Scala analysis: 401_D6
Diatonic tetrachord 40/39 * 91/80 * 8/7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 40/39 43.8311 tridecimal minor diesis 2: 91/80 223.0399 3: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 91/80 223.040 cents 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 320/273 275.005 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 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 : 43.8 266.9 498.0 43.8 : 223.0 454.2 498.0 266.9: 231.2 275.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 231.1741 cents 39/35, 187.3430 cents 40/39, 43.8311 cents 2: 266.8709 .. 454.2139 cents 39/35, 187.3430 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 3.787612 Largest / Average step : 1.392489 Largest / Smallest step : 5.274208 Median interval of one step : 91/80, 223.0399 cents, amount: 1 Least squares average step : 147.97913 cents, oct.: 443.93740 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1284-tone equal temperament with octave 4/3 degrees: 113 688 1284 Least number of segments generator : 643 of 249.410 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1171 of 454.214 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 35.69681 cents Scale diversity : 0.596405 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.247686 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 : 640/637, 8.1342 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 179.2088 cents: 1 -- Rational properties -- Prime limit : 13 Odd number limit : 273 (O: 91 U: 273) Highest odd numerator or denominator: 39 Scale harmonicity : 0.021975 Average absolute harmonicity : 0.105060 Specific harmonicity : 0.115507 Fundamental : 1/78, -6.2854 octaves, 3.3542 Hz. Guide tone : 280, 8.1293 octaves, 73255.158 Hz. Exponens Consonantiae : 2.184000E+04, 14.41469 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 49.5, average 16.50000 Mersenne's string divisions : 7189 Sum of van Prooijen's expressibility: 2.91328, average 0.97109 Sum of Tenney's harmonic distance : 5.89556, average 1.96519 Vogel's harmonic complexity : 15.00000 Wille's k value : 45 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 16.68545, average 2.78091 Lattice compactness (without 2's) : 8.29253, average 1.38209 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -1 ..-1 -1.00000 3 1 5: 0 .. 1 0.33333 1 7: 0 .. 1 0.33333 1 1 13: -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 15 19 25| Scale is weakly epimorphic with val: <6 10 15 19 28| Scale is weakly epimorphic with val: <6 10 16 19 26| Scale is weakly epimorphic with val: <6 10 16 19 29| Scale is weakly epimorphic with val: <6 10 17 19 27| Scale is weakly epimorphic with val: <6 10 17 19 30| Scale is weakly epimorphic with val: <6 10 18 19 25| Scale is weakly epimorphic with val: <6 10 18 19 28| Scale is weakly epimorphic with val: <6 10 19 19 26| Scale is weakly epimorphic with val: <6 10 19 19 29| Scale is weakly epimorphic with val: <6 11 15 20 26| Scale is weakly epimorphic with val: <6 11 15 20 29| Scale is weakly epimorphic with val: <6 11 16 20 27| Scale is weakly epimorphic with val: <6 11 16 20 30| Scale is weakly epimorphic with val: <6 11 17 20 25| Scale is weakly epimorphic with val: <6 11 17 20 28| Scale is weakly epimorphic with val: <6 11 18 20 26| Scale is weakly epimorphic with val: <6 11 18 20 29| Scale is weakly epimorphic with val: <6 11 19 20 27| Scale is weakly epimorphic with val: <6 11 19 20 30| Scale is weakly epimorphic with val: <7 10 15 20 27| Scale is weakly epimorphic with val: <7 10 15 20 30| Scale is weakly epimorphic with val: <7 10 16 20 25| Scale is weakly epimorphic with val: <7 10 16 20 28| Scale is weakly epimorphic with val: <7 10 17 19 25| Scale is weakly epimorphic with val: <7 10 17 20 26| Scale is weakly epimorphic with val: <7 10 17 20 29| Scale is weakly epimorphic with val: <7 10 17 22 25| Scale is weakly epimorphic with val: <7 10 18 19 26| Scale is weakly epimorphic with val: <7 10 18 20 27| Scale is weakly epimorphic with val: <7 10 18 20 30| Scale is weakly epimorphic with val: <7 10 18 22 26| Scale is weakly epimorphic with val: <7 10 19 19 27| Scale is weakly epimorphic with val: <7 10 19 20 25| Scale is weakly epimorphic with val: <7 10 19 20 28| Scale is weakly epimorphic with val: <7 10 19 22 27| Scale is weakly epimorphic with val: <7 11 15 19 26| Scale is weakly epimorphic with val: <7 11 15 19 29| Scale is weakly epimorphic with val: <7 11 15 20 27| Scale is weakly epimorphic with val: <7 11 15 20 30| Scale is weakly epimorphic with val: <7 11 15 22 26| Scale is weakly epimorphic with val: <7 11 15 22 29| Scale is weakly epimorphic with val: <7 11 16 19 27| Scale is weakly epimorphic with val: <7 11 16 19 30| Scale is JI-epimorphic with val: <7 11 16 20 25| Scale is weakly epimorphic with val: <7 11 16 20 28| Scale is weakly epimorphic with val: <7 11 16 22 27| Scale is weakly epimorphic with val: <7 11 16 22 30| Scale is weakly epimorphic with val: <7 11 17 19 25| Scale is weakly epimorphic with val: <7 11 17 19 28| Scale is JI-epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 22 25| Scale is weakly epimorphic with val: <7 11 17 22 28| Scale is weakly epimorphic with val: <7 11 18 19 26| Scale is weakly epimorphic with val: <7 11 18 19 29| Scale is JI-epimorphic with val: <7 11 18 20 27| Scale is weakly epimorphic with val: <7 11 18 20 30| Scale is weakly epimorphic with val: <7 11 18 22 26| Scale is weakly epimorphic with val: <7 11 18 22 29| Scale is weakly epimorphic with val: <7 11 19 19 27| Scale is weakly epimorphic with val: <7 11 19 19 30| Scale is weakly epimorphic with val: <7 11 19 20 25| Scale is JI-epimorphic with val: <7 11 19 20 28| Scale is weakly epimorphic with val: <7 11 19 22 27| Scale is weakly epimorphic with val: <7 11 19 22 30| Scale is weakly epimorphic with val: <7 12 15 22 26| Scale is weakly epimorphic with val: <7 12 15 22 29| Scale is weakly epimorphic with val: <7 12 16 22 27| Scale is weakly epimorphic with val: <7 12 16 22 30| Scale is weakly epimorphic with val: <7 12 17 22 25| Scale is weakly epimorphic with val: <7 12 17 22 28| Scale is weakly epimorphic with val: <7 12 18 22 26| Scale is weakly epimorphic with val: <7 12 18 22 29| Scale is weakly epimorphic with val: <7 12 19 20 25| Scale is weakly epimorphic with val: <7 12 19 22 27| Scale is weakly epimorphic with val: <7 12 19 22 30| Scale is weakly epimorphic with val: <8 11 15 20 25| Scale is weakly epimorphic with val: <8 11 15 22 27| Scale is weakly epimorphic with val: <8 11 15 22 30| Scale is weakly epimorphic with val: <8 11 16 20 26| Scale is weakly epimorphic with val: <8 11 16 22 25| Scale is weakly epimorphic with val: <8 11 16 22 28| Scale is weakly epimorphic with val: <8 11 17 20 27| Scale is weakly epimorphic with val: <8 11 17 22 26| Scale is weakly epimorphic with val: <8 11 17 22 29| Scale is weakly epimorphic with val: <8 11 18 20 28| Scale is weakly epimorphic with val: <8 11 18 22 27| Scale is weakly epimorphic with val: <8 11 18 22 30| Scale is weakly epimorphic with val: <8 11 19 20 29| Scale is weakly epimorphic with val: <8 11 19 22 25| Scale is weakly epimorphic with val: <8 11 19 22 28| Scale is weakly epimorphic with val: <8 12 16 19 25| Scale is weakly epimorphic with val: <8 12 16 22 25| Scale is weakly epimorphic with val: <8 12 17 19 26| Scale is weakly epimorphic with val: <8 12 17 22 26| Scale is weakly epimorphic with val: <8 12 18 19 27| Scale is weakly epimorphic with val: <8 12 18 22 27| Scale is weakly epimorphic with val: <8 12 19 19 28| Scale is weakly epimorphic with val: <8 12 19 22 28|
FIT/MODE
3: 0 1 2 N G T3 SD: 63.4904 c. M: 100.8559 c. 4: 0 2 2 P M DE S SD: 27.3235 c. M: 43.8311 c. 6: 0 3 3 P M DE S SD: 27.3235 c. M: 43.8311 c. 7: 1 3 3 SP M DE S SD: 18.8016 c. M:-27.3182 c. 8: 1 3 4 P T3 SD: 14.8102 c. M:-18.4246 c. 9: 1 4 4 SP M DE S SD: 8.7343 c. M:-11.5073 c. 11: 1 5 5 SP M DE S SD: 2.8887 c. M:-4.7900 c. 24: 2 11 11 SP M DE S SD: 2.1484 c. M:-2.9035 c. 32: 3 14 15 SP T3 SD: 2.1136 c. M:-2.8607 c. 34: 3 15 16 SP T3 SD: 1.8487 c. M: 3.2000 c. 43: 4 19 20 SP T3 SD: 1.4684 c. M:-2.4987 c. 45: 4 20 21 SP T3 SD: 0.7633 c. M: 1.2469 c. 56: 5 25 26 SP T3 SD: 0.3696 c. M:-0.6373 c. 69: 6 31 32 SP T3 SD: 0.3225 c. M: 0.5228 c. 114: 10 51 53 SP T3 SD: 0.2307 c. M: 0.3731 c. 125: 11 56 58 SP T3 SD: 0.0469 c. M:-0.0812 c. 364: 32 163 169 SP T3 SD: 0.0445 c. M: 0.0611 c. 420: 37 188 195 SP T3 SD: 0.0436 c. M: 0.0611 c. 489: 43 219 227 SP T3 SD: 0.0251 c. M: 0.0357 c. 545: 48 244 253 SP T3 SD: 0.0254 c. M:-0.0335 c. 614: 54 275 285 SP T3 SD: 0.0169 c. M: 0.0290 c. 670: 59 300 311 SP T3 SD: 0.0161 c. M:-0.0266 c. 739: 65 331 343 SP T3 SD: 0.0156 c. M: 0.0247 c. 795: 70 356 369 SP T3 SD: 0.0132 c. M:-0.0220 c. 864: 76 387 401 SP T3 SD: 0.0175 c. M: 0.0215 c. 920: 81 412 427 SP T3 SD: 0.0142 c. M:-0.0186 c. 1159: 102 519 538 SP T3 SD: 0.0087 c. M: 0.0150 c. 1284: 113 575 596 SP T3 SD: 0.0033 c. M: 0.0057 c. 1409: 124 631 654 SP T3 SD: 0.0012 c. M:-0.0020 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: 48.7680 cents 6 x 7:8 S SD: 0.0000 cents 7 x 8:9 S SD: 36.1882 cents 8 x 9:11 SD: 41.2374 cents 9 x 11:12 SD: 40.2685 cents 10 x 12:13 S SD: 32.7861 cents 12:13:14:16 S SD: 31.5805 cents 13:14:15:17 SD: 30.9673 cents 14:15:16:19 SD: 29.6842 cents 15:16:18:20 S SD: 27.8667 cents 16:17:19:21 SD: 24.5367 cents 17:18:20:23 SD: 20.7826 cents 18:19:21:24 SD: 16.5907 cents 22:23:26:29 SD: 14.8615 cents 23:24:27:31 SD: 12.2756 cents 24:25:28:32 SD: 8.9471 cents 29:30:34:39 SD: 7.5575 cents 30:31:35:40 SD: 4.3119 cents 36:37:42:48 SD: 1.2010 cents 42:43:49:56 SD: 1.0314 cents 78:80:91:104 SD: 0.0000 cents