Scala analysis: xen09-chalmers-tritriadic-10-14-15
Tritriadic scale built from 10:14:15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 3/2 701.955001 perfect fifth 6: 28/15 1080.557192 grave major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 21/20 84.4672 minor semitone 2: 15/14 119.4428 major diatonic semitone 3: 32/27 294.1350 Pythagorean minor third 4: 21/20 84.4672 minor semitone 5: 15/14 119.4428 major diatonic semitone 6: 56/45 378.6022 septimal narrow major third 7: 15/14 119.4428 major diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 21/20 84.467 cents minor semitone 1: 3 15/14 119.443 cents major diatonic semitone 1: 1 32/27 294.135 cents Pythagorean minor third 1: 1 56/45 378.602 cents septimal narrow major third 2: 3 9/8 203.910 cents major whole tone 2: 1 56/45 378.602 cents septimal narrow major third 2: 1 80/63 413.578 cents wide major third 2: 2 4/3 498.045 cents perfect fourth 3: 1 135/112 323.353 cents septimal wide minor third 3: 3 4/3 498.045 cents perfect fourth 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: 3 3/2 701.955 cents perfect fifth 4: 1 224/135 876.647 cents narrow septimal major sixth 5: 2 3/2 701.955 cents perfect fifth 5: 1 63/40 786.422 cents narrow minor sixth 5: 1 45/28 821.398 cents septimale wide minor sixth 5: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 45/28 821.398 cents septimale wide minor sixth 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 28/15 1080.557 cents grave major seventh 6: 2 40/21 1115.533 cents acute major seventh 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 : 84.5 203.9 498.0 582.5 702.0 1080.6 1200.0 84.5 : 119.4 413.6 498.0 617.5 996.1 1115.5 1200.0 203.9 : 294.1 378.6 498.0 876.6 996.1 1080.6 1200.0 498.0 : 84.5 203.9 582.5 702.0 786.4 905.9 1200.0 582.5 : 119.4 498.0 617.5 702.0 821.4 1115.5 1200.0 702.0 : 378.6 498.0 582.5 702.0 996.1 1080.6 1200.0 1080.6: 119.4 203.9 323.4 617.5 702.0 821.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 378.6022 cents 32/27, 294.1350 cents 21/20, 84.4672 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 405/448,-174.6922 cents 3: 323.3528 .. 617.4878 cents 32/27, 294.1350 cents 405/448,-174.6922 cents 4: 582.5122 .. 876.6472 cents 32/27, 294.1350 cents 49/50,-34.9756 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 405/448,-174.6922 cents 6: 821.3978 .. 1115.5328 cents 32/27, 294.1350 cents 405/448,-174.6922 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 56/45, 378.6022 cents Average / Smallest step : 2.029528 Largest / Average step : 2.208513 Largest / Smallest step : 4.482239 Median interval of one step : 15/14, 119.4428 cents, amount: 3 Most common interval of one step : 15/14, 119.4428 cents, amount: 3 Least squares average step : 162.21135 cents, oct.: 1135.47946 cents Scale is not proper Step pattern alph. order: ABCABDB Step pattern size order : ABCABDB Scale is not a Constant Structure Scale diversity : 1.440555 Lumma stability : 0.140779 Lumma impropriety factor : 0.519371 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 : 3645/3584, 29.2178 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 582.512 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 3 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 21 Scale harmonicity : 0.033686 Average absolute harmonicity : 0.251515 Specific harmonicity : 0.159222 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 3.024000E+04, 14.88417 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 64.0, average 9.14286 Mersenne's string divisions : 12587820 Sum of van Prooijen's expressibility: 5.25189, average 0.75027 Sum of Tenney's harmonic distance : 10.80626, average 1.54375 Vogel's harmonic complexity : 12.57143 Wille's k value : 67 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 79.12536, average 2.82591 Lattice compactness (without 2's) : 46.44630, average 1.65880 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.14286 11 1 3: -1 .. 2 0.28571 6 3 5: -1 .. 0 -0.42857 3 7: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 15 20| Scale is weakly epimorphic with val: <7 10 16 21| Scale is weakly epimorphic with val: <7 10 17 22| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 12 15 21| Scale is weakly epimorphic with val: <7 12 16 22|
FIT/MODE
7: 0 1 2 0 1 2 1 N T3 SD: 47.9205 c. M: 84.4672 c. 8: 1 0 2 1 1 2 1 N T3 SD: 43.1890 c. M:-65.5328 c. 10: 1 1 2 1 1 3 1 N T3 SD: 22.4323 c. M:-36.0900 c. 12: 1 1 3 1 1 4 1 N T3 SD: 11.6377 c. M:-19.4428 c. 19: 1 2 5 1 2 6 2 N SD: 12.0267 c. M: 21.3093 c. 26: 2 2 7 2 2 8 3 N SD: 13.5617 c. M: 19.2946 c. 27: 2 3 6 2 3 8 3 N SD: 10.2673 c. M:-18.3122 c. 28: 2 3 7 2 2 9 3 N SD: 12.1060 c. M:-17.4878 c. 29: 2 3 7 2 3 9 3 N SD: 2.6348 c. M: 4.6951 c. 41: 3 4 10 3 4 13 4 N SD: 1.9385 c. M:-3.3377 c. 70: 5 7 17 5 7 22 7 N SD: 0.9905 c. M:-1.8043 c. 111: 8 11 27 8 11 35 11 N SD: 1.1541 c. M:-2.0193 c. 130: 9 13 32 9 13 41 13 N SD: 0.7776 c. M: 1.3903 c. 142: 10 14 35 10 14 45 14 N SD: 0.6991 c. M:-1.1329 c. 171: 12 17 42 12 17 54 17 N SD: 0.2176 c. M: 0.4012 c. 241: 17 24 59 17 24 76 24 N SD: 0.1339 c. M:-0.2394 c. 412: 29 41 101 29 41 130 41 N SD: 0.0162 c. M: 0.0265 c. 1477: 104 147 362 104 147 466 147 N SD: 0.0159 c. M:-0.0284 c. 1889: 133 188 463 133 188 596 188 N SD: 0.0126 c. M:-0.0220 c. 2301: 162 229 564 162 229 726 229 N SD: 0.0112 c. M:-0.0178 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 60.8012 cents 4 x x 5 x 6:7:8 S SD: 39.5030 cents 5 x 6 x 7:8:9:10 S SD: 34.0187 cents 6 x 7:8 x 9:11:12 SD: 14.0530 cents 7 x 8:9:10:11:13:14 SD: 18.6304 cents 8 x 9 x 11:12:15:16 SD: 6.4267 cents 9 x 10:12:13:14:17:18 SD: 14.6948 cents 10 x 11:13:14:15:19:20 SD: 11.0224 cents 11 x 12:15 x 17:21:22 SD: 18.4785 cents 12:13:14:16:17:18:22:24 SD: 13.0026 cents 13:14:15:17:18:20:24:26 SD: 12.4749 cents 14:15:16:19:20:21:26:28 SD: 9.2662 cents 15:16:17:20:21:23:28:30 SD: 6.9318 cents 16:17:18:21:22:24:30:32 S SD: 6.6940 cents 18:19:20:24:25:27:34:36 SD: 4.8572 cents 22:23:25:29:31:33:41:44 SD: 4.2477 cents 24:25:27:32:34:36:45:48 SD: 3.6965 cents 38:40:43:51:53:57:71:76 SD: 2.4525 cents 40:42:45:53:56:60:75:80 SD: 1.9021 cents 58:61:65:77:81:87:108:116 SD: 1.7179 cents 62:65:70:83:87:93:116:124 SD: 1.6019 cents 72:76:81:96:101:108:134:144 SD: 1.5770 cents 78:82:88:104:109:117:146:156 SD: 1.1190 cents 80:84:90:107:112:120:149:160 SD: 0.9492 cents 96:101:108:128:134:144:179:192 SD: 0.9274 cents 102:107:115:136:143:153:190:204 SD: 0.8564 cents 118:124:133:157:165:177:220:236 SD: 0.8432 cents 120:126:135:160:168:180:224:240 SD: 0.0000 cents