Scala analysis: fractal-10-triple-trouble
Sevish: Triple Trouble, One With the Fractal
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/21 301.846520 BP second, quasi-equal minor third 2: 9/7 435.084095 septimal major third, BP third 3: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 4: 5/3 884.358713 major sixth, BP sixth 5: 9/5 1017.596288 just minor seventh, BP seventh 6: 15/7 1319.442808 septimal minor ninth, BP ninth 7: 7/3 1466.870906 minimal tenth, BP tenth 8: 25/9 1768.717426 classic augmented eleventh, BP twelfth 9: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 1: 25/21 301.8465 BP second, quasi-equal minor third 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 49/45 147.4281 BP minor semitone 4: 25/21 301.8465 BP second, quasi-equal minor third 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 25/21 301.8465 BP second, quasi-equal minor third 7: 49/45 147.4281 BP minor semitone 8: 25/21 301.8465 BP second, quasi-equal minor third 9: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 2 49/45 147.428 cents BP minor semitone 1: 4 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 147/125 280.666 cents 2: 5 9/7 435.084 cents septimal major third, BP third 2: 3 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 1 243/175 568.322 cents 3: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 2 75/49 736.931 cents BP fifth 3: 1 125/81 751.121 cents 4: 2 189/125 715.750 cents 4: 1 81/49 870.168 cents two (septimal major third, BP third) 4: 6 5/3 884.359 cents major sixth, BP sixth 5: 6 9/5 1017.596 cents just minor seventh, BP seventh 5: 1 49/27 1031.787 cents 5: 2 125/63 1186.205 cents 6: 1 243/125 1150.834 cents octave - maximal diesis 6: 2 49/25 1165.024 cents BP eighth 6: 5 15/7 1319.443 cents septimal minor ninth, BP ninth 6: 1 175/81 1333.633 cents 7: 3 81/35 1452.680 cents Al-Hwarizmi's lute middle finger +1 octave 7: 5 7/3 1466.871 cents minimal tenth, BP tenth 7: 1 125/49 1621.289 cents 8: 4 63/25 1600.108 cents quasi-equal major tenth, BP eleventh 8: 2 135/49 1754.527 cents 8: 3 25/9 1768.717 cents classic augmented eleventh, BP twelfth Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.25000 = 13/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 301.8 435.1 582.5 884.4 1017.6 1319.4 1466.9 1768.7 1902.0 301.8 : 133.2 280.7 582.5 715.7 1017.6 1165.0 1466.9 1600.1 1902.0 435.1 : 147.4 449.3 582.5 884.4 1031.8 1333.6 1466.9 1768.7 1902.0 582.5 : 301.8 435.1 736.9 884.4 1186.2 1319.4 1621.3 1754.5 1902.0 884.4 : 133.2 435.1 582.5 884.4 1017.6 1319.4 1452.7 1600.1 1902.0 1017.6: 301.8 449.3 751.1 884.4 1186.2 1319.4 1466.9 1768.7 1902.0 1319.4: 147.4 449.3 582.5 884.4 1017.6 1165.0 1466.9 1600.1 1902.0 1466.9: 301.8 435.1 736.9 870.2 1017.6 1319.4 1452.7 1754.5 1902.0 1768.7: 133.2 435.1 568.3 715.7 1017.6 1150.8 1452.7 1600.1 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 301.8465 cents 625/567, 168.6089 cents 27/25, 133.2376 cents 2: 280.6657 .. 449.2746 cents 625/567, 168.6089 cents 3087/3125,-21.1808 cents 3: 568.3217 .. 751.1211 cents 21875/19683, 182.7995 cents 6561/6125, 119.0471 cents 4: 715.7498 .. 884.3587 cents 625/567, 168.6089 cents 15309/15625,-35.3714 cents 5: 1017.5963 .. 1186.2052 cents 625/567, 168.6089 cents 27/25, 133.2376 cents 6: 1150.8339 .. 1333.6333 cents 21875/19683, 182.7995 cents 15309/15625,-35.3714 cents 7: 1452.6804 .. 1621.2893 cents 625/567, 168.6089 cents 6561/6125, 119.0471 cents 8: 1600.1085 .. 1768.7174 cents 625/567, 168.6089 cents 3087/3125,-21.1808 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 211.3283 cents Largest one step interval : 25/21, 301.8465 cents Average / Smallest step : 1.586102 Largest / Average step : 1.428330 Largest / Smallest step : 2.265476 Median interval of one step : 49/45, 147.4281 cents, amount: 2 Most common interval of one step : 25/21, 301.8465 cents, amount: 4 Least squares average step : 214.02476 cents, oct.: 1926.22280 cents Scale is not proper Step pattern alph. order: ABCABACAB Step pattern size order : LSMLSLMLS Scale is a Constant Structure, by a margin of 21.18085 cents Scale diversity : 0.329301 Lumma stability : 0.335343 Lumma impropriety factor : 0.059467 Rothenberg efficiency : 0.445767 redundancy: 0.554233 Efficiency x scale size : 4.011905 Number of different interval sizes : 26 = 3.25000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.25000 = 13/4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 245/243, 14.1905 cents Most common intervals : 5/3, 884.3587 cents & inv., amount: 6 Number of recognisable fifths : 2, average 715.7498 cents Number of appreciable fifths : 0 Number of recognisable fourths : 0 Scale contains two identical disjunct "tetrachords" of 3 notes Best major thirds form a closed circle Formal octave complements present : 7 = 77.7778% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 168.6089 cents: 4 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 175) Highest odd numerator or denominator: 25 Scale harmonicity : 0.019826 Average absolute harmonicity : 0.101926 Specific harmonicity : 0.107107 Fundamental : 1/315, -8.2992 octaves, 0.8306 Hz. Guide tone : 1575, 10.6211 octaves, 412060.265 Hz. Exponens Consonantiae : 4.961250E+05, 18.92034 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 83.0, average 9.22222 Mersenne's string divisions : 7225680 Sum of van Prooijen's expressibility: 8.74674, average 0.97186 Sum of Tenney's harmonic distance : 15.06558, average 1.67395 Vogel's harmonic complexity : 19.77778 Wille's k value : 472 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 9 Triangular lattice diameter : 4 Lattice compactness : 111.75304, average 2.48340 Lattice compactness (without 2's) : 111.75304, average 2.48340 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 3: -2 .. 2 0.11111 11 1 5: -1 .. 2 0.44444 8 3 7: -1 .. 1 -0.11111 5 5 Average exponent except 2's : 4 / 9 = 0.44444 Average absolute exponent except 2's: 24 / 9 = 2.66667 Scale is JI-epimorphic with val: <9 13 16| = patent
FIT/MODE
9: 1 1 1 1 1 1 1 1 1 SP B ME I SD: 50.4960 c. M: 90.5182 c. Pelog Nawanada: Sunda 10: 2 0 1 2 0 2 1 1 1 N D3 SD: 52.2352 c. M:-78.5445 c. 13: 2 1 1 2 1 2 1 2 1 P M ME S SD: 6.5438 c. M: 13.0667 c. Lambda 43: 7 3 3 7 3 7 3 7 3 N M DE S SD: 5.5581 c. M:-7.7741 c. 56: 9 4 4 9 4 9 4 9 4 N M DE S SD: 4.2239 c. M: 6.4412 c. 69: 11 5 5 11 5 11 5 11 5 N M DE S SD: 3.8139 c. M: 5.9489 c. 75: 12 5 6 12 5 12 6 12 5 N SD: 3.3505 c. M:-6.4406 c. 82: 13 6 6 13 6 13 6 13 6 N M DE S SD: 3.7988 c. M: 5.9299 c. 88: 14 6 7 14 6 14 7 14 6 N SD: 2.0450 c. M:-3.5588 c. 101: 16 7 8 16 7 16 8 16 7 N SD: 1.2562 c. M: 1.9656 c. 114: 18 8 9 18 8 18 9 18 8 N SD: 1.0484 c. M: 1.5378 c. 157: 25 11 12 25 11 25 12 25 11 N SD: 0.7639 c. M: 1.0330 c. 245: 39 17 19 39 17 39 19 39 17 N SD: 0.6360 c. M:-1.2652 c. 258: 41 18 20 41 18 41 20 41 18 N SD: 0.2744 c. M:-0.5430 c. 271: 43 19 21 43 19 43 21 43 19 N SD: 0.0545 c. M: 0.1098 c. 800: 127 56 62 127 56 127 62 127 56 N SD: 0.0541 c. M:-0.1007 c. 1071: 170 75 83 170 75 170 83 170 75 N SD: 0.0289 c. M:-0.0511 c. 1342: 213 94 104 213 94 213 104 213 94 N SD: 0.0163 c. M:-0.0286 c. 1613: 256 113 125 256 113 256 125 256 113 N SD: 0.0129 c. M: 0.0191 c.
FIT/HARMONIC
1 x x x x x 2 x x 3 S SD: 59.7214 cents 2 x x 3 x x 4:5 x 6 S SD: 51.7203 cents 3 x 4 x 5 x 6:7:8:9 S SD: 25.3997 cents 4 x 5:6 x 7 x 9:11:12 SD: 25.4354 cents 5:6 x 7:8:9:11:12:14:15 SD: 12.3930 cents 6:7:8 x 10:11:13:14:17:18 SD: 10.9956 cents 8 x 10:11:13:14:17:19:22:24 SD: 11.9261 cents 9:11:12:13:15:16:19:21:25:27 SD: 11.1652 cents 10:12:13:14:17:18:21:23:28:30 SD: 6.8183 cents 14:17:18:20:23:25:30:33:39:42 SD: 6.6134 cents 15:18:19:21:25:27:32:35:42:45 SD: 3.6981 cents 21:25:27:29:35:38:45:49:58:63 SD: 3.0314 cents 27:32:35:38:45:49:58:63:75:81 SD: 2.6385 cents 32:38:41:45:53:58:69:75:89:96 SD: 2.6208 cents 35:42:45:49:58:63:75:82:97:105 SD: 2.0910 cents 42:50:54:59:70:76:90:98:117:126 SD: 1.3260 cents 57:68:73:80:95:103:122:133:158:171 SD: 1.3173 cents 63:75:81:88:105:113:135:147:175:189 SD: 0.8079 cents 84:100:108:118:140:151:180:196:233:252 SD: 0.7531 cents 90:107:116:126:150:162:193:210:250:270 SD: 0.5578 cents 105:125:135:147:175:189:225:245:292:315 SD: 0.2197 cents 210:250:270:294:350:378:450:490:583:630 SD: 0.1100 cents 315:375:405:441:525:567:675:735:875:945 SD: 0.0000 cents