Scala analysis: 380_D3
Diatonic tetrachord 24/23 * 23/20 * 10/9, Schlesinger
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: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 24/23 73.6807 vicesimotertial minor semitone 2: 23/20 241.9606 3: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 10/9 182.404 cents minor whole tone 1: 1 23/20 241.961 cents 2: 1 80/69 256.084 cents 2: 1 6/5 315.641 cents 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 : 73.7 315.6 498.0 73.7 : 242.0 424.4 498.0 315.6: 182.4 256.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 241.9606 cents 529/480, 168.2800 cents 24/23, 73.6807 cents 2: 256.0844 .. 424.3643 cents 529/480, 168.2800 cents 1600/1587, 14.1237 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 : 23/20, 241.9606 cents Average / Smallest step : 2.253169 Largest / Average step : 1.457462 Largest / Smallest step : 3.283910 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 157.07844 cents, oct.: 471.23533 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 14.12373 cents Scale diversity : 0.988455 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.324238 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 : 1600/1587, 14.1237 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 23 Odd number limit : 69 (O: 23 U: 69) Highest odd numerator or denominator: 23 Scale harmonicity : 0.017599 Average absolute harmonicity : 0.111521 Specific harmonicity : 0.091886 Fundamental : 1/345, -8.4305 octaves, 0.7583 Hz. Guide tone : 24, 4.5850 octaves, 6279.014 Hz. Exponens Consonantiae : 8.280000E+03, 13.01542 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 32.5, average 10.83333 Mersenne's string divisions : 3619 Sum of van Prooijen's expressibility: 2.53782, average 0.84594 Sum of Tenney's harmonic distance : 5.29824, average 1.76608 Vogel's harmonic complexity : 24.66667 Wille's k value : 103 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 14.63321, average 2.43887 Lattice compactness (without 2's) : 9.71478, average 1.61913 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 .. 1 0.33333 3 1 5: -1 .. 0 -0.33333 1 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is JI-epimorphic with val: <7 11 16 31| Scale is weakly epimorphic with val: <7 11 16 34| Scale is weakly epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 17 33| = patent Scale is weakly epimorphic with val: <7 11 17 36| Scale is weakly epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 11 19 34| Scale is weakly epimorphic with val: <7 12 15 30| Scale is weakly epimorphic with val: <7 12 16 32| Scale is weakly epimorphic with val: <7 12 16 35| Scale is weakly epimorphic with val: <7 12 18 30| Scale is weakly epimorphic with val: <8 11 15 32| Scale is weakly epimorphic with val: <8 11 16 31| Scale is weakly epimorphic with val: <8 11 16 34| Scale is weakly epimorphic with val: <8 11 18 32| Scale is weakly epimorphic with val: <8 12 15 33| Scale is weakly epimorphic with val: <8 12 17 31| Scale is weakly epimorphic with val: <8 12 17 34| Scale is weakly epimorphic with val: <8 12 18 33|
FIT/MODE
3: 0 2 1 N G T3 SD: 43.5792 c. M: 73.6807 c. 5: 1 2 2 SP M ME S SD: 17.8419 c. M:-25.9283 c. 6: 1 3 2 P T3 SD: 10.8870 c. M:-16.3887 c. 8: 1 4 3 P T3 SD: 7.0609 c. M: 11.4250 c. 13: 2 6 5 SP T3 SD: 5.5502 c. M: 9.1521 c. 14: 2 7 5 P T3 SD: 2.9963 c. M:-4.5305 c. 19: 3 9 7 SP T3 SD: 2.9305 c. M:-4.9580 c. 27: 4 13 10 SP T3 SD: 1.1894 c. M: 2.0574 c. 33: 5 16 12 SP T3 SD: 1.2717 c. M:-1.7807 c. 41: 6 20 15 SP T3 SD: 0.4728 c. M: 0.7960 c. 68: 10 33 25 SP T3 SD: 0.4775 c. M: 0.7011 c. 74: 11 36 27 SP T3 SD: 0.4447 c. M:-0.6846 c. 101: 15 49 37 SP T3 SD: 0.1677 c. M:-0.2864 c. 142: 21 69 52 SP T3 SD: 0.0194 c. M: 0.0261 c. 527: 78 256 193 SP T3 SD: 0.0200 c. M:-0.0338 c. 669: 99 325 245 SP T3 SD: 0.0136 c. M:-0.0211 c. 811: 120 394 297 SP T3 SD: 0.0103 c. M:-0.0128 c. 953: 141 463 349 SP T3 SD: 0.0089 c. M:-0.0137 c. 1095: 162 532 401 SP T3 SD: 0.0086 c. M:-0.0146 c. 1764: 261 857 646 SP T3 SD: 0.0094 c. M:-0.0131 c. 1832: 271 890 671 SP T3 SD: 0.0087 c. M: 0.0134 c. 1974: 292 959 723 SP T3 SD: 0.0079 c. M: 0.0109 c. 2116: 313 1028 775 SP T3 SD: 0.0075 c. M: 0.0095 c. 2217: 328 1077 812 SP T3 SD: 0.0065 c. M: 0.0106 c. 2359: 349 1146 864 SP T3 SD: 0.0052 c. M: 0.0087 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: 70.6724 cents 5 x 6:7 S SD: 42.2336 cents 6 x 7:8 S SD: 24.3852 cents 7 x 8:9 S SD: 52.6754 cents 8 x 10:11 S SD: 44.2510 cents 9:10:11:12 H SD: 37.7563 cents 10:11:12:13 H SD: 33.7658 cents 11:12:13:15 SD: 30.0640 cents 12:13:14:16 S SD: 27.0586 cents 13:14:16:17 S SD: 25.8937 cents 14:15:17:19 SD: 19.5871 cents 15:16:18:20 S SD: 12.6835 cents 18:19:22:24 SD: 12.4990 cents 19:20:23:25 SD: 10.4512 cents 20:21:24:27 S SD: 8.0199 cents 21:22:25:28 SD: 5.1349 cents 24:25:29:32 SD: 4.1176 cents 44:46:53:59 SD: 4.0795 cents 45:47:54:60 SD: 0.5341 cents 210:219:252:280 SD: 0.3436 cents 255:266:306:340 SD: 0.1886 cents 300:313:360:400 SD: 0.0802 cents 345:360:414:460 SD: 0.0000 cents