Scala analysis: xen12-wilson-08-4C3-tetrany-08
1-7-11-15 4C3 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 15/11 536.950772 undecimal augmented fourth 3: 15/8 1088.268715 classic major seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 15/14 119.4428 major diatonic semitone 2: 14/11 417.5080 undecimal diminished fourth or major third 3: 11/8 551.3179 undecimal semi-augmented fourth 4: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 14/11 417.508 cents undecimal diminished fourth or major third 1: 1 11/8 551.318 cents undecimal semi-augmented fourth 2: 1 8/7 231.174 cents septimal whole tone 2: 1 15/11 536.951 cents undecimal augmented fourth 2: 1 22/15 663.049 cents undecimal diminished fifth 2: 1 7/4 968.826 cents harmonic seventh 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 11/7 782.492 cents undecimal augmented fifth 3: 1 28/15 1080.557 cents grave major seventh 3: 1 15/8 1088.269 cents classic major seventh 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 : 119.4 537.0 1088.3 1200.0 119.4 : 417.5 968.8 1080.6 1200.0 537.0 : 551.3 663.0 782.5 1200.0 1088.3: 111.7 231.2 648.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 551.3179 cents 165/128, 439.5867 cents 16/15, 111.7313 cents 2: 231.1741 .. 968.8259 cents 49/32, 737.6518 cents 64/77,-320.1438 cents 3: 648.6821 .. 1088.2687 cents 165/128, 439.5867 cents 64/77,-320.1438 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 11/8, 551.3179 cents Average / Smallest step : 2.685013 Largest / Average step : 1.837726 Largest / Smallest step : 4.934320 Median interval of one step : 268.47539 cents, amount: 0 Least squares average step : 308.60502 cents, oct.: 1234.42007 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 14.36717 cents Scale diversity : 1.594398 Lumma stability : 0.186219 Lumma impropriety factor : 0.533573 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 : 225/224, 7.7115 cents Number of recognisable fifths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 25.0000% -- Rational properties -- Prime limit : 11 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.024077 Average absolute harmonicity : 0.292176 Specific harmonicity : 0.134213 Fundamental : 1/616, -9.2668 octaves, 0.4247 Hz. Guide tone : 30, 4.9069 octaves, 7848.767 Hz. Exponens Consonantiae : 1.848000E+04, 14.17368 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 40.5, average 10.12500 Mersenne's string divisions : 52026 Sum of van Prooijen's expressibility: 3.52827, average 0.88207 Sum of Tenney's harmonic distance : 6.91991, average 1.72998 Vogel's harmonic complexity : 21.75000 Wille's k value : 577 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 24.06746, average 2.40675 Lattice compactness (without 2's) : 13.17084, average 1.31708 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.75000 5 1 3: 0 .. 1 0.75000 3 5: 0 .. 1 0.75000 3 1 7: -1 .. 0 -0.25000 1 1 11: -1 .. 0 -0.25000 1 1 Average exponent except 2's : 4 / 4 = 1.00000 Average absolute exponent except 2's: 8 / 4 = 2.00000 Scale is weakly epimorphic with val: <4 5 8 10 15| Scale is weakly epimorphic with val: <4 5 8 11 14| Scale is weakly epimorphic with val: <4 5 9 11 13| Scale is JI-epimorphic with val: <4 5 10 10 13| Scale is weakly epimorphic with val: <4 6 8 11 13| Scale is JI-epimorphic with val: <4 6 9 10 13| Scale is JI-epimorphic with val: <4 7 8 10 13| Scale is weakly epimorphic with val: <4 7 10 10 15| Scale is weakly epimorphic with val: <4 7 10 11 14|
FIT/MODE
4: 0 2 2 0 N D3 I SD: 87.6437 c. M: 119.4428 c. 5: 0 2 2 1 N G SD: 92.1450 c. M: 128.2687 c. 7: 1 2 3 1 N SD: 41.1703 c. M: 59.6973 c. 8: 1 3 3 1 N D3 I SD: 39.9169 c. M:-63.0492 c. 9: 1 3 4 1 N SD: 12.9680 c. M: 21.6020 c. 11: 1 4 5 1 N SD: 6.8273 c. M: 10.3519 c. 20: 2 7 9 2 N SD: 4.4153 c. M: 8.2687 c. 31: 3 11 14 3 N SD: 3.7138 c. M:-4.9847 c. 51: 5 18 23 5 N SD: 3.7442 c. M: 5.9158 c. 52: 5 18 24 5 N SD: 4.1239 c. M: 6.1815 c. 63: 6 22 29 6 N SD: 3.3988 c. M: 5.1571 c. 72: 7 25 33 7 N SD: 3.3597 c. M: 4.9354 c. 74: 7 26 34 7 N SD: 3.2260 c. M: 5.9293 c. 78: 8 27 36 7 N SD: 2.8197 c. M:-4.0390 c. 83: 8 29 38 8 N SD: 2.9064 c. M: 3.9314 c. 87: 9 30 40 8 N SD: 2.4964 c. M:-4.6951 c. 89: 9 31 41 8 N SD: 2.4606 c. M:-3.8661 c. 98: 10 34 45 9 N SD: 1.9170 c. M:-3.0062 c. 109: 11 38 50 10 N SD: 1.7089 c. M:-2.4988 c. 118: 12 41 54 11 N SD: 1.6478 c. M:-2.5911 c. 119: 12 41 55 11 N SD: 1.5278 c. M: 2.4970 c. 121: 12 42 56 11 N SD: 1.5132 c. M:-2.6404 c. 129: 13 45 59 12 N SD: 1.4917 c. M:-2.5841 c. 130: 13 45 60 12 N SD: 0.9603 c. M: 1.5662 c. 141: 14 49 65 13 N SD: 0.6874 c. M:-1.0930 c. 150: 15 52 69 14 N SD: 0.5672 c. M: 0.9508 c. 161: 16 56 74 15 N SD: 0.1825 c. M: 0.3048 c. 592: 59 206 272 55 N SD: 0.1786 c. M:-0.2448 c. 612: 61 213 281 57 N SD: 0.1738 c. M:-0.3041 c. 742: 74 258 341 69 N SD: 0.1370 c. M:-0.2337 c. 753: 75 262 346 70 N SD: 0.1095 c. M:-0.1775 c. 773: 77 269 355 72 N SD: 0.1018 c. M:-0.1773 c. 903: 90 314 415 84 N SD: 0.1015 c. M:-0.1585 c. 914: 91 318 420 85 N SD: 0.0704 c. M:-0.1339 c. 934: 93 325 429 87 N SD: 0.0567 c. M:-0.0942 c. 1075: 107 374 494 100 N SD: 0.0527 c. M:-0.1034 c. 1095: 109 381 503 102 N SD: 0.0308 c. M: 0.0495 c. 1256: 125 437 577 117 N SD: 0.0276 c. M: 0.0522 c. 2009: 200 699 923 187 N SD: 0.0256 c. M:-0.0339 c. 2170: 216 755 997 202 N SD: 0.0138 c. M:-0.0262 c. 2331: 232 811 1071 217 N SD: 0.0128 c. M:-0.0196 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 82.5021 cents 3 x 4 x 6 S SD: 19.4529 cents 4 x 5 x 8 SD: 75.3185 cents 5:6:7:9:10 SD: 53.3645 cents 6:7:8:11:12 SD: 39.3402 cents 7:8:10:13:14 SD: 34.6812 cents 8:9:11:15:16 SD: 21.4201 cents 9:10:12:17:18 SD: 18.7766 cents 10:11:14:19:20 SD: 17.0981 cents 11:12:15:21:22 SD: 11.0288 cents 13:14:18:24:26 SD: 9.6744 cents 14:15:19:26:28 SD: 4.6284 cents 25:27:34:47:50 SD: 3.8154 cents 30:32:41:56:60 SD: 2.8908 cents 39:42:53:73:78 SD: 2.7652 cents 41:44:56:77:82 SD: 1.2179 cents 55:59:75:103:110 SD: 0.7419 cents 96:103:131:180:192 SD: 0.6717 cents 113:121:154:212:226 SD: 0.4423 cents 154:165:210:289:308 SD: 0.3746 cents 168:180:229:315:336 SD: 0.1718 cents 352:377:480:660:704 SD: 0.1640 cents 377:404:514:707:754 SD: 0.1326 cents 393:421:536:737:786 SD: 0.1272 cents 407:436:555:763:814 SD: 0.1003 cents 448:480:611:840:896 SD: 0.0644 cents