Scala analysis: xen07-harrison-thoughts-4
Slendro with steps 8/7, 7/6, 9/8, 8/7, 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 12/7 933.129094 septimal major sixth 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 8/7 231.1741 septimal whole tone 2: 7/6 266.8709 septimal minor third 3: 9/8 203.9100 major whole tone 4: 8/7 231.1741 septimal whole tone 5: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 9/8 203.910 cents major whole tone 1: 2 8/7 231.174 cents septimal whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 21/16 470.781 cents narrow fourth 2: 3 4/3 498.045 cents perfect fourth 3: 3 3/2 701.955 cents perfect fifth 3: 1 32/21 729.219 cents wide fifth 3: 1 14/9 764.916 cents septimal minor sixth 4: 2 12/7 933.129 cents septimal major sixth 4: 2 7/4 968.826 cents harmonic seventh 4: 1 16/9 996.090 cents Pythagorean minor seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 231.2 498.0 702.0 933.1 1200.0 231.2 : 266.9 470.8 702.0 968.8 1200.0 498.0 : 203.9 435.1 702.0 933.1 1200.0 702.0 : 231.2 498.0 729.2 996.1 1200.0 933.1 : 266.9 498.0 764.9 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 203.9100 .. 266.8709 cents 28/27, 62.9609 cents 9/8, 203.9100 cents 2: 435.0841 .. 498.0450 cents 28/27, 62.9609 cents 54/49, 168.2132 cents 3: 701.9550 .. 764.9159 cents 28/27, 62.9609 cents 9/8, 203.9100 cents 4: 933.1291 .. 996.0900 cents 28/27, 62.9609 cents 54/49, 168.2132 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 9/8, 203.9100 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.176990 Largest / Average step : 1.111962 Largest / Smallest step : 1.308768 Median interval of one step : 8/7, 231.1741 cents, amount: 2 Least squares average step : 237.55719 cents, oct.: 1187.78595 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCAB Step pattern size order : MLSML Scale is a Constant Structure, by a margin of 168.21319 cents Scale diversity : 1.260402 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.790130 Rothenberg efficiency : 0.580000 redundancy: 0.420000 Efficiency x scale size : 2.900000 Number of different interval sizes : 12 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 64/63, 27.2641 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 3 Scale is a chain of 2 triads 0.0 231.174 498.045 cents Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 3 at degree 2 Formal octave complements present : 3 = 60.0000% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Limited transpositions with margin 62.9609 cents: 1 Limited inverse transpositions with margin 62.9609 cents: 1 3 -- Rational properties -- Prime limit : 7 Odd number limit : 21 (O: 21 U: 21) Highest odd numerator or denominator: 7 Scale harmonicity : 0.050971 Average absolute harmonicity : 0.325832 Specific harmonicity : 0.250082 Fundamental : 1/42, -5.3923 octaves, 6.2292 Hz. Guide tone : 24, 4.5850 octaves, 6279.014 Hz. Exponens Consonantiae : 1.008000E+03, 9.97728 octaves Euler's gradus suavitatis : 15 Sum of Mann's harmonic distance : 24.5, average 4.90000 Mersenne's string divisions : 1995 Sum of van Prooijen's expressibility: 2.64444, average 0.52889 Sum of Tenney's harmonic distance : 5.83083, average 1.16617 Vogel's harmonic complexity : 10.20000 Wille's k value : 31 Wilson's harmonic complexity : 13 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 34.27325, average 2.28488 Lattice compactness (without 2's) : 17.89292, average 1.19286 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.40000 9 1 3: -1 .. 1 0.20000 3 2 7: -1 .. 0 -0.40000 2 2 Average exponent except 2's :-1 / 5 =-0.20000 Average absolute exponent except 2's: 5 / 5 = 1.00000 Scale is JI-epimorphic with val: <5 8 14| = patent
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 17.0364 c. M:-26.8709 c. 14: 3 3 2 3 3 SP M ME I SD: 16.1030 c. M:-25.9688 c. Semaphore-5 17: 3 4 3 3 4 SP M ME S SD: 11.3777 c. M: 19.4094 c. 21: 4 5 3 4 5 SP T3 SD: 13.3369 c. M: 18.8434 c. 22: 4 5 4 4 5 SP M ME S SD: 7.8095 c. M: 12.9923 c. Raga Durga 26: 5 6 4 5 6 SP T3 SD: 7.5809 c. M: 10.0522 c. 27: 5 6 5 5 6 SP M ME S SD: 7.0405 c. M: 9.1561 c. 31: 6 7 5 6 7 SP T3 SD: 3.7853 c. M: 5.1808 c. Slendro M 36: 7 8 6 7 8 SP T3 SD: 1.5715 c. M:-2.1592 c. 77: 15 17 13 15 17 SP T3 SD: 1.5052 c. M:-2.5921 c. 94: 18 21 16 18 21 SP T3 SD: 0.8315 c. M: 1.3869 c. 99: 19 22 17 19 22 SP T3 SD: 0.7891 c. M:-1.0753 c. 130: 25 29 22 25 29 SP T3 SD: 0.4870 c. M: 0.8214 c. 135: 26 30 23 26 30 SP T3 SD: 0.1942 c. M:-0.2672 c. 265: 51 59 45 51 59 SP T3 SD: 0.1743 c. M: 0.2989 c. 306: 59 68 52 59 68 SP T3 SD: 0.1274 c. M:-0.2042 c. 400: 77 89 68 77 89 SP T3 SD: 0.1010 c. M: 0.1741 c. 436: 84 97 74 84 97 SP T3 SD: 0.0889 c. M:-0.1201 c. 571: 110 127 97 110 127 SP T3 SD: 0.0223 c. M: 0.0293 c. 706: 136 157 120 136 157 SP T3 SD: 0.0198 c. M:-0.0280 c. 1277: 246 284 217 246 284 SP T3 SD: 0.0042 c. M: 0.0073 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 5:6 S SD: 16.2568 cents 4 x 5:6:7:8 S SD: 29.3238 cents 6:7:8:9:10:12 S SD: 12.0877 cents 12:14:16:18:21:24 S SD: 10.0966 cents 14:16:19:21:24:28 SD: 6.1284 cents 20:23:27:30:34:40 SD: 5.6170 cents 21:24:28:32:36:42 S SD: 5.4528 cents 22:25:29:33:38:44 SD: 5.1362 cents 27:31:36:41:46:54 SD: 5.0203 cents 28:32:37:42:48:56 SD: 3.1054 cents 36:41:48:54:62:72 SD: 2.0020 cents 42:48:56:63:72:84 S SD: 0.0000 cents