Scala analysis: xen12-chalmers-tritriadic-dm-9-5-1
Tritriadic D->M scale built from 9:5:1
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: 5/4 386.313714 major third 3: 25/18 568.717426 classic augmented fourth 4: 64/45 609.776284 2nd tritone 5: 8/5 813.686286 minor sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 3: 10/9 182.4037 minor whole tone 4: 128/125 41.0589 minor diesis, diesis 5: 9/8 203.9100 major whole tone 6: 10/9 182.4037 minor whole tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128/125 41.059 cents minor diesis, diesis 1: 3 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 144/125 244.969 cents classic diminished third 2: 5 5/4 386.314 cents major third 3: 3 32/25 427.373 cents classic diminished fourth 3: 2 25/18 568.717 cents classic augmented fourth 3: 2 45/32 590.224 cents diatonic tritone 4: 2 64/45 609.776 cents 2nd tritone 4: 2 36/25 631.283 cents classic diminished fifth 4: 3 25/16 772.627 cents classic augmented fifth 5: 5 8/5 813.686 cents minor sixth 5: 1 125/72 955.031 cents classic augmented sixth 5: 1 225/128 976.537 cents augmented sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 125/64 1158.941 cents classic augmented seventh, octave - minor diesis 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 6 7 0.0 : 182.4 386.3 568.7 609.8 813.7 996.1 1200.0 182.4 : 203.9 386.3 427.4 631.3 813.7 1017.6 1200.0 386.3 : 182.4 223.5 427.4 609.8 813.7 996.1 1200.0 568.7 : 41.1 245.0 427.4 631.3 813.7 1017.6 1200.0 609.8 : 203.9 386.3 590.2 772.6 976.5 1158.9 1200.0 813.7 : 182.4 386.3 568.7 772.6 955.0 996.1 1200.0 996.1 : 203.9 386.3 590.2 772.6 813.7 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 203.9100 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 2: 223.4626 .. 386.3137 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 3: 427.3726 .. 590.2237 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 4: 609.7763 .. 772.6274 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 976.5374 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 6: 996.0900 .. 1158.9411 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 128/125, 41.0589 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 4.175191 Largest / Average step : 1.189475 Largest / Smallest step : 4.966285 Median interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 168.18043 cents, oct.: 1177.26300 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAB Step pattern size order : MLMSLML Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.233743 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.185744 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 : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 203.910 386.314 cents Most common triad is 0.0 386.314 813.686 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 5 Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 5 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 45 Scale harmonicity : 0.030738 Average absolute harmonicity : 0.217109 Specific harmonicity : 0.162877 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 1600, 10.6439 octaves, 418600.904 Hz. Exponens Consonantiae : 2.880000E+05, 18.13571 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 110.5, average 15.78571 Mersenne's string divisions : 260480025 Sum of van Prooijen's expressibility: 6.35758, average 0.90823 Sum of Tenney's harmonic distance : 13.42933, average 1.91848 Vogel's harmonic complexity : 12.71429 Wille's k value : 112 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 110.15782, average 3.93421 Lattice compactness (without 2's) : 54.57174, average 1.94899 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 6 1.71429 18 1 3: -2 .. 0 -1.14286 8 1 5: -1 .. 2 0.28571 6 5 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 44.2103 c. M:-75.9380 c. Lebeng 9: 1 2 1 0 2 1 2 N T3 SD: 44.4273 c. M: 76.4430 c. 10: 2 1 2 0 2 1 2 N T3 I SD: 31.8003 c. M:-57.5963 c. 12: 2 2 2 0 2 2 2 P M DE I SD: 15.9182 c. M:-31.2826 c. 19: 3 3 3 1 3 3 3 SP M DE I SD: 10.9698 c. M:-21.8027 c. 24: 4 4 3 1 4 4 4 P SD: 12.7921 c. M: 18.7174 c. 25: 4 4 4 1 4 4 4 SP M DE I SD: 8.4515 c. M:-14.2237 c. 28: 4 5 4 1 5 4 5 P T3 SD: 8.0921 c. M: 11.5746 c. 34: 5 6 5 1 6 5 6 P T3 SD: 5.5543 c. M: 9.7763 c. 40: 6 7 6 1 7 6 7 P T3 SD: 4.8882 c. M: 9.7763 c. 47: 7 8 7 2 8 7 8 SP T3 SD: 3.6657 c. M: 7.0153 c. 53: 8 9 8 2 9 8 9 SP T3 SD: 1.4720 c. M: 2.6797 c. 59: 9 10 9 2 10 9 10 SP T3 SD: 0.4591 c. M:-0.7741 c. 171: 26 29 26 6 29 26 29 SP T3 SD: 0.3887 c. M:-0.7500 c. 230: 35 39 35 8 39 35 39 SP T3 SD: 0.3307 c. M:-0.6585 c. 289: 44 49 44 10 49 44 49 SP T3 SD: 0.3212 c. M:-0.6043 c. 323: 49 55 49 11 55 49 55 SP T3 SD: 0.3034 c. M: 0.4884 c. 382: 58 65 58 13 65 58 65 SP T3 SD: 0.1970 c. M: 0.3522 c. 441: 67 75 67 15 75 67 75 SP T3 SD: 0.1280 c. M: 0.2525 c. 500: 76 85 76 17 85 76 85 SP T3 SD: 0.0933 c. M: 0.1763 c. 553: 84 94 84 19 94 84 94 SP T3 SD: 0.0927 c. M: 0.1822 c. 559: 85 95 85 19 95 85 95 SP T3 SD: 0.0918 c. M:-0.1556 c. 612: 93 104 93 21 104 93 104 SP T3 SD: 0.0457 c. M: 0.0900 c. 671: 102 114 102 23 114 102 114 SP T3 SD: 0.0301 c. M:-0.0598 c. 1112: 169 189 169 38 189 169 189 SP T3 SD: 0.0336 c. M: 0.0641 c. 1171: 178 199 178 40 199 178 199 SP T3 SD: 0.0233 c. M: 0.0410 c. 1724: 262 293 262 59 293 262 293 SP T3 SD: 0.0271 c. M: 0.0399 c. 1783: 271 303 271 61 303 271 303 SP T3 SD: 0.0116 c. M: 0.0175 c. 1842: 280 313 280 63 313 280 313 SP T3 SD: 0.0063 c. M:-0.0122 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: 46.0894 cents 3 x x 4 x 5 x 6 S SD: 33.3153 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 15.0298 cents 6:7 x 8:9:10:11:12 S SD: 28.1162 cents 7:8:9 x 10:11:12:14 S SD: 16.4602 cents 8:9:10:11 x 13:14:16 SD: 7.8688 cents 9:10:11 x 13:14:16:18 SD: 11.3194 cents 10:11:13:14 x 16:18:20 SD: 12.4343 cents 11:12:14:15:16:18:20:22 S SD: 12.3984 cents 12:13:15 x 17:19:21:24 SD: 9.1879 cents 13:14:16:18 x 21:23:26 SD: 10.5678 cents 15:17:19:21 x 24:27:30 SD: 8.0863 cents 16:18:20:22:23:26:28:32 SD: 7.2439 cents 17:19:21 x 24:27:30:34 SD: 5.3036 cents 20:22:25:28 x 32:36:40 SD: 5.1520 cents 22:24:28 x 31:35:39:44 SD: 8.0995 cents 23:26:29:32:33:37:41:46 SD: 5.4708 cents 24:27:30:33:34:38:43:48 SD: 5.1929 cents 26:29:33:36:37:42:46:52 SD: 4.7733 cents 27:30:34 x 38:43:48:54 SD: 3.9314 cents 28:31:35:39:40:45:50:56 SD: 2.2185 cents 36:40:45:50:51:58:64:72 SD: 1.9663 cents 52:58:65:72:74:83:92:104 SD: 1.8109 cents 64:71:80:89:91:102:114:128 SD: 1.1910 cents 72:80:90:100:102:115:128:144 SD: 1.0591 cents 80:89:100:111:114:128:142:160 SD: 0.7343 cents 100:111:125:139:142:160:178:200 SD: 0.5877 cents 144:160:180:200:205:230:256:288 SD: 0.4929 cents 152:169:190:211:216:243:270:304 SD: 0.4094 cents 180:200:225:250:256:288:320:360 SD: 0.0000 cents