Scala analysis: 584_M92
Miscellaneous tetrachord 19/17 * 17/16 * 64/57
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/17 192.557607 quasi-meantone 2: 19/16 297.513016 19th harmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/57 200.5320 1: 19/17 192.5576 quasi-meantone 2: 17/16 104.9554 17th harmonic 3: 64/57 200.5320
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 17/16 104.955 cents 17th harmonic 1: 1 19/17 192.558 cents quasi-meantone 1: 1 64/57 200.532 cents 2: 1 19/16 297.513 cents 19th harmonic 2: 1 68/57 305.487 cents 2: 1 64/51 393.090 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 : 192.6 297.5 498.0 192.6: 105.0 305.5 498.0 297.5: 200.5 393.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.9554 .. 200.5320 cents 1024/969, 95.5766 cents 17/16, 104.9554 cents 2: 297.5130 .. 393.0896 cents 1024/969, 95.5766 cents 1083/1024, 96.9810 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 17/16, 104.9554 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 64/57, 200.5320 cents Average / Smallest step : 1.581767 Largest / Average step : 1.207915 Largest / Smallest step : 1.910640 Median interval of one step : 19/17, 192.5576 cents, amount: 1 Least squares average step : 162.97990 cents, oct.: 488.93971 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1751-tone equal temperament with octave 4/3 degrees: 677 1046 1751 Least number of segments generator : 876 of 249.165 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1158 of 329.375 cents and inv. generated superset size: 24 = 21 more = 800.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 96.98103 cents Scale diversity : 1.143354 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.616193 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 : 1088/1083, 7.9744 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 19 Odd number limit : 57 (O: 19 U: 57) Highest odd numerator or denominator: 19 Scale harmonicity : 0.013719 Average absolute harmonicity : 0.085366 Specific harmonicity : 0.063297 Fundamental : 1/816, -9.6724 octaves, 0.3206 Hz. Guide tone : 76, 6.2479 octaves, 19883.543 Hz. Exponens Consonantiae : 6.201600E+04, 15.92035 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 39.0, average 13.00000 Mersenne's string divisions : 1260 Sum of van Prooijen's expressibility: 3.03463, average 1.01154 Sum of Tenney's harmonic distance : 6.07126, average 2.02375 Vogel's harmonic complexity : 29.33333 Wille's k value : 484 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 20.70666, average 3.45111 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.66667 6 3: -1 .. 0 -0.33333 1 1 17: -1 .. 0 -0.33333 1 19: 0 .. 1 0.66667 2 2 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <6 10 28 31| Scale is weakly epimorphic with val: <6 10 31 34| Scale is weakly epimorphic with val: <6 11 29 32| Scale is weakly epimorphic with val: <7 10 27 30| Scale is weakly epimorphic with val: <7 10 29 31| Scale is weakly epimorphic with val: <7 10 30 33| Scale is weakly epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 11 27 32| Scale is JI-epimorphic with val: <7 11 29 30| Scale is weakly epimorphic with val: <7 11 29 33| Scale is weakly epimorphic with val: <7 11 30 32| Scale is weakly epimorphic with val: <7 11 32 33| Scale is weakly epimorphic with val: <7 12 27 31| Scale is weakly epimorphic with val: <7 12 29 32| Scale is weakly epimorphic with val: <7 12 30 31| Scale is weakly epimorphic with val: <8 11 27 30| Scale is weakly epimorphic with val: <8 11 30 33| Scale is weakly epimorphic with val: <8 12 28 31| Scale is weakly epimorphic with val: <8 12 31 34|
FIT/MODE
3: 1 1 1 SP B ME I SD: 25.1392 c. M:-34.5170 c. 5: 2 1 2 SP M ME I SD: 3.9195 c. M:-6.6604 c. 23: 9 5 9 SP M DE I SD: 3.5257 c. M:-5.6448 c. 28: 11 6 11 SP M DE I SD: 3.3346 c. M:-4.8714 c. 33: 13 7 13 SP M DE I SD: 3.2677 c. M:-4.3324 c. 34: 13 7 14 SP T3 SD: 2.8978 c. M: 4.5454 c. 37: 14 8 15 SP T3 SD: 2.5017 c. M: 4.1081 c. 38: 15 8 15 SP M DE I SD: 3.2558 c. M:-4.0391 c. 39: 15 8 16 SP T3 SD: 2.2656 c. M: 3.7942 c. 42: 16 9 17 SP T3 SD: 1.7422 c. M: 2.8262 c. 47: 18 10 19 SP T3 SD: 1.1475 c. M: 1.8170 c. 52: 20 11 21 SP T3 SD: 0.6747 c. M: 1.0018 c. 57: 22 12 23 SP T3 SD: 0.3145 c. M: 0.4335 c. 62: 24 13 25 SP T3 SD: 0.2163 c. M: 0.2926 c. 119: 46 25 48 SP T3 SD: 0.2090 c. M: 0.3601 c. 176: 68 37 71 SP T3 SD: 0.2342 c. M: 0.3839 c. 181: 70 38 73 SP T3 SD: 0.1973 c. M: 0.3370 c. 189: 73 40 76 SP T3 SD: 0.1862 c. M:-0.2599 c. 194: 75 41 78 SP T3 SD: 0.1660 c. M:-0.2871 c. 246: 95 52 99 SP T3 SD: 0.1410 c. M: 0.2232 c. 251: 97 53 101 SP T3 SD: 0.0869 c. M:-0.1234 c. 256: 99 54 103 SP T3 SD: 0.0887 c. M:-0.1467 c. 308: 119 65 124 SP T3 SD: 0.0766 c. M: 0.1311 c. 313: 121 66 126 SP T3 SD: 0.0271 c. M:-0.0410 c. 375: 145 79 151 SP T3 SD: 0.0140 c. M:-0.0198 c. 688: 266 145 277 SP T3 SD: 0.0063 c. M:-0.0110 c. 1063: 411 224 428 SP T3 SD: 0.0044 c. M:-0.0073 c. 1751: 677 369 705 SP T3 SD: 0.0042 c. M:-0.0056 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: 88.8007 cents 5 x 6:7 S SD: 43.1953 cents 6 x 7:8 S SD: 15.3211 cents 7:8 x 9 S SD: 36.9300 cents 8:9:10:11 H SD: 34.7250 cents 9:10:11:12 H SD: 16.9725 cents 13 x 15:17 SD: 30.0307 cents 14:16:17:19 SD: 20.8737 cents 15:17:18:20 SD: 10.0601 cents 16:18:19:21 SD: 9.8444 cents 25:28:30:33 SD: 8.4632 cents 26:29:31:35 SD: 6.1074 cents 27:30:32:36 S SD: 3.5670 cents 33:37:39:44 SD: 3.3224 cents 42:47:50:56 SD: 1.6152 cents 69:77:82:92 SD: 0.9848 cents 102:114:121:136 SD: 0.5958 cents 144:161:171:192 SD: 0.2109 cents 213:238:253:284 SD: 0.2017 cents 315:352:374:420 SD: 0.1364 cents 357:399:424:476 SD: 0.0851 cents 459:513:545:612 SD: 0.0662 cents