Scala analysis: xen18-schulter-707-17
Temperament with fifth of 707.22045
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63.898 cents 63.897750 2: 150.543 cents 150.543150 3: 214.441 cents 214.440900 4: 278.339 cents 278.338650 5: 364.984 cents 364.984050 6: 428.882 cents 428.881800 7: 492.780 cents 492.779550 8: 556.677 cents 556.677300 9: 643.323 cents 643.322700 10: 707.220 cents 707.220450 11: 771.118 cents 771.118200 12: 857.764 cents 857.763600 13: 921.661 cents 921.661350 14: 985.559 cents 985.559100 15: 1072.205 cents 1072.204500 16: 1136.102 cents 1136.102250 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 63.8978 cents 63.8978 1: 63.8977 cents 63.8977 2: 86.6454 cents 86.6454 3: 63.8978 cents 63.8978 4: 63.8977 cents 63.8977 5: 86.6454 cents 86.6454 6: 63.8977 cents 63.8977 7: 63.8978 cents 63.8978 8: 63.8977 cents 63.8977 9: 86.6454 cents 86.6454 10: 63.8977 cents 63.8977 11: 63.8977 cents 63.8977 12: 86.6454 cents 86.6454 13: 63.8978 cents 63.8978 14: 63.8977 cents 63.8977 15: 86.6454 cents 86.6454 16: 63.8977 cents 63.8977 17: 63.8978 cents 63.8978
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 63.89775 cents 1: 5 86.64540 cents 2: 7 127.79550 cents 2: 10 150.54315 cents 3: 2 191.69325 cents 3: 15 214.44090 cents 4: 14 278.33865 cents 4: 3 301.08630 cents 5: 9 342.23640 cents 5: 8 364.98405 cents 6: 4 406.13415 cents 6: 13 428.88180 cents 7: 16 492.77955 cents 7: 1 515.52720 cents 8: 11 556.67730 cents 8: 6 579.42495 cents 9: 6 620.57505 cents 9: 11 643.32270 cents 10: 1 684.47280 cents 10: 16 707.22045 cents 11: 13 771.11820 cents 11: 4 793.86585 cents 12: 8 835.01595 cents 12: 9 857.76360 cents 13: 3 898.91370 cents 13: 14 921.66135 cents 14: 15 985.55910 cents 14: 2 1008.30675 cents 15: 10 1049.45685 cents 15: 7 1072.20450 cents 16: 5 1113.35460 cents 16: 12 1136.10225 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 0.0 : 63.9 150.5 214.4 278.3 365.0 428.9 492.8 556.7 643.3 707.2 771.1 857.8 921.7 985.6 1072.2 1136.1 1200.0 63.9 : 86.6 150.5 214.4 301.1 365.0 428.9 492.8 579.4 643.3 707.2 793.9 857.8 921.7 1008.3 1072.2 1136.1 1200.0 150.5 : 63.9 127.8 214.4 278.3 342.2 406.1 492.8 556.7 620.6 707.2 771.1 835.0 921.7 985.6 1049.5 1113.4 1200.0 214.4 : 63.9 150.5 214.4 278.3 342.2 428.9 492.8 556.7 643.3 707.2 771.1 857.8 921.7 985.6 1049.5 1136.1 1200.0 278.3 : 86.6 150.5 214.4 278.3 365.0 428.9 492.8 579.4 643.3 707.2 793.9 857.8 921.7 985.6 1072.2 1136.1 1200.0 365.0 : 63.9 127.8 191.7 278.3 342.2 406.1 492.8 556.7 620.6 707.2 771.1 835.0 898.9 985.6 1049.5 1113.4 1200.0 428.9 : 63.9 127.8 214.4 278.3 342.2 428.9 492.8 556.7 643.3 707.2 771.1 835.0 921.7 985.6 1049.5 1136.1 1200.0 492.8 : 63.9 150.5 214.4 278.3 365.0 428.9 492.8 579.4 643.3 707.2 771.1 857.8 921.7 985.6 1072.2 1136.1 1200.0 556.7 : 86.6 150.5 214.4 301.1 365.0 428.9 515.5 579.4 643.3 707.2 793.9 857.8 921.7 1008.3 1072.2 1136.1 1200.0 643.3 : 63.9 127.8 214.4 278.3 342.2 428.9 492.8 556.7 620.6 707.2 771.1 835.0 921.7 985.6 1049.5 1113.4 1200.0 707.2 : 63.9 150.5 214.4 278.3 365.0 428.9 492.8 556.7 643.3 707.2 771.1 857.8 921.7 985.6 1049.5 1136.1 1200.0 771.1 : 86.6 150.5 214.4 301.1 365.0 428.9 492.8 579.4 643.3 707.2 793.9 857.8 921.7 985.6 1072.2 1136.1 1200.0 857.8 : 63.9 127.8 214.4 278.3 342.2 406.1 492.8 556.7 620.6 707.2 771.1 835.0 898.9 985.6 1049.5 1113.4 1200.0 921.7 : 63.9 150.5 214.4 278.3 342.2 428.9 492.8 556.7 643.3 707.2 771.1 835.0 921.7 985.6 1049.5 1136.1 1200.0 985.6 : 86.6 150.5 214.4 278.3 365.0 428.9 492.8 579.4 643.3 707.2 771.1 857.8 921.7 985.6 1072.2 1136.1 1200.0 1072.2: 63.9 127.8 191.7 278.3 342.2 406.1 492.8 556.7 620.6 684.5 771.1 835.0 898.9 985.6 1049.5 1113.4 1200.0 1136.1: 63.9 127.8 214.4 278.3 342.2 428.9 492.8 556.7 620.6 707.2 771.1 835.0 921.7 985.6 1049.5 1136.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.8977 .. 86.6454 cents 22.74765 cents 63.89775 cents 2: 127.7955 .. 150.5431 cents 22.74765 cents 41.15010 cents 3: 191.6933 .. 214.4409 cents 22.74765 cents 41.15010 cents 4: 278.3386 .. 301.0863 cents 22.74765 cents 63.89775 cents 5: 342.2364 .. 364.9841 cents 22.74765 cents 41.15010 cents 6: 406.1342 .. 428.8818 cents 22.74765 cents 41.15010 cents 7: 492.7796 .. 515.5272 cents 22.74765 cents 63.89775 cents 8: 556.6773 .. 579.4250 cents 22.74765 cents 41.15010 cents 9: 620.5750 .. 643.3227 cents 22.74765 cents 41.15010 cents 10: 684.4728 .. 707.2205 cents 22.74765 cents 41.15010 cents 11: 771.1182 .. 793.8658 cents 22.74765 cents 63.89775 cents 12: 835.0159 .. 857.7636 cents 22.74765 cents 41.15010 cents 13: 898.9137 .. 921.6613 cents 22.74765 cents 41.15010 cents 14: 985.5591 .. 1008.3068 cents 22.74765 cents 63.89775 cents 15: 1049.4569 .. 1072.2045 cents 22.74765 cents 41.15010 cents 16: 1113.3546 .. 1136.1022 cents 22.74765 cents 41.15010 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 63.89775 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 86.64540 cents Average / Smallest step : 1.104706 Largest / Average step : 1.227477 Largest / Smallest step : 1.356001 Median interval of one step : 63.89775 cents, amount: 12 Most common interval of one step : 63.89775 cents, amount: 12 Least squares average step : 70.86860 cents, oct.: 1204.76617 cents Scale is strictly proper Scale has Myhill's property chromas: 22.74765 cents and 41.15010 cents, ratio: 1.808982 generators: 7 of 492.77955 cents and 10 of 707.22045 cents ET pair of linear temperament : 17&39 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1108-tone equal temperament with octave 1200.000 cents degrees: 59 139 198 257 337 396 455 514 594 653 712 792 851 910 990 1049 1108 generators: 455 and 653 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAAABAABAABAA Step pattern size order : SLSSLSSSLSSLSSLSS Scale is a Constant Structure, by a margin of 41.15010 cents Ratio Whole / Half tone : 3.356001 Scale diversity : 1.176294 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.696698 Rothenberg efficiency : 0.705882 redundancy: 0.294118 Efficiency x scale size : 12.000000 Number of different interval sizes : 32 = 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 : 22.74765 cents Most common intervals : 492.77955 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 492.780 985.559 cents Most common triad is 0.0 492.780 707.220 cents, amount: 15 Number of recognisable fifths : 16, average 707.2205 cents Scale contains two identical disjunct "tetrachords" of 8 notes Best fifths form a closed circle Formal octave complements present : 13 = 76.4706% Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 Inversional symmetry on intervals : 11-12 -- Rational properties --
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.0805 c. M: 13.3810 c. 39: 2 3 2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 SP M ME S SD: 2.4968 c. M:-4.7186 c. 56: 3 4 3 3 4 3 3 3 4 3 3 4 3 3 4 3 3 SP M ME S SD: 0.4106 c. M: 0.7759 c. 151: 8 11 8 8 11 8 8 8 11 8 8 11 8 8 11 8 8 SP M DE S SD: 0.3403 c. M:-0.6432 c. 207: 11 15 11 11 15 11 11 11 15 11 11 15 11 11 15 11 11 SP M DE S SD: 0.1372 c. M:-0.2593 c. 263: 14 19 14 14 19 14 14 14 19 14 14 19 14 14 19 14 14 SP M DE S SD: 0.0206 c. M:-0.0388 c. 845: 45 61 45 45 61 45 45 45 61 45 45 61 45 45 61 45 45 SP M DE S SD: 0.0080 c. M: 0.0152 c. 1108: 59 80 59 59 80 59 59 59 80 59 59 80 59 59 80 59 59 SP M DE S SD: 0.0012 c. M: 0.0023 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 2.6327 cents 3 .. 6 match: 3 H SD: 9.0371 cents 4 .. 8 match: 4 H SD: 6.9042 cents 5 .. 10 match: 5 H SD: 13.9962 cents 6 .. 12 match: 6 H SD: 6.2716 cents 7 .. 14 match: 7 H SD: 5.0448 cents 8 .. 16 match: 8 H SD: 4.7721 cents 9 .. 18 match: 9 H SD: 6.1716 cents 10 .. 20 match: 10 H SD: 8.0032 cents 11 .. 22 match: 11 H SD: 5.1914 cents 12 .. 24 match: 12 H SD: 5.6600 cents 13 .. 26 match: 13 H SD: 4.9557 cents 14 .. 28 match: 14 H SD: 4.6261 cents 15 .. 30 match: 14 SD: 6.4316 cents 16 .. 32 match: 15 S SD: 4.4983 cents 17 .. 34 match: 15 SD: 5.1477 cents 18 .. 36 match: 16 SD: 4.2343 cents 19 .. 38 match: 16 SD: 5.3291 cents 20 .. 40 match: 16 SD: 4.3659 cents 21 .. 42 match: 17 SD: 3.5627 cents 22 .. 44 match: 17 SD: 2.8637 cents 29 .. 58 match: 17 SD: 2.5486 cents 30 .. 60 match: 17 SD: 2.4228 cents 34 .. 68 match: 17 SD: 2.2308 cents 42 .. 84 match: 17 SD: 1.9994 cents 43 .. 86 match: 17 SD: 1.9539 cents 44 .. 88 match: 17 SD: 1.9398 cents 45 .. 90 match: 17 SD: 1.7863 cents 46 .. 92 match: 17 SD: 1.6702 cents 47 .. 94 match: 17 SD: 1.5768 cents 51 .. 102 match: 17 SD: 1.4425 cents 53 .. 106 match: 17 SD: 1.3909 cents 55 .. 110 match: 17 SD: 1.2782 cents 64 .. 128 match: 17 SD: 1.1228 cents 69 .. 138 match: 17 SD: 1.1130 cents 75 .. 150 match: 17 SD: 1.0197 cents 76 .. 152 match: 17 SD: 0.9526 cents 82 .. 164 match: 17 SD: 0.9025 cents 85 .. 170 match: 17 SD: 0.7589 cents 97 .. 194 match: 17 SD: 0.7520 cents 98 .. 196 match: 17 SD: 0.6654 cents 107 .. 214 match: 17 SD: 0.6084 cents 128 .. 256 match: 17 SD: 0.5992 cents 131 .. 262 match: 17 SD: 0.5467 cents 142 .. 284 match: 17 SD: 0.4977 cents 153 .. 306 match: 17 SD: 0.4281 cents 166 .. 332 match: 17 SD: 0.4174 cents 167 .. 334 match: 17 SD: 0.3612 cents 189 .. 378 match: 17 SD: 0.3097 cents 218 .. 436 match: 17 SD: 0.2866 cents 242 .. 484 match: 17 SD: 0.2527 cents 264 .. 528 match: 17 SD: 0.2261 cents 316 .. 632 match: 17 SD: 0.2236 cents 317 .. 634 match: 17 SD: 0.2184 cents 319 .. 638 match: 17 SD: 0.2120 cents 340 .. 680 match: 17 SD: 0.2076 cents 349 .. 698 match: 17 SD: 0.1706 cents 371 .. 742 match: 17 SD: 0.1700 cents 374 .. 748 match: 17 SD: 0.1548 cents 477 .. 954 match: 17 SD: 0.1336 cents 498 .. 996 match: 17 SD: 0.1318 cents 529 .. 1058 match: 17 SD: 0.1200 cents 538 .. 1076 match: 17 SD: 0.1185 cents 562 .. 1124 match: 17 SD: 0.0931 cents 583 .. 1166 match: 17 SD: 0.0883 cents