Scala analysis: 370_D1
Diatonic tetrachord 28/27 * 39/35 * 15/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 52/45 250.303946 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 39/35 187.3430 3: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 39/35 187.343 cents 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 140/117 310.702 cents 2: 1 9/7 435.084 cents septimal major third, BP 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 : 63.0 250.3 498.0 63.0 : 187.3 435.1 498.0 250.3: 247.7 310.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 247.7411 cents 405/364, 184.7801 cents 28/27, 62.9609 cents 2: 250.3039 .. 435.0841 cents 405/364, 184.7801 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 2.636795 Largest / Average step : 1.492281 Largest / Smallest step : 3.934840 Median interval of one step : 39/35, 187.3430 cents, amount: 1 Least squares average step : 146.97884 cents, oct.: 440.93653 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 973-tone equal temperament with octave 4/3 degrees: 123 489 973 Least number of segments generator : 487 of 249.278 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 608 of 311.214 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 : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 0.879713 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.257978 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 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% -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 39 U: 117) Highest odd numerator or denominator: 45 Scale harmonicity : 0.020475 Average absolute harmonicity : 0.097148 Specific harmonicity : 0.107249 Fundamental : 1/135, -7.0768 octaves, 1.9380 Hz. Guide tone : 364, 8.5078 octaves, 95231.706 Hz. Exponens Consonantiae : 4.914000E+04, 15.58461 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 79.5, average 26.50000 Mersenne's string divisions : 37345 Sum of van Prooijen's expressibility: 3.56170, average 1.18723 Sum of Tenney's harmonic distance : 7.32692, average 2.44231 Vogel's harmonic complexity : 15.00000 Wille's k value : 22 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 15.10812, average 2.51802 Lattice compactness (without 2's) : 12.57989, average 2.09665 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -3 ..-1 -2.00000 6 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.33333 1 1 13: 0 .. 1 0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 19 26| Scale is weakly epimorphic with val: <6 10 15 21 27| Scale is weakly epimorphic with val: <6 10 15 21 30| Scale is weakly epimorphic with val: <6 10 15 22 26| Scale is weakly epimorphic with val: <6 10 16 19 27| Scale is weakly epimorphic with val: <6 10 16 21 25| Scale is weakly epimorphic with val: <6 10 16 21 28| Scale is weakly epimorphic with val: <6 10 16 22 27| Scale is weakly epimorphic with val: <6 10 17 19 28| Scale is weakly epimorphic with val: <6 10 17 21 26| Scale is weakly epimorphic with val: <6 10 17 21 29| Scale is weakly epimorphic with val: <6 10 17 22 28| Scale is weakly epimorphic with val: <6 10 18 19 29| Scale is weakly epimorphic with val: <6 10 18 21 27| Scale is weakly epimorphic with val: <6 10 18 21 30| Scale is weakly epimorphic with val: <6 10 18 22 29| Scale is weakly epimorphic with val: <6 10 19 19 30| Scale is weakly epimorphic with val: <6 10 19 21 25| Scale is weakly epimorphic with val: <6 10 19 21 28| Scale is weakly epimorphic with val: <6 10 19 22 30| Scale is weakly epimorphic with val: <6 11 15 20 28| Scale is weakly epimorphic with val: <6 11 16 20 29| Scale is weakly epimorphic with val: <6 11 17 20 30| Scale is weakly epimorphic with val: <7 10 15 19 26| Scale is weakly epimorphic with val: <7 10 15 19 29| Scale is weakly epimorphic with val: <7 10 16 18 25| Scale is weakly epimorphic with val: <7 10 16 19 27| Scale is weakly epimorphic with val: <7 10 16 19 30| Scale is weakly epimorphic with val: <7 10 16 21 25| Scale is weakly epimorphic with val: <7 10 17 18 26| Scale is weakly epimorphic with val: <7 10 17 19 25| Scale is weakly epimorphic with val: <7 10 17 19 28| Scale is weakly epimorphic with val: <7 10 17 21 26| Scale is weakly epimorphic with val: <7 10 18 18 27| Scale is weakly epimorphic with val: <7 10 18 19 26| Scale is weakly epimorphic with val: <7 10 18 19 29| Scale is weakly epimorphic with val: <7 10 18 21 27| Scale is weakly epimorphic with val: <7 10 19 19 27| Scale is weakly epimorphic with val: <7 10 19 19 30| Scale is weakly epimorphic with val: <7 10 19 21 28| Scale is weakly epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 18 30| Scale is JI-epimorphic with val: <7 11 15 20 25| Scale is weakly epimorphic with val: <7 11 15 20 28| Scale is weakly epimorphic with val: <7 11 15 21 27| Scale is weakly epimorphic with val: <7 11 15 21 30| Scale is weakly epimorphic with val: <7 11 16 18 25| Scale is weakly epimorphic with val: <7 11 16 18 28| Scale is JI-epimorphic with val: <7 11 16 20 26| Scale is weakly epimorphic with val: <7 11 16 20 29| Scale is weakly epimorphic with val: <7 11 16 21 25| Scale is weakly epimorphic with val: <7 11 16 21 28| Scale is weakly epimorphic with val: <7 11 17 18 26| Scale is weakly epimorphic with val: <7 11 17 18 29| Scale is JI-epimorphic with val: <7 11 17 20 27| = patent Scale is weakly epimorphic with val: <7 11 17 20 30| Scale is weakly epimorphic with val: <7 11 17 21 26| Scale is weakly epimorphic with val: <7 11 17 21 29| Scale is weakly epimorphic with val: <7 11 18 18 27| Scale is weakly epimorphic with val: <7 11 18 18 30| Scale is weakly epimorphic with val: <7 11 18 20 25| Scale is JI-epimorphic with val: <7 11 18 20 28| Scale is weakly epimorphic with val: <7 11 18 21 27| Scale is weakly epimorphic with val: <7 11 18 21 30| Scale is weakly epimorphic with val: <7 11 19 20 26| Scale is JI-epimorphic with val: <7 11 19 20 29| Scale is weakly epimorphic with val: <7 11 19 21 25| Scale is weakly epimorphic with val: <7 11 19 21 28| Scale is weakly epimorphic with val: <7 12 15 20 28| Scale is weakly epimorphic with val: <7 12 16 20 29| Scale is weakly epimorphic with val: <7 12 17 20 30| Scale is weakly epimorphic with val: <8 11 15 20 25| Scale is weakly epimorphic with val: <8 11 15 20 28| Scale is weakly epimorphic with val: <8 11 16 18 25| Scale is weakly epimorphic with val: <8 11 16 20 26| Scale is weakly epimorphic with val: <8 11 16 20 29| Scale is weakly epimorphic with val: <8 11 16 21 25| Scale is weakly epimorphic with val: <8 11 17 18 26| Scale is weakly epimorphic with val: <8 11 17 20 27| Scale is weakly epimorphic with val: <8 11 17 20 30| Scale is weakly epimorphic with val: <8 11 17 21 26| Scale is weakly epimorphic with val: <8 11 18 18 27| Scale is weakly epimorphic with val: <8 11 18 20 25| Scale is weakly epimorphic with val: <8 11 18 20 28| Scale is weakly epimorphic with val: <8 11 18 21 27| Scale is weakly epimorphic with val: <8 11 19 20 26| Scale is weakly epimorphic with val: <8 11 19 20 29| Scale is weakly epimorphic with val: <8 11 19 21 28| Scale is weakly epimorphic with val: <8 12 15 19 26| Scale is weakly epimorphic with val: <8 12 15 22 26| Scale is weakly epimorphic with val: <8 12 16 19 27| Scale is weakly epimorphic with val: <8 12 16 22 27| Scale is weakly epimorphic with val: <8 12 17 19 28| Scale is weakly epimorphic with val: <8 12 17 22 28| Scale is weakly epimorphic with val: <8 12 18 19 29| Scale is weakly epimorphic with val: <8 12 18 22 29| Scale is weakly epimorphic with val: <8 12 19 19 30| Scale is weakly epimorphic with val: <8 12 19 22 30|
FIT/MODE
3: 0 1 2 N G T3 SD: 60.7418 c. M: 84.2889 c. 4: 0 2 2 P M DE S SD: 36.3580 c. M: 62.9609 c. 6: 1 2 3 P T3 SD: 11.5975 c. M:-20.0466 c. 8: 1 3 4 P T3 SD: 0.8445 c. M: 1.2814 c. 78: 10 29 39 P T3 SD: 0.9011 c. M: 1.2814 c. 86: 11 32 43 P T3 SD: 0.8551 c. M: 1.2814 c. 94: 12 35 47 P T3 SD: 0.8217 c. M: 1.2814 c. 95: 12 36 47 SP T3 SD: 0.7741 c. M:-1.3398 c. 101: 13 38 50 SP T3 SD: 0.9506 c. M:-1.1841 c. 102: 13 38 51 P T3 SD: 0.7974 c. M: 1.2814 c. 103: 13 39 51 SP T3 SD: 0.6586 c. M:-1.1362 c. 109: 14 41 54 SP T3 SD: 0.8211 c. M:-1.0082 c. 110: 14 41 55 P T3 SD: 0.7798 c. M: 1.2814 c. 111: 14 42 55 SP T3 SD: 0.5616 c. M:-0.9620 c. 117: 15 44 58 SP T3 SD: 0.7098 c. M:-0.8910 c. 119: 15 45 59 SP T3 SD: 0.4800 c. M:-0.8112 c. 125: 16 47 62 SP T3 SD: 0.6130 c. M:-0.7889 c. 127: 16 48 63 SP T3 SD: 0.4114 c. M:-0.6794 c. 135: 17 51 67 SP T3 SD: 0.3544 c. M:-0.5632 c. 143: 18 54 71 SP T3 SD: 0.3079 c. M:-0.4600 c. 151: 19 57 75 SP T3 SD: 0.2714 c. M:-0.3677 c. 159: 20 60 79 SP T3 SD: 0.2446 c. M: 0.3137 c. 165: 21 62 82 SP T3 SD: 0.2792 c. M:-0.4266 c. 167: 21 63 83 SP T3 SD: 0.2270 c. M: 0.3325 c. 173: 22 65 86 SP T3 SD: 0.2346 c. M:-0.3743 c. 175: 22 66 87 SP T3 SD: 0.2177 c. M: 0.3495 c. 181: 23 68 90 SP T3 SD: 0.1963 c. M:-0.3266 c. 189: 24 71 94 SP T3 SD: 0.1647 c. M:-0.2829 c. 197: 25 74 98 SP T3 SD: 0.1405 c. M:-0.2428 c. 205: 26 77 102 SP T3 SD: 0.1249 c. M:-0.2058 c. 213: 27 80 106 SP T3 SD: 0.1184 c. M:-0.1716 c. 221: 28 83 110 SP T3 SD: 0.1204 c. M: 0.1546 c. 332: 42 125 165 SP T3 SD: 0.1289 c. M:-0.2187 c. 340: 43 128 169 SP T3 SD: 0.1070 c. M:-0.1834 c. 348: 44 131 173 SP T3 SD: 0.0866 c. M:-0.1497 c. 356: 45 134 177 SP T3 SD: 0.0680 c. M:-0.1176 c. 364: 46 137 181 SP T3 SD: 0.0516 c. M:-0.0868 c. 372: 47 140 185 SP T3 SD: 0.0391 c. M:-0.0574 c. 380: 48 143 189 SP T3 SD: 0.0334 c. M: 0.0500 c. 388: 49 146 193 SP T3 SD: 0.0367 c. M: 0.0635 c. 569: 72 214 283 SP T3 SD: 0.0394 c. M:-0.0606 c. 577: 73 217 287 SP T3 SD: 0.0299 c. M:-0.0500 c. 585: 74 220 291 SP T3 SD: 0.0230 c. M:-0.0397 c. 593: 75 223 295 SP T3 SD: 0.0212 c. M:-0.0296 c. 949: 120 357 472 SP T3 SD: 0.0200 c. M:-0.0306 c. 957: 121 360 476 SP T3 SD: 0.0128 c. M:-0.0196 c. 965: 122 363 480 SP T3 SD: 0.0057 c. M:-0.0088 c. 973: 123 366 484 SP T3 SD: 0.0013 c. M: 0.0018 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 10 x 12:13 S SD: 39.3387 cents 11:12:13:15 SD: 34.5035 cents 12:13:14:16 S SD: 25.8018 cents 13:14:15:17 SD: 24.5077 cents 14:15:16:19 SD: 22.3485 cents 15:16:17:20 SD: 19.7447 cents 17:18:20:23 SD: 17.9465 cents 18:19:21:24 SD: 11.6113 cents 19:20:22:25 SD: 11.5747 cents 20:21:23:27 SD: 10.5127 cents 21:22:24:28 S SD: 8.6594 cents 24:25:28:32 SD: 6.0913 cents 26:27:30:35 S SD: 5.6439 cents 27:28:31:36 SD: 3.7111 cents 51:53:59:68 SD: 1.3756 cents 78:81:90:104 SD: 1.1650 cents 84:87:97:112 SD: 0.8365 cents 135:140:156:180 SD: 0.0000 cents