Scala analysis: First_Five_Golden_Cuts_of_Phi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93.886 cents 93.885970 2: 149.464 cents 149.463660 3: 235.774 cents 235.774410 4: 366.910 cents 366.909700 5: 560.067 cents 560.066560 6: 833.090 cents 833.090300
SHOW/INTERVAL
0: 273.0237 cents 273.0237 1: 93.8860 cents 93.8860 2: 55.5777 cents 55.5777 3: 86.3108 cents 86.3108 4: 131.1353 cents 131.1353 5: 193.1569 cents 193.1569 6: 273.0237 cents 273.0237
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55.57769 cents 1: 1 86.31075 cents 1: 1 93.88597 cents 1: 1 131.13529 cents 1: 1 193.15686 cents 1: 1 273.02374 cents 2: 1 141.88844 cents 2: 1 149.46366 cents 2: 1 217.44604 cents 2: 1 324.29215 cents 2: 1 366.90971 cents 2: 1 466.18060 cents 3: 1 235.77441 cents 3: 1 273.02373 cents 3: 1 410.60290 cents 3: 1 422.48740 cents 3: 1 560.06657 cents 3: 1 597.31589 cents 4: 1 366.90970 cents 4: 1 466.18059 cents 4: 1 508.79815 cents 4: 1 615.64426 cents 4: 1 683.62664 cents 4: 1 691.20186 cents 5: 1 560.06656 cents 5: 1 639.93344 cents 5: 1 701.95501 cents 5: 1 739.20433 cents 5: 1 746.77955 cents 5: 1 777.51261 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 93.9 149.5 235.8 366.9 560.1 833.1 93.9 : 55.6 141.9 273.0 466.2 739.2 833.1 149.5: 86.3 217.4 410.6 683.6 777.5 833.1 235.8: 131.1 324.3 597.3 691.2 746.8 833.1 366.9: 193.2 466.2 560.1 615.6 702.0 833.1 560.1: 273.0 366.9 422.5 508.8 639.9 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 55.5777 .. 273.0237 cents 217.44605 cents 55.57769 cents 2: 141.8884 .. 466.1806 cents 324.29216 cents -131.13530 cents 3: 235.7744 .. 597.3159 cents 361.54148 cents -230.40619 cents 4: 366.9097 .. 691.2019 cents 324.29216 cents -230.40619 cents 5: 560.0666 .. 777.5126 cents 217.44605 cents -131.13530 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 55.57769 cents, class 1 Average step (divided formal octave): 138.8484 cents Largest one step interval : 273.02374 cents Average / Smallest step : 2.498276 Largest / Average step : 1.966344 Largest / Smallest step : 4.912470 Median interval of one step : 112.51063 cents, amount: 0 Least squares average step : 113.91923 cents, oct.: 683.51538 cents Scale is not proper Step pattern alph. order: ABCDEF Step pattern size order : CABDEF Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.287007 Lumma stability : 0.133425 Lumma impropriety factor : 0.659368 Rothenberg efficiency : 0.377778 redundancy: 0.622222 Efficiency x scale size : 2.266667 Number of different interval sizes : 26 = 5.20000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 6.00000 = 6 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 7.57522 cents Number of recognisable fifths : 2, average 696.5784 cents Number of recognisable fourths : 1, average 508.7982 cents Formal octave complements present : 1 = 16.6667% 2/1 octave complements present : 1 = 16.6667% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval class 4 Scale is n-1 differentially coherent in interval class 5 -- Rational properties --
FIT/MODE
6: 1 0 1 1 1 2 N T3 SD: 32.6019 c. M:-49.6354 c. 7: 1 0 1 1 2 2 N SD: 21.9316 c. M:-34.9979 c. 9: 1 1 1 1 2 3 N SD: 22.5997 c. M:-41.9224 c. 10: 1 1 1 1 3 3 N D3 S SD: 19.4671 c. M: 33.6736 c. 11: 1 1 1 2 2 4 N SD: 15.4944 c. M: 29.9182 c. 12: 1 1 1 2 3 4 N SD: 17.7052 c. M: 27.5018 c. 15: 2 1 1 3 3 5 N SD: 14.5787 c. M:-21.8658 c. 16: 2 1 2 2 4 5 N SD: 12.3881 c. M:-24.5663 c. 18: 2 1 2 3 4 6 N SD: 5.2681 c. M: 10.6153 c. 28: 3 2 3 4 7 9 N SD: 5.0316 c. M: 9.8710 c. 34: 4 2 4 5 8 11 N SD: 4.4947 c. M:-9.2521 c. 39: 4 3 4 6 9 13 N SD: 4.2412 c. M: 8.4408 c. 43: 5 3 4 7 10 14 N SD: 3.0249 c. M:-5.5299 c. 45: 5 3 5 7 10 15 N SD: 3.1791 c. M:-4.8961 c. 46: 5 3 5 7 11 15 N SD: 3.0577 c. M: 4.6965 c. 57: 6 4 6 9 13 19 N SD: 3.5854 c. M: 6.1923 c. 61: 7 4 6 10 14 20 N SD: 1.8203 c. M: 3.6017 c. 71: 8 5 7 11 17 23 N SD: 2.2585 c. M: 3.1660 c. 73: 8 5 8 11 17 24 N SD: 2.1095 c. M:-3.8817 c. 77: 9 5 8 12 18 25 N SD: 2.1839 c. M:-3.4882 c. 79: 9 5 8 13 18 26 N SD: 2.0302 c. M: 3.7746 c. 82: 9 6 8 13 19 27 N SD: 1.9156 c. M:-2.9309 c. 88: 10 6 9 14 20 29 N SD: 1.4746 c. M:-2.3008 c. 89: 10 6 9 14 21 29 N SD: 1.2343 c. M: 1.8477 c. 95: 11 6 10 15 22 31 N SD: 1.3622 c. M:-2.5771 c. 106: 12 7 11 17 24 35 N SD: 1.3269 c. M:-2.4794 c. 107: 12 7 11 17 25 35 N SD: 1.1971 c. M: 2.1977 c. 116: 13 8 12 18 27 38 N SD: 0.8194 c. M:-1.3544 c. 134: 15 9 14 21 31 44 N SD: 0.4033 c. M: 0.6296 c. 311: 35 21 32 49 72 102 N SD: 0.2472 c. M:-0.5462 c. 329: 37 22 34 52 76 108 N SD: 0.2557 c. M: 0.4527 c. 434: 49 29 45 68 101 142 N SD: 0.2834 c. M:-0.4458 c. 445: 50 30 46 70 103 146 N SD: 0.2152 c. M:-0.3054 c. 452: 51 30 47 71 105 148 N SD: 0.1518 c. M:-0.2420 c. 586: 66 39 61 92 136 192 N SD: 0.1337 c. M:-0.2205 c. 629: 71 42 65 99 146 206 N SD: 0.1280 c. M:-0.2012 c. 647: 73 43 67 102 150 212 N SD: 0.0893 c. M: 0.1399 c. 763: 86 51 79 120 177 250 N SD: 0.0644 c. M:-0.1214 c. 781: 88 52 81 123 181 256 N SD: 0.0593 c. M: 0.1261 c. 958: 108 64 99 151 222 314 N SD: 0.0716 c. M:-0.1100 c. 1092: 123 73 113 172 253 358 N SD: 0.0568 c. M: 0.0956 c. 1410: 159 94 146 222 327 462 N SD: 0.0353 c. M:-0.0583 c. 1544: 174 103 160 243 358 506 N SD: 0.0071 c. M:-0.0160 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 366.9097 cents 2 x x x x x 3 S SD: 131.1353 cents 3 x x x x 4:5 S SD: 40.2341 cents 4 x x x 5 x 6 S SD: 66.2816 cents 5 x x x 6:7:8 S SD: 19.7450 cents 6 x x 7 x 8:10 S SD: 28.7559 cents 7 x x 8:9:10:11 S SD: 25.6494 cents 8 x x 9:10:11:13 SD: 9.7587 cents 9 x 10 x 11:12:15 S SD: 22.2774 cents 10 x 11 x 12:14:16 S SD: 15.3099 cents 11 x 12:13:14:15:18 S SD: 15.9142 cents 12 x 13:14:15:17:19 SD: 13.7319 cents 13 x 14:15:16:18:21 S SD: 5.1596 cents 14:15 x 16:17:19:23 SD: 11.4911 cents 15:16 x 17:19:21:24 SD: 11.5851 cents 16:17 x 18:20:22:26 SD: 8.1148 cents 17:18:19 x 21:23:28 SD: 12.9333 cents 18:19:20:21:22:25:29 SD: 8.4367 cents 20:21:22:23:25:28:32 SD: 6.7192 cents 21:22:23:24:26:29:34 SD: 2.7622 cents 27 x 29:31:33:37:44 SD: 7.5382 cents 29:31:32:33:36:40:47 SD: 5.5897 cents 32:34:35:37:40:44:52 SD: 5.0153 cents 33:35:36:38:41:46:53 SD: 4.0960 cents 34:36:37:39:42:47:55 SD: 1.0515 cents 55:58:60:63:68:76:89 SD: 0.4021 cents 89:94:97:102:110:123:144 SD: 0.1535 cents 144:152:157:165:178:199:233 SD: 0.0587 cents 233:246:254:267:288:322:377 SD: 0.0224 cents 377:398:411:432:466:521:610 SD: 0.0086 cents