17 22 17 17 SP M DE S SD: 0.0635 c. M:-0.1088 c. 663: 31 24 31 24 24 31 24 24 31 24 24 31 24 31 24 24 31 24 24 31 24 24 31 24 24 SP M DE S SD: 0.0260 c. M:-0.0446 c. 856: 40 31 40 31 31 40 31 31 40 31 31 40 31 40 31 31 40 31 31 40 31 31 40 31 31 SP M DE S SD: 0.0055 c. M:-0.0094 c. 1905: 89 69 89 69 69 89 69 69 89 69 69 89 69 89 69 69 89 69 69 89 69 69 89 69 69 SP M DE S SD: 0.0017 c. M: 0.0029 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 366.9097 cents 2 .. 3 match: 1 H SD: 1.6906 cents 3 .. 5 match: 2 H SD: 25.8760 cents 4 .. 6 match: 2 H SD: 9.7388 cents 5 .. 8 match: 3 H SD: 5.4518 cents 6 .. 10 match: 4 H SD: 12.9463 cents 7 .. 11 match: 4 H SD: 4.3834 cents 8 .. 13 match: 5 H SD: 5.3044 cents 9 .. 15 match: 6 H SD: 9.2116 cents 10 .. 16 match: 6 H SD: 4.1271 cents 11 .. 18 match: 7 H SD: 5.6063 cents 12 .. 19 match: 7 H SD: 3.1492 cents 13 .. 21 match: 8 H SD: 3.7692 cents 14 .. 23 match: 9 H SD: 3.8157 cents 15 .. 24 match: 9 H SD: 2.6711 cents 16 .. 26 match: 10 H SD: 2.9177 cents 17 .. 28 match: 11 H SD: 3.8370 cents 18 .. 29 match: 11 H SD: 2.6633 cents 19 .. 31 match: 12 H SD: 2.7157 cents 20 .. 32 match: 12 H SD: 3.4635 cents 21 .. 34 match: 13 H SD: 2.3037 cents 22 .. 36 match: 14 H SD: 3.2573 cents 23 .. 37 match: 14 H SD: 2.0719 cents 24 .. 39 match: 15 H SD: 2.6122 cents 25 .. 40 match: 15 H SD: 1.8895 cents 26 .. 42 match: 16 H SD: 2.5385 cents 27 .. 44 match: 17 H SD: 2.3824 cents 28 .. 45 match: 17 H SD: 2.4419 cents 29 .. 47 match: 18 H SD: 2.2722 cents 30 .. 49 match: 19 H SD: 2.0618 cents 31 .. 50 match: 19 H SD: 2.1525 cents 32 .. 52 match: 20 H SD: 2.1457 cents 33 .. 53 match: 19 S SD: 2.5316 cents 34 .. 55 match: 21 H SD: 1.8475 cents 35 .. 57 match: 20 SD: 2.2813 cents 36 .. 58 match: 22 H SD: 1.8803 cents 37 .. 60 match: 21 SD: 2.3339 cents 38 .. 61 match: 23 H SD: 1.7152 cents 39 .. 63 match: 23 S SD: 2.0461 cents 40 .. 65 match: 21 SD: 2.1629 cents 41 .. 66 match: 24 S SD: 1.5887 cents 42 .. 68 match: 24 SD: 1.5810 cents 43 .. 70 match: 24 SD: 2.0171 cents 44 .. 71 match: 22 SD: 1.8899 cents 45 .. 73 match: 25 SD: 1.7519 cents 46 .. 74 match: 25 SD: 1.3628 cents 47 .. 76 match: 25 SD: 1.3336 cents 48 .. 78 match: 25 SD: 1.1730 cents 71 .. 115 match: 25 SD: 1.0924 cents 72 .. 116 match: 25 SD: 1.0745 cents 73 .. 118 match: 25 SD: 1.0682 cents 74 .. 120 match: 25 SD: 1.0399 cents 76 .. 123 match: 25 SD: 0.8430 cents 88 .. 142 match: 25 SD: 0.7734 cents 94 .. 152 match: 25 SD: 0.6532 cents 118 .. 191 match: 25 SD: 0.5876 cents 124 .. 201 match: 25 SD: 0.5348 cents 136 .. 220 match: 25 SD: 0.5105 cents 143 .. 231 match: 25 SD: 0.5028 cents 144 .. 233 match: 25 SD: 0.4236 cents 168 .. 272 match: 25 SD: 0.3918 cents 171 .. 277 match: 25 SD: 0.3905 cents 174 .. 282 match: 25 SD: 0.3851 cents 190 .. 307 match: 25 SD: 0.3755 cents 196 .. 317 match: 25 SD: 0.3403 cents 204 .. 330 match: 25 SD: 0.3304 cents 215 .. 348 match: 25 SD: 0.3085 cents 227 .. 367 match: 25 SD: 0.2907 cents 246 .. 398 match: 25 SD: 0.2875 cents 251 .. 406 match: 25 SD: 0.2458 cents 265 .. 429 match: 25 SD: 0.2200 cents 311 .. 503 match: 25 SD: 0.2193 cents 313 .. 506 match: 25 SD: 0.2043 cents 339 .. 549 match: 25 SD: 0.1965 cents 345 .. 558 match: 25 SD: 0.1732 cents 387 .. 626 match: 25 SD: 0.1659 cents 402 .. 650 match: 25 SD: 0.1524 cents 443 .. 717 match: 25 SD: 0.1504 cents 448 .. 725 match: 25 SD: 0.1491 cents 469 .. 759 match: 25 SD: 0.1396 cents 481 .. 778 match: 25 SD: 0.1346 cents 496 .. 803 match: 25 SD: 0.1314 cents 517 .. 837 match: 25 SD: 0.1177 cents 558 .. 903 match: 25 SD: 0.1172 cents 576 .. 932 match: 25 SD: 0.1159 cents 587 .. 950 match: 25 SD: 0.1117 cents