Scala analysis: 582_M90
Miscellaneous tetrachord 4096/3645 * 35/32 * 243/224
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 4096/3645 201.956281 narrow diminished third 2: 896/729 357.095901 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 243/224 140.9491 Archytas' 2/3-tone 1: 4096/3645 201.9563 narrow diminished third 2: 35/32 155.1396 septimal neutral second 3: 243/224 140.9491 Archytas' 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 243/224 140.949 cents Archytas' 2/3-tone 1: 1 35/32 155.140 cents septimal neutral second 1: 1 4096/3645 201.956 cents narrow diminished third 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 128/105 342.905 cents septimal neutral third 2: 1 896/729 357.096 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 : 202.0 357.1 498.0 202.0: 155.1 296.1 498.0 357.1: 140.9 342.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 140.9491 .. 201.9563 cents 917504/885735, 61.0072 cents 243/224, 140.9491 cents 2: 296.0887 .. 357.0959 cents 917504/885735, 61.0072 cents 4428675/4194304, 94.1324 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 243/224, 140.9491 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 4096/3645, 201.9563 cents Average / Smallest step : 1.177837 Largest / Average step : 1.216494 Largest / Smallest step : 1.432831 Median interval of one step : 35/32, 155.1396 cents, amount: 1 Least squares average step : 172.16308 cents, oct.: 516.48923 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 947-tone equal temperament with octave 4/3 degrees: 384 679 947 Least number of segments generator : 474 of 249.285 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 813 of 427.572 cents and inv. generated superset size: 20 = 17 more = 666.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LMS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 94.13244 cents Scale diversity : 1.352565 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.755013 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 : 245/243, 14.1905 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 decreasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 46.8167 cents: 1 -- Rational properties -- Prime limit : 7 Odd number limit : 3645 (O: 1215 U: 3645) Highest odd numerator or denominator: 3645 Scale harmonicity : 0.022379 Average absolute harmonicity : 0.091132 Specific harmonicity : 0.104993 Fundamental : 1/3645, -11.8317 octaves, 0.0718 Hz. Guide tone : 28672, 14.8074 octaves, 7501328.208 Hz. Exponens Consonantiae : 1.045094E+08, 26.63906 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 4686.5, average 1562.16667 Mersenne's string divisions : 88053875 Sum of van Prooijen's expressibility: 6.90155, average 2.30052 Sum of Tenney's harmonic distance : 14.06827, average 4.68942 Vogel's harmonic complexity : 17.66667 Wille's k value : 607 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 48.52586, average 8.08764 Lattice compactness (without 2's) : 24.77778, average 4.12963 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 12 7.00000 21 3: -6 ..-1 -4.33333 13 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-13 / 3 =-4.33333 Average absolute exponent except 2's: 15 / 3 = 5.00000 Scale is weakly epimorphic with val: <6 10 17 21| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 11 16 21| Scale is JI-epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 11 19 21| Scale is weakly epimorphic with val: <8 12 16 19| Scale is weakly epimorphic with val: <8 12 19 19|
FIT/MODE
3: 1 1 1 SP B ME I SD: 25.2987 c. M: 35.9413 c. 5: 2 2 1 SP M ME S SD: 23.9200 c. M:-41.3401 c. 7: 3 2 2 SP M ME S SD: 6.6803 c. M:-11.4916 c. 10: 4 3 3 SP M ME S SD: 5.1363 c. M: 8.4644 c. 15: 6 5 4 SP T3 SD: 4.9568 c. M:-8.1371 c. 17: 7 5 5 SP M DE S SD: 3.6685 c. M: 5.5347 c. 22: 9 7 6 SP T3 SD: 3.1306 c. M:-5.1186 c. 25: 10 8 7 SP T3 SD: 1.8016 c. M: 2.7383 c. 32: 13 10 9 SP T3 SD: 0.5489 c. M:-0.8739 c. 74: 30 23 21 SP T3 SD: 0.2256 c. M: 0.3880 c. 106: 43 33 30 SP T3 SD: 0.0469 c. M:-0.0808 c. 392: 159 122 111 SP T3 SD: 0.0562 c. M: 0.0790 c. 449: 182 140 127 SP T3 SD: 0.0624 c. M:-0.0767 c. 498: 202 155 141 SP T3 SD: 0.0513 c. M: 0.0636 c. 523: 212 163 148 SP T3 SD: 0.0420 c. M: 0.0719 c. 555: 225 173 157 SP T3 SD: 0.0440 c. M:-0.0607 c. 597: 242 186 169 SP T3 SD: 0.0455 c. M: 0.0687 c. 629: 255 196 178 SP T3 SD: 0.0270 c. M: 0.0461 c. 735: 298 229 208 SP T3 SD: 0.0164 c. M: 0.0278 c. 841: 341 262 238 SP T3 SD: 0.0085 c. M: 0.0141 c. 947: 384 295 268 SP T3 SD: 0.0026 c. M: 0.0035 c. 1053: 427 328 298 SP T3 SD: 0.0031 c. M:-0.0050 c. 2000: 811 623 566 SP T3 SD: 0.0015 c. M:-0.0024 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: 29.2178 cents 5 x 6:7 S SD: 47.0457 cents 6:7 x 8 S SD: 32.4573 cents 7:8 x 9 S SD: 34.7050 cents 8:9:10:11 H SD: 20.2636 cents 9:10:11:12 H SD: 7.2737 cents 26:29:32:35 SD: 7.0451 cents 30:34:37:40 SD: 5.2993 cents 39:44:48:52 SD: 2.4260 cents 48:54:59:64 SD: 0.6525 cents 105:118:129:140 SD: 0.2426 cents 258:290:317:344 SD: 0.2424 cents 363:408:446:484 SD: 0.2358 cents 468:526:575:624 SD: 0.2344 cents 501:563:616:668 SD: 0.2162 cents 510:573:627:680 SD: 0.1867 cents 558:627:686:744 SD: 0.1505 cents