Scala analysis: xid1
Semisixth in two octaves
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 73.185 cents 73.184740 2: 258.101 cents 258.100770 3: 443.017 cents 443.016790 4: 627.933 cents 627.932820 5: 701.118 cents 701.117560 6: 886.034 cents 886.033590 7: 1070.950 cents 1070.949620 8: 1144.134 cents 1144.134360 9: 1329.050 cents 1329.050380 10: 1513.966 cents 1513.966410 11: 1587.151 cents 1587.151150 12: 1772.067 cents 1772.067180 13: 1956.983 cents 1956.983210 14: 2030.168 cents 2030.167950 15: 2215.084 cents 2215.083970 16: 4/1 2400.000000 2 octaves
SHOW/INTERVAL
0: 184.9160 cents 184.9160 1: 73.1847 cents 73.1847 2: 184.9160 cents 184.9160 3: 184.9160 cents 184.9160 4: 184.9160 cents 184.9160 5: 73.1847 cents 73.1847 6: 184.9160 cents 184.9160 7: 184.9160 cents 184.9160 8: 73.1847 cents 73.1847 9: 184.9160 cents 184.9160 10: 184.9160 cents 184.9160 11: 73.1847 cents 73.1847 12: 184.9160 cents 184.9160 13: 184.9160 cents 184.9160 14: 73.1847 cents 73.1847 15: 184.9160 cents 184.9160 16: 184.9160 cents 184.9160
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 73.18474 cents 1: 11 184.91603 cents 2: 10 258.10077 cents 2: 6 369.83205 cents 3: 15 443.01679 cents 3: 1 554.74808 cents 4: 4 516.20154 cents 4: 12 627.93282 cents 5: 9 701.11756 cents 5: 7 812.84885 cents 6: 14 886.03359 cents 6: 2 997.76488 cents 7: 3 959.21833 cents 7: 13 1070.94962 cents 8: 8 1144.13436 cents 8: 8 1255.86564 cents 9: 13 1329.05038 cents 9: 3 1440.78167 cents 10: 2 1402.23513 cents 10: 14 1513.96641 cents 11: 7 1587.15115 cents 11: 9 1698.88244 cents 12: 12 1772.06718 cents 12: 4 1883.79847 cents 13: 1 1845.25192 cents 13: 15 1956.98321 cents 14: 6 2030.16795 cents 14: 10 2141.89923 cents 15: 11 2215.08397 cents 15: 5 2326.81526 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 : 73.2 258.1 443.0 627.9 701.1 886.0 1070.9 1144.1 1329.1 1514.0 1587.2 1772.1 1957.0 2030.2 2215.1 2400.0 73.2 : 184.9 369.8 554.7 627.9 812.8 997.8 1070.9 1255.9 1440.8 1514.0 1698.9 1883.8 1957.0 2141.9 2326.8 2400.0 258.1 : 184.9 369.8 443.0 627.9 812.8 886.0 1070.9 1255.9 1329.1 1514.0 1698.9 1772.1 1957.0 2141.9 2215.1 2400.0 443.0 : 184.9 258.1 443.0 627.9 701.1 886.0 1070.9 1144.1 1329.1 1514.0 1587.2 1772.1 1957.0 2030.2 2215.1 2400.0 627.9 : 73.2 258.1 443.0 516.2 701.1 886.0 959.2 1144.1 1329.1 1402.2 1587.2 1772.1 1845.3 2030.2 2215.1 2400.0 701.1 : 184.9 369.8 443.0 627.9 812.8 886.0 1070.9 1255.9 1329.1 1514.0 1698.9 1772.1 1957.0 2141.9 2326.8 2400.0 886.0 : 184.9 258.1 443.0 627.9 701.1 886.0 1070.9 1144.1 1329.1 1514.0 1587.2 1772.1 1957.0 2141.9 2215.1 2400.0 1070.9: 73.2 258.1 443.0 516.2 701.1 886.0 959.2 1144.1 1329.1 1402.2 1587.2 1772.1 1957.0 2030.2 2215.1 2400.0 1144.1: 184.9 369.8 443.0 627.9 812.8 886.0 1070.9 1255.9 1329.1 1514.0 1698.9 1883.8 1957.0 2141.9 2326.8 2400.0 1329.1: 184.9 258.1 443.0 627.9 701.1 886.0 1070.9 1144.1 1329.1 1514.0 1698.9 1772.1 1957.0 2141.9 2215.1 2400.0 1514.0: 73.2 258.1 443.0 516.2 701.1 886.0 959.2 1144.1 1329.1 1514.0 1587.2 1772.1 1957.0 2030.2 2215.1 2400.0 1587.2: 184.9 369.8 443.0 627.9 812.8 886.0 1070.9 1255.9 1440.8 1514.0 1698.9 1883.8 1957.0 2141.9 2326.8 2400.0 1772.1: 184.9 258.1 443.0 627.9 701.1 886.0 1070.9 1255.9 1329.1 1514.0 1698.9 1772.1 1957.0 2141.9 2215.1 2400.0 1957.0: 73.2 258.1 443.0 516.2 701.1 886.0 1070.9 1144.1 1329.1 1514.0 1587.2 1772.1 1957.0 2030.2 2215.1 2400.0 2030.2: 184.9 369.8 443.0 627.9 812.8 997.8 1070.9 1255.9 1440.8 1514.0 1698.9 1883.8 1957.0 2141.9 2326.8 2400.0 2215.1: 184.9 258.1 443.0 627.9 812.8 886.0 1070.9 1255.9 1329.1 1514.0 1698.9 1772.1 1957.0 2141.9 2215.1 2400.0 2400.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.1847 .. 184.9160 cents 111.73129 cents 73.18474 cents 2: 258.1008 .. 369.8321 cents 111.73128 cents 73.18474 cents 3: 443.0168 .. 554.7481 cents 111.73129 cents 73.18474 cents 4: 516.2015 .. 627.9328 cents 111.73128 cents -38.54654 cents 5: 701.1176 .. 812.8489 cents 111.73129 cents 73.18474 cents 6: 886.0336 .. 997.7649 cents 111.73129 cents 73.18474 cents 7: 959.2183 .. 1070.9496 cents 111.73129 cents -38.54655 cents 8: 1144.1344 .. 1255.8656 cents 111.73128 cents 73.18474 cents 9: 1329.0504 .. 1440.7817 cents 111.73129 cents 73.18474 cents 10: 1402.2351 .. 1513.9664 cents 111.73128 cents -38.54654 cents 11: 1587.1512 .. 1698.8824 cents 111.73129 cents 73.18474 cents 12: 1772.0672 .. 1883.7985 cents 111.73129 cents 73.18474 cents 13: 1845.2519 .. 1956.9832 cents 111.73129 cents -38.54655 cents 14: 2030.1680 .. 2141.8992 cents 111.73128 cents 73.18474 cents 15: 2215.0840 .. 2326.8153 cents 111.73129 cents 73.18474 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 73.18474 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 184.91603 cents Average / Smallest step : 2.049608 Largest / Average step : 1.232774 Largest / Smallest step : 2.526702 Median interval of one step : 184.91603 cents, amount: 11 Most common interval of one step : 184.91603 cents, amount: 11 Least squares average step : 147.87143 cents, oct.: 2365.94287 cents Scale is not proper Scale has Myhill's property chromas: 111.73129 cents and 38.54655 cents, ratio: 2.898607 generators: 3 of 443.01679 cents and 13 of 1956.98321 cents ET pair of linear temperament : 11&27 Scale is distributional even Step pattern alph. order: ABBBABBABBABBABB Step pattern size order : SLLLSLLSLLSLLSLL Scale is a Constant Structure, by a margin of 38.54654 cents Scale diversity :-0.032992 Lumma stability : 0.365924 Lumma impropriety factor : 0.064244 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 : 38.54654 cents Most common intervals : 443.01679 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 1255.866 1956.983 cents Most common triad is 0.0 443.017 1956.983 cents, amount: 14 Number of recognisable fifths : 9, average 701.1176 cents Number of recognisable fourths : 0 Scale contains two identical disjunct tetrachords Formal octave complements present : 9 = 56.2500% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 10-11 -- 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: 40.4182 c. M:-76.8153 c. 18: 1 1 1 2 0 2 1 1 1 1 1 1 2 0 2 1 N D3 S SD: 37.8713 c. M:-60.1486 c. 20: 1 1 2 1 1 1 2 1 1 2 0 2 1 1 1 2 N D3 SD: 34.0615 c. M:-55.8656 c. 22: 0 2 2 2 0 2 2 0 2 2 0 2 2 0 2 2 N M DE SD: 38.5079 c. M: 73.1847 c. 24: 1 2 1 2 1 2 2 0 2 2 1 2 2 0 2 2 N D3 SD: 28.5764 c. M: 44.1344 c. 26: 1 2 2 2 1 2 2 0 2 2 1 2 2 1 2 2 N T3 SD: 25.6889 c. M:-37.3440 c. 27: 1 2 2 2 1 2 2 1 2 2 1 2 2 1 2 2 P M ME SD: 8.2631 c. M:-15.7041 c. 38: 1 3 3 3 1 3 3 1 3 3 1 3 3 1 3 3 N M DE SD: 5.2759 c. M: 10.0268 c. 65: 2 5 5 5 2 5 5 2 5 5 2 5 5 2 5 5 N M DE SD: 0.3480 c. M:-0.6614 c. 363: 11 28 28 28 11 28 28 11 28 28 11 28 28 11 28 28 N M DE SD: 0.2407 c. M: 0.4575 c. 428: 13 33 33 33 13 33 33 13 33 33 13 33 33 13 33 33 N M DE SD: 0.1513 c. M: 0.2875 c. 493: 15 38 38 38 15 38 38 15 38 38 15 38 38 15 38 38 N M DE SD: 0.0855 c. M: 0.1624 c. 558: 17 43 43 43 17 43 43 17 43 43 17 43 43 17 43 43 N M DE SD: 0.0350 c. M: 0.0665 c. 623: 19 48 48 48 19 48 48 19 48 48 19 48 48 19 48 48 N M DE SD: 0.0050 c. M:-0.0095 c.
FIT/HARMONIC
1 .. 4 match: 3 H SD: 26.1387 cents 2 .. 8 match: 6 H SD: 15.1752 cents 3 .. 12 match: 9 H SD: 16.0973 cents 4 .. 16 match: 11 S SD: 14.2301 cents 5 .. 20 match: 13 S SD: 12.3518 cents 6 .. 24 match: 13 SD: 8.5432 cents 7 .. 28 match: 15 SD: 9.2512 cents 8 .. 32 match: 14 SD: 8.2958 cents 9 .. 36 match: 14 SD: 9.5904 cents 10 .. 40 match: 15 SD: 8.8857 cents 11 .. 44 match: 15 SD: 8.0131 cents 12 .. 48 match: 16 SD: 6.1533 cents 13 .. 52 match: 15 SD: 5.3081 cents 14 .. 56 match: 16 SD: 4.3258 cents 15 .. 60 match: 15 SD: 5.6348 cents 16 .. 64 match: 16 SD: 4.7484 cents 17 .. 68 match: 16 SD: 4.6114 cents 18 .. 72 match: 16 SD: 2.5957 cents 20 .. 80 match: 16 SD: 2.4500 cents 27 .. 108 match: 16 SD: 2.3638 cents 30 .. 120 match: 16 SD: 1.7778 cents 42 .. 168 match: 16 SD: 1.3896 cents 44 .. 176 match: 16 SD: 1.2263 cents 48 .. 192 match: 16 SD: 0.9091 cents 62 .. 248 match: 16 SD: 0.9056 cents 64 .. 256 match: 16 SD: 0.8683 cents 68 .. 272 match: 16 SD: 0.8339 cents 69 .. 276 match: 16 SD: 0.7998 cents 76 .. 304 match: 16 SD: 0.7363 cents 92 .. 368 match: 16 SD: 0.5720 cents 96 .. 384 match: 16 SD: 0.5218 cents 112 .. 448 match: 16 SD: 0.4341 cents 124 .. 496 match: 16 SD: 0.4197 cents 138 .. 552 match: 16 SD: 0.3653 cents 144 .. 576 match: 16 SD: 0.3146 cents 162 .. 648 match: 16 SD: 0.2971 cents 186 .. 744 match: 16 SD: 0.2661 cents 188 .. 752 match: 16 SD: 0.2514 cents 206 .. 824 match: 16 SD: 0.2317 cents 236 .. 944 match: 16 SD: 0.2122 cents 250 .. 1000 match: 16 SD: 0.2093 cents 254 .. 1016 match: 16 SD: 0.1949 cents 281 .. 1124 match: 16 SD: 0.1852 cents 298 .. 1192 match: 16 SD: 0.1655 cents 299 .. 1196 match: 16 SD: 0.1379 cents 329 .. 1316 match: 16 SD: 0.1295 cents 391 .. 1564 match: 16 SD: 0.1281 cents 425 .. 1700 match: 16 SD: 0.1272 cents 443 .. 1772 match: 16 SD: 0.1207 cents 459 .. 1836 match: 16 SD: 0.1200 cents 460 .. 1840 match: 16 SD: 0.1161 cents 467 .. 1868 match: 16 SD: 0.0968 cents 503 .. 2012 match: 16 SD: 0.0966 cents 515 .. 2060 match: 16 SD: 0.0963 cents 535 .. 2140 match: 16 SD: 0.0772 cents 579 .. 2316 match: 16 SD: 0.0764 cents