Scala analysis: xen07-rosenthal-four-duets-2
Scale for part II 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: 9/8 203.910002 major whole tone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 45/32 590.223716 diatonic tritone 5: 3/2 701.955001 perfect fifth 6: 5/3 884.358713 major sixth, BP sixth 7: 15/8 1088.268715 classic major seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 135/128 92.1787 major chroma, major limma 5: 16/15 111.7313 minor diatonic semitone 6: 10/9 182.4037 minor whole tone 7: 9/8 203.9100 major whole tone 8: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135/128 92.179 cents major chroma, major limma 1: 3 16/15 111.731 cents minor diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 2 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 3: 1 6/5 315.641 cents minor third 3: 2 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 4: 2 4/3 498.045 cents perfect fourth 4: 2 45/32 590.224 cents diatonic tritone 4: 2 64/45 609.776 cents 2nd tritone 4: 2 3/2 701.955 cents perfect fifth 5: 1 40/27 680.449 cents grave fifth 5: 4 3/2 701.955 cents perfect fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 6: 2 8/5 813.686 cents minor sixth 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 2 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 7: 2 16/9 996.090 cents Pythagorean minor seventh 7: 2 9/5 1017.596 cents just minor seventh, BP seventh 7: 3 15/8 1088.269 cents classic major seventh 7: 1 256/135 1107.821 cents octave - major chroma 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 6 7 8 0.0 : 203.9 386.3 498.0 590.2 702.0 884.4 1088.3 1200.0 203.9 : 182.4 294.1 386.3 498.0 680.4 884.4 996.1 1200.0 386.3 : 111.7 203.9 315.6 498.0 702.0 813.7 1017.6 1200.0 498.0 : 92.2 203.9 386.3 590.2 702.0 905.9 1088.3 1200.0 590.2 : 111.7 294.1 498.0 609.8 813.7 996.1 1107.8 1200.0 702.0 : 182.4 386.3 498.0 702.0 884.4 996.1 1088.3 1200.0 884.4 : 203.9 315.6 519.6 702.0 813.7 905.9 1017.6 1200.0 1088.3: 111.7 315.6 498.0 609.8 702.0 813.7 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 203.9100 cents 16/15, 111.7313 cents 135/128, 92.1787 cents 2: 203.9100 .. 386.3137 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 3: 315.6413 .. 519.5513 cents 9/8, 203.9100 cents 24/25,-70.6724 cents 4: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 80/81,-21.5063 cents 5: 680.4487 .. 884.3587 cents 9/8, 203.9100 cents 80/81,-21.5063 cents 6: 813.6863 .. 996.0900 cents 10/9, 182.4037 cents 24/25,-70.6724 cents 7: 996.0900 .. 1107.8213 cents 16/15, 111.7313 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.627274 Largest / Average step : 1.359400 Largest / Smallest step : 2.212116 Median interval of one step : 147.06750 cents, amount: 0 Most common interval of one step : 16/15, 111.7313 cents, amount: 3 Least squares average step : 151.30086 cents, oct.: 1210.40689 cents Scale is not proper Step pattern alph. order: ABCDCBAC Step pattern size order : DCBABCDB Scale is not a Constant Structure Scale diversity : 1.322073 Lumma stability : 0.153631 Lumma impropriety factor : 0.153631 Rothenberg efficiency : 0.546429 redundancy: 0.453571 Efficiency x scale size : 4.371429 Number of different interval sizes : 20 = 2.85714 / 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 : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 6, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale is a complete genus musicum : 2^m 3^3 5^1 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 3 = 37.5000% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 7-8 -- Rational properties -- Prime limit : 5 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.046729 Average absolute harmonicity : 0.247373 Specific harmonicity : 0.230113 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 1.728000E+04, 14.07682 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 74.5, average 9.31250 Mersenne's string divisions : 10838520 Sum of van Prooijen's expressibility: 6.13573, average 0.76697 Sum of Tenney's harmonic distance : 11.73036, average 1.46629 Vogel's harmonic complexity : 10.62500 Wille's k value : 67 Wilson's harmonic complexity : 14 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 115.71945, average 3.21443 Lattice compactness (without 2's) : 57.81860, average 1.60607 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.37500 17 1 3: -1 .. 2 0.50000 8 3 5: 0 .. 1 0.50000 4 4 Average exponent except 2's : 8 / 8 = 1.00000 Average absolute exponent except 2's: 12 / 8 = 1.50000 Scale is weakly epimorphic with val: <8 13 20| Scale is weakly epimorphic with val: <8 14 17| Scale is weakly epimorphic with val: <8 14 19| Scale is weakly epimorphic with val: <8 14 21|
FIT/MODE
8: 1 2 0 1 1 1 1 1 N T3 SD: 40.9017 c. M:-63.6863 c. 10: 2 1 1 1 1 1 2 1 N D3 SD: 24.4382 c. M: 44.3587 c. 12: 2 2 1 1 1 2 2 1 N D3 SD: 9.2743 c. M:-15.6413 c. Ishikotsucho: Japan, Raga Yaman Kalyan, Chayanat, Bihag, Hamir Kalyani, Kedar, Gaud Sarang, Genus diatonicum veterum correctum, Gregorian nr.5, Kubilai's Mongol scale, Ionian/Lydian mixed 22: 4 3 2 2 2 3 4 2 N SD: 8.3933 c. M:-14.2718 c. Raga Suddha Kalyan 29: 5 4 3 2 3 4 5 3 N SD: 9.4642 c. M: 15.3932 c. 31: 5 5 3 2 3 5 5 3 N G SD: 6.2080 c. M: 10.3616 c. 34: 6 5 3 3 3 5 6 3 N SD: 5.3624 c. M:-9.7763 c. 41: 7 6 4 3 4 6 7 4 N SD: 3.9890 c. M: 6.3099 c. 53: 9 8 5 4 5 8 9 5 N SD: 1.0229 c. M: 1.5445 c. 65: 11 10 6 5 6 10 11 6 N SD: 0.9609 c. M:-1.7951 c. 118: 20 18 11 9 11 18 20 11 N SD: 0.3050 c. M: 0.5202 c. 289: 49 44 27 22 27 44 49 27 N SD: 0.3243 c. M: 0.6043 c. 323: 55 49 30 25 30 49 55 30 N SD: 0.2763 c. M:-0.4884 c. 376: 64 57 35 29 35 57 64 35 N SD: 0.2065 c. M:-0.3453 c. 441: 75 67 41 34 41 67 75 41 N SD: 0.1334 c. M:-0.2525 c. 494: 84 75 46 38 46 75 84 46 N SD: 0.0871 c. M: 0.1482 c. 559: 95 85 52 43 52 85 95 52 N SD: 0.0702 c. M:-0.1162 c. 612: 104 93 57 47 57 93 104 57 N SD: 0.0266 c. M: 0.0450 c. 1171: 199 178 109 90 109 178 199 109 N SD: 0.0221 c. M:-0.0410 c. 1783: 303 271 166 137 166 271 303 166 N SD: 0.0101 c. M:-0.0175 c. 2395: 407 364 223 184 223 364 407 223 N SD: 0.0094 c. M: 0.0163 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x x 5 x 6 S SD: 0.0000 cents 4 x 5 x x 6:7 x 8 S SD: 21.1168 cents 5 x 6 x 7 x 8:9:10 S SD: 24.5302 cents 6:7 x 8 x 9:10:11:12 S SD: 12.3353 cents 7:8:9 x 10:11:12:13:14 S SD: 16.2910 cents 8:9:10 x 11:12:13:15:16 SD: 8.3725 cents 10:11 x 13:14:15:17:19:20 SD: 10.2970 cents 11:12:14:15 x 17:18:21:22 SD: 14.2700 cents 12:14:15:16:17:18:20:23:24 SD: 9.3334 cents 15:17:19:20:21:23:25:28:30 SD: 5.9370 cents 22:25:28:29:31:33:37:41:44 SD: 5.6399 cents 23:26:29:31:32:35:38:43:46 SD: 5.3926 cents 24:27:30:32:34:36:40:45:48 S SD: 1.5971 cents 56:63:70:75:79:84:93:105:112 SD: 1.4139 cents 64:72:80:85:90:96:107:120:128 SD: 1.0832 cents 72:81:90:96:101:108:120:135:144 SD: 0.5350 cents 96:108:120:128:135:144:160:180:192 SD: 0.0000 cents