Scala analysis: 375_D3
Diatonic tetrachord 160/149 * 149/138 * 23/20
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 160/149 123.311489 2: 80/69 256.084366 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 23/20 241.9606 1: 160/149 123.3115 2: 149/138 132.7729 3: 23/20 241.9606
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 160/149 123.311 cents 1: 1 149/138 132.773 cents 1: 1 23/20 241.961 cents 2: 1 80/69 256.084 cents 2: 1 184/149 365.272 cents 2: 1 149/120 374.734 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 : 123.3 256.1 498.0 123.3: 132.8 374.7 498.0 256.1: 242.0 365.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 123.3115 .. 241.9606 cents 3427/3200, 118.6491 cents 160/149, 123.3115 cents 2: 256.0844 .. 374.7335 cents 3427/3200, 118.6491 cents 1600/1587, 14.1237 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 160/149, 123.3115 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/20, 241.9606 cents Average / Smallest step : 1.346306 Largest / Average step : 1.457462 Largest / Smallest step : 1.962191 Median interval of one step : 149/138, 132.7729 cents, amount: 1 Least squares average step : 152.11537 cents, oct.: 456.34612 cents Scale is strictly proper Scale has trivalence property 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 14.12373 cents Scale diversity : 1.182507 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.523540 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 : 22201/22080, 9.4614 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% Limited inverse transpositions with margin 109.1878 cents: 2 -- Rational properties -- Prime limit : 149 Odd number limit : 149 (O: 149 U: 149) Highest odd numerator or denominator: 149 Scale harmonicity : 0.017808 Fundamental : 1/10281, -13.3277 octaves, 0.0254 Hz. Guide tone : 160, 7.3219 octaves, 41860.090 Hz. Exponens Consonantiae : 1.644960E+06, 20.64962 octaves Euler's gradus suavitatis : 182 Sum of Mann's harmonic distance : 232.5, average 77.50000 Mersenne's string divisions : 322287 Sum of van Prooijen's expressibility: 4.48916, average 1.49639 Sum of Tenney's harmonic distance : 9.19843, average 3.06614 Vogel's harmonic complexity : 122.66667 Wille's k value : 1713 Wilson's harmonic complexity : 180 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 19.19215, average 3.19869 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.66667 11 3: -1 .. 0 -0.66667 2 1 5: 0 .. 1 0.66667 2 23: -1 .. 0 -0.33333 1 1 149: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 19 30 51| Scale is weakly epimorphic with val: <7 10 15 30 51| Scale is weakly epimorphic with val: <7 10 16 31 52| Scale is weakly epimorphic with val: <7 10 17 32 53| Scale is weakly epimorphic with val: <7 10 18 33 51| Scale is weakly epimorphic with val: <7 10 19 32 51| Scale is weakly epimorphic with val: <7 10 19 34 52| Scale is weakly epimorphic with val: <7 10 19 35 51| Scale is weakly epimorphic with val: <7 11 15 30 52| Scale is weakly epimorphic with val: <7 11 15 31 51| Scale is weakly epimorphic with val: <7 11 15 33 52| Scale is weakly epimorphic with val: <7 11 15 34 51| Scale is weakly epimorphic with val: <7 11 15 36 52| Scale is weakly epimorphic with val: <7 11 16 31 53| Scale is weakly epimorphic with val: <7 11 16 32 52| Scale is weakly epimorphic with val: <7 11 16 34 53| Scale is weakly epimorphic with val: <7 11 16 35 52| Scale is weakly epimorphic with val: <7 11 17 30 53| Scale is JI-epimorphic with val: <7 11 17 32 51| Scale is weakly epimorphic with val: <7 11 17 33 53| Scale is weakly epimorphic with val: <7 11 17 35 51| Scale is weakly epimorphic with val: <7 11 17 36 53| Scale is weakly epimorphic with val: <7 11 18 30 52| Scale is weakly epimorphic with val: <7 11 18 31 51| Scale is JI-epimorphic with val: <7 11 18 33 52| Scale is weakly epimorphic with val: <7 11 18 34 51| Scale is weakly epimorphic with val: <7 11 18 36 52| Scale is weakly epimorphic with val: <7 11 19 31 53| Scale is weakly epimorphic with val: <7 11 19 32 52| Scale is JI-epimorphic with val: <7 11 19 34 53| Scale is weakly epimorphic with val: <7 11 19 35 52| Scale is weakly epimorphic with val: <7 12 17 30 51| Scale is weakly epimorphic with val: <7 12 18 31 52| Scale is weakly epimorphic with val: <7 12 19 31 51| Scale is weakly epimorphic with val: <7 12 19 32 53| Scale is weakly epimorphic with val: <7 12 19 34 51| Scale is weakly epimorphic with val: <8 11 15 32 52| Scale is weakly epimorphic with val: <8 11 15 33 51| Scale is weakly epimorphic with val: <8 11 15 35 52| Scale is weakly epimorphic with val: <8 11 16 30 53| Scale is weakly epimorphic with val: <8 11 16 33 53| Scale is weakly epimorphic with val: <8 11 16 34 52| Scale is weakly epimorphic with val: <8 11 16 36 53| Scale is weakly epimorphic with val: <8 11 17 35 53| Scale is weakly epimorphic with val: <8 11 18 36 51| Scale is weakly epimorphic with val: <8 12 15 30 52| Scale is weakly epimorphic with val: <8 12 15 32 53| Scale is weakly epimorphic with val: <8 12 15 33 52| Scale is weakly epimorphic with val: <8 12 15 36 52| Scale is weakly epimorphic with val: <8 12 16 31 53| Scale is weakly epimorphic with val: <8 12 16 33 51| Scale is weakly epimorphic with val: <8 12 16 34 53| Scale is weakly epimorphic with val: <8 12 17 34 52| Scale is weakly epimorphic with val: <8 12 18 35 53| Scale is weakly epimorphic with val: <8 12 19 36 51|
FIT/MODE
3: 1 1 1 SP B ME I SD: 50.3035 c. M:-75.9456 c. 4: 1 1 2 P M ME S SD: 4.1356 c. M: 7.0619 c. 21: 5 6 10 SP T3 SD: 3.8889 c. M:-4.7963 c. 23: 6 6 11 SP M DE S SD: 4.3936 c. M:-6.6133 c. 25: 6 7 12 SP T3 SD: 2.7506 c. M: 3.7807 c. 29: 7 8 14 SP T3 SD: 1.9914 c. M: 3.0937 c. 33: 8 9 16 SP T3 SD: 1.5118 c. M: 2.5733 c. 37: 9 10 18 SP T3 SD: 1.2648 c. M: 2.1654 c. 41: 10 11 20 SP T3 SD: 1.2043 c. M: 1.8371 c. 45: 11 12 22 SP T3 SD: 1.2637 c. M: 1.5672 c. 60: 15 16 29 SP T3 SD: 0.9957 c. M:-1.2389 c. 64: 16 17 31 SP T3 SD: 0.8079 c. M:-1.1998 c. 68: 17 18 33 SP T3 SD: 0.7090 c. M:-1.1998 c. 72: 18 19 35 SP T3 SD: 0.6977 c. M:-1.1998 c. 80: 20 21 39 SP T3 SD: 0.8444 c. M:-1.1998 c. 89: 22 24 43 SP T3 SD: 0.7777 c. M:-1.3322 c. 93: 23 25 45 SP T3 SD: 0.5664 c. M:-0.9711 c. 97: 24 26 47 SP T3 SD: 0.3726 c. M:-0.6399 c. 101: 25 27 49 SP T3 SD: 0.1943 c. M:-0.3348 c. 105: 26 28 51 SP T3 SD: 0.0317 c. M:-0.0531 c. 319: 79 85 155 SP T3 SD: 0.0267 c. M: 0.0362 c. 424: 105 113 206 SP T3 SD: 0.0166 c. M:-0.0251 c. 529: 131 141 257 SP T3 SD: 0.0132 c. M:-0.0229 c. 634: 157 169 308 SP T3 SD: 0.0132 c. M:-0.0214 c. 739: 183 197 359 SP T3 SD: 0.0144 c. M:-0.0204 c. 844: 209 225 410 SP T3 SD: 0.0159 c. M:-0.0196 c. 953: 236 254 463 SP T3 SD: 0.0143 c. M:-0.0239 c. 1163: 288 310 565 SP T3 SD: 0.0130 c. M:-0.0221 c. 1373: 340 366 667 SP T3 SD: 0.0138 c. M:-0.0208 c. 1692: 419 451 822 SP T3 SD: 0.0130 c. M:-0.0223 c. 1834: 454 489 891 SP T3 SD: 0.0129 c. M: 0.0223 c. 1939: 480 517 942 SP T3 SD: 0.0118 c. M: 0.0203 c. 1943: 481 518 944 SP T3 SD: 0.0127 c. M: 0.0178 c. 2044: 506 545 993 SP T3 SD: 0.0110 c. M: 0.0185 c. 2048: 507 546 995 SP T3 SD: 0.0108 c. M: 0.0162 c. 2149: 532 573 1044 SP T3 SD: 0.0105 c. M: 0.0170 c. 2153: 533 574 1046 SP T3 SD: 0.0093 c. M: 0.0147 c. 2258: 559 602 1097 SP T3 SD: 0.0080 c. M: 0.0134 c. 2363: 585 630 1148 SP T3 SD: 0.0070 c. M: 0.0122 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 x 9:11 SD: 37.2833 cents 9:10 x 12 S SD: 29.5461 cents 10:11:12:13 H SD: 28.2970 cents 11:12:13:15 SD: 19.3150 cents 12:13:14:16 S SD: 6.2294 cents 27:29:31:36 SD: 5.6395 cents 30:32:35:40 SD: 5.2752 cents 38:41:44:51 SD: 4.7368 cents 39:42:45:52 SD: 3.2400 cents 51:55:59:68 SD: 2.7793 cents 57:61:66:76 SD: 2.1067 cents 69:74:80:92 SD: 0.7323 cents 81:87:94:108 SD: 0.5505 cents 150:161:174:200 SD: 0.3914 cents 189:203:219:252 SD: 0.3686 cents 258:277:299:344 SD: 0.2700 cents 270:290:313:360 SD: 0.1558 cents 339:364:393:452 SD: 0.0767 cents 420:451:487:560 SD: 0.0522 cents