Scala analysis: xen09-chalmers-tritriadic-5-6-7
Tritriadic scale built from 5:6:7
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: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 3: 10/7 617.487807 Euler's tritone 4: 42/25 898.153480 quasi-equal major sixth 5: 12/7 933.129094 septimal major sixth 6: 49/25 1165.024385 BP eighth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 1: 6/5 315.6413 minor third 2: 7/6 266.8709 septimal minor third 3: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 4: 147/125 280.6657 5: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 6: 343/300 231.8953 7: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 1 343/300 231.895 cents 1: 1 7/6 266.871 cents septimal minor third 1: 1 147/125 280.666 cents 1: 1 6/5 315.641 cents minor third 2: 2 7/6 266.871 cents septimal minor third 2: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 2 6/5 315.641 cents minor third 2: 1 60/49 350.617 cents smaller approximation to neutral third 2: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 1 60/49 350.617 cents smaller approximation to neutral third 3: 1 343/250 547.537 cents 3: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 2 10/7 617.488 cents Euler's tritone 4: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 10/7 617.488 cents Euler's tritone 4: 1 500/343 652.463 cents 4: 1 49/30 849.383 cents larger approximation to neutral sixth 4: 1 42/25 898.153 cents quasi-equal major sixth 5: 1 10/7 617.488 cents Euler's tritone 5: 1 49/30 849.383 cents larger approximation to neutral sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 42/25 898.153 cents quasi-equal major sixth 5: 2 12/7 933.129 cents septimal major sixth 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 250/147 919.334 cents 6: 1 12/7 933.129 cents septimal major sixth 6: 1 600/343 968.105 cents 6: 3 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 315.6 582.5 617.5 898.2 933.1 1165.0 1200.0 315.6 : 266.9 301.8 582.5 617.5 849.4 884.4 1200.0 582.5 : 35.0 315.6 350.6 582.5 617.5 933.1 1200.0 617.5 : 280.7 315.6 547.5 582.5 898.2 1165.0 1200.0 898.2 : 35.0 266.9 301.8 617.5 884.4 919.3 1200.0 933.1 : 231.9 266.9 582.5 849.4 884.4 1165.0 1200.0 1165.0: 35.0 350.6 617.5 652.5 933.1 968.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 315.6413 cents 147/125, 280.6657 cents 50/49, 34.9756 cents 2: 266.8709 .. 582.5122 cents 6/5, 315.6413 cents 35/36,-48.7704 cents 3: 301.8465 .. 617.4878 cents 6/5, 315.6413 cents 125/147,-280.6657 cents 4: 582.5122 .. 898.1535 cents 6/5, 315.6413 cents 49/50,-34.9756 cents 5: 617.4878 .. 933.1291 cents 6/5, 315.6413 cents 125/147,-280.6657 cents 6: 884.3587 .. 1165.0244 cents 147/125, 280.6657 cents 35/36,-48.7704 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 4.901374 Largest / Average step : 1.841241 Largest / Smallest step : 9.024610 Median interval of one step : 343/300, 231.8953 cents, amount: 1 Most common interval of one step : 50/49, 34.9756 cents, amount: 3 Least squares average step : 192.72525 cents, oct.: 1349.07674 cents Scale is not proper Step pattern alph. order: ABCDCEC Step pattern size order : ECADABA Scale is not a Constant Structure Scale diversity : 1.104758 Lumma stability : 0.058293 Lumma impropriety factor : 0.555215 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 : 5.00000 = 5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 126/125, 13.7948 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 315.641 582.512 cents Most common triad is 0.0 582.512 617.488 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 5 7 Length of longest harmonic part : 2 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 classes 2 and 3 combined -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.018274 Average absolute harmonicity : 0.192862 Specific harmonicity : 0.100674 Fundamental : 1/175, -7.4512 octaves, 1.4950 Hz. Guide tone : 2940, 11.5216 octaves, 769179.162 Hz. Exponens Consonantiae : 5.145000E+05, 18.97281 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 101.5, average 14.50000 Mersenne's string divisions : 105694644 Sum of van Prooijen's expressibility: 6.32240, average 0.90320 Sum of Tenney's harmonic distance : 13.20092, average 1.88585 Vogel's harmonic complexity : 17.57143 Wille's k value : 171 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 63.63340, average 2.27262 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.85714 6 1 3: 0 .. 1 0.42857 3 5: -2 .. 1 -0.71429 7 1 7: -1 .. 2 0.28571 6 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 15 19| Scale is weakly epimorphic with val: <7 10 16 18| Scale is weakly epimorphic with val: <7 11 15 21| Scale is weakly epimorphic with val: <7 11 16 20| = patent Scale is weakly epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 12 16 22| Scale is weakly epimorphic with val: <7 12 17 21| Scale is weakly epimorphic with val: <7 12 18 20|
FIT/MODE
7: 2 1 1 1 0 2 0 N T3 SD: 51.7266 c. M: 75.9862 c. 8: 2 2 0 2 0 2 0 N M DE S SD: 21.3158 c. M:-34.9756 c. 16: 4 4 0 4 0 3 1 N SD: 22.5490 c. M: 40.0244 c. 18: 5 4 0 4 1 3 1 N SD: 20.4256 c. M: 31.6911 c. 19: 5 4 1 4 1 3 1 N SD: 15.0644 c. M: 28.1823 c. 23: 6 5 1 5 1 4 1 N SD: 9.3489 c. M: 17.1983 c. 27: 7 6 1 6 1 5 1 N SD: 5.8662 c. M: 9.4688 c. 31: 8 7 1 7 1 6 1 N SD: 4.3849 c. M: 7.8309 c. 35: 9 8 1 8 1 7 1 N SD: 4.6430 c. M: 7.4148 c. 60: 16 13 2 14 2 11 2 N SD: 3.9185 c. M:-6.8709 c. 64: 17 14 2 15 2 12 2 N SD: 2.4418 c. M:-4.3709 c. 68: 18 15 2 16 2 13 2 N SD: 1.3241 c. M:-2.1650 c. 72: 19 16 2 17 2 14 2 N SD: 1.1051 c. M:-1.8465 c. 99: 26 22 3 23 3 19 3 N SD: 0.8082 c. M: 1.3880 c. 103: 27 23 3 24 3 20 3 N SD: 0.7060 c. M: 1.0903 c. 167: 44 37 5 39 5 32 5 N SD: 0.6148 c. M:-1.0026 c. 171: 45 38 5 40 5 33 5 N SD: 0.1140 c. M:-0.2042 c. 445: 117 99 13 104 13 86 13 N SD: 0.0987 c. M: 0.1760 c. 517: 136 115 15 121 15 100 15 N SD: 0.0869 c. M:-0.1594 c. 616: 162 137 18 144 18 119 18 N SD: 0.0605 c. M: 0.1015 c. 787: 207 175 23 184 23 152 23 N SD: 0.0510 c. M: 0.0943 c. 859: 226 191 25 201 25 166 25 N SD: 0.0560 c. M:-0.1003 c. 958: 252 213 28 224 28 185 28 N SD: 0.0532 c. M: 0.0975 c. 962: 253 214 28 225 28 186 28 N SD: 0.0411 c. M: 0.0730 c. 1133: 298 252 33 265 33 219 33 N SD: 0.0180 c. M: 0.0311 c. 1304: 343 290 38 305 38 252 38 N SD: 0.0039 c. M:-0.0063 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 42.2336 cents 3 x 4 x 5 x x 6 S SD: 28.5287 cents 4:5 x 6 x 7 x 8 S SD: 28.9434 cents 5:6:7 x 8:9 x 10 S SD: 23.8909 cents 6:7:8:9:10 x x 12 S SD: 25.9525 cents 7:8 x 10 x 12 x 14 S SD: 21.1168 cents 8:10:11 x 13:14 x 16 SD: 20.5550 cents 9:11 x 13:15 x x 18 SD: 9.8912 cents 10:12:14 x x 17 x 20 SD: 3.6218 cents 11:13:15:16:18:19 x 22 SD: 12.9036 cents 12:14 x 17:20:21 x 24 SD: 12.7326 cents 13:16:18:19:22 x 25:26 SD: 11.8917 cents 14:17 x 20 x 24:27:28 SD: 6.9367 cents 15:18:21 x 25:26:29:30 SD: 5.5745 cents 16:19:22:23:27 x 31:32 SD: 7.2209 cents 17:20:24 x x 29:33:34 SD: 8.3347 cents 18:22:25:26:30:31:35:36 SD: 6.4046 cents 19:23 x 27:32:33:37:38 SD: 5.1863 cents 20:24:28:29 x 34:39:40 SD: 5.1443 cents 21:25:29:30:35:36:41:42 SD: 4.4915 cents 22:26:31 x 37:38:43:44 SD: 5.3273 cents 23:28:32:33:39 x 45:46 SD: 5.4275 cents 24:29 x 34:40:41:47:48 SD: 4.0213 cents 25:30:35:36:42:43:49:50 SD: 2.1356 cents 29:35:41 x 49:50:57:58 SD: 4.1064 cents 30:36:42:43:50:51:59:60 SD: 3.0902 cents 35:42:49:50:59:60:69:70 SD: 1.6652 cents 56:67:78:80:94:96:110:112 SD: 1.5748 cents 60:72:84:86:101:103:118:120 SD: 1.3194 cents 70:84:98:100:118:120:137:140 SD: 0.9140 cents 75:90:105:107:126:129:147:150 SD: 0.8867 cents 95:114:133:136:160:163:186:190 SD: 0.8783 cents 100:120:140:143:168:171:196:200 SD: 0.6666 cents 105:126:147:150:176:180:206:210 SD: 0.6107 cents 140:168:196:200:235:240:274:280 SD: 0.4177 cents 150:180:210:214:252:257:294:300 SD: 0.3575 cents 175:210:245:250:294:300:343:350 SD: 0.0000 cents