Scala analysis: xen10-chalmers-tritriadic-7-19-25
Tritriadic scale built from 7:19:25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/25 196.198479 middle second 2: 475/392 332.488631 3: 19/14 528.687110 4: 38/25 724.885588 5: 625/392 807.603043 6: 25/14 1003.801521 middle minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/25 196.1985 middle second 1: 28/25 196.1985 middle second 2: 11875/10976 136.2902 3: 28/25 196.1985 middle second 4: 28/25 196.1985 middle second 5: 15625/14896 82.7175 6: 28/25 196.1985 middle second 7: 28/25 196.1985 middle second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 15625/14896 82.717 cents 1: 1 11875/10976 136.290 cents 1: 5 28/25 196.198 cents middle second 2: 2 625/532 278.916 cents 2: 2 475/392 332.489 cents 2: 3 784/625 392.397 cents two (middle second) 3: 3 25/19 475.114 cents 3: 3 19/14 528.687 cents 3: 1 21952/15625 588.595 cents 4: 1 15625/10976 611.405 cents 4: 3 28/19 671.313 cents 4: 3 38/25 724.886 cents 5: 3 625/392 807.603 cents 5: 2 784/475 867.511 cents 5: 2 1064/625 921.084 cents 6: 5 25/14 1003.802 cents middle minor seventh 6: 1 21952/11875 1063.710 cents 6: 1 29792/15625 1117.283 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 : 196.2 332.5 528.7 724.9 807.6 1003.8 1200.0 196.2 : 136.3 332.5 528.7 611.4 807.6 1003.8 1200.0 332.5 : 196.2 392.4 475.1 671.3 867.5 1063.7 1200.0 528.7 : 196.2 278.9 475.1 671.3 867.5 1003.8 1200.0 724.9 : 82.7 278.9 475.1 671.3 807.6 1003.8 1200.0 807.6 : 196.2 392.4 588.6 724.9 921.1 1117.3 1200.0 1003.8: 196.2 392.4 528.7 724.9 921.1 1003.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.7175 .. 196.1985 cents 417088/390625, 113.4810 cents 15625/14896, 82.7175 cents 2: 278.9159 .. 392.3970 cents 417088/390625, 113.4810 cents 15625/14896, 82.7175 cents 3: 475.1144 .. 588.5954 cents 417088/390625, 113.4810 cents 15625/14896, 82.7175 cents 4: 611.4046 .. 724.8856 cents 417088/390625, 113.4810 cents 244140625/240945152, 22.8091 cents 5: 807.6030 .. 921.0841 cents 417088/390625, 113.4810 cents 15625/14896, 82.7175 cents 6: 1003.8015 .. 1117.2825 cents 417088/390625, 113.4810 cents 15625/14896, 82.7175 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 15625/14896, 82.7175 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 28/25, 196.1985 cents Average / Smallest step : 2.072459 Largest / Average step : 1.144491 Largest / Smallest step : 2.371911 Median interval of one step : 28/25, 196.1985 cents, amount: 5 Most common interval of one step : 28/25, 196.1985 cents, amount: 5 Least squares average step : 170.05431 cents, oct.: 1190.38019 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : LMLLSLL Scale is a Constant Structure, by a margin of 22.80913 cents Scale diversity : 1.483257 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.432595 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 : 244140625/240945152, 22.8091 cents Most common intervals : 28/25, 196.1985 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 528.687 1003.802 cents Most common triad is 0.0 196.198 1003.802 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 : 7 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 : 0.009228 Average absolute harmonicity : 0.165544 Specific harmonicity : 0.046757 Fundamental : 1/9800, -13.2586 octaves, 0.0267 Hz. Guide tone : 332500, 18.3430 octaves, 86990500.463 Hz. Exponens Consonantiae : 3.258500E+09, 31.60156 octaves Euler's gradus suavitatis : 66 Sum of Mann's harmonic distance : 1037.5, average 148.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.94515, average 1.56359 Sum of Tenney's harmonic distance : 21.75195, average 3.10742 Vogel's harmonic complexity : 32.42857 Wille's k value : 7812 Wilson's harmonic complexity : 70 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 107.11406, average 3.82550 Lattice compactness (without 2's) : 83.83777, average 2.99421 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.57143 12 1 5: -2 .. 4 0.57143 12 7: -2 .. 1 -0.71429 7 3 19: 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 15 18 31| Scale is weakly epimorphic with val: <7 15 19 28| Scale is weakly epimorphic with val: <7 15 20 32| Scale is weakly epimorphic with val: <7 15 21 29| Scale is weakly epimorphic with val: <7 15 22 33| Scale is JI-epimorphic with val: <7 16 19 29| Scale is weakly epimorphic with val: <7 16 20 33| Scale is weakly epimorphic with val: <7 16 21 30| Scale is weakly epimorphic with val: <7 16 22 27| Scale is weakly epimorphic with val: <7 17 18 33| Scale is weakly epimorphic with val: <7 17 19 30| Scale is JI-epimorphic with val: <7 17 21 31| Scale is weakly epimorphic with val: <7 17 22 28| Scale is weakly epimorphic with val: <7 18 18 27| Scale is weakly epimorphic with val: <7 18 19 31| Scale is weakly epimorphic with val: <7 18 20 28| Scale is weakly epimorphic with val: <7 18 21 32|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 28.1084 c. M:-49.5398 c. Lebeng 10: 2 1 1 2 1 1 2 P D3 I SD: 33.8861 c. M: 48.6871 c. 11: 2 1 2 2 0 2 2 N T3 SD: 25.9383 c. M: 43.9667 c. 12: 2 1 2 2 1 2 2 P M ME S SD: 19.2148 c. M: 32.4886 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 18: 3 2 3 3 1 3 3 P T3 SD: 5.0762 c. M:-8.4477 c. 25: 4 3 4 4 2 4 4 SP T3 SD: 4.5108 c. M:-8.3970 c. 43: 7 5 7 7 3 7 7 SP T3 SD: 1.3596 c. M:-2.3951 c. 104: 17 12 17 17 7 17 17 SP T3 SD: 1.3639 c. M:-2.1268 c. 116: 19 13 19 19 8 19 19 SP T3 SD: 0.8137 c. M: 1.4541 c. 159: 26 18 26 26 11 26 26 SP T3 SD: 0.2539 c. M: 0.4132 c. 202: 33 23 33 33 14 33 33 SP T3 SD: 0.1707 c. M:-0.3177 c. 361: 59 41 59 59 25 59 59 SP T3 SD: 0.1305 c. M: 0.2318 c. 379: 62 43 62 62 26 62 62 SP T3 SD: 0.1245 c. M: 0.2152 c. 422: 69 48 69 69 29 69 69 SP T3 SD: 0.1463 c. M:-0.2329 c. 538: 88 61 88 88 37 88 88 SP T3 SD: 0.0987 c. M: 0.1681 c. 581: 95 66 95 95 40 95 95 SP T3 SD: 0.0403 c. M:-0.0714 c. 740: 121 84 121 121 51 121 121 SP T3 SD: 0.0315 c. M: 0.0562 c. 942: 154 107 154 154 65 154 154 SP T3 SD: 0.0269 c. M: 0.0448 c. 1321: 216 150 216 216 91 216 216 SP T3 SD: 0.0178 c. M: 0.0330 c. 1523: 249 173 249 249 105 249 249 SP T3 SD: 0.0083 c. M:-0.0135 c. 2263: 370 257 370 370 156 370 370 SP T3 SD: 0.0056 c. M: 0.0096 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: 11.4653 cents 3 x x 4 x 5 x 6 S SD: 27.5487 cents 4 x 5 x 6 x 7:8 S SD: 17.0408 cents 5 x 6:7 x 8:9:10 S SD: 11.6761 cents 6 x 7:8:9:10:11:12 S SD: 19.5347 cents 7:8 x 10 x 11:13:14 SD: 23.9582 cents 8:9:10:11:12:13:14:16 S SD: 11.3406 cents 9:10:11:12:14 x 16:18 S SD: 9.1496 cents 14:16:17:19:21:22:25:28 SD: 6.9882 cents 15:17:18:20:23:24:27:30 SD: 6.5441 cents 17:19:21:23:26:27:30:34 SD: 5.9457 cents 19:21:23:26:29:30:34:38 SD: 4.7006 cents 23:26:28:31:35:37:41:46 SD: 3.8258 cents 25:28:30:34:38:40:45:50 SD: 3.2714 cents 33:37:40:45:50:53:59:66 SD: 2.3324 cents 42:47:51:57:64:67:75:84 SD: 0.8458 cents 109:122:132:148:166:174:195:218 SD: 0.7658 cents 118:132:143:160:179:188:211:236 SD: 0.7288 cents 123:138:149:167:187:196:220:246 SD: 0.6206 cents 160:179:194:217:243:255:286:320 SD: 0.4893 cents 165:185:200:224:251:263:295:330 SD: 0.4663 cents 185:207:224:251:281:295:330:370 SD: 0.4485 cents 202:226:245:274:307:322:361:404 SD: 0.4258 cents 227:254:275:308:345:362:405:454 SD: 0.3347 cents 266:298:322:361:404:424:475:532 SD: 0.3279 cents 269:301:326:365:409:429:480:538 SD: 0.3153 cents 283:317:343:384:430:451:505:566 SD: 0.2426 cents 308:345:373:418:468:491:550:616 SD: 0.1716 cents 350:392:424:475:532:558:625:700 SD: 0.0645 cents