Scala analysis: 422_D9
Diatonic tetrachord 24/23 * 9/8 * 92/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 2: 27/23 277.590655 vicesimotertial minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 92/81 220.4543 1: 24/23 73.6807 vicesimotertial minor semitone 2: 9/8 203.9100 major whole tone 3: 92/81 220.4543
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 9/8 203.910 cents major whole tone 1: 1 92/81 220.454 cents 2: 1 27/23 277.591 cents vicesimotertial minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 23/18 424.364 cents vicesimotertial 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 : 73.7 277.6 498.0 73.7 : 203.9 424.4 498.0 277.6: 220.5 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 220.4543 cents 529/486, 146.7737 cents 24/23, 73.6807 cents 2: 277.5907 .. 424.3643 cents 529/486, 146.7737 cents 2187/2116, 57.1363 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 92/81, 220.4543 cents Average / Smallest step : 2.253169 Largest / Average step : 1.327918 Largest / Smallest step : 2.992025 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 151.64264 cents, oct.: 454.92792 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1656-tone equal temperament with octave 4/3 degrees: 245 923 1656 Least number of segments generator : 829 of 249.323 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 923 of 277.594 cents and inv. generated superset size: 43 = 40 more = 1433.333% 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 : 0.917423 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.410601 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 : 736/729, 16.5443 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 Limited inverse transpositions with margin 130.2293 cents: 1 -- Rational properties -- Prime limit : 23 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.017936 Average absolute harmonicity : 0.085063 Specific harmonicity : 0.074761 Fundamental : 1/69, -6.1085 octaves, 3.7917 Hz. Guide tone : 216, 7.7549 octaves, 56511.122 Hz. Exponens Consonantiae : 1.490400E+04, 13.86341 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 52.0, average 17.33333 Mersenne's string divisions : 16450 Sum of van Prooijen's expressibility: 3.27021, average 1.09007 Sum of Tenney's harmonic distance : 6.61421, average 2.20474 Vogel's harmonic complexity : 15.33333 Wille's k value : 40 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 19.35259, average 3.22543 Lattice compactness (without 2's) : 13.93566, average 2.32261 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.66667 5 3: -1 .. 3 1.00000 5 1 23: -1 .. 0 -0.66667 2 2 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 11 30| Scale is JI-epimorphic with val: <7 11 31| Scale is weakly epimorphic with val: <7 11 34| Scale is weakly epimorphic with val: <8 11 32|
FIT/MODE
3: 0 2 1 N G T3 SD: 52.8913 c. M: 73.6807 c. 4: 0 2 2 P M DE S SD: 45.6252 c. M: 73.6807 c. 5: 1 2 2 SP M ME S SD: 19.3499 c. M:-25.9283 c. 6: 1 2 3 P T3 SD: 17.3506 c. M: 28.5682 c. 7: 1 3 3 SP M DE S SD: 4.3011 c. M:-7.0065 c. 20: 3 8 9 SP T3 SD: 2.1979 c. M: 3.6659 c. 27: 4 11 12 SP T3 SD: 0.5225 c. M: 0.8990 c. 34: 5 14 15 SP T3 SD: 0.4910 c. M:-0.7286 c. 61: 9 25 27 SP T3 SD: 0.1148 c. M: 0.1986 c. 149: 22 61 66 SP T3 SD: 0.1226 c. M: 0.1562 c. 210: 31 86 93 SP T3 SD: 0.1115 c. M: 0.1597 c. 271: 40 111 120 SP T3 SD: 0.1082 c. M: 0.1685 c. 332: 49 136 147 SP T3 SD: 0.1074 c. M: 0.1740 c. 359: 53 147 159 SP T3 SD: 0.1153 c. M: 0.1531 c. 393: 58 161 174 SP T3 SD: 0.1073 c. M: 0.1778 c. 425: 63 174 188 SP T3 SD: 0.1184 c. M:-0.1472 c. 445: 66 182 197 SP T3 SD: 0.1090 c. M:-0.1867 c. 452: 67 185 200 SP T3 SD: 0.0955 c. M:-0.1446 c. 479: 71 196 212 SP T3 SD: 0.0834 c. M:-0.1423 c. 486: 72 199 215 SP T3 SD: 0.0942 c. M:-0.1258 c. 506: 75 207 224 SP T3 SD: 0.0822 c. M:-0.1402 c. 513: 76 210 227 SP T3 SD: 0.0729 c. M:-0.1038 c. 540: 80 221 239 SP T3 SD: 0.0614 c. M:-0.1038 c. 567: 84 232 251 SP T3 SD: 0.0611 c. M:-0.1038 c. 574: 85 235 254 SP T3 SD: 0.0559 c. M:-0.0717 c. 601: 89 246 266 SP T3 SD: 0.0440 c. M:-0.0731 c. 635: 94 260 281 SP T3 SD: 0.0434 c. M:-0.0596 c. 662: 98 271 293 SP T3 SD: 0.0302 c. M:-0.0481 c. 723: 107 296 320 SP T3 SD: 0.0193 c. M:-0.0273 c. 750: 111 307 332 SP T3 SD: 0.0190 c. M:-0.0300 c. 784: 116 321 347 SP T3 SD: 0.0121 c. M:-0.0186 c. 811: 120 332 359 SP T3 SD: 0.0101 c. M:-0.0128 c. 872: 129 357 386 SP T3 SD: 0.0062 c. M: 0.0105 c. 1656: 245 678 733 SP T3 SD: 0.0028 c. M:-0.0035 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 x 11:12 SD: 34.9086 cents 11:12:13:15 SD: 29.0037 cents 12:13:14:16 S SD: 21.9238 cents 15:16:18:20 S SD: 17.9372 cents 16:17:19:21 SD: 15.3418 cents 17:18:20:23 SD: 11.9803 cents 18:19:21:24 SD: 7.5411 cents 23:24:27:31 SD: 6.2387 cents 24:25:28:32 SD: 3.7113 cents 45:47:53:60 SD: 1.9705 cents 69:72:81:92 SD: 0.0000 cents