Scala analysis: 581_M89
Miscellaneous tetrachord 14/13 * 260/231 * 11/10
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 40/33 333.040771 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 11/10 165.0042 Ptolemy's second, 4/5-tone 1: 14/13 128.2982 2/3-tone 2: 260/231 204.7425 3: 11/10 165.0042 Ptolemy's second, 4/5-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 14/13 128.298 cents 2/3-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 260/231 204.743 cents 2: 1 77/65 293.302 cents 2: 1 40/33 333.041 cents 2: 1 26/21 369.747 cents 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 : 128.3 333.0 498.0 128.3: 204.7 369.7 498.0 333.0: 165.0 293.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 204.7425 cents 1690/1617, 76.4443 cents 14/13, 128.2982 cents 2: 293.3025 .. 369.7468 cents 1690/1617, 76.4443 cents 17787/16900, 88.5599 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 14/13, 128.2982 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 260/231, 204.7425 cents Average / Smallest step : 1.293977 Largest / Average step : 1.233277 Largest / Smallest step : 1.595833 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 163.46534 cents, oct.: 490.39603 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1316-tone equal temperament with octave 4/3 degrees: 339 880 1316 Least number of segments generator : 659 of 249.401 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 767 of 290.274 cents and inv. generated superset size: 16 = 13 more = 533.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 88.55995 cents Scale diversity : 1.342767 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.693023 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 : 143/140, 36.7060 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 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 -- Rational properties -- Prime limit : 13 Odd number limit : 231 (O: 77 U: 231) Highest odd numerator or denominator: 33 Scale harmonicity : 0.015952 Average absolute harmonicity : 0.092416 Specific harmonicity : 0.083450 Fundamental : 1/429, -8.7448 octaves, 0.6098 Hz. Guide tone : 280, 8.1293 octaves, 73255.158 Hz. Exponens Consonantiae : 1.201200E+05, 16.87412 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 53.5, average 17.83333 Mersenne's string divisions : 13797 Sum of van Prooijen's expressibility: 3.10958, average 1.03653 Sum of Tenney's harmonic distance : 6.45983, average 2.15328 Vogel's harmonic complexity : 23.00000 Wille's k value : 115 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.16427, average 2.36071 Lattice compactness (without 2's) : 9.52860, average 1.58810 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 .. 0 -0.66667 2 1 5: 0 .. 1 0.33333 1 7: 0 .. 1 0.33333 1 11: -1 .. 0 -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: <7 11 16 19 24 28| Scale is weakly epimorphic with val: <7 11 16 19 25 27| Scale is JI-epimorphic with val: <7 11 16 20 24 26| Scale is weakly epimorphic with val: <7 11 16 20 25 28| Scale is JI-epimorphic with val: <7 11 16 21 24 27| Scale is weakly epimorphic with val: <7 11 16 21 25 26| Scale is weakly epimorphic with val: <7 11 17 19 25 28| Scale is weakly epimorphic with val: <7 11 17 19 26 27| Scale is JI-epimorphic with val: <7 11 17 20 25 26| Scale is weakly epimorphic with val: <7 11 17 20 26 28| Scale is JI-epimorphic with val: <7 11 17 21 25 27| Scale is weakly epimorphic with val: <7 11 17 21 26 26| Scale is weakly epimorphic with val: <7 11 18 19 24 27| Scale is weakly epimorphic with val: <7 11 18 19 26 28| Scale is weakly epimorphic with val: <7 11 18 20 24 28| Scale is JI-epimorphic with val: <7 11 18 20 26 26| Scale is weakly epimorphic with val: <7 11 18 21 24 26| Scale is JI-epimorphic with val: <7 11 18 21 26 27| Scale is weakly epimorphic with val: <7 12 18 19 24 28| Scale is weakly epimorphic with val: <7 12 18 20 24 26| Scale is weakly epimorphic with val: <7 12 18 21 24 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 21.7836 c. M:-37.7168 c. 5: 1 2 2 SP M ME S SD: 25.7789 c. M: 34.2138 c. 7: 2 3 2 SP M ME I SD: 15.4008 c. M:-22.7057 c. 8: 2 3 3 SP M ME S SD: 12.7535 c. M: 21.7626 c. 9: 2 4 3 SP T3 SD: 10.1905 c. M: 17.6216 c. 11: 3 4 4 SP M ME S SD: 10.2639 c. M: 16.1030 c. 12: 3 5 4 SP T3 SD: 2.2630 c. M: 3.7870 c. 27: 7 11 9 SP T3 SD: 0.7531 c. M: 1.0108 c. 39: 10 16 13 SP T3 SD: 0.6770 c. M: 1.0108 c. 66: 17 27 22 SP T3 SD: 0.5836 c. M: 1.0108 c. 85: 22 35 28 SP T3 SD: 0.6473 c. M:-0.9423 c. 93: 24 38 31 SP T3 SD: 0.5984 c. M: 1.0108 c. 97: 25 40 32 SP T3 SD: 0.4062 c. M:-0.7007 c. 109: 28 45 36 SP T3 SD: 0.3615 c. M:-0.5123 c. 124: 32 51 41 SP T3 SD: 0.2312 c. M:-0.3281 c. 136: 35 56 45 SP T3 SD: 0.1410 c. M:-0.2099 c. 163: 42 67 54 SP T3 SD: 0.0192 c. M:-0.0324 c. 827: 213 340 274 SP T3 SD: 0.0139 c. M: 0.0231 c. 990: 255 407 328 SP T3 SD: 0.0085 c. M: 0.0139 c. 1153: 297 474 382 SP T3 SD: 0.0046 c. M: 0.0074 c. 1316: 339 541 436 SP T3 SD: 0.0017 c. M: 0.0025 c. 1479: 381 608 490 SP T3 SD: 0.0009 c. M:-0.0014 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: 53.2729 cents 5 x 6:7 S SD: 43.1203 cents 6 x 7:8 S SD: 33.0849 cents 7 x 8:9 S SD: 59.8767 cents 8:9:10:11 H SD: 35.5796 cents 9:10:11:12 H SD: 18.6602 cents 12:13:15:16 SD: 18.0849 cents 13:14:16:17 S SD: 14.2546 cents 14:15:17:19 SD: 10.6817 cents 15:16:18:20 S SD: 8.0084 cents 24:26:29:32 SD: 3.8719 cents 39:42:47:52 SD: 3.3389 cents 42:45:51:56 SD: 3.1262 cents 51:55:62:68 SD: 1.8774 cents 66:71:80:88 SD: 0.6249 cents 156:168:189:208 SD: 0.2775 cents 222:239:269:296 SD: 0.2693 cents 273:294:331:364 SD: 0.1585 cents 363:391:440:484 SD: 0.1135 cents 429:462:520:572 SD: 0.0000 cents