Scala analysis: edo-16
16 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75.000 cents 75.000000 2: 150.000 cents 150.000000 3: 225.000 cents 225.000000 4: 300.000 cents 300.000000 5: 375.000 cents 375.000000 6: 450.000 cents 450.000000 7: 525.000 cents 525.000000 8: 600.000 cents 600.000000 9: 675.000 cents 675.000000 10: 750.000 cents 750.000000 11: 825.000 cents 825.000000 12: 900.000 cents 900.000000 13: 975.000 cents 975.000000 14: 1050.000 cents 1050.000000 15: 1125.000 cents 1125.000000 16: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 75.0000 cents 75.0000 1: 75.0000 cents 75.0000 2: 75.0000 cents 75.0000 3: 75.0000 cents 75.0000 4: 75.0000 cents 75.0000 5: 75.0000 cents 75.0000 6: 75.0000 cents 75.0000 7: 75.0000 cents 75.0000 8: 75.0000 cents 75.0000 9: 75.0000 cents 75.0000 10: 75.0000 cents 75.0000 11: 75.0000 cents 75.0000 12: 75.0000 cents 75.0000 13: 75.0000 cents 75.0000 14: 75.0000 cents 75.0000 15: 75.0000 cents 75.0000 16: 75.0000 cents 75.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 16 75.00000 cents 2: 16 150.00000 cents 3: 16 225.00000 cents 4: 16 300.00000 cents 5: 16 375.00000 cents 6: 16 450.00000 cents 7: 16 525.00000 cents 8: 16 600.00000 cents 9: 16 675.00000 cents 10: 16 750.00000 cents 11: 16 825.00000 cents 12: 16 900.00000 cents 13: 16 975.00000 cents 14: 16 1050.00000 cents 15: 16 1125.00000 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 75.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 150.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 225.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 300.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 375.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 450.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 525.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 600.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 675.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 750.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 825.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 900.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 975.0 : 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 1050.0: 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 1125.0: 75.0 150.0 225.0 300.0 375.0 450.0 525.0 600.0 675.0 750.0 825.0 900.0 975.0 1050.0 1125.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.0000 .. 75.0000 cents 1/1, 0.0000 cents 75.00000 cents 2: 150.0000 .. 150.0000 cents 1/1, 0.0000 cents 75.00000 cents 3: 225.0000 .. 225.0000 cents 1/1, 0.0000 cents 75.00000 cents 4: 300.0000 .. 300.0000 cents 1/1, 0.0000 cents 75.00000 cents 5: 375.0000 .. 375.0000 cents 1/1, 0.0000 cents 75.00000 cents 6: 450.0000 .. 450.0000 cents 1/1, 0.0000 cents 75.00000 cents 7: 525.0000 .. 525.0000 cents 1/1, 0.0000 cents 75.00000 cents 8: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 75.00000 cents 9: 675.0000 .. 675.0000 cents 1/1, 0.0000 cents 75.00000 cents 10: 750.0000 .. 750.0000 cents 1/1, 0.0000 cents 75.00000 cents 11: 825.0000 .. 825.0000 cents 1/1, 0.0000 cents 75.00000 cents 12: 900.0000 .. 900.0000 cents 1/1, 0.0000 cents 75.00000 cents 13: 975.0000 .. 975.0000 cents 1/1, 0.0000 cents 75.00000 cents 14: 1050.0000 .. 1050.0000 cents 1/1, 0.0000 cents 75.00000 cents 15: 1125.0000 .. 1125.0000 cents 1/1, 0.0000 cents 75.00000 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 75.00000 cents, class 1 Average step (divided formal octave): 75.0000 cents Largest one step interval : 75.00000 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 75.00000 cents, amount: 16 Most common interval of one step : 75.00000 cents, amount: 16 Least squares average step : 75.00000 cents, oct.: 1200.00000 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 75.00000 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.062500 redundancy: 0.937500 Efficiency x scale size : 1.000000 Number of different interval sizes : 15 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 0 Scale contains two identical disjunct "tetrachords" of 8 notes Best fifths form a closed circle Best major thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
16: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I 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: 13.4775 cents 3 .. 6 match: 3 H SD: 10.3881 cents 4 .. 8 match: 4 H SD: 7.4695 cents 5 .. 10 match: 5 H SD: 8.3150 cents 6 .. 12 match: 6 H SD: 8.8125 cents 7 .. 14 match: 7 H SD: 8.0694 cents 8 .. 16 match: 8 H SD: 7.5212 cents 9 .. 18 match: 9 H SD: 8.1381 cents 10 .. 20 match: 10 H SD: 5.6885 cents 11 .. 22 match: 11 H SD: 5.6540 cents 12 .. 24 match: 12 H SD: 5.2507 cents 13 .. 26 match: 13 H SD: 4.6205 cents 14 .. 28 match: 14 H SD: 6.5196 cents 15 .. 30 match: 14 S SD: 5.6244 cents 16 .. 32 match: 15 SD: 5.0644 cents 17 .. 34 match: 15 SD: 4.3424 cents 18 .. 36 match: 15 SD: 5.8993 cents 19 .. 38 match: 16 SD: 4.8504 cents 20 .. 40 match: 16 SD: 3.4579 cents 21 .. 42 match: 16 SD: 3.2856 cents 26 .. 52 match: 16 SD: 3.1904 cents 28 .. 56 match: 16 SD: 3.1001 cents 29 .. 58 match: 16 SD: 3.0306 cents 31 .. 62 match: 16 SD: 2.6975 cents 34 .. 68 match: 16 SD: 2.5986 cents 36 .. 72 match: 16 SD: 2.2906 cents 37 .. 74 match: 16 SD: 1.9662 cents 41 .. 82 match: 16 SD: 1.9549 cents 42 .. 84 match: 16 SD: 1.8208 cents 44 .. 88 match: 16 SD: 1.5103 cents 48 .. 96 match: 16 SD: 1.5095 cents 53 .. 106 match: 16 SD: 1.4937 cents 57 .. 114 match: 16 SD: 1.3570 cents 63 .. 126 match: 16 SD: 1.2722 cents 65 .. 130 match: 16 SD: 1.0263 cents 70 .. 140 match: 16 SD: 1.0126 cents 74 .. 148 match: 16 SD: 1.0023 cents 85 .. 170 match: 16 SD: 0.9034 cents 87 .. 174 match: 16 SD: 0.8767 cents 90 .. 180 match: 16 SD: 0.7996 cents 107 .. 214 match: 16 SD: 0.6135 cents 111 .. 222 match: 16 SD: 0.6049 cents 131 .. 262 match: 16 SD: 0.5652 cents 132 .. 264 match: 16 SD: 0.5041 cents 144 .. 288 match: 16 SD: 0.4636 cents 157 .. 314 match: 16 SD: 0.4272 cents 164 .. 328 match: 16 SD: 0.3756 cents 186 .. 372 match: 16 SD: 0.3489 cents 201 .. 402 match: 16 SD: 0.3201 cents 222 .. 444 match: 16 SD: 0.3144 cents 223 .. 446 match: 16 SD: 0.2523 cents 273 .. 546 match: 16 SD: 0.2472 cents 290 .. 580 match: 16 SD: 0.2268 cents 317 .. 634 match: 16 SD: 0.2248 cents 319 .. 638 match: 16 SD: 0.2127 cents 339 .. 678 match: 16 SD: 0.2115 cents 364 .. 728 match: 16 SD: 0.2077 cents 365 .. 730 match: 16 SD: 0.1832 cents 367 .. 734 match: 16 SD: 0.1783 cents 398 .. 796 match: 16 SD: 0.1741 cents 411 .. 822 match: 16 SD: 0.1650 cents 434 .. 868 match: 16 SD: 0.1400 cents 475 .. 950 match: 16 SD: 0.1337 cents 518 .. 1036 match: 16 SD: 0.1324 cents 541 .. 1082 match: 16 SD: 0.1254 cents 562 .. 1124 match: 16 SD: 0.0981 cents