Scala analysis: 376_D3
Diatonic tetrachord 120/109 * 218/207 * 23/20
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 120/109 166.447525 2: 80/69 256.084366 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 23/20 241.9606 1: 120/109 166.4475 2: 218/207 89.6368 3: 23/20 241.9606
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 218/207 89.637 cents 1: 1 120/109 166.448 cents 1: 1 23/20 241.961 cents 2: 1 80/69 256.084 cents 2: 1 109/90 331.597 cents 2: 1 138/109 408.408 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 : 166.4 256.1 498.0 166.4: 89.6 331.6 498.0 256.1: 242.0 408.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.6368 .. 241.9606 cents 4761/4360, 152.3238 cents 218/207, 89.6368 cents 2: 256.0844 .. 408.4082 cents 4761/4360, 152.3238 cents 1600/1587, 14.1237 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 218/207, 89.6368 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/20, 241.9606 cents Average / Smallest step : 1.852084 Largest / Average step : 1.457462 Largest / Smallest step : 2.699344 Median interval of one step : 120/109, 166.4475 cents, amount: 1 Least squares average step : 155.19652 cents, oct.: 465.58955 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1517-tone equal temperament with octave 4/3 degrees: 507 780 1517 Least number of segments generator : 759 of 249.187 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1478 of 485.241 cents and inv. generated superset size: 21 = 18 more = 700.000% 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 14.12373 cents Scale diversity : 1.124392 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.388313 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 Best fifths form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 109 Odd number limit : 207 (O: 109 U: 207) Highest odd numerator or denominator: 109 Scale harmonicity : 0.017295 Fundamental : 1/7521, -12.8767 octaves, 0.0348 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 1.805040E+06, 20.78360 octaves Euler's gradus suavitatis : 143 Sum of Mann's harmonic distance : 192.5, average 64.16667 Mersenne's string divisions : 238847 Sum of van Prooijen's expressibility: 4.35340, average 1.45113 Sum of Tenney's harmonic distance : 8.93773, average 2.97924 Vogel's harmonic complexity : 96.33333 Wille's k value : 1253 Wilson's harmonic complexity : 143 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 17.26006, average 2.87668 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 1 -0.33333 3 1 5: 0 .. 1 0.66667 2 23: -1 .. 0 -0.33333 1 1 109: -1 .. 0 -0.33333 1 1 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 10 19 30 49| Scale is weakly epimorphic with val: <7 10 15 30 50| Scale is weakly epimorphic with val: <7 10 16 31 48| Scale is weakly epimorphic with val: <7 10 17 32 49| Scale is weakly epimorphic with val: <7 10 18 33 50| Scale is weakly epimorphic with val: <7 10 19 34 48| Scale is weakly epimorphic with val: <7 11 15 30 49| Scale is weakly epimorphic with val: <7 11 15 31 48| Scale is weakly epimorphic with val: <7 11 15 33 49| Scale is weakly epimorphic with val: <7 11 15 34 48| Scale is weakly epimorphic with val: <7 11 15 36 49| Scale is weakly epimorphic with val: <7 11 16 31 50| Scale is weakly epimorphic with val: <7 11 16 32 49| Scale is weakly epimorphic with val: <7 11 16 34 50| Scale is weakly epimorphic with val: <7 11 16 35 49| Scale is weakly epimorphic with val: <7 11 17 30 50| Scale is JI-epimorphic with val: <7 11 17 32 48| Scale is weakly epimorphic with val: <7 11 17 33 50| Scale is weakly epimorphic with val: <7 11 17 35 48| Scale is weakly epimorphic with val: <7 11 17 36 50| Scale is weakly epimorphic with val: <7 11 18 30 49| Scale is weakly epimorphic with val: <7 11 18 31 48| Scale is JI-epimorphic with val: <7 11 18 33 49| Scale is weakly epimorphic with val: <7 11 18 34 48| Scale is weakly epimorphic with val: <7 11 18 36 49| Scale is weakly epimorphic with val: <7 11 19 31 50| Scale is weakly epimorphic with val: <7 11 19 32 49| Scale is JI-epimorphic with val: <7 11 19 34 50| Scale is weakly epimorphic with val: <7 11 19 35 49| Scale is weakly epimorphic with val: <7 12 17 30 49| Scale is weakly epimorphic with val: <7 12 18 30 48| Scale is weakly epimorphic with val: <7 12 18 31 50| Scale is weakly epimorphic with val: <7 12 18 33 48| Scale is weakly epimorphic with val: <7 12 18 36 48| Scale is weakly epimorphic with val: <7 12 19 31 49| Scale is weakly epimorphic with val: <7 12 19 32 48| Scale is weakly epimorphic with val: <7 12 19 34 49| Scale is weakly epimorphic with val: <8 11 15 33 49| Scale is weakly epimorphic with val: <8 11 16 30 48| Scale is weakly epimorphic with val: <8 11 16 33 48| Scale is weakly epimorphic with val: <8 11 16 34 50| Scale is weakly epimorphic with val: <8 11 16 36 48| Scale is weakly epimorphic with val: <8 11 17 31 49| Scale is weakly epimorphic with val: <8 11 17 34 49| Scale is weakly epimorphic with val: <8 11 17 35 48| Scale is weakly epimorphic with val: <8 11 18 32 50| Scale is weakly epimorphic with val: <8 11 18 35 50| Scale is weakly epimorphic with val: <8 11 18 36 49| Scale is weakly epimorphic with val: <8 12 15 30 48| Scale is weakly epimorphic with val: <8 12 15 32 49| Scale is weakly epimorphic with val: <8 12 15 33 48| Scale is weakly epimorphic with val: <8 12 15 36 48| Scale is weakly epimorphic with val: <8 12 16 31 49| Scale is weakly epimorphic with val: <8 12 16 33 50| Scale is weakly epimorphic with val: <8 12 16 34 49| Scale is weakly epimorphic with val: <8 12 17 32 50| Scale is weakly epimorphic with val: <8 12 17 34 48| Scale is weakly epimorphic with val: <8 12 17 35 50| Scale is weakly epimorphic with val: <8 12 18 35 49| Scale is weakly epimorphic with val: <8 12 19 36 50|
FIT/MODE
3: 1 1 1 SP B ME I SD: 43.8479 c. M:-75.9456 c. 4: 1 1 2 P M ME S SD: 24.5528 c. M: 41.9363 c. 6: 2 1 3 P T3 SD: 4.0848 c. M: 7.0619 c. 21: 7 4 10 SP T3 SD: 2.7804 c. M:-4.7963 c. 27: 9 5 13 SP T3 SD: 1.2725 c. M:-2.1612 c. 33: 11 6 16 SP T3 SD: 0.3749 c. M:-0.4843 c. 72: 24 13 35 SP T3 SD: 0.2633 c. M: 0.4325 c. 105: 35 19 51 SP T3 SD: 0.2516 c. M: 0.4325 c. 177: 59 32 86 SP T3 SD: 0.2502 c. M: 0.4325 c. 183: 61 33 89 SP T3 SD: 0.2908 c. M: 0.4325 c. 200: 67 36 97 SP T3 SD: 0.3292 c. M:-0.4088 c. 204: 68 37 99 SP T3 SD: 0.2921 c. M: 0.4325 c. 206: 69 37 100 SP T3 SD: 0.2422 c. M:-0.3734 c. 212: 71 38 103 SP T3 SD: 0.2026 c. M:-0.3506 c. 218: 73 39 106 SP T3 SD: 0.2247 c. M:-0.3290 c. 239: 80 43 116 SP T3 SD: 0.2020 c. M:-0.2621 c. 245: 82 44 119 SP T3 SD: 0.1448 c. M:-0.2451 c. 251: 84 45 122 SP T3 SD: 0.1484 c. M:-0.2289 c. 278: 93 50 135 SP T3 SD: 0.1125 c. M:-0.1647 c. 284: 95 51 138 SP T3 SD: 0.0919 c. M:-0.1520 c. 311: 104 56 151 SP T3 SD: 0.1019 c. M:-0.1446 c. 317: 106 57 154 SP T3 SD: 0.0529 c. M:-0.0912 c. 350: 117 63 170 SP T3 SD: 0.0390 c. M:-0.0531 c. 389: 130 70 189 SP T3 SD: 0.0121 c. M: 0.0201 c. 739: 247 133 359 SP T3 SD: 0.0128 c. M:-0.0168 c. 1128: 377 203 548 SP T3 SD: 0.0054 c. M:-0.0090 c. 1517: 507 273 737 SP T3 SD: 0.0035 c. M:-0.0052 c. 1939: 648 349 942 SP T3 SD: 0.0027 c. M: 0.0044 c. 2328: 778 419 1131 SP T3 SD: 0.0029 c. M: 0.0047 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: 51.6762 cents 6 x 7:8 S SD: 5.3933 cents 7 x 8:9 S SD: 33.8548 cents 8:9 x 11 SD: 32.5632 cents 9:10 x 12 S SD: 7.9781 cents 15 x 17:20 SD: 19.6988 cents 17:19:20:23 SD: 14.7546 cents 18:20:21:24 S SD: 6.4200 cents 30:33:35:40 SD: 3.6276 cents 39:43:45:52 SD: 2.9118 cents 51:56:59:68 SD: 1.9764 cents 69:76:80:92 SD: 0.2787 cents 258:284:299:344 SD: 0.2625 cents 288:317:334:384 SD: 0.1904 cents 357:393:414:476 SD: 0.1278 cents 426:469:494:568 SD: 0.1022 cents 495:545:574:660 SD: 0.1000 cents