Scala analysis: xen12-chalmers-tritriadic-mt-25-19-17
Tritriadic M->T scale built from 25:19:17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 646/625 57.213570 2: 722/625 249.771177 3: 25/19 475.114412 4: 34/25 532.327982 5: 38/25 724.885588 6: 34/19 1007.442393 quasi-mean seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 19/17 192.5576 quasi-meantone 1: 646/625 57.2136 2: 19/17 192.5576 quasi-meantone 3: 15625/13718 225.3432 4: 646/625 57.2136 5: 19/17 192.5576 quasi-meantone 6: 425/361 282.5568 7: 19/17 192.5576 quasi-meantone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 646/625 57.214 cents 1: 3 19/17 192.558 cents quasi-meantone 1: 1 15625/13718 225.343 cents 1: 1 425/361 282.557 cents 2: 3 722/625 249.771 cents 2: 1 425/361 282.557 cents 2: 1 15625/12274 417.901 cents 2: 2 25/19 475.114 cents 3: 1 13718/10625 442.329 cents 3: 3 25/19 475.114 cents 3: 2 34/25 532.328 cents 3: 1 25/17 667.672 cents 4: 1 34/25 532.328 cents 4: 2 25/17 667.672 cents 4: 3 38/25 724.886 cents 4: 1 10625/6859 757.671 cents 5: 2 38/25 724.886 cents 5: 1 24548/15625 782.099 cents 5: 1 722/425 917.443 cents 5: 3 625/361 950.229 cents 6: 1 722/425 917.443 cents 6: 1 27436/15625 974.657 cents 6: 3 34/19 1007.442 cents quasi-mean seventh 6: 2 625/323 1142.786 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 : 57.2 249.8 475.1 532.3 724.9 1007.4 1200.0 57.2 : 192.6 417.9 475.1 667.7 950.2 1142.8 1200.0 249.8 : 225.3 282.6 475.1 757.7 950.2 1007.4 1200.0 475.1 : 57.2 249.8 532.3 724.9 782.1 974.7 1200.0 532.3 : 192.6 475.1 667.7 724.9 917.4 1142.8 1200.0 724.9 : 282.6 475.1 532.3 724.9 950.2 1007.4 1200.0 1007.4: 192.6 249.8 442.3 667.7 724.9 917.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.2136 .. 282.5568 cents 15625/13718, 225.3432 cents 646/625, 57.2136 cents 2: 249.7712 .. 475.1144 cents 15625/13718, 225.3432 cents 260642/265625,-32.7856 cents 3: 442.3288 .. 667.6720 cents 15625/13718, 225.3432 cents 260642/265625,-32.7856 cents 4: 532.3280 .. 757.6712 cents 15625/13718, 225.3432 cents 578/625,-135.3440 cents 5: 724.8856 .. 950.2288 cents 15625/13718, 225.3432 cents 260642/265625,-32.7856 cents 6: 917.4432 .. 1142.7864 cents 15625/13718, 225.3432 cents 260642/265625,-32.7856 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 646/625, 57.2136 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 425/361, 282.5568 cents Average / Smallest step : 2.996292 Largest / Average step : 1.648248 Largest / Smallest step : 4.938633 Median interval of one step : 19/17, 192.5576 cents, amount: 3 Most common interval of one step : 19/17, 192.5576 cents, amount: 3 Least squares average step : 158.43210 cents, oct.: 1109.02467 cents Scale is not proper Scale is a mode of a 1720-tone equal temperament with octave 2/1 degrees: 82 358 681 763 1039 1444 1720 Least number of segments generator : 861 of 600.698 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1403 of 978.837 cents and inv. generated superset size: 68 = 61 more = 971.429% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABDB Step pattern size order : ABCABDB Scale is not a Constant Structure Scale diversity : 1.305518 Lumma stability : 0.095356 Lumma impropriety factor : 0.222072 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 : 9904396/9765625, 24.4279 cents Most common intervals : 25/19, 475.1144 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 532.328 724.886 cents Most common triad is 0.0 475.114 724.886 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 19 25 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 19 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.005820 Average absolute harmonicity : 0.157407 Specific harmonicity : 0.030897 Fundamental : 1/11875, -13.5356 octaves, 0.0220 Hz. Guide tone : 306850, 18.2272 octaves, 80279804.713 Hz. Exponens Consonantiae : 3.643844E+09, 31.76281 octaves Euler's gradus suavitatis : 96 Sum of Mann's harmonic distance : 1420.0, average 202.85714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.06433, average 1.58062 Sum of Tenney's harmonic distance : 22.95563, average 3.27938 Vogel's harmonic complexity : 45.42857 Wille's k value : 7812 Wilson's harmonic complexity : 104 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 87.85708, average 3.13775 Lattice compactness (without 2's) : 85.08042, average 3.03859 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.85714 6 1 5: -4 .. 2 -1.42857 14 17: 0 .. 1 0.42857 3 1 19: -1 .. 2 0.28571 6 5 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 23 / 7 = 3.28571 Scale is weakly epimorphic with val: <7 15 26 29| Scale is weakly epimorphic with val: <7 15 27 31| Scale is weakly epimorphic with val: <7 15 28 33| Scale is weakly epimorphic with val: <7 15 31 32| Scale is weakly epimorphic with val: <7 16 26 27| Scale is weakly epimorphic with val: <7 16 27 29| Scale is weakly epimorphic with val: <7 16 28 31| Scale is weakly epimorphic with val: <7 16 29 33| Scale is weakly epimorphic with val: <7 17 26 32| Scale is weakly epimorphic with val: <7 17 28 29| Scale is weakly epimorphic with val: <7 17 29 31| Scale is weakly epimorphic with val: <7 17 30 33| Scale is weakly epimorphic with val: <7 18 26 30| Scale is weakly epimorphic with val: <7 18 27 32| Scale is weakly epimorphic with val: <7 18 30 31| Scale is weakly epimorphic with val: <7 18 31 33|
FIT/MODE
7: 0 1 2 0 1 2 1 N T3 SD: 43.5098 c. M: 78.3426 c. 10: 0 2 2 0 2 2 2 N M DE S SD: 34.6526 c. M: 57.2136 c. 13: 1 2 2 1 2 3 2 N G T3 S SD: 20.2257 c. M:-35.0941 c. 15: 1 2 3 1 2 4 2 N SD: 18.8535 c. M:-32.5576 c. 18: 1 3 3 1 3 4 3 N G T3 S SD: 9.0550 c. M:-16.8955 c. 20: 1 3 4 1 3 5 3 N SD: 7.2460 c. M:-12.5576 c. 25: 1 4 5 1 4 6 4 N SD: 5.9419 c. M: 9.7712 c. 38: 2 6 7 2 6 9 6 N SD: 3.3273 c. M:-5.9443 c. 43: 2 7 8 2 7 10 7 N SD: 1.5605 c. M: 2.7912 c. 63: 3 10 12 3 10 15 10 N SD: 1.3253 c. M: 2.1521 c. 81: 4 13 15 4 13 19 13 N SD: 1.2923 c. M:-2.0807 c. 106: 5 17 20 5 17 25 17 N SD: 0.4162 c. M: 0.7146 c. 187: 9 30 35 9 30 44 30 N SD: 0.3271 c. M:-0.5404 c. 250: 12 40 47 12 40 59 40 N SD: 0.3223 c. M:-0.5576 c. 293: 14 47 55 14 47 69 47 N SD: 0.0697 c. M:-0.1243 c. 692: 33 111 130 33 111 163 111 N SD: 0.0423 c. M:-0.0721 c. 985: 47 158 185 47 158 232 158 N SD: 0.0401 c. M:-0.0703 c. 1028: 49 165 193 49 165 242 165 N SD: 0.0280 c. M: 0.0494 c. 1321: 63 212 248 63 212 311 212 N SD: 0.0213 c. M:-0.0396 c. 1427: 68 229 268 68 229 336 229 N SD: 0.0171 c. M: 0.0307 c. 1720: 82 276 323 82 276 405 276 N SD: 0.0025 c. M: 0.0043 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 11.4653 cents 3 x x 4 x x 5:6 S SD: 41.7338 cents 4 x x 5 x 6:7:8 S SD: 24.8780 cents 5 x 6 x 7:8:9:10 S SD: 24.3688 cents 6 x 7:8 x 9:11:12 SD: 11.1380 cents 7 x 8:9:10:11:13:14 SD: 21.5047 cents 8 x 9 x 11:12:14:16 SD: 13.3879 cents 9 x 10:12 x 14:16:18 S SD: 16.4870 cents 10 x 12:13:14:15:18:20 S SD: 14.8353 cents 12:13:14:16 x 18:21:24 S SD: 16.2058 cents 13:14:15:17:18:20:23:26 SD: 11.9185 cents 14:15:16:18:19:21:25:28 SD: 11.4045 cents 15:16:17:20 x 23:27:30 SD: 11.6956 cents 16:17:18:21:22:24:29:32 SD: 10.8587 cents 17:18:20:22:23:26:30:34 SD: 9.4159 cents 18:19:21:24 x 27:32:36 SD: 8.8146 cents 19:20:22:25:26:29:34:38 SD: 4.9068 cents 25:26:29:33:34:38:45:50 SD: 2.4720 cents 50:52:58:66:68:76:89:100 SD: 2.3938 cents 52:54:60:68:71:79:93:104 SD: 2.1799 cents 53:55:61:70:72:81:95:106 SD: 2.1763 cents 56:58:65:74:76:85:100:112 SD: 1.8504 cents 58:60:67:76:79:88:104:116 SD: 1.3002 cents 83:86:96:109:113:126:149:166 SD: 1.2159 cents 85:88:98:112:116:129:152:170 SD: 1.1942 cents 86:89:99:113:117:131:154:172 SD: 1.1309 cents 89:92:103:117:121:135:159:178 SD: 0.8301 cents 114:118:132:150:155:173:204:228 SD: 0.7891 cents 117:121:135:154:159:178:209:234 SD: 0.6205 cents 123:127:142:162:167:187:220:246 SD: 0.5812 cents 142:147:164:187:193:216:254:284 SD: 0.5130 cents 148:153:171:195:201:225:265:296 SD: 0.5076 cents 175:181:202:230:238:266:313:350 SD: 0.4010 cents 181:187:209:238:246:275:324:362 SD: 0.3068 cents 298:308:344:392:405:453:533:596 SD: 0.2851 cents 323:334:373:425:439:491:578:646 SD: 0.2110 cents 361:373:417:475:491:549:646:722 SD: 0.1548 cents 450:465:520:592:612:684:805:900 SD: 0.1354 cents 475:491:549:625:646:722:850:950 SD: 0.1278 cents 561:580:648:738:763:853:1004:1122 SD: 0.1225 cents 567:586:655:746:771:862:1015:1134 SD: 0.1115 cents