Scala analysis: 364_D1
Diatonic tetrachord 256/243 * 351/320 * 15/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 52/45 250.303946 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 256/243 90.2250 limma, Pythagorean minor second 2: 351/320 160.0790 3: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 351/320 160.079 cents 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 1280/1053 337.966 cents 2: 1 81/64 407.820 cents Pythagorean 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 : 90.2 250.3 498.0 90.2 : 160.1 407.8 498.0 250.3: 247.7 338.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 247.7411 cents 3645/3328, 157.5161 cents 256/243, 90.2250 cents 2: 250.3039 .. 407.8200 cents 3645/3328, 157.5161 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 1.840011 Largest / Average step : 1.492281 Largest / Smallest step : 2.745814 Median interval of one step : 351/320, 160.0790 cents, amount: 1 Least squares average step : 148.92628 cents, oct.: 446.77883 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2324-tone equal temperament with octave 4/3 degrees: 421 1168 2324 Least number of segments generator : 1163 of 249.237 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1307 of 280.097 cents and inv. generated superset size: 84 = 81 more = 2800.000% 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 2.56289 cents Scale diversity : 1.104417 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.367463 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 : 676/675, 2.5629 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% -- Rational properties -- Prime limit : 13 Odd number limit : 1053 (O: 351 U: 1053) Highest odd numerator or denominator: 243 Scale harmonicity : 0.020045 Average absolute harmonicity : 0.096341 Specific harmonicity : 0.105036 Fundamental : 1/1215, -10.2467 octaves, 0.2153 Hz. Guide tone : 3328, 11.7004 octaves, 870689.881 Hz. Exponens Consonantiae : 4.043520E+06, 21.94718 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 301.5, average 100.50000 Mersenne's string divisions : 338821 Sum of van Prooijen's expressibility: 4.51594, average 1.50531 Sum of Tenney's harmonic distance : 9.24224, average 3.08075 Vogel's harmonic complexity : 18.66667 Wille's k value : 202 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 30.63113, average 5.10519 Lattice compactness (without 2's) : 17.49817, average 2.91636 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 4.00000 12 3: -5 ..-1 -2.66667 8 2 5: -1 .. 0 -0.33333 1 13: 0 .. 1 0.33333 1 1 Average exponent except 2's :-8 / 3 =-2.66667 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 10 15 26| Scale is weakly epimorphic with val: <6 10 16 27| Scale is weakly epimorphic with val: <6 10 17 28| Scale is weakly epimorphic with val: <6 10 18 29| Scale is weakly epimorphic with val: <6 10 19 30| Scale is weakly epimorphic with val: <6 11 15 28| Scale is weakly epimorphic with val: <6 11 16 29| Scale is weakly epimorphic with val: <6 11 17 30| Scale is JI-epimorphic with val: <7 11 15 25| Scale is weakly epimorphic with val: <7 11 15 28| Scale is JI-epimorphic with val: <7 11 16 26| Scale is weakly epimorphic with val: <7 11 16 29| Scale is JI-epimorphic with val: <7 11 17 27| = patent Scale is weakly epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 18 25| Scale is JI-epimorphic with val: <7 11 18 28| Scale is weakly epimorphic with val: <7 11 19 26| Scale is JI-epimorphic with val: <7 11 19 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 71.2862 c. M: 90.2250 c. 4: 1 1 2 P M ME S SD: 19.8090 c. M:-34.2863 c. 6: 1 2 3 P T3 SD: 4.2322 c. M: 7.2175 c. 16: 3 5 8 P T3 SD: 1.9679 c. M:-3.1584 c. 22: 4 7 11 P T3 SD: 0.7638 c. M: 1.2814 c. 50: 9 16 25 P T3 SD: 0.8114 c. M: 1.2814 c. 72: 13 23 36 P T3 SD: 0.7599 c. M: 1.2814 c. 94: 17 30 47 P T3 SD: 0.7451 c. M: 1.2814 c. 99: 18 32 49 SP T3 SD: 0.7372 c. M:-1.2339 c. 105: 19 34 52 SP T3 SD: 0.6322 c. M:-1.0902 c. 111: 20 36 55 SP T3 SD: 0.6226 c. M:-0.9620 c. 115: 21 37 57 SP T3 SD: 0.6591 c. M:-0.8840 c. 117: 21 38 58 SP T3 SD: 0.6856 c. M:-0.8470 c. 121: 22 39 60 SP T3 SD: 0.4869 c. M:-0.7766 c. 127: 23 41 63 SP T3 SD: 0.3926 c. M:-0.6794 c. 133: 24 43 66 SP T3 SD: 0.3972 c. M:-0.5909 c. 143: 26 46 71 SP T3 SD: 0.3264 c. M:-0.4600 c. 149: 27 48 74 SP T3 SD: 0.2255 c. M:-0.3898 c. 155: 28 50 77 SP T3 SD: 0.2388 c. M:-0.3252 c. 165: 30 53 82 SP T3 SD: 0.2309 c. M:-0.3286 c. 171: 31 55 85 SP T3 SD: 0.1075 c. M:-0.1748 c. 193: 35 62 96 SP T3 SD: 0.0545 c. M:-0.0940 c. 364: 66 117 181 SP T3 SD: 0.0681 c. M:-0.0868 c. 370: 67 119 184 SP T3 SD: 0.0434 c. M:-0.0646 c. 392: 71 126 195 SP T3 SD: 0.0121 c. M: 0.0179 c. 585: 106 188 291 SP T3 SD: 0.0113 c. M:-0.0191 c. 977: 177 314 486 SP T3 SD: 0.0047 c. M: 0.0070 c. 1369: 248 440 681 SP T3 SD: 0.0049 c. M: 0.0081 c. 1932: 350 621 961 SP T3 SD: 0.0043 c. M:-0.0075 c. 2324: 421 747 1156 SP T3 SD: 0.0029 c. M:-0.0044 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: 53.3940 cents 6 x 7:8 S SD: 8.2835 cents 7 x 8:9 S SD: 32.9015 cents 8 x 9:11 SD: 35.3214 cents 9 x 10:12 S SD: 33.9501 cents 11:12:13:15 SD: 27.2375 cents 12:13:14:16 S SD: 17.0358 cents 13:14:15:17 SD: 16.9518 cents 14:15:16:19 SD: 15.4868 cents 15:16:17:20 SD: 13.3026 cents 18:19:21:24 SD: 5.6359 cents 33:35:38:44 SD: 4.3754 cents 38:40:44:51 SD: 3.9883 cents 39:41:45:52 SD: 1.4853 cents 57:60:66:76 SD: 1.2599 cents 90:95:104:120 SD: 1.1260 cents 96:101:111:128 SD: 0.8494 cents 129:136:149:172 SD: 0.4923 cents 168:177:194:224 SD: 0.3985 cents 186:196:215:248 SD: 0.2306 cents 225:237:260:300 SD: 0.0902 cents 411:433:475:548 SD: 0.0827 cents 579:610:669:772 SD: 0.0621 cents