Scala analysis: xen12-wilson-38-4C3-tetrany-10
3-5-7-9 4C3 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/7 435.084095 septimal major third, BP third 2: 3/2 701.955001 perfect fifth 3: 9/5 1017.596288 just minor seventh, BP seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 9/7 435.0841 septimal major third, BP third 2: 7/6 266.8709 septimal minor third 3: 6/5 315.6413 minor third 4: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 10/9 182.404 cents minor whole tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 6/5 315.641 cents minor third 1: 1 9/7 435.084 cents septimal major third, BP third 2: 1 4/3 498.045 cents perfect fourth 2: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 2: 1 10/7 617.488 cents Euler's tritone 2: 1 3/2 701.955 cents perfect fifth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 5/3 884.359 cents major sixth, BP sixth 3: 1 12/7 933.129 cents septimal major sixth 3: 1 9/5 1017.596 cents just minor seventh, BP 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 : 435.1 702.0 1017.6 1200.0 435.1 : 266.9 582.5 764.9 1200.0 702.0 : 315.6 498.0 933.1 1200.0 1017.6: 182.4 617.5 884.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 182.4037 .. 435.0841 cents 81/70, 252.6804 cents 10/9, 182.4037 cents 2: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 28/27, 62.9609 cents 3: 764.9159 .. 1017.5963 cents 81/70, 252.6804 cents 28/27, 62.9609 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 10/9, 182.4037 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 1.644703 Largest / Average step : 1.450280 Largest / Smallest step : 2.385281 Median interval of one step : 291.25610 cents, amount: 0 Least squares average step : 323.05943 cents, oct.: 1292.23773 cents Scale is strictly proper Step pattern alph. order: ABCD Step pattern size order : DBCA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 62.96090 cents Scale diversity : 1.694163 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.408941 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 : 50/49, 34.9756 cents Number of recognisable fifths : 1, average 701.9550 cents Best major thirds form a closed circle Best minor thirds form a closed circle Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 25.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 9 (O: 9 U: 9) Highest odd numerator or denominator: 9 Scale harmonicity : 0.041634 Average absolute harmonicity : 0.355494 Specific harmonicity : 0.234207 Fundamental : 1/70, -6.1293 octaves, 3.7375 Hz. Guide tone : 18, 4.1699 octaves, 4709.260 Hz. Exponens Consonantiae : 1.260000E+03, 10.29921 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 19.0, average 4.75000 Mersenne's string divisions : 1680 Sum of van Prooijen's expressibility: 2.38561, average 0.59640 Sum of Tenney's harmonic distance : 4.53173, average 1.13293 Vogel's harmonic complexity : 13.75000 Wille's k value : 52 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 18.89971, average 1.88997 Lattice compactness (without 2's) : 15.18691, average 1.51869 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.00000 2 1 3: 0 .. 2 1.25000 5 1 5: -1 .. 0 -0.25000 1 1 7: -1 .. 0 -0.25000 1 1 Average exponent except 2's : 3 / 4 = 0.75000 Average absolute exponent except 2's: 7 / 4 = 1.75000 Scale is weakly epimorphic with val: <4 5 8 11| Scale is JI-epimorphic with val: <4 6 9 11| = patent Scale is weakly epimorphic with val: <4 7 9 12|
FIT/MODE
4: 1 1 1 1 SP B ME I SD: 103.0430 c. M: 135.0841 c. 5: 2 1 1 1 P M ME SD: 37.6178 c. M: 57.5963 c. 7: 3 1 2 1 P G D3 SD: 40.7956 c. M:-79.2016 c. 8: 3 2 2 1 P T3 SD: 29.9199 c. M:-48.0450 c. 11: 4 2 3 2 SP D3 SD: 29.7043 c. M: 47.4095 c. 12: 4 3 3 2 SP T3 SD: 19.6491 c. M: 35.0841 c. Raga Mahathi, Antara Kaishiaki 14: 5 3 4 2 SP SD: 10.3275 c. M: 16.2407 c. 19: 7 4 5 3 SP SD: 6.1519 c. M: 7.2182 c. 27: 10 6 7 4 SP SD: 6.9435 c. M:-9.3603 c. 33: 12 7 9 5 SP SD: 5.5676 c. M: 11.0459 c. 39: 14 9 10 6 SP SD: 3.7559 c. M:-5.7373 c. 41: 15 9 11 6 SP SD: 3.9344 c. M:-6.7940 c. 53: 19 12 14 8 SP SD: 2.5292 c. M: 4.8954 c. 58: 21 13 15 9 SP SD: 2.0649 c. M: 3.8032 c. 72: 26 16 19 11 SP SD: 1.3921 c. M: 1.9550 c. 99: 36 22 26 15 SP SD: 0.8855 c. M:-1.2795 c. 152: 55 34 40 23 SP SD: 0.6894 c. M: 0.8736 c. 171: 62 38 45 26 SP SD: 0.1037 c. M: 0.2006 c. 665: 241 148 175 101 SP SD: 0.1232 c. M: 0.1969 c. 783: 284 174 206 119 SP SD: 0.0859 c. M:-0.1649 c. 836: 303 186 220 127 SP SD: 0.0968 c. M: 0.1559 c. 935: 339 208 246 142 SP SD: 0.0878 c. M:-0.1577 c. 954: 346 212 251 145 SP SD: 0.0764 c. M:-0.1360 c. 1007: 365 224 265 153 SP SD: 0.0831 c. M: 0.1288 c. 1106: 401 246 291 168 SP SD: 0.0649 c. M:-0.1252 c. 1125: 408 250 296 171 SP SD: 0.0729 c. M:-0.1159 c. 1164: 422 259 306 177 SP SD: 0.0660 c. M:-0.1069 c. 1277: 463 284 336 194 SP SD: 0.0507 c. M:-0.1014 c. 1335: 484 297 351 203 SP SD: 0.0500 c. M: 0.0682 c. 1448: 525 322 381 220 SP SD: 0.0430 c. M:-0.0833 c. 1506: 546 335 396 229 SP SD: 0.0399 c. M: 0.0664 c. 1619: 587 360 426 246 SP SD: 0.0399 c. M:-0.0689 c. 1677: 608 373 441 255 SP SD: 0.0348 c. M: 0.0650 c. 1790: 649 398 471 272 SP SD: 0.0399 c. M:-0.0573 c. 1848: 670 411 486 281 SP SD: 0.0335 c. M: 0.0638 c. 1947: 706 433 512 296 SP SD: 0.0369 c. M:-0.0481 c. 2019: 732 449 531 307 SP SD: 0.0346 c. M: 0.0629 c. 2118: 768 471 557 322 SP SD: 0.0305 c. M:-0.0434 c. 2289: 830 509 602 348 SP SD: 0.0270 c. M:-0.0404 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 0.0000 cents 3:4 x 5:6 S SD: 49.1215 cents 4:5:6:7:8 H SD: 17.2429 cents 10:13:15:18:20 SD: 4.7825 cents 14:18:21:25:28 SD: 3.4487 cents 24:31:36:43:48 SD: 2.8337 cents 42:54:63:76:84 SD: 2.2840 cents 46:59:69:83:92 SD: 1.4785 cents 56:72:84:101:112 SD: 0.8579 cents 60:77:90:108:120 SD: 0.8022 cents 70:90:105:126:140 SD: 0.0000 cents