Scala analysis: 585_M93
Miscellaneous tetrachord 11/10 * 95/88 * 64/57
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 19/16 297.513016 19th harmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/57 200.5320 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 95/88 132.5088 3: 64/57 200.5320
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 95/88 132.509 cents 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 64/57 200.532 cents 2: 1 19/16 297.513 cents 19th harmonic 2: 1 40/33 333.041 cents 2: 1 352/285 365.536 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 : 165.0 297.5 498.0 165.0: 132.5 333.0 498.0 297.5: 200.5 365.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 132.5088 .. 200.5320 cents 5632/5415, 68.0232 cents 95/88, 132.5088 cents 2: 297.5130 .. 365.5362 cents 5632/5415, 68.0232 cents 1083/1024, 96.9810 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 95/88, 132.5088 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 64/57, 200.5320 cents Average / Smallest step : 1.252860 Largest / Average step : 1.207915 Largest / Smallest step : 1.513349 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 161.01180 cents, oct.: 483.03541 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1977-tone equal temperament with octave 4/3 degrees: 655 1181 1977 Least number of segments generator : 989 of 249.148 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1502 of 378.383 cents and inv. generated superset size: 54 = 51 more = 1800.000% 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 : 1.341344 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.726839 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 : 484/475, 32.4954 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% -- Rational properties -- Prime limit : 19 Odd number limit : 285 (O: 95 U: 285) Highest odd numerator or denominator: 19 Scale harmonicity : 0.014847 Average absolute harmonicity : 0.093206 Specific harmonicity : 0.078794 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 836, 9.7074 octaves, 218718.973 Hz. Exponens Consonantiae : 2.006400E+05, 17.61425 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 31.5, average 10.50000 Mersenne's string divisions : 105 Sum of van Prooijen's expressibility: 2.79727, average 0.93242 Sum of Tenney's harmonic distance : 5.60345, average 1.86782 Vogel's harmonic complexity : 18.33333 Wille's k value : 142 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 21.18384, average 3.53064 Lattice compactness (without 2's) : 8.29253, average 1.38209 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.00000 7 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 11: 0 .. 1 0.33333 1 1 19: 0 .. 1 0.33333 1 1 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 15 24 28| Scale is weakly epimorphic with val: <6 10 15 24 31| Scale is weakly epimorphic with val: <6 10 15 24 34| Scale is weakly epimorphic with val: <6 10 16 25 28| Scale is weakly epimorphic with val: <6 10 16 25 31| Scale is weakly epimorphic with val: <6 10 16 25 34| Scale is weakly epimorphic with val: <6 10 17 26 28| Scale is weakly epimorphic with val: <6 10 17 26 31| Scale is weakly epimorphic with val: <6 10 17 26 34| Scale is weakly epimorphic with val: <6 10 18 27 28| Scale is weakly epimorphic with val: <6 10 18 27 31| Scale is weakly epimorphic with val: <6 10 18 27 34| Scale is weakly epimorphic with val: <6 11 15 24 29| Scale is weakly epimorphic with val: <6 11 15 24 32| Scale is weakly epimorphic with val: <6 11 16 25 29| Scale is weakly epimorphic with val: <6 11 16 25 32| Scale is weakly epimorphic with val: <6 11 17 26 29| Scale is weakly epimorphic with val: <6 11 17 26 32| Scale is weakly epimorphic with val: <6 11 18 27 29| Scale is weakly epimorphic with val: <6 11 18 27 32| Scale is weakly epimorphic with val: <7 10 15 24 31| Scale is weakly epimorphic with val: <7 10 15 25 30| Scale is weakly epimorphic with val: <7 10 15 25 33| Scale is weakly epimorphic with val: <7 10 15 27 31| Scale is weakly epimorphic with val: <7 10 16 25 31| Scale is weakly epimorphic with val: <7 10 16 26 30| Scale is weakly epimorphic with val: <7 10 16 26 33| Scale is weakly epimorphic with val: <7 10 17 23 31| Scale is weakly epimorphic with val: <7 10 17 26 31| Scale is weakly epimorphic with val: <7 10 17 27 30| Scale is weakly epimorphic with val: <7 10 17 27 33| Scale is weakly epimorphic with val: <7 10 18 24 31| Scale is weakly epimorphic with val: <7 10 18 27 31| Scale is weakly epimorphic with val: <7 10 19 25 31| Scale is JI-epimorphic with val: <7 11 15 23 30| Scale is weakly epimorphic with val: <7 11 15 23 33| Scale is weakly epimorphic with val: <7 11 15 24 29| Scale is weakly epimorphic with val: <7 11 15 24 32| Scale is weakly epimorphic with val: <7 11 15 26 30| Scale is weakly epimorphic with val: <7 11 15 26 33| Scale is weakly epimorphic with val: <7 11 15 27 29| Scale is weakly epimorphic with val: <7 11 15 27 32| Scale is JI-epimorphic with val: <7 11 16 24 30| Scale is weakly epimorphic with val: <7 11 16 24 33| Scale is weakly epimorphic with val: <7 11 16 25 29| Scale is weakly epimorphic with val: <7 11 16 25 32| Scale is weakly epimorphic with val: <7 11 16 27 30| Scale is weakly epimorphic with val: <7 11 16 27 33| Scale is weakly epimorphic with val: <7 11 17 23 29| Scale is weakly epimorphic with val: <7 11 17 23 32| Scale is JI-epimorphic with val: <7 11 17 25 30| Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is weakly epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 17 26 32| Scale is weakly epimorphic with val: <7 11 18 23 30| Scale is weakly epimorphic with val: <7 11 18 23 33| Scale is weakly epimorphic with val: <7 11 18 24 29| Scale is weakly epimorphic with val: <7 11 18 24 32| Scale is JI-epimorphic with val: <7 11 18 26 30| Scale is weakly epimorphic with val: <7 11 18 26 33| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 19 24 30| Scale is weakly epimorphic with val: <7 11 19 24 33| Scale is weakly epimorphic with val: <7 11 19 25 29| Scale is weakly epimorphic with val: <7 11 19 25 32| Scale is JI-epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is weakly epimorphic with val: <7 12 15 23 31| Scale is weakly epimorphic with val: <7 12 15 25 29| Scale is weakly epimorphic with val: <7 12 15 25 32| Scale is weakly epimorphic with val: <7 12 15 26 31| Scale is weakly epimorphic with val: <7 12 16 24 31| Scale is weakly epimorphic with val: <7 12 16 26 29| Scale is weakly epimorphic with val: <7 12 16 26 32| Scale is weakly epimorphic with val: <7 12 16 27 31| Scale is weakly epimorphic with val: <7 12 17 25 31| Scale is weakly epimorphic with val: <7 12 17 27 29| Scale is weakly epimorphic with val: <7 12 17 27 32| Scale is weakly epimorphic with val: <7 12 18 23 31| Scale is weakly epimorphic with val: <7 12 18 26 31| Scale is weakly epimorphic with val: <7 12 19 24 31| Scale is weakly epimorphic with val: <7 12 19 27 31| Scale is weakly epimorphic with val: <8 11 15 26 30| Scale is weakly epimorphic with val: <8 11 15 26 33| Scale is weakly epimorphic with val: <8 11 16 27 30| Scale is weakly epimorphic with val: <8 11 16 27 33| Scale is weakly epimorphic with val: <8 12 15 26 28| Scale is weakly epimorphic with val: <8 12 15 26 31| Scale is weakly epimorphic with val: <8 12 15 26 34| Scale is weakly epimorphic with val: <8 12 16 27 28| Scale is weakly epimorphic with val: <8 12 16 27 31| Scale is weakly epimorphic with val: <8 12 16 27 34|
FIT/MODE
3: 1 1 1 SP B ME I SD: 19.9369 c. M:-34.5170 c. 5: 2 1 2 SP M ME I SD: 19.7679 c. M:-34.2138 c. 7: 2 2 3 SP M ME S SD: 15.0816 c. M: 22.7057 c. 8: 3 2 3 SP M ME I SD: 14.8671 c. M:-21.7626 c. 9: 3 2 4 SP T3 SD: 12.0354 c. M: 20.8213 c. 10: 3 3 4 SP M ME S SD: 9.0332 c. M: 15.5907 c. 12: 4 3 5 SP T3 SD: 4.0758 c. M: 6.9868 c. Raga Malasri, Peruvian tritonic 1 15: 5 4 6 SP T3 SD: 0.9571 c. M:-1.3140 c. 42: 14 11 17 SP T3 SD: 0.8447 c. M: 1.0577 c. 57: 19 15 23 SP T3 SD: 0.6350 c. M:-1.0108 c. 72: 24 19 29 SP T3 SD: 0.5849 c. M:-1.0108 c. 87: 29 23 35 SP T3 SD: 0.5917 c. M:-1.0108 c. 94: 31 25 38 SP T3 SD: 0.6375 c. M: 0.8054 c. 97: 32 26 39 SP T3 SD: 0.4372 c. M: 0.7007 c. 109: 36 29 44 SP T3 SD: 0.4189 c. M: 0.5137 c. 112: 37 30 45 SP T3 SD: 0.3663 c. M: 0.4715 c. 124: 41 33 50 SP T3 SD: 0.2538 c. M: 0.3281 c. 139: 46 37 56 SP T3 SD: 0.1264 c. M: 0.1836 c. 154: 51 41 62 SP T3 SD: 0.0406 c. M: 0.0672 c. 477: 158 127 192 SP T3 SD: 0.0402 c. M:-0.0610 c. 519: 172 138 209 SP T3 SD: 0.0341 c. M:-0.0511 c. 631: 209 168 254 SP T3 SD: 0.0381 c. M:-0.0511 c. 658: 218 175 265 SP T3 SD: 0.0280 c. M: 0.0484 c. 673: 223 179 271 SP T3 SD: 0.0174 c. M:-0.0241 c. 827: 274 220 333 SP T3 SD: 0.0075 c. M: 0.0109 c. 981: 325 261 395 SP T3 SD: 0.0044 c. M: 0.0060 c. 1977: 655 526 796 SP T3 SD: 0.0029 c. M:-0.0040 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: 45.6687 cents 8:9:10:11 H SD: 36.8740 cents 9:10:11:12 H SD: 17.6139 cents 10:11:12:13 H SD: 15.8107 cents 11:12:13:15 SD: 14.0989 cents 12:13:14:16 S SD: 13.4890 cents 18:20:21:24 S SD: 11.7458 cents 20:22:24:27 S SD: 9.3758 cents 21:23:25:28 SD: 2.8904 cents 48:53:57:64 SD: 2.1818 cents 60:66:71:80 SD: 2.0284 cents 69:76:82:92 SD: 0.8780 cents 90:99:107:120 SD: 0.6746 cents 150:165:178:200 SD: 0.4051 cents 171:188:203:228 SD: 0.3546 cents 219:241:260:292 SD: 0.2768 cents 240:264:285:320 SD: 0.0000 cents