Scala analysis: xen10-chalmers-tritriadic-7-9-25
Tritriadic scale built from 7:9:25
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: 225/196 238.885617 two (major diatonic semitone) 3: 9/7 435.084095 septimal major third, BP third 4: 36/25 631.282574 classic diminished fifth 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: 5625/5488 42.6871 3: 28/25 196.1985 middle second 4: 28/25 196.1985 middle second 5: 15625/14112 176.3205 6: 28/25 196.1985 middle second 7: 28/25 196.1985 middle second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 5625/5488 42.687 cents 1: 1 15625/14112 176.320 cents 1: 5 28/25 196.198 cents middle second 2: 2 225/196 238.886 cents two (major diatonic semitone) 2: 2 625/504 372.519 cents 2: 3 784/625 392.397 cents two (middle second) 3: 3 9/7 435.084 cents septimal major third, BP third 3: 3 25/18 568.717 cents classic augmented fourth 3: 1 21952/15625 588.595 cents 4: 1 15625/10976 611.405 cents 4: 3 36/25 631.283 cents classic diminished fifth 4: 3 14/9 764.916 cents septimal minor sixth 5: 3 625/392 807.603 cents 5: 2 1008/625 827.481 cents 5: 2 392/225 961.114 cents 6: 5 25/14 1003.802 cents middle minor seventh 6: 1 28224/15625 1023.680 cents 6: 1 10976/5625 1157.313 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 : 196.2 238.9 435.1 631.3 807.6 1003.8 1200.0 196.2 : 42.7 238.9 435.1 611.4 807.6 1003.8 1200.0 238.9 : 196.2 392.4 568.7 764.9 961.1 1157.3 1200.0 435.1 : 196.2 372.5 568.7 764.9 961.1 1003.8 1200.0 631.3 : 176.3 372.5 568.7 764.9 807.6 1003.8 1200.0 807.6 : 196.2 392.4 588.6 631.3 827.5 1023.7 1200.0 1003.8: 196.2 392.4 435.1 631.3 827.5 1003.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 42.6871 .. 196.1985 cents 153664/140625, 153.5113 cents 5625/5488, 42.6871 cents 2: 238.8856 .. 392.3970 cents 153664/140625, 153.5113 cents 5625/5488, 42.6871 cents 3: 435.0841 .. 588.5954 cents 153664/140625, 153.5113 cents 5625/5488, 42.6871 cents 4: 611.4046 .. 764.9159 cents 153664/140625, 153.5113 cents 244140625/240945152, 22.8091 cents 5: 807.6030 .. 961.1144 cents 153664/140625, 153.5113 cents 5625/5488, 42.6871 cents 6: 1003.8015 .. 1157.3129 cents 153664/140625, 153.5113 cents 5625/5488, 42.6871 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 5625/5488, 42.6871 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 28/25, 196.1985 cents Average / Smallest step : 4.015930 Largest / Average step : 1.144491 Largest / Smallest step : 4.596197 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 : 164.03698 cents, oct.: 1148.25883 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : LSLLMLL Scale is a Constant Structure, by a margin of 22.80913 cents Scale diversity : 1.272846 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.232443 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 : 395136/390625, 19.8780 cents Most common intervals : 28/25, 196.1985 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 435.084 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% Limited inverse transpositions with margin 153.5113 cents: 3 -- Rational properties -- Prime limit : 7 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.012564 Average absolute harmonicity : 0.177139 Specific harmonicity : 0.068361 Fundamental : 1/9800, -13.2586 octaves, 0.0267 Hz. Guide tone : 157500, 17.2650 octaves, 41206026.535 Hz. Exponens Consonantiae : 1.543500E+09, 30.52356 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 805.0, average 115.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.29613, average 1.47088 Sum of Tenney's harmonic distance : 20.47738, average 2.92534 Vogel's harmonic complexity : 27.28571 Wille's k value : 7812 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 11 Triangular lattice diameter : 6 Lattice compactness : 112.42298, average 4.01511 Lattice compactness (without 2's) : 92.08307, average 3.28868 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.14286 11 1 3: 0 .. 2 0.85714 6 5: -2 .. 4 0.57143 12 1 7: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 25 / 7 = 3.57143 Scale is weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 10 18 18| Scale is weakly epimorphic with val: <7 11 15 21| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 12 15 18| Scale is JI-epimorphic with val: <7 12 17 21| Scale is weakly epimorphic with val: <7 12 18 19|
FIT/MODE
7: 1 0 1 1 1 1 2 N T3 SD: 95.4117 c. M: 146.6587 c. 8: 1 1 1 1 1 2 1 P M ME S SD: 42.2962 c. M:-61.1144 c. 10: 2 0 2 1 2 1 2 N T3 SD: 33.5602 c. M:-44.9159 c. 11: 2 0 2 2 1 2 2 N T3 SD: 23.5161 c. M: 43.9667 c. 12: 2 0 2 2 2 2 2 P M DE S SD: 23.3247 c. M: 38.8856 c. 13: 2 1 2 2 2 2 2 SP M ME S SD: 21.2900 c. M:-38.0375 c. Tamashian 14: 2 1 2 2 2 3 2 P T3 SD: 23.5737 c. M: 36.1745 c. 16: 3 0 3 2 3 2 3 N SD: 21.8946 c. M: 31.2826 c. 17: 3 0 3 3 2 3 3 N T3 SD: 18.2795 c. M: 31.1325 c. 19: 3 1 3 3 3 3 3 SP M DE S SD: 8.5329 c. M:-13.7460 c. 25: 4 1 4 4 4 4 4 SP M DE S SD: 4.9216 c. M:-8.3970 c. 36: 6 1 6 6 5 6 6 P T3 SD: 4.2225 c. M: 7.6030 c. 49: 8 2 8 8 7 8 8 SP T3 SD: 3.7646 c. M:-6.0123 c. 55: 9 2 9 9 8 9 9 SP T3 SD: 0.8561 c. M:-1.4447 c. 116: 19 4 19 19 17 19 19 SP T3 SD: 0.5455 c. M: 0.9546 c. 171: 28 6 28 28 25 28 28 SP T3 SD: 0.3130 c. M: 0.5855 c. 226: 37 8 37 37 33 37 37 SP T3 SD: 0.3472 c. M:-0.5758 c. 251: 41 9 41 41 37 41 41 SP T3 SD: 0.1958 c. M:-0.3651 c. 306: 50 11 50 50 45 50 50 SP T3 SD: 0.1881 c. M:-0.3301 c. 367: 60 13 60 60 54 60 60 SP T3 SD: 0.1361 c. M: 0.2199 c. 422: 69 15 69 69 62 69 69 SP T3 SD: 0.0137 c. M: 0.0231 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: 35.3362 cents 3 x x 4 x 5 x 6 S SD: 33.0916 cents 4 x x 5:6 x 7:8 S SD: 23.1792 cents 5 x 6 x 7:8:9:10 S SD: 18.4361 cents 6 x 7:8:9:10:11:12 S SD: 22.1793 cents 7 x 8:9:10:11:13:14 SD: 12.3500 cents 8:9 x 10:12:13:14:16 S SD: 16.4485 cents 9:10 x 12:13:14:16:18 S SD: 12.9791 cents 10:11 x 13:14:16:18:20 SD: 10.4681 cents 13 x 15:17:19:21:23:26 SD: 8.1153 cents 14 x 16:18:20:22:25:28 SD: 4.9450 cents 15:17 x 19:22:24:27:30 SD: 8.0344 cents 16:18 x 21:23:26:29:32 SD: 9.2664 cents 17:19:20:22:24:27:30:34 SD: 8.5527 cents 18:20:21:23:26:29:32:36 SD: 5.5377 cents 21 x 24:27:30:33:38:42 SD: 6.2498 cents 22 x 25:28:32:35:39:44 SD: 5.5140 cents 23:26 x 30:33:37:41:46 SD: 5.6913 cents 24:27:28:31:35:38:43:48 SD: 5.6506 cents 25:28:29:32:36:40:45:50 SD: 3.5372 cents 27:30:31:35:39:43:48:54 SD: 3.1412 cents 30:34 x 39:43:48:54:60 SD: 5.4710 cents 31:35:36:40:45:49:55:62 SD: 4.8965 cents 32:36:37:41:46:51:57:64 SD: 2.3872 cents 34:38:39:44:49:54:61:68 SD: 2.2820 cents 41:46:47:53:59:65:73:82 SD: 2.1488 cents 52:58:60:67:75:83:93:104 SD: 1.8162 cents 59:66:68:76:85:94:105:118 SD: 1.4244 cents 66:74:76:85:95:105:118:132 SD: 1.1055 cents 94:105:108:121:135:150:168:188 SD: 1.0420 cents 101:113:116:130:145:161:180:202 SD: 0.9806 cents 102:114:117:131:147:163:182:204 SD: 0.8828 cents 108:121:124:139:156:172:193:216 SD: 0.8747 cents 109:122:125:140:157:174:195:218 SD: 0.6736 cents 116:130:133:149:167:185:207:232 SD: 0.4568 cents 150:168:172:193:216:239:268:300 SD: 0.3941 cents 168:188:193:216:242:268:300:336 SD: 0.3192 cents 182:204:209:234:262:290:325:364 SD: 0.2714 cents 284:318:326:365:409:453:507:568 SD: 0.1736 cents 318:356:365:409:458:507:568:636 SD: 0.1637 cents 350:392:402:450:504:558:625:700 SD: 0.1328 cents 434:486:498:558:625:692:775:868 SD: 0.1157 cents 466:522:535:599:671:743:832:932 SD: 0.0867 cents