Scala analysis: xen09-chalmers-tritriadic-5-7-9
Tritriadic scale built from 5:7:9
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: 63/50 400.108480 quasi-equal major third 3: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 4: 14/9 764.915905 septimal minor sixth 5: 81/50 835.192576 acute 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: 10/9 182.4037 minor whole tone 2: 567/500 217.7048 3: 10/9 182.4037 minor whole tone 4: 10/9 182.4037 minor whole tone 5: 729/700 70.2767 6: 10/9 182.4037 minor whole tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 729/700 70.277 cents 1: 5 10/9 182.404 cents minor whole tone 1: 1 567/500 217.705 cents 2: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 3 100/81 364.807 cents grave major third 2: 2 63/50 400.108 cents quasi-equal major third 3: 3 9/7 435.084 cents septimal major third, BP third 3: 1 1000/729 547.211 cents 3: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 3 10/7 617.488 cents Euler's tritone 4: 1 729/500 652.789 cents 4: 3 14/9 764.916 cents septimal minor sixth 5: 2 100/63 799.892 cents quasi-equal minor sixth 5: 3 81/50 835.193 cents acute minor sixth 5: 2 140/81 947.320 cents 6: 1 1000/567 982.295 cents 6: 5 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 1400/729 1129.723 cents 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 : 182.4 400.1 582.5 764.9 835.2 1017.6 1200.0 182.4 : 217.7 400.1 582.5 652.8 835.2 1017.6 1200.0 400.1 : 182.4 364.8 435.1 617.5 799.9 982.3 1200.0 582.5 : 182.4 252.7 435.1 617.5 799.9 1017.6 1200.0 764.9 : 70.3 252.7 435.1 617.5 835.2 1017.6 1200.0 835.2 : 182.4 364.8 547.2 764.9 947.3 1129.7 1200.0 1017.6: 182.4 364.8 582.5 764.9 947.3 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.2767 .. 217.7048 cents 49/45, 147.4281 cents 729/700, 70.2767 cents 2: 252.6804 .. 400.1085 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 3: 435.0841 .. 582.5122 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 4: 617.4878 .. 764.9159 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 5: 799.8915 .. 947.3196 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 6: 982.2952 .. 1129.7233 cents 49/45, 147.4281 cents 50/49, 34.9756 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 729/700, 70.2767 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 567/500, 217.7048 cents Average / Smallest step : 2.439338 Largest / Average step : 1.269944 Largest / Smallest step : 3.097824 Median interval of one step : 10/9, 182.4037 cents, amount: 5 Most common interval of one step : 10/9, 182.4037 cents, amount: 5 Least squares average step : 174.79544 cents, oct.: 1223.56807 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : MLMMSMM Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.376338 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.262860 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 : 50/49, 34.9756 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 582.512 1017.596 cents Most common triad is 0.0 182.404 1017.596 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 : 5 9 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% -- Rational properties -- Prime limit : 7 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 81 Scale harmonicity : 0.021059 Average absolute harmonicity : 0.194104 Specific harmonicity : 0.109099 Fundamental : 1/450, -8.8138 octaves, 0.5814 Hz. Guide tone : 5670, 12.4691 octaves, 1483416.955 Hz. Exponens Consonantiae : 2.551500E+06, 21.28291 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 157.5, average 22.50000 Mersenne's string divisions : 543388524 Sum of van Prooijen's expressibility: 7.41565, average 1.05938 Sum of Tenney's harmonic distance : 14.65869, average 2.09410 Vogel's harmonic complexity : 18.28571 Wille's k value : 364 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 89.96625, average 3.21308 Lattice compactness (without 2's) : 83.83777, average 2.99421 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.14286 5 1 3: -2 .. 4 0.57143 12 5: -2 .. 1 -0.71429 7 3 7: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 Scale is weakly epimorphic with val: <7 10 15 21| Scale is weakly epimorphic with val: <7 10 16 18| Scale is weakly epimorphic with val: <7 10 17 22| Scale is weakly epimorphic with val: <7 10 18 19| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 12 16 20| Scale is JI-epimorphic with val: <7 12 18 21|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 46.1801 c. M: 79.2016 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 36.4838 c. M:-64.8074 c. 10: 1 2 2 1 1 1 2 N D3 SD: 39.9403 c. M: 62.4037 c. 12: 2 2 2 2 0 2 2 P M DE S SD: 22.0211 c. M: 35.1926 c. 13: 2 2 2 2 1 2 2 SP M ME S SD: 18.9147 c. M: 30.8777 c. Glacial-7, Lobonian 14: 2 3 2 2 1 2 2 P T3 SD: 16.3929 c. M:-28.4629 c. 19: 3 3 3 3 1 3 3 SP M DE S SD: 11.9257 c. M: 21.1611 c. Glacial-7 20: 3 4 3 3 1 3 3 P T3 SD: 11.7333 c. M:-19.8915 c. 24: 4 4 4 3 2 3 4 P S SD: 13.9736 c. M: 17.5963 c. 25: 4 4 4 4 1 4 4 SP M DE S SD: 11.1094 c. M: 19.1926 c. 27: 4 5 4 4 2 4 4 SP T3 SD: 5.8363 c. M: 9.3603 c. 33: 5 6 5 5 2 5 5 SP T3 SD: 0.7735 c. M: 1.2795 c. 105: 16 19 16 16 6 16 16 SP T3 SD: 0.5348 c. M: 0.9069 c. 138: 21 25 21 21 8 21 21 SP T3 SD: 0.2281 c. M: 0.4100 c. 171: 26 31 26 26 10 26 26 SP T3 SD: 0.0670 c. M: 0.1085 c. 546: 83 99 83 83 32 83 83 SP T3 SD: 0.0637 c. M: 0.1085 c. 717: 109 130 109 109 42 109 109 SP T3 SD: 0.0611 c. M: 0.1085 c. 888: 135 161 135 135 52 135 135 SP T3 SD: 0.0606 c. M: 0.1085 c. 921: 140 167 140 140 54 140 140 SP T3 SD: 0.0670 c. M: 0.1085 c. 1059: 161 192 161 161 62 161 161 SP T3 SD: 0.0607 c. M: 0.1085 c. 1605: 244 291 244 244 94 244 244 SP T3 SD: 0.0607 c. M: 0.1085 c. 1862: 283 338 283 283 109 283 283 SP T3 SD: 0.0606 c. M:-0.1063 c. 1895: 288 344 288 288 111 288 288 SP T3 SD: 0.0573 c. M:-0.1026 c. 1928: 293 350 293 293 113 293 293 SP T3 SD: 0.0571 c. M:-0.0990 c. 1961: 298 356 298 298 115 298 298 SP T3 SD: 0.0599 c. M:-0.0955 c. 2000: 304 363 304 304 117 304 304 SP T3 SD: 0.0576 c. M:-0.0915 c. 2033: 309 369 309 309 119 309 309 SP T3 SD: 0.0511 c. M:-0.0883 c. 2066: 314 375 314 314 121 314 314 SP T3 SD: 0.0475 c. M:-0.0851 c. 2099: 319 381 319 319 123 319 319 SP T3 SD: 0.0471 c. M:-0.0821 c. 2132: 324 387 324 324 125 324 324 SP T3 SD: 0.0497 c. M:-0.0795 c. 2171: 330 394 330 330 127 330 330 SP T3 SD: 0.0501 c. M:-0.0772 c. 2204: 335 400 335 335 129 335 335 SP T3 SD: 0.0434 c. M:-0.0730 c. 2237: 340 406 340 340 131 340 340 SP T3 SD: 0.0394 c. M:-0.0703 c. 2270: 345 412 345 345 133 345 345 SP T3 SD: 0.0387 c. M:-0.0677 c. 2303: 350 418 350 350 135 350 350 SP T3 SD: 0.0410 c. M:-0.0658 c. 2375: 361 431 361 361 139 361 361 SP T3 SD: 0.0370 c. M:-0.0599 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: 31.4805 cents 3 x x 4 x 5 x 6 S SD: 32.5781 cents 4 x 5 x 6 x 7:8 S SD: 20.2066 cents 5 x 6:7 x 8:9:10 S SD: 17.4324 cents 6:7 x 8:9:10:11:12 S SD: 24.5288 cents 7:8:9:10:11 x 13:14 SD: 14.9643 cents 8:9:10:11:12:13:14:16 S SD: 12.7751 cents 10:11:13:14 x 16:18:20 SD: 10.1279 cents 11:12:14:15:17:18:20:22 SD: 9.1700 cents 12:13:15:17:19 x 22:24 SD: 11.1546 cents 14:16:18:20:22:23:25:28 SD: 10.9849 cents 15:17:19:21:23:24:27:30 SD: 6.9132 cents 16:18:20:22:25:26:29:32 SD: 6.1567 cents 18:20:23:25:28:29:32:36 SD: 5.2136 cents 20:22:25:28:31:32:36:40 SD: 4.5038 cents 27:30:34:38:42:44:49:54 SD: 2.8253 cents 35:39:44:49:54:57:63:70 SD: 2.5741 cents 43:48:54:60:67:70:77:86 SD: 2.4357 cents 45:50:57:63:70:73:81:90 SD: 1.3484 cents 65:72:82:91:101:105:117:130 SD: 1.1153 cents 81:90:102:113:126:131:146:162 SD: 1.0354 cents 90:100:113:126:140:146:162:180 SD: 0.9374 cents 92:102:116:129:143:149:166:184 SD: 0.9292 cents 100:111:126:140:156:162:180:200 SD: 0.7477 cents 108:120:136:151:168:175:194:216 SD: 0.6253 cents 135:150:170:189:210:219:243:270 SD: 0.3689 cents 200:222:252:280:311:324:360:400 SD: 0.2627 cents 250:278:315:350:389:405:450:500 SD: 0.2100 cents 315:350:397:441:490:510:567:630 SD: 0.1582 cents 405:450:510:567:630:656:729:810 SD: 0.1502 cents 450:500:567:630:700:729:810:900 SD: 0.0000 cents