Scala analysis: xen12-chalmers-tritriadic-mt-7-9-5
Tritriadic M->T scale built from 7:9:5
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: 9/7 435.084095 septimal major third, BP third 3: 10/7 617.487807 Euler's tritone 4: 14/9 764.915905 septimal minor sixth 5: 81/49 870.168191 two (septimal major third, BP third) 6: 90/49 1052.571903 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 49/45 147.4281 BP minor semitone 1: 10/9 182.4037 minor whole tone 2: 81/70 252.6804 Al-Hwarizmi's lute middle finger 3: 10/9 182.4037 minor whole tone 4: 49/45 147.4281 BP minor semitone 5: 729/686 105.2523 6: 10/9 182.4037 minor whole tone 7: 49/45 147.4281 BP minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 729/686 105.252 cents 1: 2 49/45 147.428 cents BP minor semitone 1: 3 10/9 182.404 cents minor whole tone 1: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 405/343 287.656 cents 2: 3 98/81 329.832 cents 2: 2 9/7 435.084 cents septimal major third, BP third 3: 3 9/7 435.084 cents septimal major third, BP third 3: 1 980/729 512.236 cents 3: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 10/7 617.488 cents Euler's tritone 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 10/7 617.488 cents Euler's tritone 4: 1 729/490 687.764 cents 4: 3 14/9 764.916 cents septimal minor sixth 5: 2 14/9 764.916 cents septimal minor sixth 5: 3 81/49 870.168 cents two (septimal major third, BP third) 5: 1 686/405 912.344 cents 5: 1 140/81 947.320 cents 6: 1 140/81 947.320 cents 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 90/49 1052.572 cents 6: 1 1372/729 1094.748 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 435.1 617.5 764.9 870.2 1052.6 1200.0 182.4 : 252.7 435.1 582.5 687.8 870.2 1017.6 1200.0 435.1 : 182.4 329.8 435.1 617.5 764.9 947.3 1200.0 617.5 : 147.4 252.7 435.1 582.5 764.9 1017.6 1200.0 764.9 : 105.3 287.7 435.1 617.5 870.2 1052.6 1200.0 870.2 : 182.4 329.8 512.2 764.9 947.3 1094.7 1200.0 1052.6: 147.4 329.8 582.5 764.9 912.3 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 105.2523 .. 252.6804 cents 49/45, 147.4281 cents 729/686, 105.2523 cents 2: 252.6804 .. 435.0841 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 3: 435.0841 .. 617.4878 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 4: 582.5122 .. 764.9159 cents 10/9, 182.4037 cents 49/50,-34.9756 cents 5: 764.9159 .. 947.3196 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 6: 947.3196 .. 1094.7477 cents 49/45, 147.4281 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 729/686, 105.2523 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 81/70, 252.6804 cents Average / Smallest step : 1.628740 Largest / Average step : 1.473969 Largest / Smallest step : 2.400712 Median interval of one step : 10/9, 182.4037 cents, amount: 3 Most common interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 178.79265 cents, oct.: 1251.54857 cents Scale is not proper Step pattern alph. order: ABACDAC Step pattern size order : CDCBACB Scale is not a Constant Structure Scale diversity : 1.429395 Lumma stability : 0.175420 Lumma impropriety factor : 0.029146 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 50/49, 34.9756 cents Most common intervals : 9/7, 435.0841 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 182.404 764.916 cents Most common triad is 0.0 435.084 764.916 cents, amount: 3 Number of recognisable fifths : 1, average 687.7645 cents Number of appreciable fifths : 0 Scale contains a complete diamond : 7 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 : 0.018431 Average absolute harmonicity : 0.188758 Specific harmonicity : 0.098109 Fundamental : 1/441, -8.7846 octaves, 0.5933 Hz. Guide tone : 5670, 12.4691 octaves, 1483416.955 Hz. Exponens Consonantiae : 2.500470E+06, 21.25377 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 173.5, average 24.78571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.30651, average 1.04379 Sum of Tenney's harmonic distance : 15.24320, average 2.17760 Vogel's harmonic complexity : 19.57143 Wille's k value : 364 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 87.30797, average 3.11814 Lattice compactness (without 2's) : 83.83777, average 2.99421 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.71429 5 1 3: -2 .. 4 0.57143 12 5: 0 .. 1 0.42857 3 1 7: -2 .. 1 -0.71429 7 5 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 16 19| Scale is weakly epimorphic with val: <7 10 17 21| Scale is weakly epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 12 15 20| Scale is weakly epimorphic with val: <7 12 16 22| Scale is weakly epimorphic with val: <7 12 18 19|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 61.2903 c. M: 103.2021 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 19.6299 c. M: 32.4037 c. 14: 2 3 2 2 1 2 2 P T3 SD: 13.3993 c. M: 24.0005 c. 19: 3 4 3 2 2 3 2 N SD: 11.8927 c. M:-21.1123 c. 22: 3 5 3 3 2 3 3 P T3 SD: 11.5299 c. M: 18.7673 c. 25: 4 5 4 3 2 4 3 N SD: 5.3894 c. M:-9.5963 c. 33: 5 7 5 4 3 5 4 N SD: 1.4414 c. M:-2.5591 c. 80: 12 17 12 10 7 12 10 N SD: 1.6311 c. M: 2.5719 c. 91: 14 19 14 11 8 14 11 N SD: 1.5032 c. M:-2.3732 c. 105: 16 22 16 13 9 16 13 N SD: 0.8829 c. M: 1.5968 c. 138: 21 29 21 17 12 21 17 N SD: 0.3284 c. M: 0.6030 c. 171: 26 36 26 21 15 26 21 N SD: 0.0369 c. M:-0.0597 c. 1677: 255 353 255 206 147 255 206 N SD: 0.0366 c. M:-0.0650 c. 1790: 272 377 272 220 157 272 220 N SD: 0.0377 c. M: 0.0579 c. 1848: 281 389 281 227 162 281 227 N SD: 0.0357 c. M:-0.0638 c. 1961: 298 413 298 241 172 298 241 N SD: 0.0312 c. M: 0.0478 c. 2132: 324 449 324 262 187 324 262 N SD: 0.0258 c. M: 0.0397 c. 2303: 350 485 350 283 202 350 283 N SD: 0.0212 c. M: 0.0329 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 4 x x 5 x 6 S SD: 21.5134 cents 4 x 5 x 6 x 7:8 S SD: 28.8921 cents 5 x 6:7:8 x 9:10 S SD: 27.6346 cents 6:7:8 x 9:10:11:12 S SD: 20.5984 cents 7:8:9:10:11:12:13:14 H SD: 11.9672 cents 9:10:12:13:14:15:17:18 SD: 11.8503 cents 11:12:14:16:17:18:20:22 S SD: 7.8716 cents 17:19:22:24:26:28:31:34 SD: 5.9020 cents 18:20:23:26:28:30:33:36 SD: 3.7594 cents 25:28:32:36:39:41:46:50 SD: 3.6770 cents 35:39:45:50:54:58:64:70 SD: 2.4886 cents 38:42:49:54:59:63:70:76 SD: 2.2776 cents 45:50:58:64:70:74:83:90 SD: 2.0807 cents 52:58:67:74:81:86:96:104 SD: 1.9539 cents 54:60:69:77:84:89:99:108 SD: 1.8186 cents 56:62:72:80:87:93:103:112 SD: 1.5184 cents 63:70:81:90:98:104:116:126 SD: 0.6980 cents 126:140:162:180:196:208:231:252 SD: 0.5704 cents 133:148:171:190:207:220:244:266 SD: 0.5151 cents 164:182:211:234:255:271:301:328 SD: 0.5143 cents 171:190:220:244:266:283:314:342 SD: 0.4419 cents 182:202:234:260:283:301:334:364 SD: 0.3767 cents 189:210:243:270:294:312:347:378 SD: 0.3544 cents 196:218:252:280:305:324:360:392 SD: 0.2679 cents 245:272:315:350:381:405:450:490 SD: 0.2145 cents 360:400:463:514:560:595:661:720 SD: 0.1832 cents 378:420:486:540:588:625:694:756 SD: 0.1164 cents 441:490:567:630:686:729:810:882 SD: 0.0000 cents