Scala analysis: xen09-chalmers-tritriadic-5-9-8
Tritriadic scale built from 5:9:8
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: 32/25 427.372572 classic diminished fourth 4: 36/25 631.282574 classic diminished fifth 5: 8/5 813.686286 minor sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 128/125 41.0589 minor diesis, diesis 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 9/8 203.9100 major whole tone 7: 10/9 182.4037 minor 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 : 203.9 386.3 427.4 631.3 813.7 1017.6 1200.0 203.9 : 182.4 223.5 427.4 609.8 813.7 996.1 1200.0 386.3 : 41.1 245.0 427.4 631.3 813.7 1017.6 1200.0 427.4 : 203.9 386.3 590.2 772.6 976.5 1158.9 1200.0 631.3 : 182.4 386.3 568.7 772.6 955.0 996.1 1200.0 813.7 : 203.9 386.3 590.2 772.6 813.7 1017.6 1200.0 1017.6: 182.4 386.3 568.7 609.8 813.7 996.1 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 : 166.84139 cents, oct.: 1167.88973 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAB Step pattern size order : LMSLMLM 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 0 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 162.8511 cents: 5 -- Rational properties -- Prime limit : 5 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 25 Scale harmonicity : 0.030738 Average absolute harmonicity : 0.219500 Specific harmonicity : 0.163265 Fundamental : 1/200, -7.6439 octaves, 1.3081 Hz. Guide tone : 1440, 10.4919 octaves, 376740.814 Hz. Exponens Consonantiae : 2.880000E+05, 18.13571 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 87.0, average 12.42857 Mersenne's string divisions : 32273514 Sum of van Prooijen's expressibility: 6.10231, average 0.87176 Sum of Tenney's harmonic distance : 12.57200, average 1.79600 Vogel's harmonic complexity : 12.85714 Wille's k value : 112 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 108.22683, average 3.86524 Lattice compactness (without 2's) : 54.33567, average 1.94056 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 0.85714 16 1 3: 0 .. 2 0.85714 6 1 5: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 0 2 1 1 1 N T3 SD: 46.3806 c. M: 84.5154 c. 8: 1 2 0 1 1 2 1 N T3 SD: 44.0110 c. M: 63.6863 c. 9: 2 1 0 2 1 2 1 N T3 SD: 35.2992 c. M:-62.7567 c. 11: 2 2 0 2 1 2 2 N SD: 31.8832 c. M: 50.0499 c. 12: 2 2 0 2 2 2 2 P M DE S SD: 18.6218 c. M: 31.2826 c. 13: 2 2 1 2 2 2 2 SP M ME S SD: 18.3197 c. M:-34.1659 c. Oukranian 18: 3 3 0 3 3 3 3 P M DE S SD: 18.6218 c. M: 31.2826 c. 19: 3 3 1 3 3 3 3 SP M DE S SD: 9.1344 c. M:-14.7327 c. 25: 4 4 1 4 4 4 4 SP M DE S SD: 6.7516 c. M: 11.9100 c. 28: 5 4 1 5 4 5 4 P T3 SD: 7.2134 c. M:-11.5746 c. 34: 6 5 1 6 5 6 5 P T3 SD: 4.3939 c. M:-7.8547 c. 40: 7 6 1 7 6 7 6 P T3 SD: 4.2434 c. M: 7.3726 c. 47: 8 7 2 8 7 8 7 SP T3 SD: 4.3030 c. M:-7.0153 c. 53: 9 8 2 9 8 9 8 SP T3 SD: 1.7201 c. M:-2.8161 c. 59: 10 9 2 10 9 10 9 SP T3 SD: 0.4449 c. M: 0.7741 c. 171: 29 26 6 29 26 29 26 SP T3 SD: 0.3745 c. M:-0.6976 c. 230: 39 35 8 39 35 39 35 SP T3 SD: 0.2771 c. M:-0.4535 c. 289: 49 44 10 49 44 49 44 SP T3 SD: 0.2543 c. M: 0.4498 c. 323: 55 49 11 55 49 55 49 SP T3 SD: 0.2456 c. M:-0.4244 c. 382: 65 58 13 65 58 65 58 SP T3 SD: 0.1555 c. M:-0.2785 c. 441: 75 67 15 75 67 75 67 SP T3 SD: 0.1049 c. M:-0.1716 c. 500: 85 76 17 85 76 85 76 SP T3 SD: 0.0923 c. M: 0.1726 c. 553: 94 84 19 94 84 94 84 SP T3 SD: 0.1021 c. M:-0.1822 c. 612: 104 93 21 104 93 104 93 SP T3 SD: 0.0535 c. M:-0.0900 c. 671: 114 102 23 114 102 114 102 SP T3 SD: 0.0272 c. M:-0.0492 c. 1112: 189 169 38 189 169 189 169 SP T3 SD: 0.0267 c. M:-0.0468 c. 1171: 199 178 40 199 178 199 178 SP T3 SD: 0.0245 c. M: 0.0455 c. 1724: 293 262 59 293 262 293 262 SP T3 SD: 0.0245 c. M:-0.0399 c. 1783: 303 271 61 303 271 303 271 SP T3 SD: 0.0096 c. M:-0.0160 c. 1842: 313 280 63 313 280 313 280 SP T3 SD: 0.0073 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: 35.3362 cents 3 x x 4 x 5 x 6 S SD: 33.3153 cents 4 x 5 x 6 x 7:8 S SD: 21.4668 cents 5 x 6 x 7:8:9:10 S SD: 17.1734 cents 6:7 x 8:9:10:11:12 S SD: 23.5449 cents 7:8 x 9:10:11:13:14 SD: 11.6590 cents 8:9:10 x 12:13:14:16 S SD: 14.9941 cents 9:10:11:12:13:14:16:18 S SD: 14.1712 cents 10:11 x 13:14:16:18:20 SD: 11.3194 cents 11:12 x 14:16:18:20:22 S SD: 11.8491 cents 12:14:15 x 17:19:22:24 SD: 13.0189 cents 13:15:16:17:19:21:23:26 SD: 10.9179 cents 14:16 x 18:20:22:25:28 SD: 7.7396 cents 15:17 x 19:22:24:27:30 SD: 6.4571 cents 16:18:20 x 23:26:29:32 SD: 4.9246 cents 18:20 x 23:26:29:32:36 SD: 5.5430 cents 19:21:24 x 27:30:34:38 SD: 8.2028 cents 20:23:25:26:29:32:36:40 SD: 6.8688 cents 21:24:26:27:30:34:38:42 SD: 6.0115 cents 22:25 x 28:32:35:40:44 SD: 5.5349 cents 23:26:29 x 33:37:41:46 SD: 4.4232 cents 25:28:31:32:36:40:45:50 SD: 2.2715 cents 26:29 x 33:37:42:47:52 SD: 5.7316 cents 27:30:34:35:39:43:49:54 SD: 5.3449 cents 28:32:35:36:40:45:50:56 SD: 5.0363 cents 29:33:36:37:42:46:52:58 SD: 4.3652 cents 30:34 x 38:43:48:54:60 SD: 3.9314 cents 32:36:40:41:46:51:58:64 SD: 2.0272 cents 40:45:50:51:58:64:72:80 SD: 1.9663 cents 55:62:69:70:79:88:99:110 SD: 1.8526 cents 57:64:71:73:82:91:103:114 SD: 1.5120 cents 64:72:80:82:92:102:115:128 SD: 1.1682 cents 80:90:100:102:115:128:144:160 SD: 1.0591 cents 89:100:111:114:128:142:160:178 SD: 1.0536 cents 96:108:120:123:138:154:173:192 SD: 0.8594 cents 104:117:130:133:150:166:187:208 SD: 0.7942 cents 120:135:150:154:173:192:216:240 SD: 0.7040 cents 128:144:160:164:184:205:230:256 SD: 0.6971 cents 136:153:170:174:196:218:245:272 SD: 0.5485 cents 160:180:200:205:230:256:288:320 SD: 0.4929 cents 168:189:210:215:242:269:302:336 SD: 0.3870 cents 175:197:219:224:252:280:315:350 SD: 0.3232 cents 200:225:250:256:288:320:360:400 SD: 0.0000 cents