Scala analysis: xen09-chalmers-tritriadic-3-4-5
Tritriadic scale built from 3:4:5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 25/18 568.717426 classic augmented fourth 5: 8/5 813.686286 minor sixth 6: 5/3 884.358713 major sixth, BP sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 10/9 182.4037 minor whole tone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 10/9 182.4037 minor whole tone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 144/125 244.9689 classic diminished third 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 2 10/9 182.404 cents minor whole tone 1: 1 144/125 244.969 cents classic diminished third 1: 1 6/5 315.641 cents minor third 2: 1 125/108 253.076 cents semi-augmented whole tone 2: 4 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 1 4/3 498.045 cents perfect fourth 3: 2 5/4 386.314 cents major third 3: 2 4/3 498.045 cents perfect fourth 3: 1 25/18 568.717 cents classic augmented fourth 3: 2 36/25 631.283 cents classic diminished fifth 4: 2 25/18 568.717 cents classic augmented fourth 4: 1 36/25 631.283 cents classic diminished fifth 4: 2 3/2 701.955 cents perfect fifth 4: 2 8/5 813.686 cents minor sixth 5: 1 3/2 701.955 cents perfect fifth 5: 1 8/5 813.686 cents minor sixth 5: 4 5/3 884.359 cents major sixth, BP sixth 5: 1 216/125 946.924 cents semi-augmented sixth 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 125/72 955.031 cents classic augmented sixth 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 50/27 1066.762 cents grave 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 : 182.4 315.6 498.0 568.7 813.7 884.4 1200.0 182.4 : 133.2 315.6 386.3 631.3 702.0 1017.6 1200.0 315.6 : 182.4 253.1 498.0 568.7 884.4 1066.8 1200.0 498.0 : 70.7 315.6 386.3 702.0 884.4 1017.6 1200.0 568.7 : 245.0 315.6 631.3 813.7 946.9 1129.3 1200.0 813.7 : 70.7 386.3 568.7 702.0 884.4 955.0 1200.0 884.4 : 315.6 498.0 631.3 813.7 884.4 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: 253.0761 .. 498.0450 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 3: 386.3137 .. 631.2826 cents 144/125, 244.9689 cents 15/16,-111.7313 cents 4: 568.7174 .. 813.6863 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 5: 701.9550 .. 946.9239 cents 144/125, 244.9689 cents 15/16,-111.7313 cents 6: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 625/648,-62.5651 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 : 10/9, 182.4037 cents, amount: 2 Least squares average step : 159.69482 cents, oct.: 1117.86373 cents Scale is not proper Step pattern alph. order: ABACDCE Step pattern size order : CBCADAE Scale is not a Constant Structure Scale diversity : 1.440469 Lumma stability : 0.117787 Lumma impropriety factor : 0.342632 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 15625/15552, 8.1073 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 498.045 884.359 cents Most common triad is 0.0 315.641 884.359 cents, amount: 3 Number of recognisable fifths : 3, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 3 5 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 125 (O: 125 U: 125) Highest odd numerator or denominator: 25 Scale harmonicity : 0.032051 Average absolute harmonicity : 0.237299 Specific harmonicity : 0.181852 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 600, 9.2288 octaves, 156975.339 Hz. Exponens Consonantiae : 5.400000E+04, 15.72067 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 52.0, average 7.42857 Mersenne's string divisions : 19627608 Sum of van Prooijen's expressibility: 4.92621, average 0.70374 Sum of Tenney's harmonic distance : 10.24294, average 1.46328 Vogel's harmonic complexity : 12.28571 Wille's k value : 62 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 70.88742, average 2.53169 Lattice compactness (without 2's) : 51.84729, average 1.85169 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.00000 9 1 3: -2 .. 1 -0.71429 7 1 5: -1 .. 2 0.28571 6 5 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 18| Scale is weakly epimorphic with val: <7 11 17| Scale is weakly epimorphic with val: <7 12 16|
FIT/MODE
7: 1 1 1 0 2 0 2 N T3 SD: 30.9767 c. M: 54.4317 c. 11: 2 1 2 0 2 1 3 N G SD: 31.2695 c. M: 50.0499 c. 12: 2 1 2 1 2 1 3 N T3 SD: 16.7701 c. M:-31.2826 c. Moravian Pistalkova, Hungarian Major inverse 15: 2 2 2 1 3 1 4 N SD: 12.6990 c. M: 22.4037 c. 19: 3 2 3 1 4 1 5 N SD: 4.7280 c. M:-7.3663 c. 34: 5 4 5 2 7 2 9 N SD: 3.3479 c. M: 5.9331 c. 46: 7 5 7 3 9 3 12 N SD: 3.1885 c. M:-5.1956 c. 53: 8 6 8 3 11 3 14 N SD: 1.4331 c. M: 2.6797 c. 99: 15 11 15 6 20 6 26 N SD: 0.8773 c. M: 1.5651 c. 118: 18 13 18 7 24 7 31 N SD: 0.4474 c. M:-0.7741 c. 152: 23 17 23 9 31 9 40 N SD: 0.4704 c. M: 0.8248 c. 171: 26 19 26 10 35 10 45 N SD: 0.2058 c. M:-0.3488 c. 270: 41 30 41 16 55 16 71 N SD: 0.1975 c. M: 0.3530 c. 289: 44 32 44 17 59 17 76 N SD: 0.1653 c. M:-0.2952 c. 441: 67 49 67 26 90 26 116 N SD: 0.0564 c. M: 0.0908 c. 612: 93 68 93 36 125 36 161 N SD: 0.0482 c. M: 0.0900 c. 730: 111 81 111 43 149 43 192 N SD: 0.0360 c. M:-0.0620 c. 1171: 178 130 178 69 239 69 308 N SD: 0.0157 c. M:-0.0272 c. 1342: 204 149 204 79 274 79 353 N SD: 0.0137 c. M:-0.0246 c. 1783: 271 198 271 105 364 105 469 N SD: 0.0087 c. M: 0.0145 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 55.8656 cents 3 x x 4 x x 5:6 S SD: 0.0000 cents 4 x 5 x x 6:7:8 S SD: 39.2215 cents 5 x 6 x 7:8 x 10 S SD: 3.4487 cents 6 x 7:8 x x 10:12 S SD: 12.1926 cents 7:8 x 9:10:11:12:14 S SD: 18.3127 cents 8:9:10 x 11:13 x 16 SD: 16.1001 cents 9:10:11:12:13:14:15:18 S SD: 12.7760 cents 10:11:12:13:14:16:17:20 SD: 8.5589 cents 11:12:13 x 15 x 18:22 SD: 12.2082 cents 12:13:14:16:17:19:20:24 SD: 10.8831 cents 14:16:17:19 x 22:23:28 SD: 12.1688 cents 15:17:18:20:21:24:25:30 SD: 5.2792 cents 18:20:22:24:25:29:30:36 SD: 4.8501 cents 25:28:30:33:35:40:42:50 SD: 4.2225 cents 30:33:36:40:42:48:50:60 S SD: 3.1721 cents 35:39:42:47:49:56:58:70 SD: 3.0804 cents 36:40:43:48:50:58:60:72 SD: 2.0607 cents 45:50:54:60:63:72:75:90 SD: 1.9707 cents 54:60:65:72:75:86:90:108 SD: 1.3777 cents 72:80:86:96:100:115:120:144 SD: 1.2255 cents 75:83:90:100:104:120:125:150 SD: 1.0674 cents 80:89:96:107:111:128:133:160 SD: 1.0656 cents 90:100:108:120:125:144:150:180 SD: 0.0000 cents