Scala analysis: xid2
Semitenth in two octaves
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 129.050 cents 129.050380 2: 258.101 cents 258.100770 3: 387.151 cents 387.151150 4: 627.933 cents 627.932820 5: 756.983 cents 756.983210 6: 886.034 cents 886.033590 7: 1015.084 cents 1015.083970 8: 1144.134 cents 1144.134360 9: 1384.916 cents 1384.916030 10: 1513.966 cents 1513.966410 11: 1643.017 cents 1643.016790 12: 1772.067 cents 1772.067180 13: 1901.118 cents 1901.117560 14: 2141.899 cents 2141.899230 15: 2270.950 cents 2270.949620 16: 4/1 2400.000000 2 octaves
SHOW/INTERVAL
0: 129.0504 cents 129.0504 1: 129.0504 cents 129.0504 2: 129.0504 cents 129.0504 3: 129.0504 cents 129.0504 4: 240.7817 cents 240.7817 5: 129.0504 cents 129.0504 6: 129.0504 cents 129.0504 7: 129.0504 cents 129.0504 8: 129.0504 cents 129.0504 9: 240.7817 cents 240.7817 10: 129.0504 cents 129.0504 11: 129.0504 cents 129.0504 12: 129.0504 cents 129.0504 13: 129.0504 cents 129.0504 14: 240.7817 cents 240.7817 15: 129.0504 cents 129.0504 16: 129.0504 cents 129.0504
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 129.05038 cents 1: 3 240.78167 cents 2: 10 258.10077 cents 2: 6 369.83205 cents 3: 7 387.15115 cents 3: 9 498.88244 cents 4: 4 516.20154 cents 4: 12 627.93282 cents 5: 1 645.25192 cents 5: 15 756.98321 cents 6: 14 886.03359 cents 6: 2 997.76488 cents 7: 11 1015.08397 cents 7: 5 1126.81526 cents 8: 8 1144.13436 cents 8: 8 1255.86565 cents 9: 5 1273.18474 cents 9: 11 1384.91603 cents 10: 2 1402.23512 cents 10: 14 1513.96641 cents 11: 15 1643.01679 cents 11: 1 1754.74808 cents 12: 12 1772.06718 cents 12: 4 1883.79846 cents 13: 9 1901.11756 cents 13: 7 2012.84885 cents 14: 6 2030.16795 cents 14: 10 2141.89923 cents 15: 3 2159.21833 cents 15: 13 2270.94962 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 0.0 : 129.1 258.1 387.2 627.9 757.0 886.0 1015.1 1144.1 1384.9 1514.0 1643.0 1772.1 1901.1 2141.9 2270.9 2400.0 129.1 : 129.1 258.1 498.9 627.9 757.0 886.0 1015.1 1255.9 1384.9 1514.0 1643.0 1772.1 2012.8 2141.9 2270.9 2400.0 258.1 : 129.1 369.8 498.9 627.9 757.0 886.0 1126.8 1255.9 1384.9 1514.0 1643.0 1883.8 2012.8 2141.9 2270.9 2400.0 387.2 : 240.8 369.8 498.9 627.9 757.0 997.8 1126.8 1255.9 1384.9 1514.0 1754.7 1883.8 2012.8 2141.9 2270.9 2400.0 627.9 : 129.1 258.1 387.2 516.2 757.0 886.0 1015.1 1144.1 1273.2 1514.0 1643.0 1772.1 1901.1 2030.2 2159.2 2400.0 757.0 : 129.1 258.1 387.2 627.9 757.0 886.0 1015.1 1144.1 1384.9 1514.0 1643.0 1772.1 1901.1 2030.2 2270.9 2400.0 886.0 : 129.1 258.1 498.9 627.9 757.0 886.0 1015.1 1255.9 1384.9 1514.0 1643.0 1772.1 1901.1 2141.9 2270.9 2400.0 1015.1: 129.1 369.8 498.9 627.9 757.0 886.0 1126.8 1255.9 1384.9 1514.0 1643.0 1772.1 2012.8 2141.9 2270.9 2400.0 1144.1: 240.8 369.8 498.9 627.9 757.0 997.8 1126.8 1255.9 1384.9 1514.0 1643.0 1883.8 2012.8 2141.9 2270.9 2400.0 1384.9: 129.1 258.1 387.2 516.2 757.0 886.0 1015.1 1144.1 1273.2 1402.2 1643.0 1772.1 1901.1 2030.2 2159.2 2400.0 1514.0: 129.1 258.1 387.2 627.9 757.0 886.0 1015.1 1144.1 1273.2 1514.0 1643.0 1772.1 1901.1 2030.2 2270.9 2400.0 1643.0: 129.1 258.1 498.9 627.9 757.0 886.0 1015.1 1144.1 1384.9 1514.0 1643.0 1772.1 1901.1 2141.9 2270.9 2400.0 1772.1: 129.1 369.8 498.9 627.9 757.0 886.0 1015.1 1255.9 1384.9 1514.0 1643.0 1772.1 2012.8 2141.9 2270.9 2400.0 1901.1: 240.8 369.8 498.9 627.9 757.0 886.0 1126.8 1255.9 1384.9 1514.0 1643.0 1883.8 2012.8 2141.9 2270.9 2400.0 2141.9: 129.1 258.1 387.2 516.2 645.3 886.0 1015.1 1144.1 1273.2 1402.2 1643.0 1772.1 1901.1 2030.2 2159.2 2400.0 2270.9: 129.1 258.1 387.2 516.2 757.0 886.0 1015.1 1144.1 1273.2 1514.0 1643.0 1772.1 1901.1 2030.2 2270.9 2400.0 2400.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 129.0504 .. 240.7817 cents 111.73129 cents 129.05038 cents 2: 258.1008 .. 369.8320 cents 111.73128 cents 17.31910 cents 3: 387.1511 .. 498.8824 cents 111.73129 cents 17.31910 cents 4: 516.2015 .. 627.9328 cents 111.73128 cents 17.31910 cents 5: 645.2519 .. 756.9832 cents 111.73129 cents 17.31910 cents 6: 886.0336 .. 997.7649 cents 111.73129 cents 129.05038 cents 7: 1015.0840 .. 1126.8153 cents 111.73129 cents 17.31909 cents 8: 1144.1344 .. 1255.8657 cents 111.73129 cents 17.31910 cents 9: 1273.1847 .. 1384.9160 cents 111.73129 cents 17.31909 cents 10: 1402.2351 .. 1513.9664 cents 111.73129 cents 17.31909 cents 11: 1643.0168 .. 1754.7481 cents 111.73129 cents 129.05038 cents 12: 1772.0672 .. 1883.7985 cents 111.73128 cents 17.31910 cents 13: 1901.1176 .. 2012.8489 cents 111.73129 cents 17.31910 cents 14: 2030.1680 .. 2141.8992 cents 111.73128 cents 17.31910 cents 15: 2159.2183 .. 2270.9496 cents 111.73129 cents 17.31910 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 129.05038 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 240.78167 cents Average / Smallest step : 1.162337 Largest / Average step : 1.605211 Largest / Smallest step : 1.865796 Median interval of one step : 129.05038 cents, amount: 13 Most common interval of one step : 129.05038 cents, amount: 13 Least squares average step : 149.58922 cents, oct.: 2393.42757 cents Scale is strictly proper Scale has Myhill's property chromas: 111.73129 cents and 17.31909 cents, ratio: 6.451337 generators: 5 of 756.98321 cents and 11 of 1643.01679 cents ET pair of linear temperament : 16&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1525-tone equal temperament with octave 4/1 degrees: 82 164 246 399 481 563 645 727 880 962 1044 1126 1208 1361 1443 1525 generators: 481 and 1044 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAAABAAAABAA Step pattern size order : SSSLSSSSLSSSSLSS Scale is a Constant Structure, by a margin of 17.31909 cents Scale diversity :-0.051111 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.301679 Rothenberg efficiency : 0.708333 redundancy: 0.291667 Efficiency x scale size : 11.333333 Number of different interval sizes : 30 = 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 : 17.31909 cents Most common intervals : 756.98321 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 498.882 1643.017 cents Most common triad is 0.0 756.983 1643.017 cents, amount: 14 Number of recognisable fifths : 0 Number of recognisable fourths : 9, average 498.8824 cents Scale contains two identical disjunct tetrachords Best fifths form a closed circle Formal octave complements present : 13 = 81.2500% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 8-9 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
16: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 33.8523 c. M:-62.8489 c. 18: 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 N D3 SD: 36.3610 c. M:-55.8656 c. 19: 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 P M ME SD: 4.4188 c. M: 8.2038 c. 73: 4 4 4 7 4 4 4 4 7 4 4 4 4 7 4 4 SP M DE SD: 3.9694 c. M:-7.3694 c. 92: 5 5 5 9 5 5 5 5 9 5 5 5 5 9 5 5 SP M DE SD: 2.2370 c. M:-4.1532 c. 111: 6 6 6 11 6 6 6 6 11 6 6 6 6 11 6 6 SP M DE SD: 1.0978 c. M:-2.0380 c. 130: 7 7 7 13 7 7 7 7 13 7 7 7 7 13 7 7 SP M DE SD: 0.2915 c. M:-0.5412 c. 279: 15 15 15 28 15 15 15 15 28 15 15 15 15 28 15 15 SP M DE SD: 0.0293 c. M: 0.0544 c. 967: 52 52 52 97 52 52 52 52 97 52 52 52 52 97 52 52 SP M DE SD: 0.0138 c. M:-0.0257 c. 1246: 67 67 67 125 67 67 67 67 125 67 67 67 67 125 67 67 SP M DE SD: 0.0042 c. M:-0.0078 c. 1525: 82 82 82 153 82 82 82 82 153 82 82 82 82 153 82 82 SP M DE SD: 0.0019 c. M: 0.0036 c.
FIT/HARMONIC
1 .. 4 match: 3 H SD: 18.6240 cents 2 .. 8 match: 6 H SD: 16.7415 cents 3 .. 12 match: 9 H SD: 17.3721 cents 4 .. 16 match: 11 S SD: 10.4927 cents 5 .. 20 match: 13 SD: 9.2666 cents 6 .. 24 match: 14 S SD: 12.2148 cents 7 .. 28 match: 15 SD: 8.6874 cents 8 .. 32 match: 14 SD: 9.0789 cents 9 .. 36 match: 15 SD: 6.2310 cents 11 .. 44 match: 16 SD: 5.5527 cents 12 .. 48 match: 16 SD: 4.5373 cents 13 .. 52 match: 16 SD: 4.0219 cents 18 .. 72 match: 16 SD: 3.7990 cents 20 .. 80 match: 16 SD: 3.3916 cents 23 .. 92 match: 16 SD: 2.9831 cents 24 .. 96 match: 16 SD: 2.5268 cents 25 .. 100 match: 16 SD: 2.1392 cents 27 .. 108 match: 16 SD: 2.1323 cents 31 .. 124 match: 16 SD: 2.0797 cents 35 .. 140 match: 16 SD: 1.9648 cents 36 .. 144 match: 16 SD: 1.3981 cents 48 .. 192 match: 16 SD: 1.1202 cents 51 .. 204 match: 16 SD: 1.0545 cents 55 .. 220 match: 16 SD: 1.0201 cents 60 .. 240 match: 16 SD: 1.0056 cents 63 .. 252 match: 16 SD: 0.9318 cents 64 .. 256 match: 16 SD: 0.7753 cents 75 .. 300 match: 16 SD: 0.6146 cents 80 .. 320 match: 16 SD: 0.5983 cents 93 .. 372 match: 16 SD: 0.5311 cents 112 .. 448 match: 16 SD: 0.5258 cents 117 .. 468 match: 16 SD: 0.5214 cents 119 .. 476 match: 16 SD: 0.4962 cents 124 .. 496 match: 16 SD: 0.4275 cents 139 .. 556 match: 16 SD: 0.4049 cents 142 .. 568 match: 16 SD: 0.3628 cents 144 .. 576 match: 16 SD: 0.2979 cents 192 .. 768 match: 16 SD: 0.2542 cents 204 .. 816 match: 16 SD: 0.2412 cents 217 .. 868 match: 16 SD: 0.2388 cents 231 .. 924 match: 16 SD: 0.2121 cents 268 .. 1072 match: 16 SD: 0.1998 cents 272 .. 1088 match: 16 SD: 0.1798 cents 286 .. 1144 match: 16 SD: 0.1734 cents 299 .. 1196 match: 16 SD: 0.1696 cents 311 .. 1244 match: 16 SD: 0.1628 cents 336 .. 1344 match: 16 SD: 0.1625 cents 347 .. 1388 match: 16 SD: 0.1544 cents 350 .. 1400 match: 16 SD: 0.1341 cents 410 .. 1640 match: 16 SD: 0.1226 cents 443 .. 1772 match: 16 SD: 0.1206 cents 455 .. 1820 match: 16 SD: 0.1193 cents 467 .. 1868 match: 16 SD: 0.1047 cents 492 .. 1968 match: 16 SD: 0.1025 cents 503 .. 2012 match: 16 SD: 0.0769 cents 554 .. 2216 match: 16 SD: 0.0744 cents 567 .. 2268 match: 16 SD: 0.0646 cents