Scala analysis: xen07-harrison-thoughts-1
Pelog based on partials 12/13/14/17/18/19/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 7/6 266.870906 septimal minor third 3: 17/12 603.000409 2nd septendecimal tritone 4: 3/2 701.955001 perfect fifth 5: 19/12 795.558015 undevicesimal minor sixth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 13/12 138.5727 tridecimal 2/3-tone 2: 14/13 128.2982 2/3-tone 3: 17/14 336.1295 supraminor third 4: 18/17 98.9546 Arabic lute index finger 5: 19/18 93.6030 undevicesimal semitone 6: 21/19 173.2679 7: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 19/18 93.603 cents undevicesimal semitone 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 14/13 128.298 cents 2/3-tone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 21/19 173.268 cents 1: 1 8/7 231.174 cents septimal whole tone 1: 1 17/14 336.130 cents supraminor third 2: 1 19/17 192.558 cents quasi-meantone 2: 2 7/6 266.871 cents septimal minor third 2: 1 26/21 369.747 cents 2: 1 24/19 404.442 cents smaller undevicesimal major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 17/13 464.428 cents 3: 1 21/17 365.825 cents submajor third 3: 2 4/3 498.045 cents perfect fourth 3: 1 19/14 528.687 cents 3: 1 26/19 543.015 cents 3: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 17/12 603.000 cents 2nd septendecimal tritone 4: 1 24/17 597.000 cents 1st septendecimal tritone 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 1 19/13 656.985 cents 4: 1 28/19 671.313 cents 4: 2 3/2 701.955 cents perfect fifth 4: 1 34/21 834.175 cents supraminor sixth 5: 1 26/17 735.572 cents 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 19/12 795.558 cents undevicesimal minor sixth 5: 1 21/13 830.253 cents 5: 2 12/7 933.129 cents septimal major sixth 5: 1 34/19 1007.442 cents quasi-mean seventh 6: 1 28/17 863.870 cents submajor sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 1 38/21 1026.732 cents 6: 1 24/13 1061.427 cents tridecimal neutral seventh 6: 1 13/7 1071.702 cents 16/3-tone 6: 1 17/9 1101.045 cents septendecimal major seventh 6: 1 36/19 1106.397 cents smaller undevicesimal major seventh Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.33333 = 19/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 138.6 266.9 603.0 702.0 795.6 968.8 1200.0 138.6 : 128.3 464.4 563.4 657.0 830.3 1061.4 1200.0 266.9 : 336.1 435.1 528.7 702.0 933.1 1071.7 1200.0 603.0 : 99.0 192.6 365.8 597.0 735.6 863.9 1200.0 702.0 : 93.6 266.9 498.0 636.6 764.9 1101.0 1200.0 795.6 : 173.3 404.4 543.0 671.3 1007.4 1106.4 1200.0 968.8 : 231.2 369.7 498.0 834.2 933.1 1026.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6030 .. 336.1295 cents 153/133, 242.5265 cents 19/18, 93.6030 cents 2: 192.5576 .. 464.4277 cents 289/247, 271.8701 cents 266/289,-143.5719 cents 3: 365.8255 .. 603.0004 cents 289/252, 237.1749 cents 273/289,-98.6022 cents 4: 596.9996 .. 834.1745 cents 289/252, 237.1749 cents 288/289,-6.0008 cents 5: 735.5723 .. 1007.4424 cents 289/247, 271.8701 cents 273/289,-98.6022 cents 6: 863.8705 .. 1106.3970 cents 153/133, 242.5265 cents 266/289,-143.5719 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 19/18, 93.6030 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 1.831443 Largest / Average step : 1.960755 Largest / Smallest step : 3.591012 Median interval of one step : 13/12, 138.5727 cents, amount: 1 Least squares average step : 167.71344 cents, oct.: 1173.99406 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : DCGBAEF Scale is a Constant Structure, by a margin of 3.92126 cents Scale diversity : 1.694371 Lumma stability : 0.156005 Lumma impropriety factor : 0.408624 Rothenberg efficiency : 0.312925 redundancy: 0.687075 Efficiency x scale size : 2.190476 Number of different interval sizes : 38 = 6.33333 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.33333 = 19/3 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 442/441, 3.9213 cents Number of recognisable fifths : 2, average 701.9550 cents Length of longest harmonic part : 2 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 class 1 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval class 4 -- Rational properties -- Prime limit : 19 Odd number limit : 21 (O: 21 U: 21) Highest odd numerator or denominator: 19 Scale harmonicity : 0.009524 Average absolute harmonicity : 0.216802 Specific harmonicity : 0.077632 Fundamental : 1/12, -3.5850 octaves, 21.8021 Hz. Guide tone : 176358, 17.4281 octaves, 46139761.445 Hz. Exponens Consonantiae : 2.116296E+06, 21.01311 octaves Euler's gradus suavitatis : 60 Sum of Mann's harmonic distance : 58.5, average 8.35714 Mersenne's string divisions : 9641775 Sum of van Prooijen's expressibility: 5.79046, average 0.82721 Sum of Tenney's harmonic distance : 11.01028, average 1.57290 Vogel's harmonic complexity : 11.42857 Wille's k value : 10 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 58.89426, average 2.10337 Lattice compactness (without 2's) : 40.35363, average 1.44120 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -1.28571 11 1 3: -1 .. 1 -0.42857 5 1 7: 0 .. 1 0.28571 2 2 13: 0 .. 1 0.14286 1 1 17: 0 .. 1 0.14286 1 1 19: 0 .. 1 0.14286 1 1 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 11 19 27 28 31| Scale is JI-epimorphic with val: <7 11 20 26 28 30|
FIT/MODE
7: 0 1 2 1 0 1 2 N T3 SD: 93.3384 c. M: 138.5727 c. 8: 1 1 2 1 0 1 2 N T3 S SD: 38.4670 c. M: 68.8259 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 32.5263 c. M: 69.6671 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 3 1 1 1 2 N T3 SD: 22.2152 c. M:-44.4420 c. 12: 1 2 3 1 1 2 2 N SD: 22.6456 c. M: 38.5727 c. Mela Bhavapriya, Raga Bhavani, Kalamurti, Neveseri ascending: Greece 14: 1 2 4 1 1 2 3 N SD: 25.1226 c. M: 52.8584 c. 15: 2 1 5 1 1 2 3 N SD: 20.6100 c. M:-36.9996 c. 16: 2 2 4 1 2 2 3 N SD: 20.2437 c. M:-33.1291 c. 17: 2 2 5 1 1 3 3 N SD: 17.0957 c. M:-32.2937 c. 18: 2 2 5 2 1 3 3 N SD: 16.9565 c. M:-31.3783 c. 21: 2 3 6 1 2 3 4 N SD: 16.4276 c. M:-25.5710 c. 22: 3 2 6 2 2 3 4 N SD: 14.1575 c. M:-25.0637 c. 24: 3 2 7 2 2 3 5 N SD: 10.7050 c. M: 18.8259 c. 26: 3 3 7 2 2 4 5 N SD: 6.7932 c. M: 10.9426 c. 36: 4 4 10 3 3 5 7 N SD: 3.0404 c. M: 5.2393 c. 62: 7 7 17 5 5 9 12 N SD: 3.1026 c. M: 5.1808 c. 68: 8 7 19 6 5 10 13 N SD: 2.4223 c. M:-3.9274 c. 77: 9 8 22 6 6 11 15 N SD: 2.3075 c. M:-4.7918 c. 89: 10 10 25 7 7 13 17 N SD: 2.4002 c. M: 3.7412 c. 94: 11 10 26 8 7 14 18 N SD: 2.1520 c. M: 4.0687 c. 103: 12 11 29 8 8 15 20 N SD: 2.1933 c. M: 3.3250 c. 104: 12 11 29 9 8 15 20 N SD: 1.4793 c. M: 3.0004 c. 113: 13 12 32 9 9 16 22 N SD: 1.4881 c. M: 2.4542 c. 130: 15 14 36 11 10 19 25 N SD: 1.3605 c. M: 3.0004 c. 145: 17 15 41 12 11 21 28 N SD: 1.3959 c. M:-2.1170 c. 157: 18 17 44 13 12 23 30 N SD: 1.0372 c. M:-1.8747 c. 181: 21 19 51 15 14 26 35 N SD: 0.8238 c. M: 1.6775 c. 207: 24 22 58 17 16 30 40 N SD: 0.6502 c. M: 1.3551 c. 243: 28 26 68 20 19 35 47 N SD: 0.5392 c. M: 0.9247 c. 338: 39 36 95 28 26 49 65 N SD: 0.5250 c. M:-1.0036 c. 364: 42 39 102 30 28 53 70 N SD: 0.4562 c. M: 1.0525 c. 374: 43 40 105 31 29 54 72 N SD: 0.4296 c. M:-0.7188 c. 400: 46 43 112 33 31 58 77 N SD: 0.3136 c. M: 0.5727 c. 513: 59 55 144 42 40 74 99 N SD: 0.3535 c. M: 0.5610 c. 535: 62 57 150 44 42 77 103 N SD: 0.3594 c. M:-0.7037 c. 561: 65 60 157 46 44 81 108 N SD: 0.3147 c. M:-0.5088 c. 581: 67 62 163 48 45 84 112 N SD: 0.2616 c. M: 0.4337 c. 617: 71 66 173 51 48 89 119 N SD: 0.2734 c. M: 0.4851 c. 643: 74 69 180 53 50 93 124 N SD: 0.3082 c. M: 0.5347 c. 665: 77 71 186 55 52 96 128 N SD: 0.2260 c. M:-0.3747 c. 742: 86 79 208 61 58 107 143 N SD: 0.2225 c. M:-0.5109 c. 778: 90 83 218 64 61 112 150 N SD: 0.1836 c. M:-0.3289 c. 899: 104 96 252 74 70 130 173 N SD: 0.1970 c. M:-0.3366 c. 908: 105 97 254 75 71 131 175 N SD: 0.1783 c. M: 0.3572 c. 935: 108 100 262 77 73 135 180 N SD: 0.1248 c. M:-0.2081 c. 1065: 123 114 298 88 83 154 205 N SD: 0.1215 c. M:-0.1882 c. 1142: 132 122 320 94 89 165 220 N SD: 0.0882 c. M:-0.1520 c. 1178: 136 126 330 97 92 170 227 N SD: 0.0498 c. M: 0.0874 c. 2243: 259 240 628 185 175 324 432 N SD: 0.0490 c. M:-0.0930 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 x 5:6 S SD: 44.9077 cents 4 x 5 x 6 x 7:8 S SD: 29.8607 cents 5 x 6:7 x 8:9:10 S SD: 14.8398 cents 6 x 7 x 9 x 11:12 SD: 20.1343 cents 7 x 8:10 x 11:12:14 S SD: 10.8243 cents 8 x 9:11:12:13:14:16 SD: 15.5075 cents 9:10:11:13 x 14:16:18 SD: 17.6539 cents 10:11:12:14:15:16:18:20 S SD: 11.2523 cents 11:12:13:16 x 17:19:22 SD: 11.7861 cents 12:13:14:17:18:19:21:24 SD: 0.0000 cents