Scala analysis: xen07-harrison-thoughts-2
Pelog based on partials 10/11/12/14/15/16/18
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: 6/5 315.641287 minor third 3: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 7/6 266.8709 septimal minor third 4: 15/14 119.4428 major diatonic semitone 5: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 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 15/14 119.443 cents major diatonic semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 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 9/8 203.910 cents major whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 2 6/5 315.641 cents minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 2 5/4 386.314 cents major third 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 3 4/3 498.045 cents perfect fourth 3: 1 15/11 536.951 cents undecimal augmented fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 10/7 617.488 cents Euler's tritone 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 22/15 663.049 cents undecimal diminished fifth 4: 3 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 1 11/7 782.492 cents undecimal augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor 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 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 28/15 1080.557 cents grave major seventh 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: 5.66667 = 17/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 165.0 315.6 582.5 702.0 813.7 1017.6 1200.0 165.0 : 150.6 417.5 537.0 648.7 852.6 1035.0 1200.0 315.6 : 266.9 386.3 498.0 702.0 884.4 1049.4 1200.0 582.5 : 119.4 231.2 435.1 617.5 782.5 933.1 1200.0 702.0 : 111.7 315.6 498.0 663.0 813.7 1080.6 1200.0 813.7 : 203.9 386.3 551.3 702.0 968.8 1088.3 1200.0 1017.6: 182.4 347.4 498.0 764.9 884.4 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 266.8709 cents 35/32, 155.1396 cents 16/15, 111.7313 cents 2: 231.1741 .. 417.5080 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 3: 435.0841 .. 582.5122 cents 49/45, 147.4281 cents 99/98, 17.5761 cents 4: 617.4878 .. 764.9159 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 5: 782.4920 .. 968.8259 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 6: 933.1291 .. 1088.2687 cents 35/32, 155.1396 cents 48/49,-35.6968 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 : 7/6, 266.8709 cents Average / Smallest step : 1.534293 Largest / Average step : 1.556747 Largest / Smallest step : 2.388507 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 170.89752 cents, oct.: 1196.28263 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : DCGBAFE Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.633918 Lumma stability : 0.244659 Lumma impropriety factor : 0.059495 Rothenberg efficiency : 0.341497 redundancy: 0.658503 Efficiency x scale size : 2.390476 Number of different interval sizes : 34 = 5.66667 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 5.66667 = 17/3 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 3 Number of recognisable fifths : 3, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 4 at degree 5 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval class 3 Scale is differentially coherent in interval class 4 Scale is differentially coherent in interval class 5 Scale is n-1 differentially coherent in interval class 6 -- Rational properties -- Prime limit : 11 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 11 Scale harmonicity : 0.022624 Average absolute harmonicity : 0.237528 Specific harmonicity : 0.162050 Fundamental : 1/10, -3.3219 octaves, 26.1626 Hz. Guide tone : 5544, 12.4367 octaves, 1450452.134 Hz. Exponens Consonantiae : 5.544000E+04, 15.75864 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 39.5, average 5.64286 Mersenne's string divisions : 60060 Sum of van Prooijen's expressibility: 4.71579, average 0.67368 Sum of Tenney's harmonic distance : 9.39704, average 1.34243 Vogel's harmonic complexity : 7.14286 Wille's k value : 7 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 62.29143, average 2.22469 Lattice compactness (without 2's) : 38.96472, average 1.39160 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 0.42857 7 1 3: 0 .. 2 0.57143 4 1 5: -1 .. 0 -0.71429 5 3 7: 0 .. 1 0.14286 1 1 11: 0 .. 1 0.14286 1 1 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 15 19 23| Scale is weakly epimorphic with val: <7 10 16 18 22| Scale is weakly epimorphic with val: <7 10 16 22 25| Scale is JI-epimorphic with val: <7 11 16 19 24| Scale is weakly epimorphic with val: <7 12 15 18 23| Scale is weakly epimorphic with val: <7 12 18 20 22|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.1867 c. M: 68.2265 c. Lebeng 8: 1 1 2 1 0 2 1 N D3 SD: 34.2050 c. M: 63.6863 c. 10: 1 2 2 1 1 1 2 N D3 SD: 35.1207 c. M: 57.5963 c. 11: 1 2 2 1 1 2 2 P D3 S SD: 39.0377 c. M: 55.9133 c. 12: 2 1 3 1 1 2 2 N T3 SD: 18.0315 c. M:-34.9958 c. Minor Gipsy, Mela Sanmukhapriya, Raga Camara, Chinthamani 15: 2 2 3 2 1 3 2 P D3 SD: 14.9557 c. M: 22.5122 c. 19: 3 2 4 2 2 3 3 P T3 SD: 11.6722 c. M:-24.4695 c. 22: 3 3 5 2 2 4 3 N SD: 11.1248 c. M:-18.7673 c. 27: 4 3 6 3 2 5 4 N SD: 8.4401 c. M: 13.6863 c. 31: 4 4 7 3 3 5 5 N SD: 6.4813 c. M: 11.1447 c. 41: 6 5 9 4 4 7 6 N SD: 5.8648 c. M:-10.6055 c. 46: 6 6 10 5 4 8 7 N SD: 5.1175 c. M: 8.5991 c. 53: 7 7 12 5 5 9 8 N SD: 3.5022 c. M: 6.5137 c. 58: 8 7 13 6 5 10 9 N SD: 3.8053 c. M: 6.7897 c. 60: 8 8 13 6 6 10 9 N SD: 3.7761 c. M:-6.3137 c. 65: 9 8 15 6 6 11 10 N SD: 3.3740 c. M:-8.2570 c. 68: 9 9 15 7 6 12 10 N SD: 3.7142 c. M: 6.1807 c. 72: 10 9 16 7 7 12 11 N SD: 1.6062 c. M:-2.9804 c. 111: 15 14 25 11 10 19 17 N SD: 1.8881 c. M: 2.8755 c. 118: 16 15 26 12 11 20 18 N SD: 1.4161 c. M: 2.8512 c. 130: 18 16 29 13 12 22 20 N SD: 1.3340 c. M: 2.2117 c. 152: 21 19 34 15 14 26 23 N SD: 0.8401 c. M:-1.6983 c. 159: 22 20 35 16 15 27 24 N SD: 1.0936 c. M:-1.4081 c. 183: 25 23 41 18 17 31 28 N SD: 0.8454 c. M: 1.2028 c. 224: 31 28 50 22 21 38 34 N SD: 0.7354 c. M:-1.4164 c. 255: 35 32 57 25 24 43 39 N SD: 0.6870 c. M: 1.1257 c. 270: 37 34 60 27 25 46 41 N SD: 0.3009 c. M: 0.5598 c. 342: 47 43 76 34 32 58 52 N SD: 0.1683 c. M:-0.3488 c. 612: 84 77 136 61 57 104 93 N SD: 0.1312 c. M: 0.2983 c. 764: 105 96 170 76 71 130 116 N SD: 0.1321 c. M:-0.2103 c. 836: 115 105 186 83 78 142 127 N SD: 0.1437 c. M:-0.2629 c. 954: 131 120 212 95 89 162 145 N SD: 0.1192 c. M: 0.2244 c. 1034: 142 130 230 103 96 176 157 N SD: 0.1418 c. M: 0.2073 c. 1053: 145 132 234 105 98 179 160 N SD: 0.1163 c. M:-0.2379 c. 1106: 152 139 246 110 103 188 168 N SD: 0.0863 c. M:-0.1280 c. 1236: 170 155 275 123 115 210 188 N SD: 0.0729 c. M: 0.1206 c. 1506: 207 189 335 150 140 256 229 N SD: 0.0775 c. M: 0.1405 c. 1578: 217 198 351 157 147 268 240 N SD: 0.0493 c. M: 0.1058 c. 1848: 254 232 411 184 172 314 281 N SD: 0.0487 c. M: 0.0692 c. 2190: 301 275 487 218 204 372 333 N SD: 0.0438 c. M: 0.0727 c. 2342: 322 294 521 233 218 398 356 N SD: 0.0282 c. M:-0.0668 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 36.7110 cents 4 x 5 x 6 x 7:8 S SD: 21.4668 cents 5 x 6:7 x 8:9:10 S SD: 0.0000 cents 6 x 7:8:9:10:11:12 S SD: 20.7612 cents 7:8 x 10 x 11:13:14 SD: 19.4959 cents 8:9:10:11:12:13:14:16 S SD: 14.6944 cents 9:10:11:13 x 14:16:18 SD: 14.0241 cents 10:11:12:14:15:16:18:20 S SD: 0.0000 cents