Scala analysis: xen18-darreg-djami-17
Seventeen-tone system
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 90.000 cents 90.000000 2: 180.000 cents 180.000000 3: 204.000 cents 204.000000 4: 294.000 cents 294.000000 5: 384.000 cents 384.000000 6: 408.000 cents 408.000000 7: 498.000 cents 498.000000 8: 588.000 cents 588.000000 9: 678.000 cents 678.000000 10: 702.000 cents 702.000000 11: 792.000 cents 792.000000 12: 882.000 cents 882.000000 13: 906.000 cents 906.000000 14: 996.000 cents 996.000000 15: 1086.000 cents 1086.000000 16: 1176.000 cents 1176.000000 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 24.0000 cents 24.0000 1: 90.0000 cents 90.0000 2: 90.0000 cents 90.0000 3: 24.0000 cents 24.0000 4: 90.0000 cents 90.0000 5: 90.0000 cents 90.0000 6: 24.0000 cents 24.0000 7: 90.0000 cents 90.0000 8: 90.0000 cents 90.0000 9: 90.0000 cents 90.0000 10: 24.0000 cents 24.0000 11: 90.0000 cents 90.0000 12: 90.0000 cents 90.0000 13: 24.0000 cents 24.0000 14: 90.0000 cents 90.0000 15: 90.0000 cents 90.0000 16: 90.0000 cents 90.0000 17: 24.0000 cents 24.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 24.00000 cents 1: 12 90.00000 cents 2: 10 114.00000 cents 2: 7 180.00000 cents 3: 15 204.00000 cents 3: 2 270.00000 cents 4: 3 228.00000 cents 4: 14 294.00000 cents 5: 8 318.00000 cents 5: 9 384.00000 cents 6: 13 408.00000 cents 6: 4 474.00000 cents 7: 1 432.00000 cents 7: 16 498.00000 cents 8: 6 522.00000 cents 8: 11 588.00000 cents 9: 11 612.00000 cents 9: 6 678.00000 cents 10: 16 702.00000 cents 10: 1 768.00000 cents 11: 4 726.00000 cents 11: 13 792.00000 cents 12: 9 816.00000 cents 12: 8 882.00000 cents 13: 14 906.00000 cents 13: 3 972.00000 cents 14: 2 930.00000 cents 14: 15 996.00000 cents 15: 7 1020.00000 cents 15: 10 1086.00000 cents 16: 12 1110.00000 cents 16: 5 1176.00000 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 : 90.0 180.0 204.0 294.0 384.0 408.0 498.0 588.0 678.0 702.0 792.0 882.0 906.0 996.0 1086.0 1176.0 1200.0 90.0 : 90.0 114.0 204.0 294.0 318.0 408.0 498.0 588.0 612.0 702.0 792.0 816.0 906.0 996.0 1086.0 1110.0 1200.0 180.0 : 24.0 114.0 204.0 228.0 318.0 408.0 498.0 522.0 612.0 702.0 726.0 816.0 906.0 996.0 1020.0 1110.0 1200.0 204.0 : 90.0 180.0 204.0 294.0 384.0 474.0 498.0 588.0 678.0 702.0 792.0 882.0 972.0 996.0 1086.0 1176.0 1200.0 294.0 : 90.0 114.0 204.0 294.0 384.0 408.0 498.0 588.0 612.0 702.0 792.0 882.0 906.0 996.0 1086.0 1110.0 1200.0 384.0 : 24.0 114.0 204.0 294.0 318.0 408.0 498.0 522.0 612.0 702.0 792.0 816.0 906.0 996.0 1020.0 1110.0 1200.0 408.0 : 90.0 180.0 270.0 294.0 384.0 474.0 498.0 588.0 678.0 768.0 792.0 882.0 972.0 996.0 1086.0 1176.0 1200.0 498.0 : 90.0 180.0 204.0 294.0 384.0 408.0 498.0 588.0 678.0 702.0 792.0 882.0 906.0 996.0 1086.0 1110.0 1200.0 588.0 : 90.0 114.0 204.0 294.0 318.0 408.0 498.0 588.0 612.0 702.0 792.0 816.0 906.0 996.0 1020.0 1110.0 1200.0 678.0 : 24.0 114.0 204.0 228.0 318.0 408.0 498.0 522.0 612.0 702.0 726.0 816.0 906.0 930.0 1020.0 1110.0 1200.0 702.0 : 90.0 180.0 204.0 294.0 384.0 474.0 498.0 588.0 678.0 702.0 792.0 882.0 906.0 996.0 1086.0 1176.0 1200.0 792.0 : 90.0 114.0 204.0 294.0 384.0 408.0 498.0 588.0 612.0 702.0 792.0 816.0 906.0 996.0 1086.0 1110.0 1200.0 882.0 : 24.0 114.0 204.0 294.0 318.0 408.0 498.0 522.0 612.0 702.0 726.0 816.0 906.0 996.0 1020.0 1110.0 1200.0 906.0 : 90.0 180.0 270.0 294.0 384.0 474.0 498.0 588.0 678.0 702.0 792.0 882.0 972.0 996.0 1086.0 1176.0 1200.0 996.0 : 90.0 180.0 204.0 294.0 384.0 408.0 498.0 588.0 612.0 702.0 792.0 882.0 906.0 996.0 1086.0 1110.0 1200.0 1086.0: 90.0 114.0 204.0 294.0 318.0 408.0 498.0 522.0 612.0 702.0 792.0 816.0 906.0 996.0 1020.0 1110.0 1200.0 1176.0: 24.0 114.0 204.0 228.0 318.0 408.0 432.0 522.0 612.0 702.0 726.0 816.0 906.0 930.0 1020.0 1110.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.0000 .. 90.0000 cents 66.00000 cents 24.00000 cents 2: 114.0000 .. 180.0000 cents 66.00000 cents 24.00000 cents 3: 204.0000 .. 270.0000 cents 66.00000 cents 24.00000 cents 4: 228.0000 .. 294.0000 cents 66.00000 cents -42.00000 cents 5: 318.0000 .. 384.0000 cents 66.00000 cents 24.00000 cents 6: 408.0000 .. 474.0000 cents 66.00000 cents 24.00000 cents 7: 432.0000 .. 498.0000 cents 66.00000 cents -42.00000 cents 8: 522.0000 .. 588.0000 cents 66.00000 cents 24.00000 cents 9: 612.0000 .. 678.0000 cents 66.00000 cents 24.00000 cents 10: 702.0000 .. 768.0000 cents 66.00000 cents 24.00000 cents 11: 726.0000 .. 792.0000 cents 66.00000 cents -42.00000 cents 12: 816.0000 .. 882.0000 cents 66.00000 cents 24.00000 cents 13: 906.0000 .. 972.0000 cents 66.00000 cents 24.00000 cents 14: 930.0000 .. 996.0000 cents 66.00000 cents -42.00000 cents 15: 1020.0000 .. 1086.0000 cents 66.00000 cents 24.00000 cents 16: 1110.0000 .. 1176.0000 cents 66.00000 cents 24.00000 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 24.00000 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 90.00000 cents Average / Smallest step : 2.941176 Largest / Average step : 1.275000 Largest / Smallest step : 3.750000 Median interval of one step : 90.00000 cents, amount: 12 Most common interval of one step : 90.00000 cents, amount: 12 Least squares average step : 71.95630 cents, oct.: 1223.25714 cents Scale is not proper Scale has Myhill's property chromas: 66.00000 cents and 42.00000 cents, ratio: 1.571429 generators: 7 of 498.00000 cents and 10 of 702.00000 cents ET pair of linear temperament : 12&41 Scale is distributional even Scale is a mode of a 200-tone equal temperament with octave 1200.000 cents degrees: 15 30 34 49 64 68 83 98 113 117 132 147 151 166 181 196 200 generators: 83 and 117 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 200-tone equal temperament Step pattern alph. order: AABAABAAABAABAAAB Step pattern size order : LLSLLSLLLSLLSLLLS Interval vector is [ 0 0 0 5 0 0 0 0 0 0 0 0 0 0 12 0 0 0 10 0 0 0 0 0 0 0 0 0 0 7 0 0 0 15 0 0 0 3 0 0 0 0 0 0 2 0 0 0 14 0 0 0 8 0 0 0 0 0 0 0 0 0 0 9 0 0 0 13 0 0 0 1 0 0 0 0 0 0 4 0 0 0 16 0 0 0 6 0 0 0 0 0 0 0 0 0 0 11 0 0 ] Scale is a Constant Structure, by a margin of 24.00000 cents Ratio Whole / Half tone : 2.266667 ( 34/15 ) Scale diversity : 1.158901 Lumma stability : 0.260000 Lumma impropriety factor : 0.140000 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 : 24.00000 cents Most common intervals : 498.00000 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 498.000 996.000 cents Most common triad is 0.0 498.000 702.000 cents, amount: 15 Number of recognisable fifths : 16, average 702.0000 cents Scale contains two identical conjunct "tetrachords" of 8 notes Formal octave complements present : 9 = 52.9412% Limited inverse transpositions : 5 Inversional symmetry on degrees : 11 Inversional symmetry on intervals : 2-3 -- 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: 24.5542 c. M: 46.5882 c. 19: 1 2 0 2 1 0 2 1 2 0 2 1 0 2 1 2 0 N T3 SD: 17.8177 c. M: 29.0526 c. 20: 2 1 0 2 1 1 1 2 1 1 1 2 0 2 1 2 0 N T3 SD: 17.2183 c. M:-30.0000 c. 21: 2 1 1 1 2 0 2 1 2 0 2 1 1 1 2 2 0 N T3 SD: 16.1803 c. M: 24.8571 c. 23: 2 1 1 2 1 1 2 1 2 0 2 2 0 2 2 2 0 N SD: 15.4825 c. M:-24.0000 c. 24: 2 2 0 2 2 0 2 2 2 0 2 2 0 2 2 2 0 N M DE S SD: 12.6491 c. M:-24.0000 c. 28: 2 2 1 2 2 1 2 2 2 0 2 3 0 2 2 2 1 N SD: 12.9492 c. M:-20.5714 c. 29: 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 1 P M ME S SD: 9.1597 c. M: 17.3793 c. 34: 3 2 1 2 3 1 2 3 2 1 2 3 1 2 3 2 1 P T3 SD: 9.6391 c. M:-15.8824 c. 38: 3 3 0 3 3 1 3 3 2 1 3 3 1 3 2 3 1 N SD: 9.2290 c. M: 14.8421 c. 41: 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 N M DE S SD: 2.7766 c. M: 5.2683 c. 53: 4 4 1 4 4 1 4 4 4 1 4 4 1 4 4 4 1 N M DE S SD: 0.7160 c. M:-1.3585 c. 147: 11 11 3 11 11 3 11 11 11 3 11 11 3 11 11 11 3 N M DE S SD: 0.2581 c. M: 0.4898 c. 200: 15 15 4 15 15 4 15 15 15 4 15 15 4 15 15 15 4 N M DE S SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.0225 cents 3 .. 6 match: 3 H SD: 0.7864 cents 4 .. 8 match: 4 H SD: 6.8181 cents 5 .. 10 match: 5 H SD: 7.5767 cents 6 .. 12 match: 6 H SD: 7.6082 cents 7 .. 14 match: 7 H SD: 8.2960 cents 8 .. 16 match: 8 H SD: 7.7202 cents 9 .. 18 match: 9 H SD: 7.0472 cents 10 .. 20 match: 10 H SD: 6.6122 cents 11 .. 22 match: 11 H SD: 9.0658 cents 12 .. 24 match: 11 S SD: 6.2862 cents 13 .. 26 match: 12 S SD: 8.4294 cents 14 .. 28 match: 13 S SD: 6.6729 cents 15 .. 30 match: 13 SD: 4.7250 cents 16 .. 32 match: 12 SD: 4.8924 cents 17 .. 34 match: 15 S SD: 4.7732 cents 18 .. 36 match: 13 SD: 4.6783 cents 19 .. 38 match: 14 SD: 4.7109 cents 20 .. 40 match: 15 SD: 4.6287 cents 21 .. 42 match: 16 SD: 4.3271 cents 22 .. 44 match: 15 SD: 3.8016 cents 23 .. 46 match: 15 SD: 3.4068 cents 24 .. 48 match: 14 SD: 3.3103 cents 25 .. 50 match: 15 SD: 3.8771 cents 26 .. 52 match: 16 SD: 3.4817 cents 27 .. 54 match: 15 SD: 3.0129 cents 28 .. 56 match: 15 SD: 3.6272 cents 29 .. 58 match: 17 SD: 3.2293 cents 30 .. 60 match: 17 SD: 2.9845 cents 31 .. 62 match: 15 SD: 3.0374 cents 32 .. 64 match: 16 SD: 2.2973 cents 33 .. 66 match: 16 SD: 2.0954 cents 34 .. 68 match: 15 SD: 2.5905 cents 35 .. 70 match: 15 SD: 2.5625 cents 36 .. 72 match: 17 SD: 2.2006 cents 37 .. 74 match: 16 SD: 2.1894 cents 38 .. 76 match: 17 SD: 1.8060 cents 39 .. 78 match: 16 SD: 1.8836 cents 42 .. 84 match: 16 SD: 1.6753 cents 43 .. 86 match: 15 SD: 2.4003 cents 44 .. 88 match: 17 SD: 1.9330 cents 45 .. 90 match: 17 SD: 1.7734 cents 47 .. 94 match: 16 SD: 2.0834 cents 48 .. 96 match: 17 SD: 1.4128 cents 51 .. 102 match: 16 SD: 2.1361 cents 52 .. 104 match: 17 SD: 1.7030 cents 53 .. 106 match: 17 SD: 1.6706 cents 54 .. 108 match: 17 SD: 1.1764 cents 64 .. 128 match: 17 SD: 1.0341 cents 71 .. 142 match: 17 SD: 0.9819 cents 72 .. 144 match: 17 SD: 0.8579 cents 90 .. 180 match: 17 SD: 0.8141 cents 96 .. 192 match: 17 SD: 0.7939 cents 98 .. 196 match: 17 SD: 0.7684 cents 102 .. 204 match: 17 SD: 0.6732 cents 109 .. 218 match: 17 SD: 0.6435 cents 112 .. 224 match: 17 SD: 0.5804 cents 128 .. 256 match: 17 SD: 0.5351 cents 129 .. 258 match: 17 SD: 0.5300 cents 136 .. 272 match: 17 SD: 0.4805 cents 146 .. 292 match: 17 SD: 0.4563 cents 150 .. 300 match: 17 SD: 0.4541 cents 166 .. 332 match: 17 SD: 0.4195 cents 173 .. 346 match: 17 SD: 0.4018 cents 184 .. 368 match: 17 SD: 0.3836 cents 190 .. 380 match: 17 SD: 0.3735 cents 202 .. 404 match: 17 SD: 0.3638 cents 210 .. 420 match: 17 SD: 0.3085 cents 226 .. 452 match: 17 SD: 0.3004 cents 238 .. 476 match: 17 SD: 0.2738 cents 265 .. 530 match: 17 SD: 0.2562 cents 282 .. 564 match: 17 SD: 0.1905 cents 319 .. 638 match: 17 SD: 0.1847 cents 336 .. 672 match: 17 SD: 0.1723 cents 390 .. 780 match: 17 SD: 0.1638 cents 400 .. 800 match: 17 SD: 0.1600 cents 410 .. 820 match: 17 SD: 0.1581 cents 426 .. 852 match: 17 SD: 0.1562 cents 432 .. 864 match: 17 SD: 0.1254 cents 448 .. 896 match: 17 SD: 0.1240 cents 486 .. 972 match: 17 SD: 0.1203 cents 512 .. 1024 match: 17 SD: 0.1199 cents 519 .. 1038 match: 17 SD: 0.1139 cents 576 .. 1152 match: 17 SD: 0.0954 cents 584 .. 1168 match: 17 SD: 0.0949 cents