Scala analysis: 420_D9
Diatonic tetrachord 81/77 * 77/69 * 92/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/77 87.676155 2: 27/23 277.590655 vicesimotertial minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 92/81 220.4543 1: 81/77 87.6762 2: 77/69 189.9145 3: 92/81 220.4543
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/77 87.676 cents 1: 1 77/69 189.915 cents 1: 1 92/81 220.454 cents 2: 1 27/23 277.591 cents vicesimotertial minor third 2: 1 92/77 308.130 cents 2: 1 308/243 410.369 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 : 87.7 277.6 498.0 87.7 : 189.9 410.4 498.0 277.6: 220.5 308.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 87.6762 .. 220.4543 cents 7084/6561, 132.7782 cents 81/77, 87.6762 cents 2: 277.5907 .. 410.3688 cents 7084/6561, 132.7782 cents 2187/2116, 57.1363 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 81/77, 87.6762 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 92/81, 220.4543 cents Average / Smallest step : 1.893502 Largest / Average step : 1.327918 Largest / Smallest step : 2.514416 Median interval of one step : 77/69, 189.9145 cents, amount: 1 Least squares average step : 152.64232 cents, oct.: 457.92696 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1778-tone equal temperament with octave 4/3 degrees: 313 991 1778 Least number of segments generator : 891 of 249.583 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1503 of 421.013 cents and inv. generated superset size: 28 = 25 more = 933.333% 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 57.13631 cents Scale diversity : 1.086342 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.466802 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 : 2116/2079, 30.5398 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 23 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.011643 Average absolute harmonicity : 0.086601 Specific harmonicity : 0.060226 Fundamental : 1/5313, -12.3753 octaves, 0.0492 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 1.721412E+06, 20.71516 octaves Euler's gradus suavitatis : 51 Sum of Mann's harmonic distance : 107.5, average 35.83333 Mersenne's string divisions : 27650 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.66725, average 2.55575 Vogel's harmonic complexity : 37.00000 Wille's k value : 3118 Wilson's harmonic complexity : 56 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 21.79133, average 3.63189 Lattice compactness (without 2's) : 19.72418, average 3.28736 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 4 2.00000 8 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 11 / 3 = 3.66667 Scale is weakly epimorphic with val: <6 11 18 23 31| Scale is weakly epimorphic with val: <6 11 18 23 34| Scale is weakly epimorphic with val: <6 11 18 24 30| Scale is weakly epimorphic with val: <6 11 18 27 30| Scale is weakly epimorphic with val: <6 11 19 23 30| Scale is weakly epimorphic with val: <6 11 19 26 30| Scale is weakly epimorphic with val: <6 11 20 25 30| Scale is weakly epimorphic with val: <6 11 21 24 30| Scale is weakly epimorphic with val: <6 11 21 27 30| Scale is weakly epimorphic with val: <6 11 22 23 30| Scale is weakly epimorphic with val: <6 11 22 26 30| Scale is weakly epimorphic with val: <7 11 18 24 32| Scale is weakly epimorphic with val: <7 11 18 24 35| Scale is JI-epimorphic with val: <7 11 18 25 31| Scale is weakly epimorphic with val: <7 11 18 25 34| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 27 35| Scale is weakly epimorphic with val: <7 11 19 23 32| Scale is weakly epimorphic with val: <7 11 19 23 35| Scale is JI-epimorphic with val: <7 11 19 24 31| Scale is weakly epimorphic with val: <7 11 19 24 34| Scale is weakly epimorphic with val: <7 11 19 26 32| Scale is weakly epimorphic with val: <7 11 19 26 35| Scale is weakly epimorphic with val: <7 11 19 27 31| Scale is weakly epimorphic with val: <7 11 19 27 34| Scale is JI-epimorphic with val: <7 11 20 23 31| Scale is weakly epimorphic with val: <7 11 20 23 34| Scale is weakly epimorphic with val: <7 11 20 25 32| Scale is weakly epimorphic with val: <7 11 20 25 35| Scale is weakly epimorphic with val: <7 11 20 26 31| Scale is weakly epimorphic with val: <7 11 20 26 34| Scale is weakly epimorphic with val: <7 11 21 24 32| Scale is weakly epimorphic with val: <7 11 21 24 35| Scale is weakly epimorphic with val: <7 11 21 25 31| Scale is weakly epimorphic with val: <7 11 21 25 34| Scale is weakly epimorphic with val: <7 11 21 27 32| Scale is weakly epimorphic with val: <7 11 21 27 35| Scale is weakly epimorphic with val: <7 11 22 23 32| Scale is weakly epimorphic with val: <7 11 22 23 35| Scale is weakly epimorphic with val: <7 11 22 24 31| Scale is weakly epimorphic with val: <7 11 22 24 34| Scale is weakly epimorphic with val: <7 11 22 26 32| Scale is weakly epimorphic with val: <7 11 22 26 35| Scale is weakly epimorphic with val: <7 11 22 27 31| Scale is weakly epimorphic with val: <7 11 22 27 34| Scale is weakly epimorphic with val: <7 12 18 23 33| Scale is weakly epimorphic with val: <7 12 18 26 33| Scale is weakly epimorphic with val: <7 12 18 27 32| Scale is weakly epimorphic with val: <7 12 18 27 35| Scale is weakly epimorphic with val: <7 12 19 25 33| Scale is weakly epimorphic with val: <7 12 19 26 32| Scale is weakly epimorphic with val: <7 12 19 26 35| Scale is weakly epimorphic with val: <7 12 20 24 33| Scale is weakly epimorphic with val: <7 12 20 25 32| Scale is weakly epimorphic with val: <7 12 20 25 35| Scale is weakly epimorphic with val: <7 12 20 27 33| Scale is weakly epimorphic with val: <7 12 21 23 33| Scale is weakly epimorphic with val: <7 12 21 24 32| Scale is weakly epimorphic with val: <7 12 21 24 35| Scale is weakly epimorphic with val: <7 12 21 26 33| Scale is weakly epimorphic with val: <7 12 22 23 32| Scale is weakly epimorphic with val: <7 12 22 23 35| Scale is weakly epimorphic with val: <7 12 22 25 33| Scale is weakly epimorphic with val: <8 11 18 23 32| Scale is weakly epimorphic with val: <8 11 18 23 35| Scale is weakly epimorphic with val: <8 11 18 25 30| Scale is weakly epimorphic with val: <8 11 19 24 30| Scale is weakly epimorphic with val: <8 11 19 27 30| Scale is weakly epimorphic with val: <8 11 20 23 30| Scale is weakly epimorphic with val: <8 11 20 26 30| Scale is weakly epimorphic with val: <8 11 21 25 30| Scale is weakly epimorphic with val: <8 11 22 24 30| Scale is weakly epimorphic with val: <8 11 22 27 30| Scale is weakly epimorphic with val: <8 12 18 25 33| Scale is weakly epimorphic with val: <8 12 18 27 31| Scale is weakly epimorphic with val: <8 12 18 27 34| Scale is weakly epimorphic with val: <8 12 19 24 33| Scale is weakly epimorphic with val: <8 12 19 26 31| Scale is weakly epimorphic with val: <8 12 19 26 34| Scale is weakly epimorphic with val: <8 12 19 27 33| Scale is weakly epimorphic with val: <8 12 20 23 33| Scale is weakly epimorphic with val: <8 12 20 25 31| Scale is weakly epimorphic with val: <8 12 20 25 34| Scale is weakly epimorphic with val: <8 12 20 26 33| Scale is weakly epimorphic with val: <8 12 21 24 31| Scale is weakly epimorphic with val: <8 12 21 24 34| Scale is weakly epimorphic with val: <8 12 21 25 33| Scale is weakly epimorphic with val: <8 12 22 23 31| Scale is weakly epimorphic with val: <8 12 22 23 34| Scale is weakly epimorphic with val: <8 12 22 24 33| Scale is weakly epimorphic with val: <8 12 22 27 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 81.9273 c. M: 111.5757 c. 4: 1 1 2 P M ME S SD: 26.9132 c. M:-36.8351 c. 5: 1 2 2 SP M ME S SD: 14.0638 c. M:-21.2363 c. 7: 1 3 3 SP M DE S SD: 10.3639 c. M: 16.5269 c. 11: 2 4 5 SP T3 SD: 3.8053 c. M: 5.9297 c. 16: 3 6 7 SP T3 SD: 3.6113 c. M:-5.7073 c. 18: 3 7 8 SP T3 SD: 2.7450 c. M: 4.6687 c. 23: 4 9 10 SP T3 SD: 2.3406 c. M:-3.9130 c. 29: 5 11 13 SP T3 SD: 1.9273 c. M: 2.8072 c. 34: 6 13 15 SP T3 SD: 0.4385 c. M:-0.7286 c. 79: 14 30 35 SP T3 SD: 0.3567 c. M:-0.5850 c. 97: 17 37 43 SP T3 SD: 0.2944 c. M: 0.3899 c. 113: 20 43 50 SP T3 SD: 0.2772 c. M:-0.4734 c. 131: 23 50 58 SP T3 SD: 0.1382 c. M: 0.2331 c. 165: 29 63 73 SP T3 SD: 0.1022 c. M: 0.1410 c. 210: 37 80 93 SP T3 SD: 0.0760 c. M: 0.1084 c. 244: 43 93 108 SP T3 SD: 0.0545 c. M:-0.0941 c. 341: 60 130 151 SP T3 SD: 0.0565 c. M: 0.0876 c. 375: 66 143 166 SP T3 SD: 0.0141 c. M: 0.0202 c. 784: 138 299 347 SP T3 SD: 0.0122 c. M:-0.0186 c. 994: 175 379 440 SP T3 SD: 0.0066 c. M: 0.0082 c. 1369: 241 522 606 SP T3 SD: 0.0056 c. M: 0.0097 c. 1403: 247 535 621 SP T3 SD: 0.0056 c. M:-0.0082 c. 1778: 313 678 787 SP T3 SD: 0.0021 c. M:-0.0036 c. 2153: 379 821 953 SP T3 SD: 0.0021 c. M: 0.0036 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 x 9:11 SD: 45.4611 cents 9:10:11:12 H SD: 39.2255 cents 10:11:12:13 H SD: 32.2295 cents 11:12:13:15 SD: 24.9727 cents 12:13:14:16 S SD: 17.3377 cents 15:16:18:20 S SD: 15.0056 cents 16:17:19:21 SD: 12.6439 cents 17:18:20:23 SD: 9.3105 cents 18:19:21:24 SD: 4.0830 cents 39:41:46:52 SD: 2.7580 cents 57:60:67:76 SD: 0.8380 cents 75:79:88:100 SD: 0.8112 cents 132:139:155:176 SD: 0.6151 cents 156:164:183:208 SD: 0.5501 cents 195:205:229:260 SD: 0.4262 cents 213:224:250:284 SD: 0.1951 cents 270:284:317:360 SD: 0.0951 cents 558:587:655:744 SD: 0.0404 cents