Scala analysis: xen07-harrison-thoughts-8
Partials 6/7/8/9/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 7/6 266.8709 septimal minor third 2: 8/7 231.1741 septimal whole tone 3: 9/8 203.9100 major whole tone 4: 11/9 347.4079 undecimal neutral third 5: 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 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 11/9 347.408 cents undecimal neutral third 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 2 4/3 498.045 cents perfect fourth 2: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 3: 2 3/2 701.955 cents perfect fifth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 11/7 782.492 cents undecimal augmented fifth 4: 1 18/11 852.592 cents undecimal neutral sixth 4: 1 12/7 933.129 cents septimal major sixth 4: 1 7/4 968.826 cents harmonic seventh 4: 1 16/9 996.090 cents Pythagorean minor seventh 4: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.50000 = 9/2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 266.9 498.0 702.0 1049.4 1200.0 266.9 : 231.2 435.1 782.5 933.1 1200.0 498.0 : 203.9 551.3 702.0 968.8 1200.0 702.0 : 347.4 498.0 764.9 996.1 1200.0 1049.4: 150.6 417.5 648.7 852.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 347.4079 cents 121/108, 196.7709 cents 12/11, 150.6371 cents 2: 417.5080 .. 551.3179 cents 121/112, 133.8100 cents 126/121, 70.1000 cents 3: 648.6821 .. 782.4920 cents 121/112, 133.8100 cents 128/121, 97.3641 cents 4: 852.5921 .. 1049.3629 cents 121/108, 196.7709 cents 126/121, 70.1000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 1.593233 Largest / Average step : 1.447533 Largest / Smallest step : 2.306258 Median interval of one step : 8/7, 231.1741 cents, amount: 1 Least squares average step : 246.65959 cents, oct.: 1233.29797 cents Scale is strictly proper Step pattern alph. order: ABCDE Step pattern size order : DCBEA Scale is a Constant Structure, by a margin of 70.10002 cents Scale diversity : 1.647401 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.449032 Rothenberg efficiency : 0.440000 redundancy: 0.560000 Efficiency x scale size : 2.200000 Number of different interval sizes : 18 = 4.50000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.50000 = 9/2 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 99/98, 17.5761 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 2 Most common triad is 0.0 498.045 701.955 cents, amount: 1 Number of recognisable fifths : 2, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 3 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 60.0000% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.027173 Average absolute harmonicity : 0.320891 Specific harmonicity : 0.178508 Fundamental : 1/6, -2.5850 octaves, 43.6043 Hz. Guide tone : 924, 9.8517 octaves, 241742.022 Hz. Exponens Consonantiae : 5.544000E+03, 12.43671 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 22.5, average 4.50000 Mersenne's string divisions : 23205 Sum of van Prooijen's expressibility: 2.84073, average 0.56815 Sum of Tenney's harmonic distance : 5.60116, average 1.12023 Vogel's harmonic complexity : 6.40000 Wille's k value : 5 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 32.48010, average 2.16534 Lattice compactness (without 2's) : 19.54320, average 1.30288 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.00000 6 1 3: -1 .. 1 -0.40000 4 2 7: 0 .. 1 0.20000 1 1 11: 0 .. 1 0.20000 1 1 Average exponent except 2's : 0 / 5 = 0.00000 Average absolute exponent except 2's: 6 / 5 = 1.20000 Scale is weakly epimorphic with val: <5 7 13 16| Scale is JI-epimorphic with val: <5 8 14 17| = patent
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 43.2644 c. M: 89.3629 c. 7: 2 1 1 2 1 P M ME S SD: 36.6980 c. M:-75.9862 c. Thai mode 6 8: 2 1 2 2 1 P M ME S SD: 33.8071 c. M:-48.0450 c. Agmon Diatonic DS1 9: 2 2 1 3 1 P D3 S SD: 23.6220 c. M:-35.2883 c. 10: 2 2 2 3 1 P T3 SD: 21.5031 c. M:-30.6371 c. 14: 3 3 2 4 2 SP D3 S SD: 14.5220 c. M: 20.7915 c. 17: 4 3 3 5 2 SP SD: 8.4858 c. M:-15.4820 c. 22: 5 4 4 6 3 SP SD: 7.8118 c. M: 12.9993 c. 24: 5 5 4 7 3 SP SD: 7.6508 c. M: 16.8709 c. 26: 6 5 4 8 3 SP SD: 9.3320 c. M:-12.1755 c. 31: 7 6 5 9 4 SP SD: 4.1981 c. M: 5.1808 c. 41: 9 8 7 12 5 SP SD: 2.4846 c. M:-4.2956 c. 58: 13 11 10 17 7 SP SD: 2.9188 c. M:-5.8095 c. 63: 14 12 11 18 8 SP SD: 1.9411 c. M: 2.8069 c. 72: 16 14 12 21 9 SP SD: 1.2721 c. M: 1.9550 c. 94: 21 18 16 27 12 SP SD: 1.2696 c. M: 2.5544 c. 104: 23 20 18 30 13 SP SD: 1.3977 c. M:-1.8912 c. 113: 25 22 19 33 14 SP SD: 1.2701 c. M:-1.9645 c. 118: 26 23 20 34 15 SP SD: 1.4027 c. M: 2.4641 c. 130: 29 25 22 38 16 SP SD: 1.3924 c. M:-2.9448 c. 135: 30 26 23 39 17 SP SD: 0.2861 c. M: 0.4741 c. 342: 76 66 58 99 43 SP SD: 0.1897 c. M: 0.2401 c. 477: 106 92 81 138 60 SP SD: 0.1702 c. M: 0.3063 c. 494: 110 95 84 143 62 SP SD: 0.1569 c. M:-0.3356 c. 629: 140 121 107 182 79 SP SD: 0.1260 c. M:-0.2197 c. 670: 149 129 114 194 84 SP SD: 0.1201 c. M:-0.1893 c. 701: 156 135 119 203 88 SP SD: 0.1013 c. M:-0.1762 c. 764: 170 147 130 221 96 SP SD: 0.1279 c. M: 0.1483 c. 805: 179 155 137 233 101 SP SD: 0.1065 c. M:-0.1568 c. 836: 186 161 142 242 105 SP SD: 0.0679 c. M:-0.1147 c. 877: 195 169 149 254 110 SP SD: 0.0611 c. M:-0.1239 c. 1012: 225 195 172 293 127 SP SD: 0.0403 c. M: 0.0725 c. 1506: 335 290 256 436 189 SP SD: 0.0402 c. M:-0.0614 c. 1641: 365 316 279 475 206 SP SD: 0.0396 c. M:-0.0560 c. 1713: 381 330 291 496 215 SP SD: 0.0248 c. M:-0.0293 c. 1848: 411 356 314 535 232 SP SD: 0.0089 c. M: 0.0123 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 0.0000 cents 3 x 4 x x 6 S SD: 0.0000 cents 4 x 5:6:7:8 S SD: 34.4330 cents 5:6:7:8:9:10 H SD: 30.3356 cents 6:7:8:9:11:12 SD: 0.0000 cents