Scala analysis: 414_D8
Diatonic tetrachord 16/15 * 11/10 * 25/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 88/75 276.735514 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/22 221.3095 undecimal acute whole tone 1: 16/15 111.7313 minor diatonic semitone 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 25/22 221.3095 undecimal acute whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 25/22 221.309 cents undecimal acute whole tone 2: 1 88/75 276.736 cents 2: 1 40/33 333.041 cents 2: 1 5/4 386.314 cents major third Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 111.7 276.7 498.0 111.7: 165.0 386.3 498.0 276.7: 221.3 333.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 221.3095 cents 375/352, 109.5782 cents 16/15, 111.7313 cents 2: 276.7355 .. 386.3137 cents 375/352, 109.5782 cents 1936/1875, 55.4260 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 25/22, 221.3095 cents Average / Smallest step : 1.485842 Largest / Average step : 1.333069 Largest / Smallest step : 1.980730 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 154.23838 cents, oct.: 462.71514 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1150-tone equal temperament with octave 4/3 degrees: 258 639 1150 Least number of segments generator : 577 of 249.889 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 639 of 276.740 cents and inv. generated superset size: 23 = 20 more = 766.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 55.42603 cents Scale diversity : 1.294454 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.559967 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 33/32, 53.2729 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Best minor thirds form a closed circle Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 75 (O: 25 U: 75) Highest odd numerator or denominator: 75 Scale harmonicity : 0.026561 Average absolute harmonicity : 0.106034 Specific harmonicity : 0.132950 Fundamental : 1/75, -6.2288 octaves, 3.4883 Hz. Guide tone : 176, 7.4594 octaves, 46046.099 Hz. Exponens Consonantiae : 1.320000E+04, 13.68825 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 100.5, average 33.50000 Mersenne's string divisions : 35371 Sum of van Prooijen's expressibility: 3.52827, average 1.17609 Sum of Tenney's harmonic distance : 7.27894, average 2.42631 Vogel's harmonic complexity : 11.66667 Wille's k value : 12 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 16.76930, average 2.79488 Lattice compactness (without 2's) : 9.51398, average 1.58566 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 ..-1 -1.00000 3 1 5: -2 .. 0 -1.00000 3 1 11: 0 .. 1 0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 16 27| Scale is weakly epimorphic with val: <7 10 15 24| Scale is weakly epimorphic with val: <7 10 15 27| Scale is weakly epimorphic with val: <7 10 16 24| Scale is weakly epimorphic with val: <7 11 15 24| Scale is weakly epimorphic with val: <7 11 15 27| Scale is JI-epimorphic with val: <7 11 16 24| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 18 24| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 12 15 24| Scale is weakly epimorphic with val: <8 11 17 24| Scale is weakly epimorphic with val: <8 11 18 24| Scale is weakly epimorphic with val: <8 11 18 27| Scale is weakly epimorphic with val: <8 12 17 24| Scale is weakly epimorphic with val: <8 12 17 27| Scale is weakly epimorphic with val: <8 12 18 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 44.7370 c. M:-55.2945 c. 4: 1 1 2 P M ME S SD: 17.6195 c. M: 27.7130 c. 5: 1 2 2 SP M ME S SD: 14.5486 c. M:-22.0915 c. 9: 2 3 4 SP T3 SD: 0.6094 c. M: 1.0546 c. 103: 23 34 46 SP T3 SD: 0.7114 c. M: 1.1184 c. 106: 24 35 47 SP T3 SD: 0.6575 c. M:-1.0336 c. 112: 25 37 50 SP T3 SD: 0.6781 c. M: 1.0320 c. 115: 26 38 51 SP T3 SD: 0.5623 c. M:-0.8702 c. 124: 28 41 55 SP T3 SD: 0.4815 c. M:-0.7305 c. 133: 30 44 59 SP T3 SD: 0.4124 c. M:-0.6097 c. 142: 32 47 63 SP T3 SD: 0.3530 c. M:-0.5042 c. 151: 34 50 67 SP T3 SD: 0.3018 c. M:-0.4113 c. 160: 36 53 71 SP T3 SD: 0.2578 c. M:-0.3288 c. 169: 38 56 75 SP T3 SD: 0.2203 c. M:-0.2836 c. 178: 40 59 79 SP T3 SD: 0.1889 c. M:-0.2670 c. 187: 42 62 83 SP T3 SD: 0.1635 c. M:-0.2521 c. 196: 44 65 87 SP T3 SD: 0.1443 c. M:-0.2385 c. 205: 46 68 91 SP T3 SD: 0.1313 c. M:-0.2261 c. 214: 48 71 95 SP T3 SD: 0.1245 c. M:-0.2147 c. 223: 50 74 99 SP T3 SD: 0.1233 c. M:-0.2043 c. 232: 52 77 103 SP T3 SD: 0.1265 c. M:-0.1947 c. 241: 54 80 107 SP T3 SD: 0.1330 c. M:-0.1858 c. 250: 56 83 111 SP T3 SD: 0.1416 c. M:-0.1775 c. 290: 65 96 129 SP T3 SD: 0.1474 c. M: 0.2347 c. 299: 67 99 133 SP T3 SD: 0.1518 c. M: 0.2289 c. 308: 69 102 137 SP T3 SD: 0.1575 c. M: 0.2235 c. 378: 85 125 168 SP T3 SD: 0.1539 c. M:-0.2630 c. 383: 86 127 170 SP T3 SD: 0.1531 c. M:-0.2451 c. 387: 87 128 172 SP T3 SD: 0.1365 c. M:-0.2323 c. 396: 89 131 176 SP T3 SD: 0.1199 c. M:-0.2031 c. 405: 91 134 180 SP T3 SD: 0.1042 c. M:-0.1751 c. 414: 93 137 184 SP T3 SD: 0.0893 c. M:-0.1484 c. 423: 95 140 188 SP T3 SD: 0.0753 c. M:-0.1228 c. 432: 97 143 192 SP T3 SD: 0.0621 c. M:-0.0983 c. 441: 99 146 196 SP T3 SD: 0.0500 c. M:-0.0747 c. 450: 101 149 200 SP T3 SD: 0.0393 c. M:-0.0521 c. 459: 103 152 204 SP T3 SD: 0.0308 c. M: 0.0438 c. 468: 105 155 208 SP T3 SD: 0.0259 c. M: 0.0438 c. 477: 107 158 212 SP T3 SD: 0.0260 c. M: 0.0438 c. 486: 109 161 216 SP T3 SD: 0.0306 c. M: 0.0438 c. 655: 147 217 291 SP T3 SD: 0.0345 c. M:-0.0437 c. 664: 149 220 295 SP T3 SD: 0.0282 c. M:-0.0395 c. 673: 151 223 299 SP T3 SD: 0.0237 c. M:-0.0384 c. 682: 153 226 303 SP T3 SD: 0.0215 c. M:-0.0373 c. 691: 155 229 307 SP T3 SD: 0.0223 c. M:-0.0362 c. 700: 157 232 311 SP T3 SD: 0.0256 c. M:-0.0352 c. 945: 212 313 420 SP T3 SD: 0.0253 c. M: 0.0438 c. 1114: 250 369 495 SP T3 SD: 0.0223 c. M:-0.0382 c. 1123: 252 372 499 SP T3 SD: 0.0173 c. M:-0.0295 c. 1132: 254 375 503 SP T3 SD: 0.0124 c. M:-0.0209 c. 1141: 256 378 507 SP T3 SD: 0.0076 c. M:-0.0124 c. 1150: 258 381 511 SP T3 SD: 0.0034 c. M:-0.0043 c. 1159: 260 384 515 SP T3 SD: 0.0033 c. M: 0.0042 c. 2309: 518 765 1026 SP T3 SD: 0.0024 c. M:-0.0041 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x 5 x S SD: 109.5782 cents 5 x 6:7 S SD: 46.4983 cents 6 x 7:8 S SD: 4.9323 cents 7 x 8:9 S SD: 38.8585 cents 8 x 9:11 SD: 45.1153 cents 9:10:11:12 H SD: 33.3153 cents 10:11:12:13 H SD: 26.4004 cents 11:12:13:15 SD: 18.8058 cents 12:13:14:16 S SD: 9.5322 cents 18:19:21:24 SD: 6.8795 cents 28:30:33:37 SD: 6.3247 cents 29:31:34:39 SD: 5.1269 cents 30:32:35:40 SD: 3.2882 cents 45:48:53:60 SD: 2.1818 cents 57:61:67:76 SD: 2.1591 cents 63:67:74:84 SD: 1.8298 cents 75:80:88:100 SD: 0.0000 cents