Scala analysis: xen07-harrison-thoughts-3
Pelog based on partials 30/32/35/40/44/47/54
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 47/30 777.237907 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 16/15 111.7313 minor diatonic semitone 2: 35/32 155.1396 septimal neutral second 3: 8/7 231.1741 septimal whole tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 47/44 114.1887 6: 54/47 240.3584 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 47/44 114.189 cents 1: 1 35/32 155.140 cents septimal neutral second 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 54/47 240.358 cents 2: 1 7/6 266.871 cents septimal minor third 2: 1 47/40 279.193 cents 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 5/4 386.314 cents major third 2: 1 44/35 396.178 cents 2: 1 60/47 422.762 cents 3: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 1 4/3 498.045 cents perfect fourth 3: 1 47/35 510.367 cents 3: 1 27/20 519.551 cents acute fourth 3: 1 64/47 534.493 cents 3: 1 15/11 536.951 cents undecimal augmented fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 22/15 663.049 cents undecimal diminished fifth 4: 1 47/32 665.507 cents 4: 1 40/27 680.449 cents grave fifth 4: 1 70/47 689.633 cents 4: 1 3/2 701.955 cents perfect fifth 4: 1 54/35 750.725 cents septimal semi-augmented fifth 5: 1 47/30 777.238 cents 5: 1 35/22 803.822 cents 5: 1 8/5 813.686 cents minor sixth 5: 1 44/27 845.453 cents neutral sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 80/47 920.807 cents 5: 1 12/7 933.129 cents septimal major sixth 6: 1 47/27 959.642 cents 6: 1 7/4 968.826 cents harmonic seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 20/11 1034.996 cents large minor seventh 6: 1 64/35 1044.860 cents septimal neutral seventh 6: 1 88/47 1085.811 cents 6: 1 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 266.9 498.0 663.0 777.2 1017.6 1200.0 111.7 : 155.1 386.3 551.3 665.5 905.9 1088.3 1200.0 266.9 : 231.2 396.2 510.4 750.7 933.1 1044.9 1200.0 498.0 : 165.0 279.2 519.6 702.0 813.7 968.8 1200.0 663.0 : 114.2 354.5 537.0 648.7 803.8 1035.0 1200.0 777.2 : 240.4 422.8 534.5 689.6 920.8 1085.8 1200.0 1017.6: 182.4 294.1 449.3 680.4 845.5 959.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 240.3584 cents 405/376, 128.6271 cents 16/15, 111.7313 cents 2: 266.8709 .. 422.7621 cents 360/329, 155.8912 cents 329/324, 26.5125 cents 3: 449.2746 .. 551.3179 cents 297/280, 102.0433 cents 329/324, 26.5125 cents 4: 648.6821 .. 750.7254 cents 297/280, 102.0433 cents 128/121, 97.3641 cents 5: 777.2379 .. 933.1291 cents 360/329, 155.8912 cents 329/324, 26.5125 cents 6: 959.6416 .. 1088.2687 cents 405/376, 128.6271 cents 329/324, 26.5125 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 54/47, 240.3584 cents Average / Smallest step : 1.534293 Largest / Average step : 1.402091 Largest / Smallest step : 2.151218 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 165.59694 cents, oct.: 1159.17861 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : ACFDBGE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 26.51253 cents Scale diversity : 1.599006 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.355731 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 705/704, 2.4574 cents Number of recognisable fifths : 2, average 695.7940 cents Best fifths form a closed circle Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 47 Odd number limit : 47 (O: 47 U: 47) Highest odd numerator or denominator: 47 Scale harmonicity : 0.020891 Fundamental : 1/30, -4.9069 octaves, 8.7209 Hz. Guide tone : 521136, 18.9913 octaves, 136342500.599 Hz. Exponens Consonantiae : 1.563408E+07, 23.89819 octaves Euler's gradus suavitatis : 78 Sum of Mann's harmonic distance : 91.0, average 13.00000 Mersenne's string divisions : 6888882 Sum of van Prooijen's expressibility: 6.30074, average 0.90011 Sum of Tenney's harmonic distance : 12.70462, average 1.81495 Vogel's harmonic complexity : 15.00000 Wille's k value : 23 Wilson's harmonic complexity : 79 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 77.62204, average 2.77222 Lattice compactness (without 2's) : 45.03739, average 1.60848 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 0.85714 10 1 3: -1 .. 2 -0.42857 7 1 5: -1 .. 0 -0.57143 4 2 7: 0 .. 1 0.14286 1 1 11: 0 .. 1 0.14286 1 1 47: 0 .. 1 0.14286 1 1 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is JI-epimorphic with val: <7 11 16 20 24 39| = patent Scale is weakly epimorphic with val: <7 11 16 20 25 38|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 48.7272 c. M:-79.9049 c. Lebeng 8: 1 1 1 1 1 2 1 P M ME S SD: 38.9825 c. M: 63.0492 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 25.7767 c. M:-49.0704 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 22.1427 c. M:-36.9508 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 13: 1 2 2 2 1 3 2 P D3 SD: 22.6936 c. M: 38.7764 c. 14: 1 2 3 2 1 3 2 P T3 SD: 15.5985 c. M: 26.0170 c. 19: 2 2 4 2 2 4 3 P SD: 16.3973 c. M: 31.4703 c. 20: 2 2 4 3 2 4 3 P SD: 12.7545 c. M: 26.8709 c. 21: 2 3 4 3 2 4 3 SP T3 SD: 15.9357 c. M:-22.7621 c. 22: 2 3 4 3 2 5 3 P SD: 10.0123 c. M:-18.7673 c. 31: 3 4 6 4 3 6 5 SP SD: 5.6225 c. M: 11.1447 c. 40: 4 5 8 5 4 8 6 SP SD: 5.9014 c. M:-11.9550 c. 45: 4 6 9 6 4 9 7 SP SD: 4.5752 c. M:-8.6217 c. 51: 5 6 10 7 5 10 8 SP SD: 4.8936 c. M: 8.0474 c. 53: 5 7 10 7 5 11 8 SP SD: 4.2055 c. M: 7.4266 c. 54: 5 7 10 8 5 11 8 SP SD: 4.1238 c. M: 9.1561 c. 63: 6 8 12 9 6 12 10 SP SD: 3.9004 c. M: 8.0725 c. 65: 6 8 13 9 6 13 10 SP SD: 3.4350 c. M: 8.4094 c. 67: 6 9 13 9 6 14 10 SP SD: 3.6754 c. M: 7.0887 c. 72: 7 9 14 10 7 14 11 SP SD: 3.3663 c. M:-6.0954 c. 73: 7 9 14 10 7 15 11 SP SD: 3.8614 c. M: 5.5150 c. 77: 7 10 15 11 7 15 12 SP SD: 3.5145 c. M:-7.0806 c. 85: 8 11 16 12 8 17 13 SP SD: 1.7253 c. M: 3.9274 c. 94: 9 12 18 13 9 19 14 SP SD: 1.9952 c. M:-3.6803 c. 99: 9 13 19 14 9 20 15 SP SD: 1.8435 c. M:-3.6174 c. 120: 11 16 23 16 12 24 18 SP SD: 2.3699 c. M:-3.1291 c. 125: 12 16 24 17 12 25 19 SP SD: 1.5875 c. M:-3.4687 c. 127: 12 16 25 17 12 26 19 SP SD: 2.1524 c. M:-2.8762 c. 130: 12 17 25 18 12 26 20 SP SD: 1.3391 c. M: 2.2117 c. 139: 13 18 27 19 13 28 21 SP SD: 1.3177 c. M:-2.6744 c. 176: 16 23 34 24 17 35 27 SP SD: 1.3983 c. M: 2.6404 c. 179: 17 23 34 25 17 36 27 SP SD: 1.3632 c. M:-2.2352 c. 184: 17 24 35 26 17 37 28 SP SD: 1.3526 c. M: 2.3928 c. 185: 17 24 36 25 18 37 28 SP SD: 1.1302 c. M: 1.4610 c. 190: 18 24 37 26 18 38 29 SP SD: 1.0657 c. M:-1.9529 c. 224: 21 29 43 31 21 45 34 SP SD: 0.6963 c. M:-1.2365 c. 270: 25 35 52 37 26 54 41 SP SD: 0.4638 c. M: 0.8270 c. 395: 37 51 76 54 38 79 60 SP SD: 0.4710 c. M: 0.7707 c. 400: 37 52 77 55 38 80 61 SP SD: 0.3719 c. M: 0.7313 c. 409: 38 53 79 56 39 82 62 SP SD: 0.3642 c. M:-0.7325 c. 462: 43 60 89 63 44 93 70 SP SD: 0.5473 c. M: 0.7116 c. 463: 43 60 89 64 44 93 70 SP SD: 0.4651 c. M:-0.9782 c. 472: 44 61 91 65 45 94 72 SP SD: 0.4311 c. M:-0.7282 c. 494: 46 64 95 68 47 99 75 SP SD: 0.1624 c. M:-0.3356 c. 764: 71 99 147 105 73 153 116 SP SD: 0.1847 c. M:-0.2490 c. 894: 83 116 172 123 85 179 136 SP SD: 0.1658 c. M: 0.3219 c. 954: 89 123 184 131 91 191 145 SP SD: 0.1379 c. M:-0.2184 c. 1053: 98 136 203 145 100 211 160 SP SD: 0.1138 c. M: 0.2042 c. 1178: 110 152 227 162 112 236 179 SP SD: 0.1353 c. M:-0.3230 c. 1323: 123 171 255 182 126 265 201 SP SD: 0.1151 c. M: 0.2042 c. 1354: 126 175 261 186 129 271 206 SP SD: 0.0923 c. M: 0.1665 c. 1448: 135 187 279 199 138 290 220 SP SD: 0.0810 c. M:-0.1472 c. 1578: 147 204 304 217 150 316 240 SP SD: 0.0621 c. M: 0.1058 c. 1848: 172 239 356 254 176 370 281 SP SD: 0.0400 c. M: 0.0638 c. 2342: 218 303 451 322 223 469 356 SP SD: 0.0386 c. M:-0.0804 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: 19.4529 cents 3 x x 4 x 5 x 6 S SD: 35.7069 cents 4 x x 5:6 x 7:8 S SD: 31.9923 cents 5 x 6 x 7:8:9:10 S SD: 20.1923 cents 6 x 7:8:9 x 11:12 SD: 10.0455 cents 7 x 8:9:10:11:13:14 SD: 16.8895 cents 8 x 9:11:12:13:14:16 SD: 20.2072 cents 9:10:11:12:13:14:16:18 S SD: 16.1585 cents 10:11:12:13:15:16:18:20 SD: 14.2713 cents 11:12:13:15:16:17:20:22 SD: 9.6811 cents 12:13:14:16:18:19:22:24 SD: 8.5462 cents 16:17:19:21:23:25:29:32 SD: 7.9569 cents 17:18:20:23:25:27:31:34 SD: 6.5452 cents 18:19:21:24:26:28:32:36 SD: 5.7881 cents 19:20:22:25:28:30:34:38 SD: 5.6721 cents 24:26:28:32:35:38:43:48 SD: 4.9856 cents 25:27:29:33:37:39:45:50 SD: 4.8732 cents 26:28:30:35:38:41:47:52 SD: 4.8102 cents 28:30:33:37:41:44:50:56 SD: 4.1288 cents 30:32:35:40:44:47:54:60 SD: 0.0000 cents