Scala analysis: xen18-erlich-semaphore-19
5L 14s MOS for Semaphore, L=76.29, s=58.73
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.730 cents 58.730000 2: 135.020 cents 135.020000 3: 193.750 cents 193.750000 4: 252.480 cents 252.480000 5: 311.210 cents 311.210000 6: 387.500 cents 387.500000 7: 446.230 cents 446.230000 8: 504.960 cents 504.960000 9: 563.690 cents 563.690000 10: 639.980 cents 639.980000 11: 698.710 cents 698.710000 12: 757.440 cents 757.440000 13: 816.170 cents 816.170000 14: 892.460 cents 892.460000 15: 951.190 cents 951.190000 16: 1009.920 cents 1009.920000 17: 1068.650 cents 1068.650000 18: 1144.940 cents 1144.940000 19: 1203.670 cents 1203.670000
SHOW/INTERVAL
0: 58.7300 cents 58.7300 1: 58.7300 cents 58.7300 2: 76.2900 cents 76.2900 3: 58.7300 cents 58.7300 4: 58.7300 cents 58.7300 5: 58.7300 cents 58.7300 6: 76.2900 cents 76.2900 7: 58.7300 cents 58.7300 8: 58.7300 cents 58.7300 9: 58.7300 cents 58.7300 10: 76.2900 cents 76.2900 11: 58.7300 cents 58.7300 12: 58.7300 cents 58.7300 13: 58.7300 cents 58.7300 14: 76.2900 cents 76.2900 15: 58.7300 cents 58.7300 16: 58.7300 cents 58.7300 17: 58.7300 cents 58.7300 18: 76.2900 cents 76.2900 19: 58.7300 cents 58.7300
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 14 58.73000 cents 1: 5 76.29000 cents 2: 9 117.46000 cents 2: 10 135.02000 cents 3: 4 176.19000 cents 3: 15 193.75000 cents 4: 18 252.48000 cents 4: 1 270.04000 cents 5: 13 311.21000 cents 5: 6 328.77000 cents 6: 8 369.94000 cents 6: 11 387.50000 cents 7: 3 428.67000 cents 7: 16 446.23000 cents 8: 17 504.96000 cents 8: 2 522.52000 cents 9: 12 563.69000 cents 9: 7 581.25000 cents 10: 7 622.42000 cents 10: 12 639.98000 cents 11: 2 681.15000 cents 11: 17 698.71000 cents 12: 16 757.44000 cents 12: 3 775.00000 cents 13: 11 816.17000 cents 13: 8 833.73000 cents 14: 6 874.90000 cents 14: 13 892.46000 cents 15: 1 933.63000 cents 15: 18 951.19000 cents 16: 15 1009.92000 cents 16: 4 1027.48000 cents 17: 10 1068.65000 cents 17: 9 1086.21000 cents 18: 5 1127.38000 cents 18: 14 1144.94000 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 0.0 : 58.7 135.0 193.7 252.5 311.2 387.5 446.2 505.0 563.7 640.0 698.7 757.4 816.2 892.5 951.2 1009.9 1068.7 1144.9 1203.7 58.7 : 76.3 135.0 193.7 252.5 328.8 387.5 446.2 505.0 581.2 640.0 698.7 757.4 833.7 892.5 951.2 1009.9 1086.2 1144.9 1203.7 135.0 : 58.7 117.5 176.2 252.5 311.2 369.9 428.7 505.0 563.7 622.4 681.1 757.4 816.2 874.9 933.6 1009.9 1068.7 1127.4 1203.7 193.7 : 58.7 117.5 193.7 252.5 311.2 369.9 446.2 505.0 563.7 622.4 698.7 757.4 816.2 874.9 951.2 1009.9 1068.7 1144.9 1203.7 252.5 : 58.7 135.0 193.8 252.5 311.2 387.5 446.2 505.0 563.7 640.0 698.7 757.4 816.2 892.5 951.2 1009.9 1086.2 1144.9 1203.7 311.2 : 76.3 135.0 193.8 252.5 328.8 387.5 446.2 505.0 581.3 640.0 698.7 757.4 833.7 892.5 951.2 1027.5 1086.2 1144.9 1203.7 387.5 : 58.7 117.5 176.2 252.5 311.2 369.9 428.7 505.0 563.7 622.4 681.2 757.4 816.2 874.9 951.2 1009.9 1068.7 1127.4 1203.7 446.2 : 58.7 117.5 193.7 252.5 311.2 369.9 446.2 505.0 563.7 622.4 698.7 757.4 816.2 892.5 951.2 1009.9 1068.6 1144.9 1203.7 505.0 : 58.7 135.0 193.7 252.5 311.2 387.5 446.2 505.0 563.7 640.0 698.7 757.4 833.7 892.5 951.2 1009.9 1086.2 1144.9 1203.7 563.7 : 76.3 135.0 193.7 252.5 328.8 387.5 446.2 505.0 581.2 640.0 698.7 775.0 833.7 892.5 951.2 1027.5 1086.2 1144.9 1203.7 640.0 : 58.7 117.5 176.2 252.5 311.2 369.9 428.7 505.0 563.7 622.4 698.7 757.4 816.2 874.9 951.2 1009.9 1068.7 1127.4 1203.7 698.7 : 58.7 117.5 193.7 252.5 311.2 369.9 446.2 505.0 563.7 640.0 698.7 757.4 816.2 892.5 951.2 1009.9 1068.7 1144.9 1203.7 757.4 : 58.7 135.0 193.7 252.5 311.2 387.5 446.2 505.0 581.3 640.0 698.7 757.4 833.7 892.5 951.2 1009.9 1086.2 1144.9 1203.7 816.2 : 76.3 135.0 193.8 252.5 328.8 387.5 446.2 522.5 581.3 640.0 698.7 775.0 833.7 892.5 951.2 1027.5 1086.2 1144.9 1203.7 892.5 : 58.7 117.5 176.2 252.5 311.2 369.9 446.2 505.0 563.7 622.4 698.7 757.4 816.2 874.9 951.2 1009.9 1068.7 1127.4 1203.7 951.2 : 58.7 117.5 193.7 252.5 311.2 387.5 446.2 505.0 563.7 640.0 698.7 757.4 816.2 892.5 951.2 1009.9 1068.6 1144.9 1203.7 1009.9: 58.7 135.0 193.8 252.5 328.8 387.5 446.2 505.0 581.3 640.0 698.7 757.4 833.7 892.5 951.2 1009.9 1086.2 1144.9 1203.7 1068.7: 76.3 135.0 193.8 270.0 328.8 387.5 446.2 522.5 581.3 640.0 698.7 775.0 833.7 892.5 951.2 1027.5 1086.2 1144.9 1203.7 1144.9: 58.7 117.5 193.8 252.5 311.2 369.9 446.2 505.0 563.7 622.4 698.7 757.4 816.2 874.9 951.2 1009.9 1068.7 1127.4 1203.7 1203.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.7300 .. 76.2900 cents 17.56000 cents 58.73000 cents 2: 117.4600 .. 135.0200 cents 17.56000 cents 41.17000 cents 3: 176.1900 .. 193.7500 cents 17.56000 cents 41.17000 cents 4: 252.4800 .. 270.0400 cents 17.56000 cents 58.73000 cents 5: 311.2100 .. 328.7700 cents 17.56000 cents 41.17000 cents 6: 369.9400 .. 387.5000 cents 17.56000 cents 41.17000 cents 7: 428.6700 .. 446.2300 cents 17.56000 cents 41.17000 cents 8: 504.9600 .. 522.5200 cents 17.56000 cents 58.73000 cents 9: 563.6900 .. 581.2500 cents 17.56000 cents 41.17000 cents 10: 622.4200 .. 639.9800 cents 17.56000 cents 41.17000 cents 11: 681.1500 .. 698.7100 cents 17.56000 cents 41.17000 cents 12: 757.4400 .. 775.0000 cents 17.56000 cents 58.73000 cents 13: 816.1700 .. 833.7300 cents 17.56000 cents 41.17000 cents 14: 874.9000 .. 892.4600 cents 17.56000 cents 41.17000 cents 15: 933.6300 .. 951.1900 cents 17.56000 cents 41.17000 cents 16: 1009.9200 .. 1027.4800 cents 17.56000 cents 58.73000 cents 17: 1068.6500 .. 1086.2100 cents 17.56000 cents 41.17000 cents 18: 1127.3800 .. 1144.9400 cents 17.56000 cents 41.17000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 58.73000 cents, class 1 Average step (divided formal octave): 63.3511 cents Largest one step interval : 76.29000 cents Average / Smallest step : 1.078683 Largest / Average step : 1.204242 Largest / Smallest step : 1.298995 Median interval of one step : 58.73000 cents, amount: 14 Most common interval of one step : 58.73000 cents, amount: 14 Least squares average step : 63.31551 cents, oct.: 1202.99462 cents Scale is strictly proper Scale has Myhill's property chromas: 17.56000 cents and 41.17000 cents, ratio: 2.344533 generators: 4 of 252.48000 cents and 15 of 951.19000 cents ET pair of linear temperament : 19&62 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1783-tone equal temperament with octave 1203.670 cents degrees: 87 200 287 374 461 574 661 748 835 948 1035 1122 1209 1322 1409 1496 1583 1696 1783 generators: 374 and 1409 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAAABAAABAAABA Step pattern size order : SLSSSLSSSLSSSLSSSLS Scale is a Constant Structure, by a margin of 41.17000 cents Scale diversity : 1.152100 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.737403 Rothenberg efficiency : 0.701754 redundancy: 0.298246 Efficiency x scale size : 13.333333 Number of different interval sizes : 36 = 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 : 17.56000 cents Most common intervals : 252.48000 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 252.480 504.960 cents Most common triad is 0.0 252.480 951.190 cents, amount: 17 Number of recognisable fifths : 17, average 698.7100 cents Number of recognisable fourths : 17, average 504.9600 cents Scale contains two identical conjunct "tetrachords" of 9 notes 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% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties --
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: 5.0621 c. M:-8.3179 c. 43: 2 3 2 2 2 3 2 2 2 3 2 2 2 3 2 2 2 3 2 SP M ME I SD: 3.0074 c. M:-4.9416 c. 62: 3 4 3 3 3 4 3 3 3 4 3 3 3 4 3 3 3 4 3 SP M ME I SD: 0.5345 c. M:-0.8782 c. 143: 7 9 7 7 7 9 7 7 7 9 7 7 7 9 7 7 7 9 7 SP M DE I SD: 0.2091 c. M:-0.3436 c. 205: 10 13 10 10 10 13 10 10 10 13 10 10 10 13 10 10 10 13 10 SP M DE I SD: 0.0158 c. M:-0.0259 c. 1168: 57 74 57 57 57 74 57 57 57 74 57 57 57 74 57 57 57 74 57 SP M DE I SD: 0.0118 c. M:-0.0193 c. 1373: 67 87 67 67 67 87 67 67 67 87 67 67 67 87 67 67 67 87 67 SP M DE I SD: 0.0077 c. M:-0.0126 c. 1578: 77 100 77 77 77 100 77 77 77 100 77 77 77 100 77 77 77 100 77 SP M DE I SD: 0.0046 c. M:-0.0076 c. 1783: 87 113 87 87 87 113 87 87 87 113 87 87 87 113 87 87 87 113 87 SP M DE I SD: 0.0023 c. M:-0.0037 c. 1988: 97 126 97 97 97 126 97 97 97 126 97 97 97 126 97 97 97 126 97 SP M DE I SD: 0.0004 c. M:-0.0007 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 3.6700 cents 2 .. 4 match: 2 H SD: 2.4494 cents 3 .. 6 match: 3 H SD: 3.7552 cents 4 .. 8 match: 4 H SD: 4.5855 cents 5 .. 10 match: 5 H SD: 4.2543 cents 6 .. 12 match: 6 H SD: 4.4614 cents 7 .. 14 match: 7 H SD: 6.4849 cents 8 .. 16 match: 8 H SD: 4.9543 cents 9 .. 18 match: 9 H SD: 5.9565 cents 10 .. 20 match: 10 H SD: 5.6365 cents 11 .. 22 match: 11 H SD: 6.4288 cents 12 .. 24 match: 12 H SD: 4.6998 cents 13 .. 26 match: 13 H SD: 4.1180 cents 14 .. 28 match: 14 H SD: 4.8903 cents 15 .. 30 match: 15 H SD: 3.7115 cents 16 .. 32 match: 16 H SD: 4.0500 cents 17 .. 34 match: 16 S SD: 5.7565 cents 18 .. 36 match: 17 SD: 3.8862 cents 19 .. 38 match: 16 SD: 4.6932 cents 20 .. 40 match: 18 SD: 3.2647 cents 21 .. 42 match: 18 SD: 3.9144 cents 22 .. 44 match: 17 SD: 4.1962 cents 23 .. 46 match: 19 SD: 3.6976 cents 24 .. 48 match: 19 SD: 2.7501 cents 26 .. 52 match: 19 SD: 2.7193 cents 27 .. 54 match: 19 SD: 2.4846 cents 33 .. 66 match: 19 SD: 2.2173 cents 34 .. 68 match: 19 SD: 2.2123 cents 36 .. 72 match: 19 SD: 1.9710 cents 40 .. 80 match: 19 SD: 1.9032 cents 44 .. 88 match: 19 SD: 1.8550 cents 45 .. 90 match: 19 SD: 1.8462 cents 47 .. 94 match: 19 SD: 1.6889 cents 49 .. 98 match: 19 SD: 1.5850 cents 50 .. 100 match: 19 SD: 1.4782 cents 51 .. 102 match: 19 SD: 1.3182 cents 52 .. 104 match: 19 SD: 1.3069 cents 60 .. 120 match: 19 SD: 1.1353 cents 62 .. 124 match: 19 SD: 1.0898 cents 71 .. 142 match: 19 SD: 1.0794 cents 75 .. 150 match: 19 SD: 1.0132 cents 76 .. 152 match: 19 SD: 0.8479 cents 83 .. 166 match: 19 SD: 0.7898 cents 91 .. 182 match: 19 SD: 0.7704 cents 96 .. 192 match: 19 SD: 0.7342 cents 101 .. 202 match: 19 SD: 0.7322 cents 108 .. 216 match: 19 SD: 0.7168 cents 109 .. 218 match: 19 SD: 0.6599 cents 111 .. 222 match: 19 SD: 0.6431 cents 116 .. 232 match: 19 SD: 0.6022 cents 127 .. 255 match: 19 SD: 0.5880 cents 135 .. 271 match: 19 SD: 0.5312 cents 145 .. 291 match: 19 SD: 0.5095 cents 151 .. 303 match: 19 SD: 0.4898 cents 153 .. 307 match: 19 SD: 0.4609 cents 159 .. 319 match: 19 SD: 0.4391 cents 171 .. 343 match: 19 SD: 0.3831 cents 177 .. 355 match: 19 SD: 0.3643 cents 197 .. 395 match: 19 SD: 0.3180 cents 224 .. 449 match: 19 SD: 0.2967 cents 234 .. 469 match: 19 SD: 0.2922 cents 235 .. 471 match: 19 SD: 0.2886 cents 239 .. 479 match: 19 SD: 0.2833 cents 254 .. 509 match: 19 SD: 0.2737 cents 255 .. 511 match: 19 SD: 0.2285 cents 286 .. 573 match: 19 SD: 0.2044 cents 319 .. 639 match: 19 SD: 0.1898 cents 370 .. 742 match: 19 SD: 0.1795 cents 382 .. 766 match: 19 SD: 0.1698 cents 431 .. 864 match: 19 SD: 0.1520 cents 432 .. 866 match: 19 SD: 0.1334 cents 467 .. 936 match: 19 SD: 0.1279 cents 523 .. 1048 match: 19 SD: 0.1103 cents