Scala analysis: jsmith17
J. Smith 17-note well-temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 71.000 cents 71.000000 2: 137.000 cents 137.000000 3: 208.000 cents 208.000000 4: 288.000 cents 288.000000 5: 345.000 cents 345.000000 6: 416.000 cents 416.000000 7: 496.000 cents 496.000000 8: 567.000 cents 567.000000 9: 633.000 cents 633.000000 10: 704.000 cents 704.000000 11: 784.000 cents 784.000000 12: 841.000 cents 841.000000 13: 912.000 cents 912.000000 14: 992.000 cents 992.000000 15: 1049.000 cents 1049.000000 16: 1120.000 cents 1120.000000 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 80.0000 cents 80.0000 1: 71.0000 cents 71.0000 2: 66.0000 cents 66.0000 3: 71.0000 cents 71.0000 4: 80.0000 cents 80.0000 5: 57.0000 cents 57.0000 6: 71.0000 cents 71.0000 7: 80.0000 cents 80.0000 8: 71.0000 cents 71.0000 9: 66.0000 cents 66.0000 10: 71.0000 cents 71.0000 11: 80.0000 cents 80.0000 12: 57.0000 cents 57.0000 13: 71.0000 cents 71.0000 14: 80.0000 cents 80.0000 15: 57.0000 cents 57.0000 16: 71.0000 cents 71.0000 17: 80.0000 cents 80.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 57.00000 cents 1: 2 66.00000 cents 1: 7 71.00000 cents 1: 5 80.00000 cents 2: 3 128.00000 cents 2: 7 137.00000 cents 2: 7 151.00000 cents 3: 11 208.00000 cents 3: 4 217.00000 cents 3: 2 222.00000 cents 4: 1 265.00000 cents 4: 2 274.00000 cents 4: 5 279.00000 cents 4: 9 288.00000 cents 5: 1 336.00000 cents 5: 7 345.00000 cents 5: 7 359.00000 cents 5: 2 368.00000 cents 6: 7 416.00000 cents 6: 6 425.00000 cents 6: 2 430.00000 cents 6: 2 439.00000 cents 7: 1 482.00000 cents 7: 2 487.00000 cents 7: 14 496.00000 cents 8: 5 553.00000 cents 8: 1 562.00000 cents 8: 7 567.00000 cents 8: 4 576.00000 cents 9: 4 624.00000 cents 9: 7 633.00000 cents 9: 1 638.00000 cents 9: 5 647.00000 cents 10: 14 704.00000 cents 10: 2 713.00000 cents 10: 1 718.00000 cents 11: 2 761.00000 cents 11: 2 770.00000 cents 11: 6 775.00000 cents 11: 7 784.00000 cents 12: 2 832.00000 cents 12: 7 841.00000 cents 12: 7 855.00000 cents 12: 1 864.00000 cents 13: 9 912.00000 cents 13: 5 921.00000 cents 13: 2 926.00000 cents 13: 1 935.00000 cents 14: 2 978.00000 cents 14: 4 983.00000 cents 14: 11 992.00000 cents 15: 7 1049.00000 cents 15: 7 1063.00000 cents 15: 3 1072.00000 cents 16: 5 1120.00000 cents 16: 7 1129.00000 cents 16: 2 1134.00000 cents 16: 3 1143.00000 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.62500 = 29/8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 71.0 137.0 208.0 288.0 345.0 416.0 496.0 567.0 633.0 704.0 784.0 841.0 912.0 992.0 1049.0 1120.0 1200.0 71.0 : 66.0 137.0 217.0 274.0 345.0 425.0 496.0 562.0 633.0 713.0 770.0 841.0 921.0 978.0 1049.0 1129.0 1200.0 137.0 : 71.0 151.0 208.0 279.0 359.0 430.0 496.0 567.0 647.0 704.0 775.0 855.0 912.0 983.0 1063.0 1134.0 1200.0 208.0 : 80.0 137.0 208.0 288.0 359.0 425.0 496.0 576.0 633.0 704.0 784.0 841.0 912.0 992.0 1063.0 1129.0 1200.0 288.0 : 57.0 128.0 208.0 279.0 345.0 416.0 496.0 553.0 624.0 704.0 761.0 832.0 912.0 983.0 1049.0 1120.0 1200.0 345.0 : 71.0 151.0 222.0 288.0 359.0 439.0 496.0 567.0 647.0 704.0 775.0 855.0 926.0 992.0 1063.0 1143.0 1200.0 416.0 : 80.0 151.0 217.0 288.0 368.0 425.0 496.0 576.0 633.0 704.0 784.0 855.0 921.0 992.0 1072.0 1129.0 1200.0 496.0 : 71.0 137.0 208.0 288.0 345.0 416.0 496.0 553.0 624.0 704.0 775.0 841.0 912.0 992.0 1049.0 1120.0 1200.0 567.0 : 66.0 137.0 217.0 274.0 345.0 425.0 482.0 553.0 633.0 704.0 770.0 841.0 921.0 978.0 1049.0 1129.0 1200.0 633.0 : 71.0 151.0 208.0 279.0 359.0 416.0 487.0 567.0 638.0 704.0 775.0 855.0 912.0 983.0 1063.0 1134.0 1200.0 704.0 : 80.0 137.0 208.0 288.0 345.0 416.0 496.0 567.0 633.0 704.0 784.0 841.0 912.0 992.0 1063.0 1129.0 1200.0 784.0 : 57.0 128.0 208.0 265.0 336.0 416.0 487.0 553.0 624.0 704.0 761.0 832.0 912.0 983.0 1049.0 1120.0 1200.0 841.0 : 71.0 151.0 208.0 279.0 359.0 430.0 496.0 567.0 647.0 704.0 775.0 855.0 926.0 992.0 1063.0 1143.0 1200.0 912.0 : 80.0 137.0 208.0 288.0 359.0 425.0 496.0 576.0 633.0 704.0 784.0 855.0 921.0 992.0 1072.0 1129.0 1200.0 992.0 : 57.0 128.0 208.0 279.0 345.0 416.0 496.0 553.0 624.0 704.0 775.0 841.0 912.0 992.0 1049.0 1120.0 1200.0 1049.0: 71.0 151.0 222.0 288.0 359.0 439.0 496.0 567.0 647.0 718.0 784.0 855.0 935.0 992.0 1063.0 1143.0 1200.0 1120.0: 80.0 151.0 217.0 288.0 368.0 425.0 496.0 576.0 647.0 713.0 784.0 864.0 921.0 992.0 1072.0 1129.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.0000 .. 80.0000 cents 23.00000 cents 57.00000 cents 2: 128.0000 .. 151.0000 cents 23.00000 cents 48.00000 cents 3: 208.0000 .. 222.0000 cents 14.00000 cents 57.00000 cents 4: 265.0000 .. 288.0000 cents 23.00000 cents 43.00000 cents 5: 336.0000 .. 368.0000 cents 32.00000 cents 48.00000 cents 6: 416.0000 .. 439.0000 cents 23.00000 cents 48.00000 cents 7: 482.0000 .. 496.0000 cents 14.00000 cents 43.00000 cents 8: 553.0000 .. 576.0000 cents 23.00000 cents 57.00000 cents 9: 624.0000 .. 647.0000 cents 23.00000 cents 48.00000 cents 10: 704.0000 .. 718.0000 cents 14.00000 cents 57.00000 cents 11: 761.0000 .. 784.0000 cents 23.00000 cents 43.00000 cents 12: 832.0000 .. 864.0000 cents 32.00000 cents 48.00000 cents 13: 912.0000 .. 935.0000 cents 23.00000 cents 48.00000 cents 14: 978.0000 .. 992.0000 cents 14.00000 cents 43.00000 cents 15: 1049.0000 .. 1072.0000 cents 23.00000 cents 57.00000 cents 16: 1120.0000 .. 1143.0000 cents 23.00000 cents 48.00000 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 57.00000 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 80.00000 cents Average / Smallest step : 1.238390 Largest / Average step : 1.133333 Largest / Smallest step : 1.403509 Median interval of one step : 71.00000 cents, amount: 7 Most common interval of one step : 71.00000 cents, amount: 7 Least squares average step : 70.36527 cents, oct.: 1196.20952 cents Scale is strictly proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 71 137 208 288 345 416 496 567 633 704 784 841 912 992 1049 1120 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1169 of 1169.000 cents and inv. generated superset size: 186 = 169 more = 1094.118% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACDACABACDACDAC Step pattern size order : CBCDACDCBCDACDACD Scale is a Constant Structure, by a margin of 43.00000 cents Scale diversity : 1.213903 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.708333 Number of different interval sizes : 58 = 3.62500 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.62500 = 29/8 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 5.00000 cents Most common intervals : 496.00000 cents & inv., amount: 14 Most common triad is 0.0 496.000 704.000 cents, amount: 11 Number of recognisable fifths : 17, average 705.8824 cents Number of appreciable fifths : 16, average 705.1250 cents Scale contains two identical conjunct "tetrachords" of 8 notes Best fifths form a closed circle Formal octave complements present : 11 = 64.7059% Limited inverse transpositions with margin 23.0000 cents: 6 9 -- 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: 5.5603 c. M:-9.8235 c. 46: 3 2 3 3 2 3 3 3 2 3 3 2 3 3 2 3 3 SP M ME S SD: 4.2377 c. M:-7.2609 c. 63: 4 3 4 4 3 4 4 4 3 4 4 3 4 4 3 4 4 SP M ME S SD: 2.9093 c. M:-5.1905 c. 70: 4 4 4 5 3 4 5 4 4 4 5 3 4 5 3 4 5 SP SD: 2.8350 c. M: 5.7143 c. 80: 5 4 5 5 4 5 5 5 4 5 5 4 5 5 4 5 5 SP M ME S SD: 2.7116 c. M:-5.0000 c. 87: 5 5 5 6 4 5 6 5 5 5 6 4 5 6 4 5 6 SP SD: 1.4547 c. M: 2.7586 c. 104: 6 6 6 7 5 6 7 6 6 6 7 5 6 7 5 6 7 SP SD: 0.9863 c. M: 1.7692 c. 150: 9 8 9 10 7 9 10 9 8 9 10 7 9 10 7 9 10 SP SD: 0.6417 c. M:-1.0000 c. 167: 10 9 10 11 8 10 11 10 9 10 11 8 10 11 8 10 11 SP SD: 0.5455 c. M:-0.9581 c. 237: 14 13 14 16 11 14 16 14 13 14 16 11 14 16 11 14 16 SP SD: 0.5497 c. M: 1.0127 c. 254: 15 14 15 17 12 15 17 15 14 15 17 12 15 17 12 15 17 SP SD: 0.1563 c. M: 0.3150 c. 421: 25 23 25 28 20 25 28 25 23 25 28 20 25 28 20 25 28 SP SD: 0.1451 c. M:-0.2589 c. 525: 31 29 31 35 25 31 35 31 29 31 35 25 31 35 25 31 35 SP SD: 0.0917 c. M:-0.1429 c. 675: 40 37 40 45 32 40 45 40 37 40 45 32 40 45 32 40 45 SP SD: 0.0713 c. M: 0.1111 c. 929: 55 51 55 62 44 55 62 55 51 55 62 44 55 62 44 55 62 SP SD: 0.0685 c. M: 0.1302 c. 946: 56 52 56 63 45 56 63 56 52 56 63 45 56 63 45 56 63 SP SD: 0.0420 c. M:-0.0846 c. 1200: 71 66 71 80 57 71 80 71 66 71 80 57 71 80 57 71 80 SP 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: 1.0225 cents 3 .. 6 match: 3 H SD: 9.2389 cents 4 .. 8 match: 4 H SD: 9.4290 cents 5 .. 10 match: 5 H SD: 9.8099 cents 6 .. 12 match: 6 H SD: 5.8190 cents 7 .. 14 match: 7 H SD: 6.5558 cents 8 .. 16 match: 8 H SD: 6.4859 cents 9 .. 18 match: 9 H SD: 5.1908 cents 10 .. 20 match: 10 H SD: 6.9110 cents 11 .. 22 match: 11 H SD: 5.5749 cents 12 .. 24 match: 12 H SD: 5.0780 cents 13 .. 26 match: 13 H SD: 5.6243 cents 14 .. 28 match: 14 H SD: 4.7032 cents 15 .. 30 match: 13 SD: 6.2432 cents 16 .. 32 match: 15 SD: 4.5373 cents 17 .. 34 match: 16 S SD: 5.5940 cents 18 .. 36 match: 16 S SD: 3.6722 cents 19 .. 38 match: 16 SD: 4.8862 cents 20 .. 40 match: 16 SD: 5.1907 cents 21 .. 42 match: 17 S SD: 3.8602 cents 22 .. 44 match: 17 SD: 3.0224 cents 23 .. 46 match: 17 SD: 2.6232 cents 32 .. 64 match: 17 SD: 2.4796 cents 36 .. 72 match: 17 SD: 2.4160 cents 37 .. 74 match: 17 SD: 2.3355 cents 38 .. 76 match: 17 SD: 2.2928 cents 39 .. 78 match: 17 SD: 2.2371 cents 40 .. 80 match: 17 SD: 1.9421 cents 45 .. 90 match: 17 SD: 1.6032 cents 48 .. 96 match: 17 SD: 1.4558 cents 49 .. 98 match: 17 SD: 1.3811 cents 54 .. 108 match: 17 SD: 1.3199 cents 66 .. 132 match: 17 SD: 1.2669 cents 70 .. 140 match: 17 SD: 0.9944 cents 72 .. 144 match: 17 SD: 0.8127 cents 88 .. 176 match: 17 SD: 0.7796 cents 96 .. 192 match: 17 SD: 0.6834 cents 100 .. 200 match: 17 SD: 0.6759 cents 117 .. 234 match: 17 SD: 0.6685 cents 118 .. 236 match: 17 SD: 0.5575 cents 133 .. 266 match: 17 SD: 0.5489 cents 136 .. 272 match: 17 SD: 0.5356 cents 144 .. 288 match: 17 SD: 0.5034 cents 145 .. 290 match: 17 SD: 0.5034 cents 147 .. 294 match: 17 SD: 0.4857 cents 150 .. 300 match: 17 SD: 0.4417 cents 166 .. 332 match: 17 SD: 0.4179 cents 173 .. 346 match: 17 SD: 0.3892 cents 181 .. 362 match: 17 SD: 0.3823 cents 195 .. 390 match: 17 SD: 0.3396 cents 209 .. 418 match: 17 SD: 0.3243 cents 217 .. 434 match: 17 SD: 0.3002 cents 235 .. 470 match: 17 SD: 0.2985 cents 243 .. 486 match: 17 SD: 0.2720 cents 265 .. 530 match: 17 SD: 0.2192 cents 281 .. 562 match: 17 SD: 0.2026 cents 313 .. 626 match: 17 SD: 0.1843 cents 353 .. 706 match: 17 SD: 0.1261 cents 508 .. 1016 match: 17 SD: 0.1177 cents 548 .. 1096 match: 17 SD: 0.1061 cents