Scala analysis: xen07-rosenthal-four-duets-3
Scale for parts III and IV of 'Four duets for bowed psaltery and harp'
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6/5 315.641287 minor third 2: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 3/2 701.955001 perfect fifth 5: 9/5 1017.596288 just minor seventh, BP seventh 6: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 6/5 315.6413 minor third 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 9/8 203.9100 major whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 6/5 315.6413 minor third 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 75/64 274.582 cents classic augmented second 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 2 32/25 427.373 cents classic diminished fourth 3: 1 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 36/25 631.283 cents classic diminished fifth 4: 1 25/18 568.717 cents classic augmented fourth 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 8/5 813.686 cents minor sixth 5: 2 25/16 772.627 cents classic augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 128/75 925.418 cents diminished seventh 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 315.6 386.3 590.2 702.0 1017.6 1088.3 1200.0 315.6 : 70.7 274.6 386.3 702.0 772.6 884.4 1200.0 386.3 : 203.9 315.6 631.3 702.0 813.7 1129.3 1200.0 590.2 : 111.7 427.4 498.0 609.8 925.4 996.1 1200.0 702.0 : 315.6 386.3 498.0 813.7 884.4 1088.3 1200.0 1017.6: 70.7 182.4 498.0 568.7 772.6 884.4 1200.0 1088.3: 111.7 427.4 498.0 702.0 813.7 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 315.6413 cents 144/125, 244.9689 cents 25/24, 70.6724 cents 2: 182.4037 .. 427.3726 cents 144/125, 244.9689 cents 25/27,-133.2376 cents 3: 386.3137 .. 631.2826 cents 144/125, 244.9689 cents 125/128,-41.0589 cents 4: 568.7174 .. 813.6863 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 5: 772.6274 .. 1017.5963 cents 144/125, 244.9689 cents 125/128,-41.0589 cents 6: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.425678 Largest / Average step : 1.841241 Largest / Smallest step : 4.466258 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Least squares average step : 183.45967 cents, oct.: 1284.21768 cents Scale is not proper Step pattern alph. order: ABCDABD Step pattern size order : DACBDAB Scale is not a Constant Structure Scale diversity : 1.537490 Lumma stability : 0.117787 Lumma impropriety factor : 0.342632 Rothenberg efficiency : 0.451701 redundancy: 0.548299 Efficiency x scale size : 3.161905 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypolydian octave species of abstract tetrachord All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 45 Scale harmonicity : 0.041436 Average absolute harmonicity : 0.245567 Specific harmonicity : 0.203951 Fundamental : 1/160, -7.3219 octaves, 1.6352 Hz. Guide tone : 90, 6.4919 octaves, 23546.301 Hz. Exponens Consonantiae : 1.440000E+04, 13.81378 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 71.0, average 10.14286 Mersenne's string divisions : 159390 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 10.74809, average 1.53544 Vogel's harmonic complexity : 12.42857 Wille's k value : 112 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 85.37683, average 3.04917 Lattice compactness (without 2's) : 43.38040, average 1.54930 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.28571 13 1 3: 0 .. 2 1.00000 7 1 5: -1 .. 1 0.14286 5 5 Average exponent except 2's : 8 / 7 = 1.14286 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 2 0 1 1 2 0 1 N T3 SD: 41.9927 c. M: 75.9380 c. 8: 2 1 1 1 2 0 1 N D3 SD: 36.2905 c. M:-63.6863 c. 10: 3 0 2 1 2 1 1 N SD: 30.3950 c. M: 57.5963 c. 11: 3 0 2 1 3 1 1 N SD: 36.1744 c. M: 59.0410 c. 12: 3 1 2 1 3 1 1 N T3 S SD: 11.8238 c. M: 17.5963 c. Mela Rasikapriya, Raga Rasamanjari, Hamsagiri 19: 5 1 3 2 5 1 2 N SD: 10.9833 c. M: 21.8027 c. 22: 6 1 4 2 6 1 2 N SD: 9.7188 c. M:-18.7673 c. 28: 7 2 5 2 8 1 3 N SD: 12.0023 c. M: 16.8401 c. 29: 8 1 5 3 8 1 3 N SD: 11.8958 c. M:-16.8865 c. 31: 8 2 5 3 8 2 3 N SD: 6.5281 c. M: 11.1447 c. 34: 9 2 6 3 9 2 3 N SD: 5.1841 c. M:-9.7763 c. 41: 11 2 7 4 11 2 4 N SD: 4.9610 c. M:-6.7940 c. 53: 14 3 9 5 14 3 5 N SD: 1.1931 c. M: 1.5445 c. 118: 31 7 20 11 31 7 11 N SD: 0.3432 c. M: 0.6471 c. 289: 76 17 49 27 76 17 27 N SD: 0.3107 c. M: 0.6043 c. 323: 85 19 55 30 85 19 30 N SD: 0.2714 c. M:-0.4884 c. 376: 99 22 64 35 99 22 35 N SD: 0.2481 c. M:-0.4888 c. 441: 116 26 75 41 116 26 41 N SD: 0.1274 c. M:-0.2525 c. 494: 130 29 84 46 130 29 46 N SD: 0.1095 c. M:-0.2175 c. 559: 147 33 95 52 147 33 52 N SD: 0.0782 c. M:-0.1162 c. 612: 161 36 104 57 161 36 57 N SD: 0.0339 c. M:-0.0508 c. 1171: 308 69 199 109 308 69 109 N SD: 0.0224 c. M:-0.0410 c. 1783: 469 105 303 166 469 105 166 N SD: 0.0101 c. M:-0.0175 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 54.0053 cents 4 x 5 x 6:7 x 8 S SD: 12.1926 cents 5:6 x 7:8:9 x 10 S SD: 22.3994 cents 6:7 x 8:9:11 x 12 SD: 21.8033 cents 7:8:9:10:11 x 13:14 SD: 21.7417 cents 8 x 10:11:12:14:15:16 S SD: 10.3979 cents 9:11 x 13:14:16:17:18 SD: 14.6736 cents 10:12:13:14:15:18:19:20 S SD: 10.2973 cents 12:14:15:17:18:22:23:24 SD: 10.1003 cents 13 x 16:18:20:23:24:26 SD: 11.7539 cents 14:17:18:20:21:25:26:28 SD: 9.0423 cents 15:18:19:21:23:27:28:30 SD: 6.5350 cents 16:19:20:23:24:29:30:32 SD: 6.2597 cents 20:24:25:28:30:36:38:40 SD: 3.4561 cents 24:29:30:34:36:43:45:48 SD: 2.7528 cents 40:48:50:56:60:72:75:80 SD: 1.1016 cents 64:77:80:90:96:115:120:128 SD: 0.7736 cents 96:115:120:135:144:173:180:192 SD: 0.5163 cents 120:144:150:169:180:216:225:240 SD: 0.3661 cents 160:192:200:225:240:288:300:320 S SD: 0.0000 cents