Scala analysis: xen07-harrison-thoughts-6
Slendro based on partials 12/14/16/19/21
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: 19/12 795.558015 undevicesimal minor sixth 4: 7/4 968.825906 harmonic seventh 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 7/6 266.8709 septimal minor third 2: 8/7 231.1741 septimal whole tone 3: 19/16 297.5130 19th harmonic 4: 21/19 173.2679 5: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/19 173.268 cents 1: 2 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 19/16 297.513 cents 19th harmonic 2: 1 24/19 404.442 cents smaller undevicesimal major third 2: 1 21/16 470.781 cents narrow fourth 2: 2 4/3 498.045 cents perfect fourth 2: 1 19/14 528.687 cents 3: 1 28/19 671.313 cents 3: 2 3/2 701.955 cents perfect fifth 3: 1 32/21 729.219 cents wide fifth 3: 1 19/12 795.558 cents undevicesimal minor sixth 4: 1 32/19 902.487 cents 19th subharmonic 4: 1 12/7 933.129 cents septimal major sixth 4: 2 7/4 968.826 cents harmonic seventh 4: 1 38/21 1026.732 cents 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 5 0.0 : 266.9 498.0 795.6 968.8 1200.0 266.9 : 231.2 528.7 702.0 933.1 1200.0 498.0 : 297.5 470.8 702.0 968.8 1200.0 795.6 : 173.3 404.4 671.3 902.5 1200.0 968.8 : 231.2 498.0 729.2 1026.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 173.2679 .. 297.5130 cents 361/336, 124.2451 cents 21/19, 173.2679 cents 2: 404.4420 .. 528.6871 cents 361/336, 124.2451 cents 384/361, 106.9290 cents 3: 671.3129 .. 795.5580 cents 361/336, 124.2451 cents 392/361, 142.6258 cents 4: 902.4870 .. 1026.7321 cents 361/336, 124.2451 cents 384/361, 106.9290 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 21/19, 173.2679 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 19/16, 297.5130 cents Average / Smallest step : 1.385138 Largest / Average step : 1.239638 Largest / Smallest step : 1.717070 Median interval of one step : 8/7, 231.1741 cents, amount: 2 Most common interval of one step : 8/7, 231.1741 cents, amount: 2 Least squares average step : 245.90797 cents, oct.: 1229.53987 cents Scale is strictly proper Step pattern alph. order: ABCDB Step pattern size order : CBDAB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 106.92897 cents Scale diversity : 1.510927 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.585850 Rothenberg efficiency : 0.480000 redundancy: 0.520000 Efficiency x scale size : 2.400000 Number of different interval sizes : 16 = 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 : 64/63, 27.2641 cents Number of recognisable fifths : 2, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 1 = 20.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 19 Odd number limit : 21 (O: 21 U: 21) Highest odd numerator or denominator: 19 Scale harmonicity : 0.019586 Average absolute harmonicity : 0.278629 Specific harmonicity : 0.117335 Fundamental : 1/12, -3.5850 octaves, 21.8021 Hz. Guide tone : 532, 9.0553 octaves, 139184.801 Hz. Exponens Consonantiae : 6.384000E+03, 12.64024 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 32.5, average 6.50000 Mersenne's string divisions : 93093 Sum of van Prooijen's expressibility: 3.44607, average 0.68921 Sum of Tenney's harmonic distance : 6.80855, average 1.36171 Vogel's harmonic complexity : 9.40000 Wille's k value : 10 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 36.40262, average 2.42684 Lattice compactness (without 2's) : 17.21733, average 1.14782 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.40000 8 1 3: -1 .. 0 -0.60000 3 1 7: 0 .. 1 0.40000 2 2 19: 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 14 23| Scale is JI-epimorphic with val: <5 8 14 21| = patent Scale is weakly epimorphic with val: <5 9 13 21|
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 36.9718 c. M: 75.5580 c. 8: 2 1 2 1 2 P M ME I SD: 45.2071 c. M: 68.8259 c. 9: 2 2 2 1 2 SP M ME S SD: 22.4711 c. M: 35.4926 c. 12: 3 2 3 2 2 SP M ME S SD: 20.4593 c. M:-33.1291 c. Blues Minor, Raga Malkauns (Malakosh), Raga Hindola, Man Gong, Quan Ming, Yi Ze, Jiao: China, Shegaye: Ethiopia 14: 3 3 3 2 3 SP M ME S SD: 17.9722 c. M: 25.9688 c. 15: 3 3 4 2 3 SP T3 SD: 15.1347 c. M: 26.8709 c. 17: 4 3 4 3 3 SP M ME S SD: 14.1150 c. M:-19.4094 c. 20: 4 4 5 3 4 SP T3 SD: 16.5385 c. M: 26.8709 c. 21: 5 4 5 3 4 SP T3 SD: 11.3608 c. M:-18.8434 c. 24: 5 5 6 3 5 SP SD: 11.5117 c. M: 18.8259 c. 26: 6 5 6 4 5 SP T3 SD: 7.9249 c. M: 10.9426 c. 27: 6 5 7 4 5 SP SD: 6.0621 c. M: 9.1561 c. 32: 7 6 8 5 6 SP SD: 6.8316 c. M: 10.5450 c. 36: 8 7 9 5 7 SP SD: 2.3773 c. M:-4.4420 c. 68: 15 13 17 10 13 SP SD: 2.2491 c. M: 3.9274 c. 77: 17 15 19 11 15 SP SD: 1.5142 c. M: 2.5921 c. 89: 20 17 22 13 17 SP SD: 1.5706 c. M:-2.7920 c. 104: 23 20 26 15 20 SP SD: 1.1229 c. M: 1.8912 c. 125: 28 24 31 18 24 SP SD: 1.1998 c. M:-1.9291 c. 130: 29 25 32 19 25 SP SD: 0.8880 c. M: 1.7119 c. 140: 31 27 35 20 27 SP SD: 0.9724 c. M:-1.5848 c. 166: 37 32 41 24 32 SP SD: 0.4662 c. M:-0.7502 c. 229: 51 44 57 33 44 SP SD: 0.5408 c. M:-0.9485 c. 234: 52 45 58 34 45 SP SD: 0.4577 c. M: 0.6862 c. 270: 60 52 67 39 52 SP SD: 0.1530 c. M: 0.2672 c. 436: 97 84 108 63 84 SP SD: 0.0961 c. M: 0.1452 c. 706: 157 136 175 102 136 SP SD: 0.0433 c. M: 0.0906 c. 1178: 262 227 292 170 227 SP SD: 0.0513 c. M:-0.0874 c. 1448: 322 279 359 209 279 SP SD: 0.0247 c. M: 0.0414 c. 1718: 382 331 426 248 331 SP SD: 0.0281 c. M: 0.0490 c. 1884: 419 363 467 272 363 SP SD: 0.0268 c. M:-0.0442 c. 2154: 479 415 534 311 415 SP SD: 0.0152 c. M: 0.0237 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 46.8015 cents 3 x 4 x 5:6 S SD: 28.1557 cents 4 x 5:6:7:8 S SD: 36.4395 cents 5:6:7:8:9:10 H SD: 22.1092 cents 6:7:8 x 11:12 SD: 20.1343 cents 7:8:9:11:12:14 SD: 16.3503 cents 11:13:15:17:19:22 SD: 13.0877 cents 12:14:16:19:21:24 SD: 0.0000 cents