Scala analysis: 421_D9
Diatonic tetrachord 81/73 * 73/69 * 92/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/73 180.030533 2: 27/23 277.590655 vicesimotertial minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 92/81 220.4543 1: 81/73 180.0305 2: 73/69 97.5601 3: 92/81 220.4543
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 73/69 97.560 cents 1: 1 81/73 180.031 cents 1: 1 92/81 220.454 cents 2: 1 27/23 277.591 cents vicesimotertial minor third 2: 1 292/243 318.014 cents 2: 1 92/73 400.485 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 : 180.0 277.6 498.0 180.0: 97.6 318.0 498.0 277.6: 220.5 400.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.5601 .. 220.4543 cents 2116/1971, 122.8942 cents 73/69, 97.5601 cents 2: 277.5907 .. 400.4849 cents 2116/1971, 122.8942 cents 2187/2116, 57.1363 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 73/69, 97.5601 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 92/81, 220.4543 cents Average / Smallest step : 1.701669 Largest / Average step : 1.327918 Largest / Smallest step : 2.259677 Median interval of one step : 81/73, 180.0305 cents, amount: 1 Least squares average step : 159.23906 cents, oct.: 477.71718 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 924-tone equal temperament with octave 4/3 degrees: 334 515 924 Least number of segments generator : 463 of 249.562 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 515 of 277.590 cents and inv. generated superset size: 48 = 45 more = 1600.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 57.13631 cents Scale diversity : 1.188686 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.506494 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 : 6716/6561, 40.4238 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 73 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.017415 Fundamental : 1/5037, -12.2983 octaves, 0.0519 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 1.631988E+06, 20.63820 octaves Euler's gradus suavitatis : 107 Sum of Mann's harmonic distance : 105.5, average 35.16667 Mersenne's string divisions : 3850 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.64408, average 2.54803 Vogel's harmonic complexity : 73.66667 Wille's k value : 2956 Wilson's harmonic complexity : 111 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 20.78030, average 3.46338 Lattice compactness (without 2's) : 18.69960, average 3.11660 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 4 2.00000 8 1 23: -1 .. 0 -0.33333 1 1 73: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 4 / 3 = 1.33333 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 11 30 45| Scale is weakly epimorphic with val: <7 11 31 46| Scale is weakly epimorphic with val: <7 11 32 45| Scale is weakly epimorphic with val: <7 11 34 46| Scale is weakly epimorphic with val: <7 11 35 45| Scale is weakly epimorphic with val: <7 12 32 45| Scale is weakly epimorphic with val: <7 12 33 44| Scale is weakly epimorphic with val: <7 12 35 45| Scale is weakly epimorphic with val: <8 11 30 46| Scale is weakly epimorphic with val: <8 12 31 45| Scale is weakly epimorphic with val: <8 12 33 46| Scale is weakly epimorphic with val: <8 12 34 45|
FIT/MODE
3: 1 1 1 SP B ME I SD: 32.4555 c. M:-54.4393 c. 4: 1 1 2 P M ME S SD: 36.0487 c. M: 55.5193 c. 5: 2 1 2 SP M ME I SD: 16.5241 c. M:-21.2363 c. 9: 3 2 4 SP T3 SD: 8.1085 c. M: 14.0155 c. 11: 4 2 5 SP T3 SD: 3.4795 c. M: 5.9297 c. 16: 6 3 7 SP T3 SD: 4.1605 c. M:-6.7363 c. 20: 7 4 9 SP T3 SD: 3.9199 c. M: 5.7148 c. 25: 9 5 11 SP T3 SD: 0.8693 c. M:-1.3145 c. 36: 13 7 16 SP T3 SD: 0.5294 c. M: 0.8990 c. 61: 22 12 27 SP T3 SD: 0.2355 c. M: 0.4077 c. 97: 35 19 43 SP T3 SD: 0.2662 c. M: 0.3285 c. 158: 57 31 70 SP T3 SD: 0.2354 c. M: 0.3561 c. 174: 63 34 77 SP T3 SD: 0.1739 c. M:-0.2961 c. 199: 72 39 88 SP T3 SD: 0.1563 c. M:-0.2133 c. 210: 76 41 93 SP T3 SD: 0.1387 c. M:-0.2143 c. 235: 85 46 104 SP T3 SD: 0.0700 c. M:-0.1134 c. 271: 98 53 120 SP T3 SD: 0.0640 c. M: 0.0822 c. 296: 107 58 131 SP T3 SD: 0.0209 c. M:-0.0358 c. 628: 227 123 278 SP T3 SD: 0.0106 c. M: 0.0178 c. 924: 334 181 409 SP T3 SD: 0.0008 c. M: 0.0013 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: 108.7231 cents 5 x 6:7 S SD: 46.3210 cents 6 x 7:8 S SD: 5.3599 cents 7 x 8:9 S SD: 39.1107 cents 8:9 x 11 SD: 29.1900 cents 9:10:11:12 H SD: 23.2859 cents 10:11:12:13 H SD: 19.9856 cents 11:12:13:15 SD: 16.7087 cents 12:13:14:16 S SD: 14.2738 cents 14 x 16:19 SD: 27.8093 cents 15:17:18:20 SD: 17.6116 cents 16:18:19:21 SD: 13.7859 cents 17:19:20:23 SD: 9.4862 cents 18:20:21:24 S SD: 3.6598 cents 45:50:53:60 SD: 2.0551 cents 63:70:74:84 SD: 0.8607 cents 120:133:141:160 SD: 0.8439 cents 138:153:162:184 SD: 0.4648 cents 201:223:236:268 SD: 0.1278 cents 420:466:493:560 SD: 0.0612 cents