Scala analysis: wier_cl
Danny Wier, ClownTone (2003)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/18 93.603014 undevicesimal semitone 2: 10/9 182.403712 minor whole tone 3: 7/6 266.870906 septimal minor third 4: 11/9 347.407941 undecimal neutral third 5: 4/3 498.044999 perfect fourth 6: 17/12 603.000409 2nd septendecimal tritone 7: 3/2 701.955001 perfect fifth 8: 19/12 795.558015 undevicesimal minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 7/4 968.825906 harmonic seventh 11: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 19/18 93.6030 undevicesimal semitone 2: 20/19 88.8007 small undevicesimal semitone 3: 21/20 84.4672 minor semitone 4: 22/21 80.5370 undecimal minor semitone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 17/16 104.9554 17th harmonic 7: 18/17 98.9546 Arabic lute index finger 8: 19/18 93.6030 undevicesimal semitone 9: 20/19 88.8007 small undevicesimal semitone 10: 21/20 84.4672 minor semitone 11: 22/21 80.5370 undecimal minor semitone 12: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 2 21/20 84.467 cents minor semitone 1: 2 20/19 88.801 cents small undevicesimal semitone 1: 2 19/18 93.603 cents undevicesimal semitone 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 17/16 104.955 cents 17th harmonic 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 2 21/19 173.268 cents 2: 2 10/9 182.404 cents minor whole tone 2: 1 19/17 192.558 cents quasi-meantone 2: 1 9/8 203.910 cents major whole tone 2: 2 8/7 231.174 cents septimal whole tone 2: 1 38/33 244.240 cents 2: 1 51/44 255.592 cents 3: 2 22/19 253.805 cents Godzilla third 3: 2 7/6 266.871 cents septimal minor third 3: 1 20/17 281.358 cents septendecimal augmented second 3: 1 19/16 297.513 cents 19th harmonic 3: 2 6/5 315.641 cents minor third 3: 1 76/63 324.777 cents 3: 1 40/33 333.041 cents 3: 1 17/14 336.130 cents supraminor third 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 4: 2 11/9 347.408 cents undecimal neutral third 4: 1 21/17 365.825 cents submajor third 4: 1 5/4 386.314 cents major third 4: 2 24/19 404.442 cents smaller undevicesimal major third 4: 1 19/15 409.244 cents undevicesimal ditone 4: 1 80/63 413.578 cents wide major third 4: 1 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 51/40 420.597 cents septendecimal diminished fourth 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 57/44 448.150 cents 5: 1 22/17 446.363 cents 5: 1 21/16 470.781 cents narrow fourth 5: 6 4/3 498.045 cents perfect fourth 5: 1 51/38 509.397 cents 5: 1 27/20 519.551 cents acute fourth 5: 1 19/14 528.687 cents 5: 1 15/11 536.951 cents undecimal augmented fourth 6: 1 11/8 551.318 cents undecimal semi-augmented fourth 6: 1 88/63 578.582 cents 6: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 80/57 586.846 cents 6: 1 38/27 591.648 cents 6: 1 24/17 597.000 cents 1st septendecimal tritone 6: 1 17/12 603.000 cents 2nd septendecimal tritone 6: 1 27/19 608.352 cents 6: 1 57/40 613.154 cents 6: 1 10/7 617.488 cents Euler's tritone 6: 1 63/44 621.418 cents 6: 1 16/11 648.682 cents undecimal semi-diminished fifth 7: 1 22/15 663.049 cents undecimal diminished fifth 7: 1 28/19 671.313 cents 7: 1 40/27 680.449 cents grave fifth 7: 1 76/51 690.603 cents 7: 6 3/2 701.955 cents perfect fifth 7: 1 32/21 729.219 cents wide fifth 7: 1 17/11 753.637 cents 8: 1 88/57 751.850 cents 8: 1 14/9 764.916 cents septimal minor sixth 8: 1 80/51 779.403 cents 8: 1 11/7 782.492 cents undecimal augmented fifth 8: 1 63/40 786.422 cents narrow minor sixth 8: 1 30/19 790.756 cents smaller undevicesimal minor sixth 8: 2 19/12 795.558 cents undevicesimal minor sixth 8: 1 8/5 813.686 cents minor sixth 8: 1 34/21 834.175 cents supraminor sixth 8: 2 18/11 852.592 cents undecimal neutral sixth 9: 1 44/27 845.453 cents neutral sixth 9: 1 28/17 863.870 cents submajor sixth 9: 1 33/20 866.959 cents 9: 1 63/38 875.223 cents 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 32/19 902.487 cents 19th subharmonic 9: 1 17/10 918.642 cents septendecimal diminished seventh 9: 2 12/7 933.129 cents septimal major sixth 9: 2 19/11 946.195 cents 10: 1 88/51 944.408 cents 10: 1 33/19 955.760 cents 10: 2 7/4 968.826 cents harmonic seventh 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 1 34/19 1007.442 cents quasi-mean seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 38/21 1026.732 cents 10: 2 20/11 1034.996 cents large minor seventh 11: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 11: 1 32/17 1095.045 cents 17th subharmonic 11: 1 17/9 1101.045 cents septendecimal major seventh 11: 2 36/19 1106.397 cents smaller undevicesimal major seventh 11: 2 19/10 1111.199 cents undevicesimal major seventh 11: 2 40/21 1115.533 cents acute major seventh 11: 2 21/11 1119.463 cents undecimal major seventh Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 8.54545 = 94/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 93.6 182.4 266.9 347.4 498.0 603.0 702.0 795.6 884.4 968.8 1049.4 1200.0 93.6 : 88.8 173.3 253.8 404.4 509.4 608.4 702.0 790.8 875.2 955.8 1106.4 1200.0 182.4 : 84.5 165.0 315.6 420.6 519.6 613.2 702.0 786.4 867.0 1017.6 1111.2 1200.0 266.9 : 80.5 231.2 336.1 435.1 528.7 617.5 702.0 782.5 933.1 1026.7 1115.5 1200.0 347.4 : 150.6 255.6 354.5 448.2 537.0 621.4 702.0 852.6 946.2 1035.0 1119.5 1200.0 498.0 : 105.0 203.9 297.5 386.3 470.8 551.3 702.0 795.6 884.4 968.8 1049.4 1200.0 603.0 : 99.0 192.6 281.4 365.8 446.4 597.0 690.6 779.4 863.9 944.4 1095.0 1200.0 702.0 : 93.6 182.4 266.9 347.4 498.0 591.6 680.4 764.9 845.5 996.1 1101.0 1200.0 795.6 : 88.8 173.3 253.8 404.4 498.0 586.8 671.3 751.8 902.5 1007.4 1106.4 1200.0 884.4 : 84.5 165.0 315.6 409.2 498.0 582.5 663.0 813.7 918.6 1017.6 1111.2 1200.0 968.8 : 80.5 231.2 324.8 413.6 498.0 578.6 729.2 834.2 933.1 1026.7 1115.5 1200.0 1049.4: 150.6 244.2 333.0 417.5 498.0 648.7 753.6 852.6 946.2 1035.0 1119.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 150.6371 cents 126/121, 70.1000 cents 22/21, 80.5370 cents 2: 165.0042 .. 255.5925 cents 255/242, 90.5882 cents 121/120, 14.3672 cents 3: 253.8049 .. 354.5471 cents 513/484, 100.7421 cents 968/969,-1.7875 cents 4: 347.4079 .. 448.1501 cents 513/484, 100.7421 cents 242/243,-7.1391 cents 5: 446.3625 .. 536.9508 cents 255/242, 90.5882 cents 968/969,-1.7875 cents 6: 551.3179 .. 648.6821 cents 128/121, 97.3641 cents 121/120, 14.3672 cents 7: 663.0492 .. 753.6375 cents 255/242, 90.5882 cents 121/120, 14.3672 cents 8: 751.8499 .. 852.5921 cents 513/484, 100.7421 cents 968/969,-1.7875 cents 9: 845.4529 .. 946.1951 cents 513/484, 100.7421 cents 242/243,-7.1391 cents 10: 944.4075 .. 1034.9958 cents 255/242, 90.5882 cents 968/969,-1.7875 cents 11: 1049.3629 .. 1119.4630 cents 126/121, 70.1000 cents 121/120, 14.3672 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 12/11, 150.6371 cents Average / Smallest step : 1.241665 Largest / Average step : 1.506371 Largest / Smallest step : 1.870407 Median interval of one step : 91.20186 cents, amount: 0 Least squares average step : 97.88540 cents, oct.: 1174.62482 cents Scale is not proper Step pattern alph. order: ABCDEFGABCDE Step pattern size order : DCBAGFEDCBAG Scale is a Constant Structure, by a margin of 1.78754 cents Scale diversity : 1.543767 Lumma stability : 0.182119 Lumma impropriety factor : 0.017857 Rothenberg efficiency : 0.231241 redundancy: 0.768759 Efficiency x scale size : 2.774892 Number of different interval sizes : 94 = 8.54545 / class Number of one step interval sizes : 7 Highest interval variety : 12 Mean interval variety : 8.54545 = 94/11 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 969/968, 1.7875 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Number of recognisable fifths : 7, average 700.3332 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 6 at degree 5 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 25.0000% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is differentially coherent in interval classes 6 and 7 combined Scale is n-1 differentially coherent in interval classes 7 and 8 combined -- Rational properties -- Prime limit : 19 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 19 Scale harmonicity : 0.009002 Average absolute harmonicity : 0.166372 Specific harmonicity : 0.076789 Fundamental : 1/36, -5.1699 octaves, 7.2674 Hz. Guide tone : 1492260, 20.5091 octaves, 390413366.076 Hz. Exponens Consonantiae : 5.372136E+07, 25.67899 octaves Euler's gradus suavitatis : 65 Sum of Mann's harmonic distance : 100.0, average 8.33333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.16839, average 0.84737 Sum of Tenney's harmonic distance : 19.37587, average 1.61466 Vogel's harmonic complexity : 13.16667 Wille's k value : 31 Wilson's harmonic complexity : 68 Rectangular lattice diameter : 8 Triangular lattice diameter : 3 Lattice compactness : 183.67588, average 2.35482 Lattice compactness (without 2's) : 125.74284, average 1.61209 Number of different primes : 7 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.50000 14 1 3: -2 .. 1 -0.91667 13 2 5: 0 .. 1 0.16667 2 2 7: 0 .. 1 0.16667 2 2 11: 0 .. 1 0.16667 2 2 17: 0 .. 1 0.08333 1 1 19: 0 .. 1 0.16667 2 2 Average exponent except 2's :-2 / 12 =-0.16667 Average absolute exponent except 2's: 22 / 12 = 1.83333 Scale is weakly epimorphic with val: <12 19 27 33 41 47 49| Scale is weakly epimorphic with val: <12 19 27 33 42 49 53| Scale is weakly epimorphic with val: <12 19 27 34 40 47 49| Scale is weakly epimorphic with val: <12 19 27 34 42 49 52| Scale is weakly epimorphic with val: <12 19 27 35 40 49 53| Scale is weakly epimorphic with val: <12 19 27 35 41 49 52| Scale is weakly epimorphic with val: <12 19 28 32 41 47 49| Scale is weakly epimorphic with val: <12 19 28 32 42 49 53| Scale is JI-epimorphic with val: <12 19 28 34 42 49 51| = patent Scale is weakly epimorphic with val: <12 19 28 35 41 49 51| Scale is weakly epimorphic with val: <12 19 28 35 44 51 53| Scale is weakly epimorphic with val: <12 19 29 32 40 47 49| Scale is weakly epimorphic with val: <12 19 29 32 42 49 52| Scale is weakly epimorphic with val: <12 19 29 33 42 49 51| Scale is weakly epimorphic with val: <12 19 29 35 40 49 51| Scale is weakly epimorphic with val: <12 19 29 35 44 51 52|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 25.8698 c. M:-52.5921 c. Twelve-tone Chromatic (1/11-comma) 14: 1 1 1 1 2 1 1 1 1 1 1 2 P D3 S SD: 16.4928 c. M: 27.2159 c. 22: 2 1 2 1 3 2 2 2 1 2 1 3 N SD: 13.3153 c. M:-22.6238 c. 24: 2 2 1 2 3 2 2 2 2 1 2 3 P T3 SD: 10.3189 c. M: 18.8259 c. 26: 2 2 2 2 3 2 2 2 2 2 2 3 SP D3 S SD: 9.5848 c. M:-21.8228 c. 27: 2 2 2 2 3 3 2 2 2 2 2 3 P D3 SD: 9.4296 c. M:-19.2218 c. 31: 2 3 2 2 4 3 2 3 2 2 2 4 N SD: 9.4880 c. M:-17.3452 c. 32: 2 3 2 2 4 3 3 2 3 2 2 4 N SD: 9.4376 c. M: 18.6030 c. 38: 3 3 2 3 5 3 3 3 3 3 2 5 P SD: 6.8276 c. M: 14.2393 c. 41: 3 3 3 3 5 4 3 3 3 3 3 5 P SD: 5.3025 c. M:-11.6337 c. 48: 4 3 4 3 6 4 4 4 3 4 3 6 P SD: 5.2522 c. M: 9.3587 c. 53: 4 4 4 3 7 5 4 4 4 4 3 7 N SD: 4.6525 c. M:-8.3203 c. 58: 5 4 4 4 7 5 5 5 4 4 4 7 P SD: 5.4092 c. M:-11.3385 c. 62: 5 4 5 4 8 5 5 5 5 4 4 8 P SD: 4.2458 c. M: 8.2102 c. 63: 5 5 4 4 8 6 5 5 4 5 4 8 N SD: 4.5016 c. M: 8.1682 c. 65: 5 5 4 5 8 6 5 5 5 4 5 8 P SD: 4.2863 c. M: 8.8259 c. 66: 5 5 5 4 8 6 6 5 5 4 5 8 N SD: 4.7696 c. M:-7.1359 c. 68: 5 5 5 5 8 6 6 5 5 5 4 9 N SD: 4.2367 c. M: 8.1865 c. 72: 6 5 5 5 9 6 6 6 5 5 5 9 P SD: 2.7544 c. M:-6.3970 c. 77: 6 6 5 5 10 7 6 6 6 5 5 10 N SD: 3.1565 c. M: 5.2071 c. 80: 6 6 6 5 10 7 7 6 6 6 5 10 N SD: 2.9032 c. M:-6.1741 c. 87: 7 6 6 6 11 8 7 7 6 6 6 11 N SD: 2.9161 c. M: 4.8019 c. 89: 7 7 6 6 11 8 7 7 7 6 6 11 P SD: 3.0821 c. M:-6.3603 c. 90: 7 7 6 6 11 8 8 7 6 7 6 11 N SD: 3.5006 c. M:-4.7117 c. 92: 7 7 6 7 11 8 8 7 7 6 6 12 N SD: 3.4024 c. M: 6.0013 c. 94: 7 7 7 6 12 8 8 7 7 7 6 12 N SD: 2.6897 c. M: 4.2413 c. 103: 8 8 7 7 13 9 8 8 8 7 7 13 P SD: 2.2945 c. M:-4.0041 c. 104: 8 8 7 7 13 9 9 8 8 7 7 13 N SD: 1.9206 c. M:-4.1028 c. 113: 9 8 8 8 14 10 9 9 8 8 8 14 P SD: 1.9472 c. M:-3.0345 c. 118: 9 9 8 8 15 10 10 9 9 8 8 15 N SD: 1.8101 c. M: 3.0004 c. 125: 10 9 9 8 16 11 10 10 9 9 8 16 N SD: 1.6048 c. M: 2.9629 c. 145: 11 11 10 10 18 13 12 11 11 10 10 18 N SD: 1.3621 c. M: 2.5685 c. 166: 13 12 12 11 21 14 14 13 12 12 11 21 N SD: 1.3251 c. M: 3.0004 c. 183: 14 14 13 12 23 16 15 14 14 13 12 23 N SD: 1.1894 c. M: 2.1154 c. 193: 15 14 14 13 24 17 16 15 14 14 13 24 N SD: 0.9844 c. M: 2.0928 c. 217: 17 16 15 15 27 19 18 17 16 15 15 27 N SD: 0.7736 c. M: 1.4331 c. 255: 20 19 18 17 32 22 21 20 19 18 17 32 N SD: 0.7214 c. M:-1.3644 c. 270: 21 20 19 18 34 24 22 21 20 19 18 34 N SD: 0.5132 c. M:-1.4440 c. 296: 23 22 21 20 37 26 24 23 22 21 20 37 N SD: 0.6872 c. M:-1.2407 c. 297: 23 22 21 20 37 26 25 23 22 21 20 37 N SD: 0.7405 c. M:-1.1421 c. 311: 24 23 22 21 39 27 26 24 23 22 21 39 N SD: 0.6490 c. M: 1.0711 c. 342: 27 25 24 23 43 30 28 27 25 24 23 43 N SD: 0.4817 c. M:-1.1338 c. 388: 30 29 27 26 49 34 32 30 29 27 26 49 N SD: 0.6135 c. M: 1.0162 c. 400: 31 30 28 27 50 35 33 31 30 28 27 50 N SD: 0.4329 c. M:-0.6413 c. 422: 33 31 30 28 53 37 35 33 31 30 28 53 N SD: 0.4237 c. M:-0.8423 c. 436: 34 32 31 29 55 38 36 34 32 31 29 55 N SD: 0.4453 c. M: 0.8725 c. 487: 38 36 34 33 61 43 40 38 36 34 33 61 N SD: 0.3785 c. M: 0.7518 c. 525: 41 39 37 35 66 46 43 41 39 37 35 66 N SD: 0.2943 c. M:-0.5577 c. 643: 50 48 45 43 81 56 53 50 48 45 43 81 N SD: 0.3226 c. M: 0.5347 c. 653: 51 48 46 44 82 57 54 51 48 46 44 82 N SD: 0.2634 c. M: 0.4742 c. 742: 58 55 52 50 93 65 61 58 55 52 50 93 N SD: 0.1979 c. M:-0.3456 c. 836: 65 62 59 56 105 73 69 65 62 59 56 105 N SD: 0.1551 c. M: 0.3427 c. 1053: 82 78 74 71 132 92 87 82 78 74 71 132 N SD: 0.1326 c. M:-0.2097 c. 1178: 92 87 83 79 148 103 97 92 87 83 79 148 N SD: 0.0819 c. M: 0.1482 c. 1578: 123 117 111 106 198 138 130 123 117 111 106 198 N SD: 0.0718 c. M: 0.1208 c. 2000: 156 148 141 134 251 175 165 156 148 141 134 251 N SD: 0.0683 c. M:-0.1741 c. 2231: 174 165 157 150 280 195 184 174 165 157 150 280 N SD: 0.0591 c. M: 0.1123 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.7264 cents 5 x x x 6 x 7 x 8 x x 9:10 S SD: 10.5198 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 0.0000 cents 7 x x 8 x 9:10 x 11 x 12:13:14 S SD: 12.2826 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 11.2375 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.2278 cents 10 x 11 x 12:13:14:15:16:17 x 18:20 S SD: 8.7248 cents 11 x 12:13 x 15:16 x 17:18:19:20:22 SD: 10.3002 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 5.3279 cents 13:14 x 15:16:17:18:20:21:22:23:24:26 S SD: 8.4999 cents 14:15 x 16:17:19:20:21:22:23:25:26:28 SD: 6.8824 cents 15:16:17 x 18:20:21:23:24:25:26:28:30 SD: 7.0164 cents 16:17:18:19:20:21:23:24:25:27:28:29:32 SD: 6.3497 cents 17:18:19:20:21:23:24:26:27:28:30:31:34 SD: 4.7362 cents 18:19:20:21:22:24:26:27:29:30:32:33:36 SD: 4.3938 cents 19:20:21:22:23:25:27:29:30:32:33:35:38 SD: 4.2541 cents 24:25:27:28:29:32:34:36:38:40:42:44:48 SD: 3.0955 cents 34:36:38:40:42:45:48:51:54:57:60:62:68 SD: 3.0137 cents 35:37:39:41:43:47:50:53:55:58:61:64:70 SD: 2.8037 cents 36:38:40:42:44:48:51:54:57:60:63:66:72 S SD: 0.0000 cents