Scala analysis: 592_M100
Miscellaneous tetrachord 68/63 * 21/19 * 19/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/63 132.219501 supraminor second 2: 68/57 305.487393 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/17 192.5576 quasi-meantone 1: 68/63 132.2195 supraminor second 2: 21/19 173.2679 3: 19/17 192.5576 quasi-meantone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/63 132.220 cents supraminor second 1: 1 21/19 173.268 cents 1: 1 19/17 192.558 cents quasi-meantone 2: 1 68/57 305.487 cents 2: 1 76/63 324.777 cents 2: 1 21/17 365.825 cents submajor 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 : 132.2 305.5 498.0 132.2: 173.3 365.8 498.0 305.5: 192.6 324.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 132.2195 .. 192.5576 cents 1197/1156, 60.3381 cents 68/63, 132.2195 cents 2: 305.4874 .. 365.8255 cents 1197/1156, 60.3381 cents 1156/1083, 112.9298 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 68/63, 132.2195 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/17, 192.5576 cents Average / Smallest step : 1.255601 Largest / Average step : 1.159881 Largest / Smallest step : 1.456348 Median interval of one step : 21/19, 173.2679 cents, amount: 1 Least squares average step : 159.80923 cents, oct.: 479.42770 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1808-tone equal temperament with octave 4/3 degrees: 480 1109 1808 Least number of segments generator : 905 of 249.298 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1179 of 324.776 cents and inv. generated superset size: 66 = 63 more = 2200.000% 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 112.92979 cents Scale diversity : 1.296938 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.757700 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 : 361/357, 19.2897 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle 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 41.0484 cents: 1 -- Rational properties -- Prime limit : 19 Odd number limit : 63 (O: 21 U: 63) Highest odd numerator or denominator: 63 Scale harmonicity : 0.012219 Average absolute harmonicity : 0.083250 Specific harmonicity : 0.058046 Fundamental : 1/1197, -10.2252 octaves, 0.2186 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 8.139600E+04, 16.31267 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 131.5, average 43.83333 Mersenne's string divisions : 114625 Sum of van Prooijen's expressibility: 4.03234, average 1.34411 Sum of Tenney's harmonic distance : 8.29941, average 2.76647 Vogel's harmonic complexity : 32.66667 Wille's k value : 199 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 12.92241, average 2.15374 Lattice compactness (without 2's) : 10.05986, average 1.67664 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -2 ..-1 -1.33333 4 1 7: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 18 29 30| Scale is weakly epimorphic with val: <6 10 18 29 33| Scale is weakly epimorphic with val: <6 10 19 30 31| Scale is weakly epimorphic with val: <6 10 19 30 34| Scale is weakly epimorphic with val: <6 10 20 31 32| Scale is weakly epimorphic with val: <6 10 21 32 33| Scale is weakly epimorphic with val: <6 10 22 33 34| Scale is weakly epimorphic with val: <6 11 18 31 33| Scale is weakly epimorphic with val: <6 11 19 32 34| Scale is weakly epimorphic with val: <7 10 18 27 29| Scale is weakly epimorphic with val: <7 10 18 27 32| Scale is weakly epimorphic with val: <7 10 18 29 30| Scale is weakly epimorphic with val: <7 10 18 32 33| Scale is weakly epimorphic with val: <7 10 19 27 28| Scale is weakly epimorphic with val: <7 10 19 28 30| Scale is weakly epimorphic with val: <7 10 19 28 33| Scale is weakly epimorphic with val: <7 10 19 30 31| Scale is weakly epimorphic with val: <7 10 19 33 34| Scale is weakly epimorphic with val: <7 10 20 28 29| Scale is weakly epimorphic with val: <7 10 20 29 31| Scale is weakly epimorphic with val: <7 10 20 29 34| Scale is weakly epimorphic with val: <7 10 20 31 32| Scale is weakly epimorphic with val: <7 10 21 29 30| Scale is weakly epimorphic with val: <7 10 21 30 32| Scale is weakly epimorphic with val: <7 10 21 32 33| Scale is weakly epimorphic with val: <7 10 22 27 28| Scale is weakly epimorphic with val: <7 10 22 30 31| Scale is weakly epimorphic with val: <7 10 22 31 33| Scale is weakly epimorphic with val: <7 10 22 33 34| Scale is JI-epimorphic with val: <7 11 18 27 28| Scale is weakly epimorphic with val: <7 11 18 27 31| Scale is weakly epimorphic with val: <7 11 18 27 34| Scale is weakly epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 28 33| Scale is weakly epimorphic with val: <7 11 18 30 31| Scale is weakly epimorphic with val: <7 11 18 30 34| Scale is weakly epimorphic with val: <7 11 18 31 33| Scale is weakly epimorphic with val: <7 11 18 33 34| Scale is JI-epimorphic with val: <7 11 19 28 29| Scale is weakly epimorphic with val: <7 11 19 28 32| Scale is weakly epimorphic with val: <7 11 19 29 31| Scale is weakly epimorphic with val: <7 11 19 29 34| Scale is weakly epimorphic with val: <7 11 19 31 32| Scale is weakly epimorphic with val: <7 11 19 32 34| Scale is weakly epimorphic with val: <7 11 20 27 29| Scale is weakly epimorphic with val: <7 11 20 27 32| Scale is JI-epimorphic with val: <7 11 20 29 30| Scale is weakly epimorphic with val: <7 11 20 29 33| Scale is weakly epimorphic with val: <7 11 20 30 32| Scale is weakly epimorphic with val: <7 11 20 32 33| Scale is weakly epimorphic with val: <7 11 21 27 28| Scale is weakly epimorphic with val: <7 11 21 27 31| Scale is weakly epimorphic with val: <7 11 21 27 34| Scale is weakly epimorphic with val: <7 11 21 28 30| Scale is weakly epimorphic with val: <7 11 21 28 33| Scale is JI-epimorphic with val: <7 11 21 30 31| Scale is weakly epimorphic with val: <7 11 21 30 34| Scale is weakly epimorphic with val: <7 11 21 31 33| Scale is weakly epimorphic with val: <7 11 21 33 34| Scale is weakly epimorphic with val: <7 11 22 28 29| Scale is weakly epimorphic with val: <7 11 22 28 32| Scale is weakly epimorphic with val: <7 11 22 29 31| Scale is weakly epimorphic with val: <7 11 22 29 34| Scale is JI-epimorphic with val: <7 11 22 31 32| Scale is weakly epimorphic with val: <7 11 22 32 34| Scale is weakly epimorphic with val: <7 12 18 31 32| Scale is weakly epimorphic with val: <7 12 19 32 33| Scale is weakly epimorphic with val: <7 12 20 33 34| Scale is weakly epimorphic with val: <8 11 18 27 28| Scale is weakly epimorphic with val: <8 11 18 27 31| Scale is weakly epimorphic with val: <8 11 18 27 34| Scale is weakly epimorphic with val: <8 11 18 28 30| Scale is weakly epimorphic with val: <8 11 18 31 33| Scale is weakly epimorphic with val: <8 11 19 28 29| Scale is weakly epimorphic with val: <8 11 19 28 32| Scale is weakly epimorphic with val: <8 11 19 29 31| Scale is weakly epimorphic with val: <8 11 19 32 34| Scale is weakly epimorphic with val: <8 11 20 27 29| Scale is weakly epimorphic with val: <8 11 20 29 30| Scale is weakly epimorphic with val: <8 11 20 29 33| Scale is weakly epimorphic with val: <8 11 20 30 32| Scale is weakly epimorphic with val: <8 11 21 28 30| Scale is weakly epimorphic with val: <8 11 21 30 31| Scale is weakly epimorphic with val: <8 11 21 30 34| Scale is weakly epimorphic with val: <8 11 21 31 33| Scale is weakly epimorphic with val: <8 11 22 29 31| Scale is weakly epimorphic with val: <8 11 22 31 32| Scale is weakly epimorphic with val: <8 11 22 32 34| Scale is weakly epimorphic with val: <8 12 18 28 29| Scale is weakly epimorphic with val: <8 12 18 29 31| Scale is weakly epimorphic with val: <8 12 18 29 34| Scale is weakly epimorphic with val: <8 12 18 31 32| Scale is weakly epimorphic with val: <8 12 19 29 30| Scale is weakly epimorphic with val: <8 12 19 30 32| Scale is weakly epimorphic with val: <8 12 19 32 33| Scale is weakly epimorphic with val: <8 12 20 27 28| Scale is weakly epimorphic with val: <8 12 20 30 31| Scale is weakly epimorphic with val: <8 12 20 31 33| Scale is weakly epimorphic with val: <8 12 20 33 34| Scale is weakly epimorphic with val: <8 12 21 28 29| Scale is weakly epimorphic with val: <8 12 21 31 32| Scale is weakly epimorphic with val: <8 12 21 32 34| Scale is weakly epimorphic with val: <8 12 22 29 30| Scale is weakly epimorphic with val: <8 12 22 32 33|
FIT/MODE
3: 1 1 1 SP B ME I SD: 24.8103 c. M:-33.7955 c. 5: 1 2 2 SP M ME S SD: 19.2164 c. M: 32.6105 c. 7: 2 2 3 SP M ME S SD: 13.3914 c. M: 20.8903 c. 8: 2 3 3 SP M ME S SD: 5.5663 c. M: 7.7083 c. 15: 4 5 6 SP T3 SD: 3.8606 c. M: 6.6604 c. 18: 5 6 7 SP T3 SD: 3.5963 c. M:-6.1263 c. 23: 6 8 9 SP T3 SD: 1.8879 c. M: 2.3296 c. 26: 7 9 10 SP T3 SD: 1.2246 c. M:-1.8695 c. 41: 11 14 16 SP T3 SD: 1.3180 c. M: 1.8014 c. 49: 13 17 19 SP T3 SD: 0.3281 c. M: 0.5619 c. 83: 22 29 32 SP T3 SD: 0.3341 c. M:-0.5403 c. 124: 33 43 48 SP T3 SD: 0.2311 c. M:-0.3247 c. 132: 35 46 51 SP T3 SD: 0.1204 c. M: 0.1621 c. 181: 48 63 70 SP T3 SD: 0.0878 c. M: 0.1413 c. 207: 55 72 80 SP T3 SD: 0.0780 c. M:-0.1113 c. 256: 68 89 99 SP T3 SD: 0.0501 c. M:-0.0737 c. 339: 90 118 131 SP T3 SD: 0.0565 c. M:-0.0977 c. 388: 103 135 150 SP T3 SD: 0.0091 c. M:-0.0144 c. 1032: 274 359 399 SP T3 SD: 0.0077 c. M:-0.0134 c. 1213: 322 422 469 SP T3 SD: 0.0076 c. M: 0.0097 c. 1420: 377 494 549 SP T3 SD: 0.0050 c. M:-0.0079 c. 1808: 480 629 699 SP T3 SD: 0.0044 c. M:-0.0059 c. 2245: 596 781 868 SP T3 SD: 0.0029 c. M: 0.0050 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 5 x S SD: 80.8263 cents 5 x 6:7 S SD: 42.5377 cents 6 x 7:8 S SD: 19.3082 cents 7 x 8:9 S SD: 48.6994 cents 8:9:10:11 H SD: 40.1531 cents 9:10:11:12 H SD: 21.7965 cents 10:11:12:13 H SD: 18.5565 cents 11:12:13:15 SD: 15.3400 cents 12:13:14:16 S SD: 13.0452 cents 15:16:18:20 S SD: 7.6221 cents 25:27:30:33 SD: 6.7238 cents 26:28:31:35 SD: 5.6843 cents 27:29:32:36 SD: 4.7288 cents 36:39:43:48 SD: 2.2325 cents 51:55:61:68 SD: 1.5768 cents 63:68:75:84 SD: 1.2136 cents 99:107:118:132 SD: 0.9269 cents 114:123:136:152 SD: 0.2234 cents 264:285:315:352 SD: 0.1364 cents 378:408:451:504 SD: 0.0673 cents