Scala analysis: 408_D7
Diatonic tetrachord 225/214 * 107/96 * 256/225
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 225/214 86.777046 2: 75/64 274.582429 classic augmented second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 256/225 223.4626 Neapolitan diminished third 1: 225/214 86.7770 2: 107/96 187.8054 3: 256/225 223.4626 Neapolitan diminished third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 225/214 86.777 cents 1: 1 107/96 187.805 cents 1: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 75/64 274.582 cents classic augmented second 2: 1 128/107 310.240 cents 2: 1 856/675 411.268 cents 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 : 86.8 274.6 498.0 86.8 : 187.8 411.3 498.0 274.6: 223.5 310.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 86.7770 .. 223.4626 cents 54784/50625, 136.6855 cents 225/214, 86.7770 cents 2: 274.5824 .. 411.2680 cents 54784/50625, 136.6855 cents 16875/16384, 51.1199 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 225/214, 86.7770 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 256/225, 223.4626 cents Average / Smallest step : 1.913121 Largest / Average step : 1.346038 Largest / Smallest step : 2.575135 Median interval of one step : 107/96, 187.8054 cents, amount: 1 Least squares average step : 152.14835 cents, oct.: 456.44505 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 419-tone equal temperament with octave 4/3 degrees: 73 231 419 Least number of segments generator : 210 of 249.617 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 334 of 397.010 cents and inv. generated superset size: 18 = 15 more = 600.000% 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 51.11986 cents Scale diversity : 1.089441 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.451112 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 : 8192/8025, 35.6572 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 107 Odd number limit : 675 (O: 225 U: 675) Highest odd numerator or denominator: 225 Scale harmonicity : 0.034722 Fundamental : 1/20544, -14.3264 octaves, 0.0127 Hz. Guide tone : 900, 9.8138 octaves, 235463.009 Hz. Exponens Consonantiae : 1.848960E+07, 24.14021 octaves Euler's gradus suavitatis : 129 Sum of Mann's harmonic distance : 292.5, average 97.50000 Mersenne's string divisions : 427147 Sum of van Prooijen's expressibility: 4.70437, average 1.56812 Sum of Tenney's harmonic distance : 9.44302, average 3.14767 Vogel's harmonic complexity : 87.33333 Wille's k value : 12037 Wilson's harmonic complexity : 126 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 29.91391, average 4.98565 Lattice compactness (without 2's) : 13.49847, average 2.24975 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 2 -1.66667 9 3: -1 .. 2 0.66667 4 1 5: 0 .. 2 1.33333 4 1 107: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 5 / 3 = 1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 11 18 49| Scale is weakly epimorphic with val: <7 11 15 50| Scale is weakly epimorphic with val: <7 11 16 48| Scale is weakly epimorphic with val: <7 11 18 50| Scale is weakly epimorphic with val: <7 11 19 48| Scale is weakly epimorphic with val: <7 12 17 48| Scale is weakly epimorphic with val: <8 11 19 49|
FIT/MODE
3: 0 1 2 N G T3 SD: 80.2437 c. M: 108.5674 c. 4: 1 1 2 P M ME S SD: 26.3134 c. M:-37.7342 c. 5: 1 2 2 SP M ME S SD: 15.8373 c. M:-24.2446 c. 6: 1 2 3 P T3 SD: 14.9167 c. M: 25.5599 c. 7: 1 3 3 SP M DE S SD: 10.7164 c. M: 15.6278 c. 11: 2 4 5 SP T3 SD: 2.7567 c. M:-3.7766 c. 18: 3 7 8 SP T3 SD: 2.4939 c. M: 3.7695 c. 29: 5 11 13 SP T3 SD: 0.5365 c. M: 0.9072 c. 40: 7 15 18 SP T3 SD: 0.4388 c. M: 0.6577 c. 69: 12 26 31 SP T3 SD: 0.1948 c. M: 0.2968 c. 167: 29 63 75 SP T3 SD: 0.2069 c. M: 0.2902 c. 212: 37 80 95 SP T3 SD: 0.1833 c. M:-0.2820 c. 236: 41 89 106 SP T3 SD: 0.1993 c. M: 0.2523 c. 241: 42 91 108 SP T3 SD: 0.1576 c. M:-0.2723 c. 252: 44 95 113 SP T3 SD: 0.1307 c. M:-0.1832 c. 281: 49 106 126 SP T3 SD: 0.0905 c. M:-0.1399 c. 310: 54 117 139 SP T3 SD: 0.0849 c. M:-0.1456 c. 321: 56 121 144 SP T3 SD: 0.0673 c. M:-0.1093 c. 350: 61 132 157 SP T3 SD: 0.0343 c. M:-0.0538 c. 419: 73 158 188 SP T3 SD: 0.0039 c. M: 0.0055 c. 2026: 353 764 909 SP T3 SD: 0.0035 c. M:-0.0061 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 x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 46.9589 cents 6 x 7:8 S SD: 3.8558 cents 7 x 8:9 S SD: 38.2373 cents 8 x 9:11 SD: 44.2510 cents 9 x 11:12 SD: 36.4128 cents 10:11:12:13 H SD: 32.8743 cents 11:12:13:15 SD: 25.3984 cents 12:13:14:16 S SD: 17.4555 cents 15:16:18:20 S SD: 16.0158 cents 16:17:19:21 SD: 13.3316 cents 17:18:20:23 SD: 9.6204 cents 18:19:21:24 SD: 3.4329 cents 42:44:49:56 SD: 3.3066 cents 57:60:67:76 SD: 1.8776 cents 75:79:88:100 SD: 1.2794 cents 81:85:95:108 SD: 1.2066 cents 99:104:116:132 SD: 0.4985 cents 117:123:137:156 SD: 0.4652 cents 174:183:204:232 SD: 0.3188 cents 273:287:320:364 SD: 0.1555 cents 291:306:341:388 SD: 0.0836 cents 390:410:457:520 SD: 0.0767 cents 564:593:661:752 SD: 0.0553 cents