Scala analysis: schisynch17
Schismatic[17] in synch (brat=-1) tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 91.361 cents 91.360882 2: 182.722 cents 182.721764 3: 203.456 cents 203.455647 4: 294.817 cents 294.816529 5: 386.177 cents 386.177411 6: 406.911 cents 406.911294 7: 498.272 cents 498.272176 8: 589.633 cents 589.633058 9: 680.994 cents 680.993940 10: 701.728 cents 701.727824 11: 793.089 cents 793.088706 12: 884.450 cents 884.449587 13: 905.183 cents 905.183471 14: 996.544 cents 996.544353 15: 1087.905 cents 1087.905235 16: 1108.639 cents 1108.639118 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 91.3609 cents 91.3609 1: 91.3609 cents 91.3609 2: 91.3609 cents 91.3609 3: 20.7339 cents 20.7339 4: 91.3609 cents 91.3609 5: 91.3609 cents 91.3609 6: 20.7339 cents 20.7339 7: 91.3609 cents 91.3609 8: 91.3609 cents 91.3609 9: 91.3609 cents 91.3609 10: 20.7339 cents 20.7339 11: 91.3609 cents 91.3609 12: 91.3609 cents 91.3609 13: 20.7339 cents 20.7339 14: 91.3609 cents 91.3609 15: 91.3609 cents 91.3609 16: 20.7339 cents 20.7339 17: 91.3609 cents 91.3609
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 20.73388 cents 1: 12 91.36088 cents 2: 10 112.09476 cents 2: 7 182.72176 cents 3: 15 203.45565 cents 3: 2 274.08265 cents 4: 3 224.18953 cents 4: 14 294.81653 cents 5: 8 315.55041 cents 5: 9 386.17741 cents 6: 13 406.91129 cents 6: 4 477.53829 cents 7: 1 427.64518 cents 7: 16 498.27218 cents 8: 6 519.00606 cents 8: 11 589.63306 cents 9: 11 610.36694 cents 9: 6 680.99394 cents 10: 16 701.72782 cents 10: 1 772.35482 cents 11: 4 722.46171 cents 11: 13 793.08871 cents 12: 9 813.82259 cents 12: 8 884.44959 cents 13: 14 905.18347 cents 13: 3 975.81047 cents 14: 2 925.91735 cents 14: 15 996.54435 cents 15: 7 1017.27824 cents 15: 10 1087.90523 cents 16: 12 1108.63912 cents 16: 5 1179.26612 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 : 91.4 182.7 203.5 294.8 386.2 406.9 498.3 589.6 681.0 701.7 793.1 884.4 905.2 996.5 1087.9 1108.6 1200.0 91.4 : 91.4 112.1 203.5 294.8 315.6 406.9 498.3 589.6 610.4 701.7 793.1 813.8 905.2 996.5 1017.3 1108.6 1200.0 182.7 : 20.7 112.1 203.5 224.2 315.6 406.9 498.3 519.0 610.4 701.7 722.5 813.8 905.2 925.9 1017.3 1108.6 1200.0 203.5 : 91.4 182.7 203.5 294.8 386.2 477.5 498.3 589.6 681.0 701.7 793.1 884.4 905.2 996.5 1087.9 1179.3 1200.0 294.8 : 91.4 112.1 203.5 294.8 386.2 406.9 498.3 589.6 610.4 701.7 793.1 813.8 905.2 996.5 1087.9 1108.6 1200.0 386.2 : 20.7 112.1 203.5 294.8 315.6 406.9 498.3 519.0 610.4 701.7 722.5 813.8 905.2 996.5 1017.3 1108.6 1200.0 406.9 : 91.4 182.7 274.1 294.8 386.2 477.5 498.3 589.6 681.0 701.7 793.1 884.4 975.8 996.5 1087.9 1179.3 1200.0 498.3 : 91.4 182.7 203.5 294.8 386.2 406.9 498.3 589.6 610.4 701.7 793.1 884.4 905.2 996.5 1087.9 1108.6 1200.0 589.6 : 91.4 112.1 203.5 294.8 315.6 406.9 498.3 519.0 610.4 701.7 793.1 813.8 905.2 996.5 1017.3 1108.6 1200.0 681.0 : 20.7 112.1 203.5 224.2 315.6 406.9 427.6 519.0 610.4 701.7 722.5 813.8 905.2 925.9 1017.3 1108.6 1200.0 701.7 : 91.4 182.7 203.5 294.8 386.2 406.9 498.3 589.6 681.0 701.7 793.1 884.4 905.2 996.5 1087.9 1179.3 1200.0 793.1 : 91.4 112.1 203.5 294.8 315.6 406.9 498.3 589.6 610.4 701.7 793.1 813.8 905.2 996.5 1087.9 1108.6 1200.0 884.4 : 20.7 112.1 203.5 224.2 315.6 406.9 498.3 519.0 610.4 701.7 722.5 813.8 905.2 996.5 1017.3 1108.6 1200.0 905.2 : 91.4 182.7 203.5 294.8 386.2 477.5 498.3 589.6 681.0 701.7 793.1 884.4 975.8 996.5 1087.9 1179.3 1200.0 996.5 : 91.4 112.1 203.5 294.8 386.2 406.9 498.3 589.6 610.4 701.7 793.1 884.4 905.2 996.5 1087.9 1108.6 1200.0 1087.9: 20.7 112.1 203.5 294.8 315.6 406.9 498.3 519.0 610.4 701.7 793.1 813.8 905.2 996.5 1017.3 1108.6 1200.0 1108.6: 91.4 182.7 274.1 294.8 386.2 477.5 498.3 589.6 681.0 772.4 793.1 884.4 975.8 996.5 1087.9 1179.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.7339 .. 91.3609 cents 70.62700 cents 20.73388 cents 2: 112.0948 .. 182.7218 cents 70.62700 cents 20.73388 cents 3: 203.4556 .. 274.0826 cents 70.62700 cents 20.73388 cents 4: 224.1895 .. 294.8165 cents 70.62700 cents -49.89312 cents 5: 315.5504 .. 386.1774 cents 70.62700 cents 20.73388 cents 6: 406.9113 .. 477.5383 cents 70.62700 cents 20.73388 cents 7: 427.6452 .. 498.2722 cents 70.62700 cents -49.89311 cents 8: 519.0061 .. 589.6331 cents 70.62700 cents 20.73388 cents 9: 610.3669 .. 680.9939 cents 70.62700 cents 20.73388 cents 10: 701.7278 .. 772.3548 cents 70.62700 cents 20.73388 cents 11: 722.4617 .. 793.0887 cents 70.62700 cents -49.89311 cents 12: 813.8226 .. 884.4496 cents 70.62700 cents 20.73388 cents 13: 905.1835 .. 975.8105 cents 70.62700 cents 20.73388 cents 14: 925.9174 .. 996.5444 cents 70.62700 cents -49.89312 cents 15: 1017.2782 .. 1087.9052 cents 70.62700 cents 20.73388 cents 16: 1108.6391 .. 1179.2661 cents 70.62700 cents 20.73388 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 20.73388 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 91.36088 cents Average / Smallest step : 3.404487 Largest / Average step : 1.294279 Largest / Smallest step : 4.406357 Median interval of one step : 91.36088 cents, amount: 12 Most common interval of one step : 91.36088 cents, amount: 12 Least squares average step : 71.41914 cents, oct.: 1214.12540 cents Scale is not proper Scale has Myhill's property chromas: 70.62700 cents and 49.89312 cents, ratio: 1.415566 generators: 7 of 498.27218 cents and 10 of 701.72782 cents ET pair of linear temperament : 12&53 Scale is distributional even Scale is a mode of a 1563-tone equal temperament with octave 1200.000 cents degrees: 119 238 265 384 503 530 649 768 887 914 1033 1152 1179 1298 1417 1444 1563 generators: 649 and 914 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAABAAABAABAABA Step pattern size order : LLSLLSLLLSLLSLLSL Scale is a Constant Structure, by a margin of 20.73388 cents Ratio Whole / Half tone : 2.226945 Scale diversity : 1.128302 Lumma stability : 0.224617 Lumma impropriety factor : 0.166310 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 : 20.73388 cents Most common intervals : 498.27218 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 498.272 996.544 cents Most common triad is 0.0 498.272 701.728 cents, amount: 15 Number of recognisable fifths : 16, average 701.7278 cents Scale contains two identical disjunct "tetrachords" of 8 notes Formal octave complements present : 11 = 64.7059% Limited inverse transpositions : 8 Inversional symmetry on degrees : 4 Inversional symmetry on intervals : 12-13 -- Rational properties --
FIT/MODE
17: 1 2 0 1 1 1 1 1 2 0 1 2 0 1 1 1 1 N T3 SD: 20.3432 c. M: 33.2362 c. 19: 1 2 0 1 2 0 2 1 2 0 1 2 0 2 1 0 2 N T3 SD: 21.2617 c. M: 42.1850 c. 20: 1 2 0 2 1 1 1 2 1 1 1 2 0 2 1 0 2 N T3 SD: 18.0087 c. M: 31.3609 c. 21: 1 2 0 2 2 0 2 1 2 0 2 1 1 1 2 0 2 N T3 S SD: 18.0682 c. M: 34.2180 c. 22: 2 1 1 1 2 0 2 2 1 1 1 2 0 2 2 0 2 N SD: 18.0620 c. M: 32.4562 c. 23: 2 1 1 1 2 1 1 2 2 0 2 2 0 2 2 0 2 N T3 SD: 17.0086 c. M: 33.9470 c. 24: 2 2 0 2 2 0 2 2 2 0 2 2 0 2 2 0 2 N M DE S SD: 9.9256 c. M:-19.0061 c. 29: 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 2 P M ME S SD: 9.8832 c. M: 18.9250 c. 30: 2 3 0 2 3 0 2 3 2 1 2 2 1 2 2 1 2 N SD: 11.2843 c. M: 18.2722 c. 32: 2 3 0 3 2 1 2 3 2 1 2 3 0 3 2 1 2 N SD: 10.6438 c. M: 16.3609 c. 34: 3 2 1 2 3 1 2 3 2 1 2 3 1 2 3 0 3 N SD: 10.1732 c. M:-16.6181 c. 35: 3 2 1 3 2 1 3 2 3 0 3 3 0 3 3 0 3 N SD: 9.7558 c. M: 16.0135 c. 37: 3 3 0 3 3 1 2 3 3 1 2 3 1 3 3 0 3 N SD: 9.1889 c. M:-14.7975 c. 38: 3 3 0 3 3 1 3 3 3 0 3 3 1 3 2 1 3 N SD: 8.9414 c. M: 14.2210 c. 39: 3 3 1 3 3 0 3 3 3 1 3 3 0 3 3 1 3 N SD: 8.4136 c. M:-13.8226 c. 41: 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 1 3 N M DE S SD: 4.0855 c. M: 7.8232 c. 53: 4 4 1 4 4 1 4 4 4 1 4 4 1 4 4 1 4 N M DE S SD: 0.9132 c. M: 1.7487 c. 118: 9 9 2 9 9 2 9 9 9 2 9 9 2 9 9 2 9 N M DE S SD: 0.1890 c. M:-0.3620 c. 171: 13 13 3 13 13 3 13 13 13 3 13 13 3 13 13 3 13 N M DE S SD: 0.1526 c. M: 0.2922 c. 289: 22 22 5 22 22 5 22 22 22 5 22 22 5 22 22 5 22 N M DE S SD: 0.0131 c. M: 0.0251 c. 985: 75 75 17 75 75 17 75 75 75 17 75 75 17 75 75 17 75 N M DE S SD: 0.0111 c. M:-0.0213 c. 1274: 97 97 22 97 97 22 97 97 97 22 97 97 22 97 97 22 97 N M DE S SD: 0.0056 c. M:-0.0108 c. 1563: 119 119 27 119 119 27 119 119 119 27 119 119 27 119 119 27 119 N M DE S SD: 0.0022 c. M:-0.0041 c. 1852: 141 141 32 141 141 32 141 141 141 32 141 141 32 141 141 32 141 N M DE S SD: 0.0002 c. M: 0.0004 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.1136 cents 3 .. 6 match: 3 H SD: 0.0816 cents 4 .. 8 match: 4 H SD: 6.9299 cents 5 .. 10 match: 5 H SD: 7.3534 cents 6 .. 12 match: 6 H SD: 7.9348 cents 7 .. 14 match: 7 H SD: 8.4439 cents 8 .. 16 match: 8 H SD: 8.0680 cents 9 .. 18 match: 9 H SD: 7.3064 cents 10 .. 20 match: 10 H SD: 6.1600 cents 11 .. 22 match: 11 H SD: 8.8897 cents 12 .. 24 match: 11 SD: 5.7467 cents 13 .. 26 match: 13 H SD: 8.1161 cents 14 .. 28 match: 14 H SD: 6.5459 cents 15 .. 30 match: 13 SD: 4.7347 cents 16 .. 32 match: 12 SD: 5.0026 cents 17 .. 34 match: 15 S SD: 4.8986 cents 18 .. 36 match: 12 SD: 4.0653 cents 19 .. 38 match: 13 SD: 4.5059 cents 20 .. 40 match: 14 SD: 4.0298 cents 21 .. 42 match: 15 SD: 4.2865 cents 22 .. 44 match: 14 SD: 3.5770 cents 23 .. 46 match: 14 SD: 3.3986 cents 24 .. 48 match: 13 SD: 3.3320 cents 25 .. 50 match: 13 SD: 4.0912 cents 26 .. 52 match: 13 SD: 3.4027 cents 27 .. 54 match: 13 SD: 2.8629 cents 28 .. 56 match: 14 SD: 3.4908 cents 29 .. 58 match: 16 SD: 3.2602 cents 30 .. 60 match: 16 SD: 3.0212 cents 31 .. 62 match: 14 SD: 2.9511 cents 32 .. 64 match: 15 SD: 2.1039 cents 33 .. 66 match: 15 SD: 2.0846 cents 34 .. 68 match: 15 SD: 2.7606 cents 35 .. 70 match: 13 SD: 2.6171 cents 36 .. 72 match: 16 SD: 2.0380 cents 37 .. 74 match: 15 SD: 2.1633 cents 38 .. 76 match: 17 SD: 2.0431 cents 39 .. 78 match: 15 SD: 1.7312 cents 40 .. 80 match: 16 SD: 2.1350 cents 41 .. 82 match: 15 SD: 1.8824 cents 42 .. 84 match: 16 SD: 1.8093 cents 43 .. 86 match: 14 SD: 2.3284 cents 44 .. 88 match: 16 SD: 1.9148 cents 45 .. 90 match: 16 SD: 1.8489 cents 47 .. 94 match: 15 SD: 1.9466 cents 48 .. 96 match: 17 SD: 1.4450 cents 49 .. 98 match: 16 SD: 1.7837 cents 50 .. 100 match: 16 SD: 1.6637 cents 51 .. 102 match: 15 SD: 1.9614 cents 52 .. 104 match: 16 SD: 1.4845 cents 53 .. 106 match: 16 SD: 1.7109 cents 54 .. 108 match: 17 SD: 1.2138 cents 55 .. 110 match: 16 SD: 1.4524 cents 56 .. 112 match: 17 SD: 1.3421 cents 59 .. 118 match: 16 SD: 1.5549 cents 60 .. 120 match: 16 SD: 1.0664 cents 64 .. 128 match: 17 SD: 1.0258 cents 68 .. 136 match: 16 SD: 1.3651 cents 69 .. 138 match: 17 SD: 1.1791 cents 71 .. 142 match: 17 SD: 0.9850 cents 72 .. 144 match: 17 SD: 0.7770 cents 96 .. 192 match: 17 SD: 0.6224 cents 108 .. 216 match: 17 SD: 0.5990 cents 128 .. 256 match: 17 SD: 0.4751 cents 144 .. 288 match: 17 SD: 0.4055 cents 162 .. 324 match: 17 SD: 0.3822 cents 189 .. 378 match: 17 SD: 0.3797 cents 200 .. 400 match: 17 SD: 0.3344 cents 207 .. 414 match: 17 SD: 0.3311 cents 216 .. 432 match: 17 SD: 0.2791 cents 264 .. 528 match: 17 SD: 0.2515 cents 279 .. 558 match: 17 SD: 0.2392 cents 280 .. 560 match: 17 SD: 0.2187 cents 312 .. 624 match: 17 SD: 0.1999 cents 313 .. 626 match: 17 SD: 0.1964 cents 351 .. 702 match: 17 SD: 0.1639 cents 384 .. 768 match: 17 SD: 0.1522 cents 441 .. 882 match: 17 SD: 0.1362 cents 456 .. 912 match: 17 SD: 0.1234 cents 513 .. 1026 match: 17 SD: 0.1164 cents 537 .. 1074 match: 17 SD: 0.1115 cents 592 .. 1184 match: 17 SD: 0.1046 cents