Scala analysis: xen18-schulter-harrison
A JI scale of Lou Harrison
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 14/9 764.915905 septimal minor sixth 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/7 435.0841 septimal major third, BP third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 9/7 435.0841 septimal major third, BP third 3: 9/8 203.9100 major whole tone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 9/7 435.0841 septimal major third, BP third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 9/7 435.084 cents septimal major third, BP third 2: 1 7/6 266.871 cents septimal minor third 2: 3 4/3 498.045 cents perfect fourth 2: 1 81/56 638.994 cents 3: 1 112/81 561.006 cents 3: 3 3/2 701.955 cents perfect fifth 3: 1 12/7 933.129 cents septimal major sixth 4: 2 14/9 764.916 cents septimal minor sixth 4: 1 16/9 996.090 cents Pythagorean minor seventh 4: 2 27/14 1137.039 cents septimal major 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 : 63.0 498.0 702.0 764.9 1200.0 63.0 : 435.1 639.0 702.0 1137.0 1200.0 498.0 : 203.9 266.9 702.0 764.9 1200.0 702.0 : 63.0 498.0 561.0 996.1 1200.0 764.9 : 435.1 498.0 933.1 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 435.0841 cents 243/196, 372.1232 cents 28/27, 62.9609 cents 2: 266.8709 .. 638.9941 cents 243/196, 372.1232 cents 49/54,-168.2132 cents 3: 561.0059 .. 933.1291 cents 243/196, 372.1232 cents 6272/6561,-77.9882 cents 4: 764.9159 .. 1137.0391 cents 243/196, 372.1232 cents 49/54,-168.2132 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 3.811889 Largest / Average step : 1.812850 Largest / Smallest step : 6.910385 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 222.26508 cents, oct.: 1111.32541 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1277-tone equal temperament with octave 2/1 degrees: 67 530 747 814 1277 Least number of segments generator : 639 of 600.470 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 680 of 638.998 cents and inv. generated superset size: 54 = 49 more = 1080.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCAB Step pattern size order : SLMSL Scale is a Constant Structure, by a margin of 62.96090 cents Scale diversity : 1.474843 Lumma stability : 0.104935 Lumma impropriety factor : 0.345345 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 : 28/27, 62.9609 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 3 Scale is a chain of 2 triads 0.0 62.961 498.045 cents Number of recognisable fifths : 3, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 60.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.041750 Average absolute harmonicity : 0.319296 Specific harmonicity : 0.205379 Fundamental : 1/54, -5.7549 octaves, 4.8449 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 4.536000E+03, 12.14720 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 46.5, average 9.30000 Mersenne's string divisions : 26565 Sum of van Prooijen's expressibility: 3.33985, average 0.66797 Sum of Tenney's harmonic distance : 7.13725, average 1.42745 Vogel's harmonic complexity : 10.80000 Wille's k value : 40 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 37.87296, average 2.52486 Lattice compactness (without 2's) : 28.73236, average 1.91549 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 7 1 3: -3 .. 1 -1.00000 7 2 7: 0 .. 1 0.40000 2 2 Average exponent except 2's :-3 / 5 =-0.60000 Average absolute exponent except 2's: 9 / 5 = 1.80000 Scale is weakly epimorphic with val: <5 7 15| Scale is JI-epimorphic with val: <5 8 15| Scale is weakly epimorphic with val: <5 9 15|
FIT/MODE
5: 0 2 1 0 2 N T3 SD: 36.4219 c. M: 62.9609 c. 10: 1 3 2 0 4 N SD: 34.4155 c. M:-57.0391 c. 12: 1 4 2 1 4 N T3 SD: 22.8492 c. M:-37.0391 c. Hon-kumoi-joshi, Sakura, Akebono II: Japan, Olympos Enharmonic, Raga Gunakri (Gunakali), Latantapriya, Salanganata, Saveri, Ambassel: Ethiopia 14: 1 5 2 1 5 N T3 SD: 14.7489 c. M:-22.7534 c. 17: 1 6 3 1 6 N T3 SD: 6.6714 c. M:-11.5547 c. 19: 1 7 3 1 7 N T3 SD: 5.5415 c. M:-7.2182 c. 36: 2 13 6 2 13 N T3 SD: 2.2110 c. M:-3.7058 c. 58: 3 21 10 3 21 N T3 SD: 1.0599 c. M: 1.4933 c. 77: 4 28 13 4 28 N T3 SD: 0.7599 c. M: 1.2795 c. 94: 5 34 16 5 34 N T3 SD: 0.6163 c. M:-1.0415 c. 135: 7 49 23 7 49 N T3 SD: 0.4268 c. M: 0.7387 c. 171: 9 62 29 9 62 N T3 SD: 0.1545 c. M:-0.2006 c. 306: 16 111 52 16 111 N T3 SD: 0.1347 c. M: 0.2158 c. 400: 21 145 68 21 145 N T3 SD: 0.0503 c. M:-0.0841 c. 571: 30 207 97 30 207 N T3 SD: 0.0499 c. M:-0.0864 c. 706: 37 256 120 37 256 N T3 SD: 0.0413 c. M: 0.0714 c. 877: 46 318 149 46 318 N T3 SD: 0.0209 c. M: 0.0356 c. 1106: 58 401 188 58 401 N T3 SD: 0.0258 c. M: 0.0341 c. 1277: 67 463 217 67 463 N T3 SD: 0.0019 c. M:-0.0027 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: 39.8143 cents 4 x 5:6 x 8 S SD: 37.2438 cents 5 x 7 x 8:10 SD: 32.5120 cents 6:7:8:9 x 12 S SD: 50.9775 cents 7:8:9 x 11:14 SD: 45.1170 cents 8:9:11:12 x 16 SD: 37.6702 cents 9:10:12 x 14:18 SD: 29.8607 cents 10:11:13:15:16:20 SD: 24.2591 cents 11:12:15 x 17:22 SD: 24.1454 cents 12:13:16:18:19:24 SD: 16.3170 cents 13:14:17 x 20:26 SD: 18.9820 cents 14:15:19:21:22:28 SD: 13.3238 cents 15:16:20 x 23:30 SD: 13.6909 cents 16:17:21:24:25:32 SD: 10.1318 cents 17:18:23 x 26:34 SD: 13.2178 cents 18:19:24:27:28:36 SD: 6.1284 cents 22:23:29:33:34:44 SD: 5.3462 cents 24:25:32:36:37:48 SD: 3.4673 cents 30:31:40:45:47:60 SD: 2.7582 cents 48:50:64:72:75:96 SD: 2.1811 cents 52:54:69:78:81:104 SD: 1.7990 cents 54:56:72:81:84:108 SD: 0.0000 cents