Scala analysis: xen12-wilson-38-4C3-tetrany-02
1-3-5-11 4C3 Tetrany, Figure 38
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: 11/8 551.317942 undecimal semi-augmented fourth 3: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 5/4 386.3137 major third 3: 4/3 498.0450 perfect fourth 4: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 5/4 386.314 cents major third 1: 1 4/3 498.045 cents perfect fourth 2: 1 6/5 315.641 cents minor third 2: 1 11/8 551.318 cents undecimal semi-augmented fourth 2: 1 16/11 648.682 cents undecimal semi-diminished fifth 2: 1 5/3 884.359 cents major sixth, BP sixth 3: 1 3/2 701.955 cents perfect fifth 3: 1 8/5 813.686 cents minor sixth 3: 1 20/11 1034.996 cents large minor seventh 3: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 0.0 : 165.0 551.3 1049.4 1200.0 165.0 : 386.3 884.4 1035.0 1200.0 551.3 : 498.0 648.7 813.7 1200.0 1049.4: 150.6 315.6 702.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 498.0450 cents 11/9, 347.4079 cents 12/11, 150.6371 cents 2: 315.6413 .. 884.3587 cents 25/18, 568.7174 cents 9/10,-182.4037 cents 3: 701.9550 .. 1049.3629 cents 11/9, 347.4079 cents 9/10,-182.4037 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 4/3, 498.0450 cents Average / Smallest step : 1.991542 Largest / Average step : 1.660150 Largest / Smallest step : 3.306258 Median interval of one step : 275.65897 cents, amount: 0 Least squares average step : 307.19096 cents, oct.: 1228.76386 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : BCDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 53.27294 cents Scale diversity : 1.674660 Lumma stability : 0.251062 Lumma impropriety factor : 0.304006 Rothenberg efficiency : 0.500000 redundancy: 0.500000 Efficiency x scale size : 2.000000 Number of different interval sizes : 12 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 121/120, 14.3672 cents Number of recognisable fifths : 1, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 25.0000% Scale is differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.032002 Average absolute harmonicity : 0.283017 Specific harmonicity : 0.153038 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 22, 4.4594 octaves, 5755.762 Hz. Exponens Consonantiae : 2.640000E+03, 11.36632 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 30.0, average 7.50000 Mersenne's string divisions : 6783 Sum of van Prooijen's expressibility: 3.12418, average 0.78104 Sum of Tenney's harmonic distance : 6.10645, average 1.52661 Vogel's harmonic complexity : 16.25000 Wille's k value : 82 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 3 Triangular lattice diameter : 1 Lattice compactness : 22.53481, average 2.25348 Lattice compactness (without 2's) : 11.07107, average 1.10711 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.00000 6 1 3: -1 .. 0 -0.25000 1 5: -1 .. 0 -0.25000 1 11: 0 .. 1 0.75000 3 3 Average exponent except 2's : 1 / 4 = 0.25000 Average absolute exponent except 2's: 5 / 4 = 1.25000 Scale is weakly epimorphic with val: <4 5 10 15| Scale is weakly epimorphic with val: <4 6 9 15| Scale is JI-epimorphic with val: <4 7 9 14| Scale is weakly epimorphic with val: <4 7 10 13|
FIT/MODE
4: 0 1 2 1 N D3 SD: 167.8514 c. M: 251.3179 c. 5: 0 2 2 1 N G SD: 100.3723 c. M: 165.0042 c. 6: 1 2 2 1 P D3 I SD: 38.8309 c. M: 49.3629 c. 7: 1 2 3 1 N SD: 21.4764 c. M: 37.0322 c. 9: 1 3 4 1 N SD: 20.1613 c. M: 31.6709 c. 13: 2 4 5 2 N SD: 19.6565 c. M: 33.9783 c. 15: 2 5 6 2 N SD: 6.8572 c. M: 9.3629 c. 22: 3 7 9 3 N SD: 7.1630 c. M: 12.9993 c. 31: 4 10 13 4 N SD: 7.2288 c. M: 10.1655 c. 37: 5 12 15 5 N SD: 5.9352 c. M: 11.5251 c. 41: 6 13 17 5 N SD: 6.2003 c. M:-10.6055 c. 42: 6 13 18 5 N SD: 6.5838 c. M: 8.4608 c. 46: 6 15 19 6 N SD: 5.4492 c. M: 8.4825 c. 48: 7 15 20 6 N SD: 5.0512 c. M:-9.9958 c. 50: 7 16 21 6 N SD: 3.6569 c. M:-6.6371 c. 56: 8 18 23 7 N SD: 4.3476 c. M:-6.4243 c. 57: 8 18 24 7 N SD: 3.0805 c. M: 3.9495 c. 65: 9 21 27 8 N SD: 2.0239 c. M:-2.9448 c. 72: 10 23 30 9 N SD: 1.1075 c. M:-1.6624 c. 87: 12 28 36 11 N SD: 0.6344 c. M: 1.0871 c. 159: 22 51 66 20 N SD: 0.5706 c. M:-1.0335 c. 183: 25 59 76 23 N SD: 0.5971 c. M: 1.0698 c. 224: 31 72 93 28 N SD: 0.6640 c. M:-1.0672 c. 233: 32 75 97 29 N SD: 0.6595 c. M:-1.2808 c. 239: 33 77 99 30 N SD: 0.5995 c. M:-0.9833 c. 246: 34 79 102 31 N SD: 0.5173 c. M:-0.8494 c. 248: 34 80 103 31 N SD: 0.4275 c. M:-0.6371 c. 255: 35 82 106 32 N SD: 0.3949 c. M: 0.7297 c. 270: 37 87 112 34 N SD: 0.3811 c. M: 0.5598 c. 320: 44 103 133 40 N SD: 0.3203 c. M:-0.6371 c. 335: 46 108 139 42 N SD: 0.2195 c. M:-0.3238 c. 342: 47 110 142 43 N SD: 0.2551 c. M: 0.4407 c. 407: 56 131 169 51 N SD: 0.1454 c. M:-0.2685 c. 494: 68 159 205 62 N SD: 0.1029 c. M:-0.1780 c. 677: 93 218 281 85 N SD: 0.0867 c. M: 0.1593 c. 764: 105 246 317 96 N SD: 0.0850 c. M: 0.1483 c. 836: 115 269 347 105 N SD: 0.0805 c. M: 0.1218 c. 1084: 149 349 450 136 N SD: 0.0530 c. M:-0.0836 c. 1171: 161 377 486 147 N SD: 0.0091 c. M: 0.0170 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 75.3185 cents 3 x 4 x 6 S SD: 26.6365 cents 4 x 6:7:8 S SD: 56.9383 cents 5:6:7:9:10 SD: 39.2697 cents 6:7:8:11:12 SD: 28.7389 cents 7:8:10:13:14 SD: 24.0519 cents 8:9:11:15:16 SD: 13.7553 cents 10:11:14:18:20 SD: 11.1305 cents 11:12:15:20:22 S SD: 6.2212 cents 18:20:25:33:36 SD: 6.1516 cents 19:21:26:35:38 SD: 3.5840 cents 29:32:40:53:58 SD: 2.3488 cents 40:44:55:73:80 SD: 1.9718 cents 48:53:66:88:96 SD: 1.6363 cents 59:65:81:108:118 SD: 1.1554 cents 61:67:84:112:122 SD: 1.1169 cents 72:79:99:132:144 SD: 1.0943 cents 80:88:110:147:160 SD: 0.9825 cents 90:99:124:165:180 SD: 0.8735 cents 91:100:125:167:182 SD: 0.7490 cents 101:111:139:185:202 SD: 0.6749 cents 109:120:150:200:218 SD: 0.6250 cents 120:132:165:220:240 S SD: 0.0000 cents