Scala analysis: xen09-chalmers-tritriadic-10-11-15
Tritriadic scale built from 10:11:15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 3/2 701.955001 perfect fifth 6: 33/20 866.959229 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 40/33 333.0408 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 45/44 38.9058 1/5-tone 3: 32/27 294.1350 Pythagorean minor third 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 45/44 38.9058 1/5-tone 6: 11/10 165.0042 Ptolemy's second, 4/5-tone 7: 40/33 333.0408
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 45/44 38.906 cents 1/5-tone 1: 3 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 32/27 294.135 cents Pythagorean minor third 1: 1 40/33 333.041 cents 2: 3 9/8 203.910 cents major whole tone 2: 1 40/33 333.041 cents 2: 1 176/135 459.139 cents 2: 2 4/3 498.045 cents perfect fourth 3: 1 99/80 368.914 cents 3: 3 4/3 498.045 cents perfect fourth 3: 2 15/11 536.951 cents undecimal augmented fourth 3: 1 22/15 663.049 cents undecimal diminished fifth 4: 1 15/11 536.951 cents undecimal augmented fourth 4: 2 22/15 663.049 cents undecimal diminished fifth 4: 3 3/2 701.955 cents perfect fifth 4: 1 160/99 831.086 cents 5: 2 3/2 701.955 cents perfect fifth 5: 1 135/88 740.861 cents 5: 1 33/20 866.959 cents 5: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 33/20 866.959 cents 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 20/11 1034.996 cents large minor seventh 6: 2 88/45 1161.094 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 : 165.0 203.9 498.0 663.0 702.0 867.0 1200.0 165.0 : 38.9 333.0 498.0 537.0 702.0 1035.0 1200.0 203.9 : 294.1 459.1 498.0 663.0 996.1 1161.1 1200.0 498.0 : 165.0 203.9 368.9 702.0 867.0 905.9 1200.0 663.0 : 38.9 203.9 537.0 702.0 740.9 1035.0 1200.0 702.0 : 165.0 498.0 663.0 702.0 996.1 1161.1 1200.0 867.0 : 333.0 498.0 537.0 831.1 996.1 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.9058 .. 333.0408 cents 32/27, 294.1350 cents 45/44, 38.9058 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 297/320,-129.1308 cents 3: 368.9142 .. 663.0492 cents 32/27, 294.1350 cents 297/320,-129.1308 cents 4: 536.9508 .. 831.0858 cents 32/27, 294.1350 cents 225/242,-126.0985 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 297/320,-129.1308 cents 6: 866.9592 .. 1161.0942 cents 32/27, 294.1350 cents 297/320,-129.1308 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 45/44, 38.9058 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 40/33, 333.0408 cents Average / Smallest step : 4.406250 Largest / Average step : 1.942738 Largest / Smallest step : 8.560189 Median interval of one step : 11/10, 165.0042 cents, amount: 3 Most common interval of one step : 11/10, 165.0042 cents, amount: 3 Least squares average step : 155.93348 cents, oct.: 1091.53433 cents Scale is not proper Step pattern alph. order: ABCABAD Step pattern size order : BACBABD Scale is not a Constant Structure Scale diversity : 1.381197 Lumma stability : 0.064843 Lumma impropriety factor : 0.535518 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 : 3267/3200, 35.8735 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 165.004 701.955 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 : 11 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 33 Scale harmonicity : 0.026609 Average absolute harmonicity : 0.245099 Specific harmonicity : 0.123936 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 4.752000E+04, 15.53625 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 71.5, average 10.21429 Mersenne's string divisions : 3500385 Sum of van Prooijen's expressibility: 5.64448, average 0.80635 Sum of Tenney's harmonic distance : 11.39515, average 1.62788 Vogel's harmonic complexity : 14.00000 Wille's k value : 67 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 76.20148, average 2.72148 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 -0.42857 11 1 3: -1 .. 2 0.28571 6 3 5: -1 .. 0 -0.42857 3 11: 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 17 22| Scale is weakly epimorphic with val: <7 10 18 23| Scale is weakly epimorphic with val: <7 11 15 24| Scale is weakly epimorphic with val: <7 11 16 25| Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 12 16 22| Scale is weakly epimorphic with val: <7 12 17 23| Scale is weakly epimorphic with val: <7 12 18 24|
FIT/MODE
7: 1 0 2 1 0 1 2 N T3 SD: 17.8642 c. M: 32.4814 c. 17: 2 1 4 2 1 2 5 N SD: 16.1541 c. M: 27.7551 c. 20: 3 0 5 3 1 2 6 N SD: 17.6631 c. M: 26.9592 c. 21: 3 1 5 3 0 3 6 N SD: 15.9779 c. M:-24.6614 c. 22: 3 1 5 3 1 3 6 N SD: 7.6810 c. M:-14.2718 c. 29: 4 1 7 4 1 4 8 N SD: 1.6313 c. M:-2.9865 c. 65: 9 2 16 9 2 9 18 N SD: 0.8745 c. M:-1.5662 c. 94: 13 3 23 13 3 13 26 N SD: 0.6508 c. M:-1.1259 c. 159: 22 5 39 22 5 22 44 N SD: 0.6805 c. M:-1.1017 c. 212: 29 7 52 29 7 29 59 N SD: 0.5633 c. M: 0.9215 c. 241: 33 8 59 33 8 33 67 N SD: 0.4688 c. M: 0.8086 c. 248: 34 8 61 34 8 34 69 N SD: 0.4856 c. M: 0.8302 c. 270: 37 9 66 37 9 37 75 N SD: 0.4647 c. M: 0.8270 c. 277: 38 9 68 38 9 38 77 N SD: 0.2978 c. M: 0.5332 c. 306: 42 10 75 42 10 42 85 N SD: 0.1954 c. M: 0.3041 c. 371: 51 12 91 51 12 51 103 N SD: 0.0786 c. M: 0.1364 c. 400: 55 13 98 55 13 55 111 N SD: 0.0482 c. M:-0.0900 c. 771: 106 25 189 106 25 106 214 N SD: 0.0185 c. M: 0.0332 c. 1171: 161 38 287 161 38 161 325 N SD: 0.0148 c. M: 0.0262 c. 1942: 267 63 476 267 63 267 539 N SD: 0.0130 c. M: 0.0214 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 x 5:6 S SD: 5.7998 cents 4 x x 5 x 6:7:8 S SD: 37.7994 cents 5 x 6 x 7 x 8:10 S SD: 36.9189 cents 6 x 7:8 x 9:10:12 S SD: 13.0642 cents 7 x 8:9:10:11:12:14 S SD: 22.1409 cents 8 x 9:11 x 12:13:16 SD: 11.8939 cents 9:10 x 12:13:14:15:18 S SD: 12.0970 cents 10:11 x 13 x 15:17:20 SD: 13.5532 cents 11:12 x 15:16:17:18:22 SD: 11.5518 cents 12:13:14:16 x 18:20:24 S SD: 11.7443 cents 14:15:16:19 x 21:23:28 SD: 10.2936 cents 15 x 17:20:22:23:25:30 SD: 7.2912 cents 16 x 18:21:23:24:26:32 SD: 8.5817 cents 17 x 19:23:25:26:28:34 SD: 7.3195 cents 18:20 x 24:26:27:30:36 S SD: 6.0187 cents 19:21 x 25:28:29:31:38 SD: 7.3536 cents 20:22:23:27:29:30:33:40 SD: 6.8539 cents 21:23:24:28:31:32:35:42 SD: 6.3429 cents 22:24:25:29:32:33:36:44 SD: 5.1774 cents 24:26:27:32:35:36:40:48 SD: 4.7352 cents 25 x 28:33:37:38:41:50 SD: 5.8790 cents 26 x 29:35:38:39:43:52 SD: 3.9027 cents 27:30 x 36:40:41:45:54 SD: 6.1452 cents 28:31:32:37:41:42:46:56 SD: 4.8954 cents 30:33:34:40:44:45:50:60 SD: 3.0838 cents 32:35:36:43:47:48:53:64 SD: 2.5861 cents 35 x 39:47:51:53:58:70 SD: 4.9405 cents 36:40:41:48:53:54:59:72 SD: 4.3651 cents 37:41:42:49:54:56:61:74 SD: 4.1804 cents 38:42:43:51:56:57:63:76 SD: 2.9817 cents 39:43:44:52:57:59:64:78 SD: 2.7977 cents 40:44:45:53:59:60:66:80 SD: 2.0899 cents 48:53:54:64:70:72:79:96 SD: 1.8031 cents 62:68:70:83:91:93:102:124 SD: 1.6916 cents 66:73:74:88:97:99:109:132 SD: 1.6895 cents 71:78:80:95:104:107:117:142 SD: 1.5964 cents 72:79:81:96:106:108:119:144 SD: 1.1993 cents 80:88:90:107:117:120:132:160 SD: 1.0443 cents 88:97:99:117:129:132:145:176 SD: 0.9424 cents 111:122:125:148:163:167:183:222 SD: 0.8863 cents 112:123:126:149:164:168:185:224 SD: 0.8366 cents 120:132:135:160:176:180:198:240 SD: 0.0000 cents