Scala analysis: xen18-erlich-helmholtz-03
2L 1s MOS for Helmholtz, L=498.28, s=203.51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 498.280 cents 498.280000 2: 701.790 cents 701.790000 3: 1200.070 cents 1200.070000
SHOW/INTERVAL
0: 498.2800 cents 498.2800 1: 498.2800 cents 498.2800 2: 203.5100 cents 203.5100 3: 498.2800 cents 498.2800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 203.51000 cents 1: 2 498.28000 cents 2: 2 701.79000 cents 2: 1 996.56000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 498.3 701.8 1200.1 498.3 : 203.5 701.8 1200.1 701.8 : 498.3 996.6 1200.1 1200.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 203.5100 .. 498.2800 cents 294.77000 cents 203.51000 cents 2: 701.7900 .. 996.5600 cents 294.77000 cents 203.51000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 203.51000 cents, class 1 Average step (divided formal octave): 400.0233 cents Largest one step interval : 498.28000 cents Average / Smallest step : 1.965620 Largest / Average step : 1.245627 Largest / Smallest step : 2.448430 Median interval of one step : 498.28000 cents, amount: 2 Most common interval of one step : 498.28000 cents, amount: 2 Least squares average step : 393.00500 cents, oct.: 1179.01500 cents Scale is strictly proper Scale has Myhill's property chromas: 294.77000 cents and 91.26000 cents, ratio: 3.230002 generators: 1 of 498.28000 cents and 2 of 701.79000 cents ET pair of linear temperament : 12&53 Scale is distributional even Scale is a mode of a 171-tone equal temperament with octave 1200.070 cents degrees: 71 100 171 generators: 71 and 100 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : LSL Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 203.51000 cents Ratio Whole / Half tone : 2.230002 Scale diversity : 1.433839 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.508745 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 203.51000 cents Most common intervals : 498.28000 cents & inv., amount: 2 Number of recognisable fifths : 2, average 701.7900 cents Number of recognisable fourths : 2, average 498.2800 cents Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 80.2262 c. M: 98.2567 c. 5: 2 1 2 SP M ME I SD: 14.9027 c. M: 18.2520 c. 7: 3 1 3 SP M DE I SD: 13.0931 c. M: 16.0357 c. 12: 5 2 5 SP M DE I SD: 1.4282 c. M: 1.7492 c. Raga Sarvasri, Warao tritonic: South America 29: 12 5 12 SP M DE I SD: 1.3875 c. M: 1.6993 c. 41: 17 7 17 SP M DE I SD: 0.5634 c. M: 0.6900 c. 53: 22 9 22 SP M DE I SD: 0.1125 c. M: 0.1377 c. 118: 49 20 49 SP M DE I SD: 0.0442 c. M: 0.0542 c. 171: 71 29 71 SP M DE I SD: 0.0043 c. M: 0.0053 c. 802: 333 136 333 SP M DE I SD: 0.0028 c. M: 0.0034 c. 973: 404 165 404 SP M DE I SD: 0.0015 c. M: 0.0019 c. 1144: 475 194 475 SP M DE I SD: 0.0007 c. M: 0.0008 c. 1315: 546 223 546 SP M DE I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 0.0700 cents 2 x 3:4 S SD: 0.0896 cents