Scala analysis: 004_H1
Hyperenharmonic tetrachord 100/99 * 66/65 * 13/10, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 100/99 17.399484 Ptolemy's comma 2: 40/39 43.831051 tridecimal minor diesis 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/10 454.2139 tridecimal semi-diminished fourth 1: 100/99 17.3995 Ptolemy's comma 2: 66/65 26.4316 Winmeanma 3: 13/10 454.2139 tridecimal semi-diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 100/99 17.399 cents Ptolemy's comma 1: 1 66/65 26.432 cents Winmeanma 1: 1 13/10 454.214 cents tridecimal semi-diminished fourth 2: 1 40/39 43.831 cents tridecimal minor diesis 2: 1 130/99 471.613 cents 2: 1 33/25 480.646 cents 2 pentatones 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 : 17.4 43.8 498.0 17.4 : 26.4 480.6 498.0 43.8 : 454.2 471.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 17.3995 .. 454.2139 cents 1287/1000, 436.8145 cents 100/99, 17.3995 cents 2: 43.8311 .. 480.6455 cents 1287/1000, 436.8145 cents 400/507,-410.3829 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 100/99, 17.3995 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 13/10, 454.2139 cents Average / Smallest step : 9.541375 Largest / Average step : 2.735981 Largest / Smallest step : 26.105025 Median interval of one step : 66/65, 26.4316 cents, amount: 1 Least squares average step : 114.22833 cents, oct.: 342.68498 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2261-tone equal temperament with octave 4/3 degrees: 79 199 2261 Least number of segments generator : 1131 of 249.133 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2201 of 484.828 cents and inv. generated superset size: 42 = 39 more = 1400.000% 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 17.39948 cents Scale diversity : 0.013014 Lumma stability : 0.069871 Lumma impropriety factor : 0.823988 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 : 3267/3250, 9.0321 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 480.6455 cents Number of appreciable 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 427.7824 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 99 (O: 65 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.016268 Average absolute harmonicity : 0.089869 Specific harmonicity : 0.083854 Fundamental : 1/1287, -10.3298 octaves, 0.2033 Hz. Guide tone : 200, 7.6439 octaves, 52325.113 Hz. Exponens Consonantiae : 2.574000E+05, 17.97365 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 142.5, average 47.50000 Mersenne's string divisions : 110047 Sum of van Prooijen's expressibility: 4.06382, average 1.35461 Sum of Tenney's harmonic distance : 8.26794, average 2.75598 Vogel's harmonic complexity : 25.33333 Wille's k value : 214 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 15.72333, average 2.62055 Lattice compactness (without 2's) : 11.59575, average 1.93263 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -2 ..-1 -1.33333 4 1 5: 0 .. 2 1.00000 3 11: -1 .. 0 -0.33333 1 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 17 23 27| Scale is weakly epimorphic with val: <6 10 17 23 30| Scale is weakly epimorphic with val: <6 10 18 25 25| Scale is weakly epimorphic with val: <6 10 18 25 28| Scale is weakly epimorphic with val: <6 10 19 27 29| Scale is weakly epimorphic with val: <6 11 18 23 26| Scale is weakly epimorphic with val: <6 11 18 23 29| Scale is weakly epimorphic with val: <6 11 19 25 27| Scale is weakly epimorphic with val: <6 11 19 25 30| Scale is weakly epimorphic with val: <7 10 16 23 25| Scale is weakly epimorphic with val: <7 10 16 23 28| Scale is weakly epimorphic with val: <7 10 17 23 25| Scale is weakly epimorphic with val: <7 10 17 25 26| Scale is weakly epimorphic with val: <7 10 17 25 29| Scale is weakly epimorphic with val: <7 10 18 25 26| Scale is weakly epimorphic with val: <7 10 18 27 27| Scale is weakly epimorphic with val: <7 10 18 27 30| Scale is weakly epimorphic with val: <7 10 19 24 27| Scale is weakly epimorphic with val: <7 10 19 27 27| Scale is weakly epimorphic with val: <7 11 15 23 27| Scale is weakly epimorphic with val: <7 11 15 23 30| Scale is weakly epimorphic with val: <7 11 15 24 26| Scale is weakly epimorphic with val: <7 11 15 24 29| Scale is weakly epimorphic with val: <7 11 15 26 27| Scale is weakly epimorphic with val: <7 11 15 26 30| Scale is weakly epimorphic with val: <7 11 15 27 29| Scale is weakly epimorphic with val: <7 11 16 23 27| Scale is weakly epimorphic with val: <7 11 16 23 30| Scale is weakly epimorphic with val: <7 11 16 25 25| Scale is weakly epimorphic with val: <7 11 16 25 28| Scale is weakly epimorphic with val: <7 11 16 26 27| Scale is weakly epimorphic with val: <7 11 16 26 30| Scale is weakly epimorphic with val: <7 11 17 24 26| Scale is weakly epimorphic with val: <7 11 17 24 29| Scale is JI-epimorphic with val: <7 11 17 25 25| Scale is weakly epimorphic with val: <7 11 17 25 28| Scale is weakly epimorphic with val: <7 11 17 27 29| Scale is weakly epimorphic with val: <7 11 18 23 27| Scale is weakly epimorphic with val: <7 11 18 23 30| Scale is weakly epimorphic with val: <7 11 18 24 26| Scale is weakly epimorphic with val: <7 11 18 24 29| Scale is weakly epimorphic with val: <7 11 18 26 27| Scale is weakly epimorphic with val: <7 11 18 26 30| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 19 23 27| Scale is weakly epimorphic with val: <7 11 19 23 30| Scale is weakly epimorphic with val: <7 11 19 25 25| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 26 27| Scale is weakly epimorphic with val: <7 11 19 26 30| Scale is weakly epimorphic with val: <7 12 18 23 26| Scale is weakly epimorphic with val: <7 12 18 23 29| Scale is weakly epimorphic with val: <7 12 19 24 25| Scale is weakly epimorphic with val: <7 12 19 25 27| Scale is weakly epimorphic with val: <7 12 19 25 30| Scale is weakly epimorphic with val: <8 11 15 23 25| Scale is weakly epimorphic with val: <8 11 16 23 25| Scale is weakly epimorphic with val: <8 11 16 23 28| Scale is weakly epimorphic with val: <8 11 16 25 26| Scale is weakly epimorphic with val: <8 11 17 24 27| Scale is weakly epimorphic with val: <8 11 17 25 26| Scale is weakly epimorphic with val: <8 11 17 25 29| Scale is weakly epimorphic with val: <8 11 17 27 27| Scale is weakly epimorphic with val: <8 11 18 23 28| Scale is weakly epimorphic with val: <8 11 18 26 28| Scale is weakly epimorphic with val: <8 11 18 27 27| Scale is weakly epimorphic with val: <8 11 18 27 30| Scale is weakly epimorphic with val: <8 11 19 25 29| Scale is weakly epimorphic with val: <8 12 16 25 25| Scale is weakly epimorphic with val: <8 12 17 23 27| Scale is weakly epimorphic with val: <8 12 17 23 30| Scale is weakly epimorphic with val: <8 12 17 24 26| Scale is weakly epimorphic with val: <8 12 18 23 27| Scale is weakly epimorphic with val: <8 12 18 25 25| Scale is weakly epimorphic with val: <8 12 18 25 28| Scale is weakly epimorphic with val: <8 12 18 26 27| Scale is weakly epimorphic with val: <8 12 19 25 28| Scale is weakly epimorphic with val: <8 12 19 27 29|
FIT/MODE
3: 0 0 3 N M DE S SD: 27.2268 c. M: 43.8311 c. 8: 0 1 7 N G T3 SD: 14.6311 c. M:-18.4246 c. 9: 0 1 8 N G T3 SD: 12.0438 c. M: 17.3995 c. 10: 0 1 9 N G T3 SD: 10.6211 c. M: 17.3995 c. 11: 0 1 10 N G T3 SD: 10.0802 c. M: 17.3995 c. 12: 0 1 11 N G T3 SD: 10.1351 c. M: 17.3995 c. 13: 0 1 12 N G T3 SD: 10.5390 c. M: 17.3995 c. 14: 0 1 13 N G T3 SD: 11.1192 c. M: 17.3995 c. 19: 1 1 17 N M DE S SD: 7.1074 c. M:-8.8134 c. 20: 1 1 18 N M DE S SD: 5.5370 c. M:-7.5028 c. 21: 1 1 19 N M DE S SD: 4.1983 c. M:-6.3169 c. 22: 1 1 20 N M DE S SD: 3.1378 c. M:-5.2389 c. 23: 1 1 21 N M DE S SD: 2.4749 c. M:-4.2546 c. 24: 1 1 22 N M DE S SD: 2.3562 c. M:-3.3524 c. 32: 1 2 29 N T3 SD: 1.9624 c. M:-2.8607 c. 33: 1 2 30 N T3 SD: 1.5720 c. M: 2.3072 c. 34: 1 2 31 N T3 SD: 1.5897 c. M: 2.7511 c. 54: 2 3 49 N T3 SD: 1.4506 c. M:-2.2842 c. 55: 2 3 50 N T3 SD: 0.9303 c. M:-1.4458 c. 56: 2 3 51 N T3 SD: 0.4307 c. M:-0.6373 c. 57: 2 3 52 N T3 SD: 0.0934 c. M: 0.1429 c. 227: 8 12 207 N T3 SD: 0.0927 c. M:-0.1528 c. 284: 10 15 259 N T3 SD: 0.0795 c. M:-0.1373 c. 341: 12 18 311 N T3 SD: 0.0738 c. M:-0.1270 c. 374: 13 20 341 N T3 SD: 0.0831 c. M:-0.1141 c. 375: 13 20 342 N T3 SD: 0.0773 c. M: 0.1339 c. 398: 14 21 363 N T3 SD: 0.0717 c. M:-0.1197 c. 431: 15 23 393 N T3 SD: 0.0600 c. M:-0.0801 c. 432: 15 23 394 N T3 SD: 0.0626 c. M: 0.1063 c. 488: 17 26 445 N T3 SD: 0.0423 c. M:-0.0541 c. 545: 19 29 497 N T3 SD: 0.0286 c. M: 0.0364 c. 602: 21 32 549 N T3 SD: 0.0178 c. M: 0.0258 c. 659: 23 35 601 N T3 SD: 0.0100 c. M: 0.0170 c. 716: 25 38 653 N T3 SD: 0.0075 c. M: 0.0096 c. 1545: 54 82 1409 N T3 SD: 0.0073 c. M:-0.0098 c. 1602: 56 85 1461 N T3 SD: 0.0065 c. M:-0.0103 c. 2204: 77 117 2010 N T3 SD: 0.0045 c. M:-0.0078 c. 2261: 79 120 2062 N T3 SD: 0.0027 c. M:-0.0040 c. 2318: 81 123 2114 N T3 SD: 0.0024 c. M:-0.0042 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 111.5199 cents 7 x 8:9 S SD: 98.8199 cents 8 x 9:11 SD: 84.3553 cents 9 x 10:12 S SD: 69.2863 cents 10 x 11:13 SD: 64.4284 cents 11 x 12:15 S SD: 56.8357 cents 12 x 13:16 SD: 47.3708 cents 13 x 14:17 SD: 45.4555 cents 14 x 15:19 SD: 40.7924 cents 15 x 16:20 S SD: 33.9501 cents 16 x 17:21 SD: 33.4646 cents 17 x 18:23 SD: 30.3207 cents 18 x 19:24 SD: 24.8860 cents 19 x 20:25 S SD: 25.2393 cents 20 x 21:27 SD: 22.9881 cents 21 x 22:28 SD: 18.3530 cents 22 x 23:29 SD: 19.2923 cents 23 x 24:31 SD: 17.6160 cents 24 x 25:32 SD: 13.4207 cents 25 x 26:33 SD: 14.8498 cents 26 x 27:35 SD: 13.5737 cents 27 x 28:36 SD: 9.5649 cents 28 x 29:37 SD: 11.4824 cents 29 x 30:39 SD: 10.5079 cents 30 x 31:40 SD: 6.4679 cents 31 x 32:41 SD: 8.9507 cents 32 x 33:43 SD: 8.2259 cents 33 x 34:44 SD: 3.9257 cents 34 x 35:45 SD: 7.1345 cents 35 x 36:47 SD: 6.6376 cents 36 x 37:48 SD: 1.8015 cents 37 x 38:49 SD: 5.9839 cents 38 x 39:51 SD: 5.7047 cents 39 x 40:52 SD: 0.0000 cents 40 x 41:53 SD: 5.4540 cents 41 x 42:55 SD: 5.3671 cents 42 x 43:56 SD: 1.5471 cents 43 x 44:57 SD: 5.4348 cents 44 x 45:59 SD: 5.4879 cents 45 x 46:60 SD: 2.8902 cents 46 x 47:61 SD: 5.7566 cents 47 x 48:63 SD: 5.8918 cents 48 x 49:64 SD: 4.0671 cents 49 x 50:65 SD: 6.2617 cents 50 x 51:67 SD: 6.4367 cents 51 x 52:68 SD: 5.1069 cents 52 x 53:69 SD: 6.8451 cents 53 x 54:71 SD: 7.0347 cents 54 x 55:72 SD: 6.0322 cents 55 x 56:73 SD: 7.4481 cents 56 x 57:75 SD: 7.6390 cents 57:58 x 76 SD: 6.3548 cents 58:59 x 77 SD: 7.1527 cents 59:60:61:79 SD: 6.5246 cents 60:61:62:80 SD: 5.7072 cents 62:63:64:83 SD: 5.5637 cents 63:64:65:84 SD: 4.7478 cents 65:66:67:87 SD: 4.7176 cents 66:67:68:88 SD: 3.8902 cents 69:70:71:92 SD: 3.1301 cents 72:73:74:96 SD: 2.4714 cents 75:76:77:100 SD: 1.9318 cents 78:79:80:104 SD: 1.5516 cents 81:82:83:108 SD: 1.3880 cents 108:109:111:144 SD: 1.2938 cents 111:112:114:148 SD: 0.9985 cents 114:115:117:152 SD: 0.8493 cents 186:188:191:248 SD: 0.7907 cents 189:191:194:252 SD: 0.5339 cents 192:194:197:256 SD: 0.2886 cents 195:197:200:260 SD: 0.0888 cents