Scala analysis: xen09-chalmers-tritriadic-6-7-8
Tritriadic scale built from 6:7:8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 14/9 764.915905 septimal minor sixth 5: 7/4 968.825906 harmonic seventh 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 7/6 266.8709 septimal minor third 2: 8/7 231.1741 septimal whole tone 3: 9/8 203.9100 major whole tone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 9/8 203.9100 major whole tone 6: 64/63 27.2641 septimal comma, Archytas' comma 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 3 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 21/16 470.781 cents narrow fourth 2: 1 4/3 498.045 cents perfect fourth 3: 1 32/27 294.135 cents Pythagorean minor third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 4: 2 4/3 498.045 cents perfect fourth 4: 2 3/2 701.955 cents perfect fifth 4: 1 32/21 729.219 cents wide fifth 4: 1 14/9 764.916 cents septimal minor sixth 4: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 3/2 701.955 cents perfect fifth 5: 1 32/21 729.219 cents wide fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 2 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/14 1137.039 cents septimal major seventh 6: 1 63/32 1172.736 cents octave - septimal comma Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 266.9 498.0 702.0 764.9 968.8 996.1 1200.0 266.9 : 231.2 435.1 498.0 702.0 729.2 933.1 1200.0 498.0 : 203.9 266.9 470.8 498.0 702.0 968.8 1200.0 702.0 : 63.0 266.9 294.1 498.0 764.9 996.1 1200.0 764.9 : 203.9 231.2 435.1 702.0 933.1 1137.0 1200.0 968.8 : 27.3 231.2 498.0 729.2 933.1 996.1 1200.0 996.1 : 203.9 470.8 702.0 905.9 968.8 1172.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 266.8709 cents 147/128, 239.6068 cents 64/63, 27.2641 cents 2: 231.1741 .. 498.0450 cents 7/6, 266.8709 cents 48/49,-35.6968 cents 3: 294.1350 .. 701.9550 cents 81/64, 407.8200 cents 8/9,-203.9100 cents 4: 498.0450 .. 905.8650 cents 81/64, 407.8200 cents 8/9,-203.9100 cents 5: 701.9550 .. 968.8259 cents 7/6, 266.8709 cents 8/9,-203.9100 cents 6: 933.1291 .. 1172.7359 cents 147/128, 239.6068 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 6.287705 Largest / Average step : 1.556747 Largest / Smallest step : 9.788366 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 183.20828 cents, oct.: 1282.45795 cents Scale is not proper Step pattern alph. order: ABCDCEC Step pattern size order : EDCBCAC Scale is not a Constant Structure Scale diversity : 1.217840 Lumma stability : 0.045440 Lumma impropriety factor : 0.569270 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 : 5 Highest interval variety : 5 Mean interval variety : 5.00000 = 5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 64/63, 27.2641 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 266.871 498.045 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 All steps are superparticular (epimoric) Length of longest harmonic part : 3 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 7 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 9 Scale harmonicity : 0.041176 Average absolute harmonicity : 0.258199 Specific harmonicity : 0.205379 Fundamental : 1/36, -5.1699 octaves, 7.2674 Hz. Guide tone : 336, 8.3923 octaves, 87906.190 Hz. Exponens Consonantiae : 1.209600E+04, 13.56224 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 43.5, average 6.21429 Mersenne's string divisions : 1726725 Sum of van Prooijen's expressibility: 4.55292, average 0.65042 Sum of Tenney's harmonic distance : 9.48750, average 1.35536 Vogel's harmonic complexity : 9.42857 Wille's k value : 31 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 81.18040, average 2.89930 Lattice compactness (without 2's) : 42.59183, average 1.52114 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 0.57143 12 1 3: -2 .. 1 -0.71429 7 3 7: 0 .. 1 0.42857 3 3 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 10 19| Scale is weakly epimorphic with val: <7 12 20|
FIT/MODE
7: 2 1 1 1 1 0 1 N T3 SD: 52.6875 c. M:-92.2270 c. 9: 2 2 1 1 1 0 2 N SD: 35.6963 c. M: 62.7567 c. 10: 2 2 2 0 2 0 2 N D3 S SD: 26.1072 c. M: 44.9159 c. 12: 3 2 2 1 2 0 2 N SD: 21.7886 c. M:-35.0841 c. 14: 3 3 2 1 2 1 2 N G S SD: 18.4932 c. M:-32.4814 c. 17: 4 3 3 1 3 0 3 N SD: 10.9706 c. M:-19.4094 c. 22: 5 4 4 1 4 0 4 N SD: 8.5378 c. M: 14.2718 c. 31: 7 6 5 2 5 1 5 N SD: 6.1537 c. M:-10.3616 c. 36: 8 7 6 2 6 1 6 N SD: 2.0943 c. M:-3.9100 c. 41: 9 8 7 2 7 1 7 N SD: 2.3211 c. M: 3.9403 c. 58: 13 11 10 3 10 1 10 N SD: 2.1045 c. M:-3.5879 c. 77: 17 15 13 4 13 2 13 N SD: 1.4486 c. M: 2.5921 c. 94: 21 18 16 5 16 2 16 N SD: 0.8160 c. M:-1.3869 c. 130: 29 25 22 7 22 3 22 N SD: 0.6982 c. M:-1.2379 c. 135: 30 26 23 7 23 3 23 N SD: 0.3154 c. M: 0.5344 c. 171: 38 33 29 9 29 4 29 N SD: 0.2527 c. M: 0.4049 c. 265: 59 51 45 14 45 6 45 N SD: 0.2088 c. M:-0.3671 c. 306: 68 59 52 16 52 7 52 N SD: 0.1338 c. M: 0.2100 c. 400: 89 77 68 21 68 9 68 N SD: 0.0972 c. M:-0.1741 c. 571: 127 110 97 30 97 13 97 N SD: 0.0360 c. M:-0.0578 c. 706: 157 136 120 37 120 16 120 N SD: 0.0316 c. M: 0.0560 c. 1277: 284 246 217 67 217 29 217 N SD: 0.0042 c. M:-0.0073 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 0.0000 cents 3 x 4 x x 5 x 6 S SD: 28.1557 cents 4 x 5:6 x 7 x 8 S SD: 27.9328 cents 5:6:7 x 8 x 9:10 S SD: 22.2300 cents 6:7:8:9 x x 11:12 SD: 10.6546 cents 7:8:9 x 11:12 x 14 SD: 16.5185 cents 8:9:11:12 x 14 x 16 SD: 16.4949 cents 9:11:12 x 14 x 16:18 SD: 16.1074 cents 10:12:13:15:16 x 18:20 SD: 14.0839 cents 11:13:15 x 17:19:20:22 SD: 10.7570 cents 12:14:16:18:19:21 x 24 SD: 5.1070 cents 13:15:17 x 20 x 23:26 SD: 8.7901 cents 14:16:19:21:22 x 25:28 SD: 8.4682 cents 15:18:20 x 23:26:27:30 SD: 10.1872 cents 16:19:21:24:25:28 x 32 SD: 6.9557 cents 17:20:23 x 26 x 30:34 SD: 8.6555 cents 18:21:24:27:28 x 32:36 S SD: 0.0000 cents 21:25:28:32:33:37 x 42 SD: 8.1876 cents 22:26:29:33:34 x 39:44 SD: 5.3799 cents 23:27:31:35:36:40:41:46 SD: 5.2276 cents 24:28:32:36:37:42:43:48 SD: 2.9367 cents 25:29:33:38:39:44 x 50 SD: 5.3972 cents 26:30:35:39:40 x 46:52 SD: 5.4670 cents 27:32:36:41:42:47:48:54 SD: 5.1089 cents 28:33:37:42:44:49:50:56 SD: 4.3293 cents 30:35:40:45:47 x 53:60 SD: 2.7368 cents 34:40:45:51:53 x 60:68 SD: 3.9072 cents 36:42:48:54:56:63:64:72 S SD: 0.0000 cents