Scala analysis: breedpump
Comma pump in breed (2401/2400 planar)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 50/49 34.975615 Erlich's decatonic comma, tritonic diesis 2: 16807/16000 85.188391 3: 343/320 120.164006 4: 400/343 266.149708 5: 20000/16807 301.125323 6: 49/40 351.338099 larger approximation to neutral third 7: 5/4 386.313714 major third 8: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 9: 10/7 617.487807 Euler's tritone 10: 2401/1600 702.676198 two (larger approximation to neutral third) 11: 49/32 737.651813 12: 80/49 848.661901 smaller approximation to neutral sixth 13: 4000/2401 883.637516 14: 7/4 968.825906 harmonic seventh 15: 25/14 1003.801521 middle minor seventh 16: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/25 196.1985 middle second 1: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 2: 823543/800000 50.2128 3: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 4: 128000/117649 145.9857 5: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 6: 823543/800000 50.2128 7: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 8: 28/25 196.1985 middle second 9: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 10: 16807/16000 85.1884 11: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 12: 2560/2401 111.0101 13: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 14: 16807/16000 85.1884 15: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 16: 28/25 196.1985 middle second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 2 823543/800000 50.213 cents 1: 2 16807/16000 85.188 cents 1: 1 2560/2401 111.010 cents 1: 1 128000/117649 145.986 cents 1: 2 28/25 196.198 cents middle second 2: 4 16807/16000 85.188 cents 2: 4 343/320 120.164 cents 2: 2 128000/117649 145.986 cents 2: 2 6400000/5764801 180.961 cents 2: 4 8/7 231.174 cents septimal whole tone 3: 2 343/320 120.164 cents 3: 2 35/32 155.140 cents septimal neutral second 3: 1 6400000/5764801 180.961 cents 3: 1 320000000/282475249 215.937 cents 3: 4 8/7 231.174 cents septimal whole tone 3: 2 400/343 266.150 cents 3: 2 117649/100000 281.387 cents 3: 2 2401/2000 316.362 cents 4: 8 400/343 266.150 cents 4: 4 2401/2000 316.362 cents 4: 4 49/40 351.338 cents larger approximation to neutral third 5: 4 20000/16807 301.125 cents 5: 1 2401/2000 316.362 cents 5: 3 49/40 351.338 cents larger approximation to neutral third 5: 2 5/4 386.314 cents major third 5: 2 40353607/32000000 401.551 cents 5: 4 64/49 462.348 cents 2 septatones or septatonic major third 6: 2 49/40 351.338 cents larger approximation to neutral third 6: 2 5/4 386.314 cents major third 6: 4 823543/640000 436.526 cents 6: 8 3200/2401 497.324 cents 7: 1 5/4 386.314 cents major third 7: 1 125/98 421.289 cents 7: 2 16807/12800 471.502 cents 7: 4 160000/117649 532.299 cents 7: 4 343/250 547.537 cents 7: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 8: 8 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 8: 8 10/7 617.488 cents Euler's tritone 9: 4 10/7 617.488 cents Euler's tritone 9: 4 500/343 652.463 cents 9: 4 117649/80000 667.701 cents 9: 2 25600/16807 728.498 cents 9: 1 196/125 778.711 cents 9: 1 8/5 813.686 cents minor sixth 10: 8 2401/1600 702.676 cents two (larger approximation to neutral third) 10: 4 1280000/823543 763.474 cents 10: 2 8/5 813.686 cents minor sixth 10: 2 80/49 848.662 cents smaller approximation to neutral sixth 11: 4 49/32 737.652 cents 11: 2 64000000/40353607 798.449 cents 11: 2 8/5 813.686 cents minor sixth 11: 3 80/49 848.662 cents smaller approximation to neutral sixth 11: 1 4000/2401 883.638 cents 11: 4 16807/10000 898.875 cents 12: 4 80/49 848.662 cents smaller approximation to neutral sixth 12: 4 4000/2401 883.638 cents 12: 8 343/200 933.850 cents 13: 2 4000/2401 883.638 cents 13: 2 200000/117649 918.613 cents 13: 2 343/200 933.850 cents 13: 4 7/4 968.826 cents harmonic seventh 13: 1 282475249/160000000 984.063 cents 13: 1 5764801/3200000 1019.039 cents 13: 2 64/35 1044.860 cents septimal neutral seventh 13: 2 640/343 1079.836 cents 14: 4 7/4 968.826 cents harmonic seventh 14: 2 5764801/3200000 1019.039 cents 14: 2 117649/64000 1054.014 cents 14: 4 640/343 1079.836 cents 14: 4 32000/16807 1114.812 cents 15: 2 25/14 1003.802 cents middle minor seventh 15: 1 117649/64000 1054.014 cents 15: 1 2401/1280 1088.990 cents 15: 2 32000/16807 1114.812 cents 15: 2 1600000/823543 1149.787 cents 15: 8 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 5.20000 = 26/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.0 : 35.0 85.2 120.2 266.1 301.1 351.3 386.3 582.5 617.5 702.7 737.7 848.7 883.6 968.8 1003.8 1200.0 35.0 : 50.2 85.2 231.2 266.1 316.4 351.3 547.5 582.5 667.7 702.7 813.7 848.7 933.9 968.8 1165.0 1200.0 85.2 : 35.0 181.0 215.9 266.1 301.1 497.3 532.3 617.5 652.5 763.5 798.4 883.6 918.6 1114.8 1149.8 1200.0 120.2 : 146.0 181.0 231.2 266.1 462.3 497.3 582.5 617.5 728.5 763.5 848.7 883.6 1079.8 1114.8 1165.0 1200.0 266.1 : 35.0 85.2 120.2 316.4 351.3 436.5 471.5 582.5 617.5 702.7 737.7 933.9 968.8 1019.0 1054.0 1200.0 301.1 : 50.2 85.2 281.4 316.4 401.6 436.5 547.5 582.5 667.7 702.7 898.9 933.9 984.1 1019.0 1165.0 1200.0 351.3 : 35.0 231.2 266.1 351.3 386.3 497.3 532.3 617.5 652.5 848.7 883.6 933.9 968.8 1114.8 1149.8 1200.0 386.3 : 196.2 231.2 316.4 351.3 462.3 497.3 582.5 617.5 813.7 848.7 898.9 933.9 1079.8 1114.8 1165.0 1200.0 582.5 : 35.0 120.2 155.1 266.1 301.1 386.3 421.3 617.5 652.5 702.7 737.7 883.6 918.6 968.8 1003.8 1200.0 617.5 : 85.2 120.2 231.2 266.1 351.3 386.3 582.5 617.5 667.7 702.7 848.7 883.6 933.9 968.8 1165.0 1200.0 702.7 : 35.0 146.0 181.0 266.1 301.1 497.3 532.3 582.5 617.5 763.5 798.4 848.7 883.6 1079.8 1114.8 1200.0 737.7 : 111.0 146.0 231.2 266.1 462.3 497.3 547.5 582.5 728.5 763.5 813.7 848.7 1044.9 1079.8 1165.0 1200.0 848.7 : 35.0 120.2 155.1 351.3 386.3 436.5 471.5 617.5 652.5 702.7 737.7 933.9 968.8 1054.0 1089.0 1200.0 883.6 : 85.2 120.2 316.4 351.3 401.6 436.5 582.5 617.5 667.7 702.7 898.9 933.9 1019.0 1054.0 1165.0 1200.0 968.8 : 35.0 231.2 266.1 316.4 351.3 497.3 532.3 582.5 617.5 813.7 848.7 933.9 968.8 1079.8 1114.8 1200.0 1003.8: 196.2 231.2 281.4 316.4 462.3 497.3 547.5 582.5 778.7 813.7 898.9 933.9 1044.9 1079.8 1165.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 196.1985 cents 686/625, 161.2229 cents 50/49, 34.9756 cents 2: 85.1884 .. 231.1741 cents 128000/117649, 145.9857 cents 2401/2560,-111.0101 cents 3: 120.1640 .. 316.3625 cents 28/25, 196.1985 cents 2401/2560,-111.0101 cents 4: 266.1497 .. 351.3381 cents 16807/16000, 85.1884 cents 800000/823543,-50.2128 cents 5: 301.1253 .. 462.3482 cents 686/625, 161.2229 cents 800000/823543,-50.2128 cents 6: 351.3381 .. 497.3238 cents 128000/117649, 145.9857 cents 2401/2560,-111.0101 cents 7: 386.3137 .. 582.5122 cents 28/25, 196.1985 cents 2401/2560,-111.0101 cents 8: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 1/1, 0.0000 cents 9: 617.4878 .. 813.6863 cents 28/25, 196.1985 cents 1/1, 0.0000 cents 10: 702.6762 .. 848.6619 cents 128000/117649, 145.9857 cents 2401/2560,-111.0101 cents 11: 737.6518 .. 898.8747 cents 686/625, 161.2229 cents 2401/2560,-111.0101 cents 12: 848.6619 .. 933.8503 cents 16807/16000, 85.1884 cents 800000/823543,-50.2128 cents 13: 883.6375 .. 1079.8360 cents 28/25, 196.1985 cents 800000/823543,-50.2128 cents 14: 968.8259 .. 1114.8116 cents 128000/117649, 145.9857 cents 2401/2560,-111.0101 cents 15: 1003.8015 .. 1165.0244 cents 686/625, 161.2229 cents 2401/2560,-111.0101 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 75.0000 cents Largest one step interval : 28/25, 196.1985 cents Average / Smallest step : 2.144351 Largest / Average step : 2.615980 Largest / Smallest step : 5.609579 Median interval of one step : 42.59420 cents, amount: 0 Most common interval of one step : 50/49, 34.9756 cents, amount: 8 Least squares average step : 68.71560 cents, oct.: 1099.44952 cents Scale is not proper Step pattern alph. order: ABACABADAEAFAEAD Step pattern size order : ABAEABAFACADACAF Scale is not a Constant Structure Scale diversity : 1.377818 Lumma stability : 0.058293 Lumma impropriety factor : 0.628600 Number of different interval sizes : 52 = 3.46667 / class Number of one step interval sizes : 6 Highest interval variety : 8 Mean interval variety : 5.20000 = 26/5 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 823543/819200, 9.1539 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 12 Most common triad is 0.0 582.512 617.488 cents, amount: 8 Number of recognisable fifths : 8, average 702.6762 cents Scale contains a complete diamond : 5 7 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 31.2500% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 11-12 -- Rational properties -- Prime limit : 7 Odd number limit : 282475249 (O: 282475249 U: 282475249) Highest odd numerator or denominator: 16807 Scale harmonicity : 0.006263 Average absolute harmonicity : 0.099590 Specific harmonicity : 0.041749 Fundamental : 1/268912000, -28.0026 octaves, 0.0000 Hz. Guide tone : 336140000, 28.3245 octaves, 87942817520.278 Hz. Exponens Consonantiae : 9.039208E+16, 56.32705 octaves Euler's gradus suavitatis : 101 Sum of Mann's harmonic distance : 40955.5, average 2559.71875 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 31.67534, average 1.97971 Sum of Tenney's harmonic distance : 63.15340, average 3.94709 Vogel's harmonic complexity : 58.81250 Wille's k value : 141237624 Wilson's harmonic complexity : 105 Rectangular lattice diameter : 17 Triangular lattice diameter : 10 Lattice compactness : 839.47159, average 6.17259 Lattice compactness (without 2's) : 530.92129, average 3.90383 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 5 -0.68750 53 1 5: -3 .. 4 0.50000 24 1 7: -5 .. 5 0.00000 36 14 Average exponent except 2's : 8 / 16 = 0.50000 Average absolute exponent except 2's: 60 / 16 = 3.75000 Scale is weakly epimorphic with val: <16 35 47| Scale is weakly epimorphic with val: <16 39 43|
FIT/MODE
16: 0 1 1 2 0 1 0 3 0 1 1 1 1 1 0 3 N SD: 21.3273 c. M: 34.9756 c. 19: 1 0 1 2 1 1 0 3 1 1 1 1 1 1 1 3 N SD: 17.0842 c. M:-28.1823 c. 20: 1 0 1 2 1 1 0 4 0 2 0 2 1 1 1 3 N SD: 16.9919 c. M: 26.3137 c. 21: 1 0 1 3 0 1 1 3 1 1 1 2 0 2 1 3 N SD: 16.0988 c. M: 28.0455 c. 23: 1 1 0 3 1 1 0 4 1 1 1 2 1 2 0 4 N SD: 14.5384 c. M: 24.4153 c. 24: 1 1 0 3 1 1 1 4 0 2 1 2 1 1 1 4 N SD: 13.0206 c. M: 20.1640 c. 27: 1 1 1 3 1 1 1 4 1 2 1 2 1 2 1 4 N SD: 9.6281 c. M:-18.4207 c. 28: 1 1 1 3 1 1 1 5 0 2 1 3 1 2 0 5 N SD: 11.7834 c. M: 18.0872 c. 31: 1 1 1 4 1 1 1 5 1 2 1 3 1 2 1 5 N SD: 4.3615 c. M:-8.5521 c. 41: 1 2 1 5 1 2 1 7 1 3 1 4 1 3 1 7 N SD: 4.5331 c. M: 8.6796 c. 57: 2 2 2 7 1 3 1 10 1 4 2 5 2 4 2 9 N SD: 5.7759 c. M: 7.9394 c. 58: 2 2 2 7 2 2 2 9 2 4 2 5 2 4 2 9 N SD: 5.1450 c. M:-9.9916 c. 68: 2 3 2 8 2 3 2 11 2 5 2 6 2 5 2 11 N SD: 2.0114 c. M:-3.5247 c. 72: 2 3 2 9 2 3 2 12 2 5 2 7 2 5 2 12 N SD: 2.2183 c. M: 4.3185 c. 99: 3 4 3 12 3 4 3 16 3 7 3 9 3 7 3 16 N SD: 1.1457 c. M:-2.2591 c. 140: 4 6 4 17 4 6 4 23 4 10 4 13 4 10 4 23 N SD: 0.5424 c. M: 1.1253 c. 171: 5 7 5 21 5 7 5 28 5 12 5 16 5 12 5 28 N SD: 0.5600 c. M: 0.9779 c. 239: 7 10 7 29 7 10 7 39 7 17 7 22 7 17 7 39 N SD: 0.2181 c. M:-0.4235 c. 379: 11 16 11 46 11 16 11 62 11 27 11 35 11 27 11 62 N SD: 0.1690 c. M: 0.3338 c. 550: 16 23 16 67 16 23 16 90 16 39 16 51 16 39 16 90 N SD: 0.1013 c. M: 0.1973 c. 789: 23 33 23 96 23 33 23 129 23 56 23 73 23 56 23 129 N SD: 0.0094 c. M: 0.0173 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.3606 cents 3 .. 6 match: 3 H SD: 28.1568 cents 4 .. 8 match: 4 H SD: 0.1803 cents 5 .. 10 match: 5 H SD: 8.0605 cents 6 .. 12 match: 6 H SD: 15.9966 cents 7 .. 14 match: 7 H SD: 15.3179 cents 8 .. 16 match: 7 S SD: 10.0138 cents 9 .. 18 match: 7 SD: 10.1604 cents 10 .. 20 match: 9 S SD: 10.8133 cents 11 .. 22 match: 10 S SD: 8.2758 cents 12 .. 24 match: 8 SD: 2.9324 cents 13 .. 26 match: 10 SD: 6.1622 cents 14 .. 28 match: 9 SD: 6.9837 cents 15 .. 30 match: 11 SD: 6.3949 cents 16 .. 32 match: 12 SD: 5.1250 cents 17 .. 34 match: 8 SD: 4.4828 cents 18 .. 36 match: 12 SD: 4.8759 cents 19 .. 38 match: 11 SD: 3.6053 cents 20 .. 40 match: 12 SD: 4.0600 cents 21 .. 42 match: 13 SD: 5.1146 cents 22 .. 44 match: 12 SD: 4.5239 cents 23 .. 46 match: 12 SD: 3.5466 cents 24 .. 48 match: 13 SD: 3.0388 cents 25 .. 50 match: 13 SD: 3.3269 cents 26 .. 52 match: 14 SD: 3.7858 cents 27 .. 54 match: 14 SD: 3.4070 cents 28 .. 56 match: 14 SD: 2.7645 cents 29 .. 58 match: 12 SD: 4.0518 cents 30 .. 60 match: 15 SD: 2.9217 cents 31 .. 62 match: 14 SD: 3.1373 cents 32 .. 64 match: 15 SD: 2.3483 cents 33 .. 66 match: 15 SD: 3.2103 cents 34 .. 68 match: 14 SD: 3.4579 cents 35 .. 70 match: 16 SD: 2.7668 cents 36 .. 72 match: 16 SD: 2.1126 cents 40 .. 80 match: 16 SD: 1.7665 cents 44 .. 88 match: 16 SD: 1.7377 cents 52 .. 104 match: 16 SD: 1.5225 cents 53 .. 106 match: 16 SD: 1.5137 cents 56 .. 112 match: 16 SD: 1.3994 cents 60 .. 120 match: 16 SD: 1.2343 cents 68 .. 136 match: 16 SD: 1.2134 cents 79 .. 158 match: 16 SD: 1.0407 cents 80 .. 160 match: 16 SD: 0.9698 cents 84 .. 168 match: 16 SD: 0.6945 cents 96 .. 192 match: 16 SD: 0.6763 cents 120 .. 240 match: 16 SD: 0.6377 cents 136 .. 272 match: 16 SD: 0.6042 cents 137 .. 274 match: 16 SD: 0.5275 cents 152 .. 304 match: 16 SD: 0.4211 cents 180 .. 360 match: 16 SD: 0.4054 cents 192 .. 384 match: 16 SD: 0.3935 cents 196 .. 392 match: 16 SD: 0.3375 cents 200 .. 400 match: 16 SD: 0.3215 cents 236 .. 472 match: 16 SD: 0.2780 cents 252 .. 504 match: 16 SD: 0.2378 cents 320 .. 640 match: 16 SD: 0.2263 cents 332 .. 664 match: 16 SD: 0.1954 cents 373 .. 746 match: 16 SD: 0.1878 cents 392 .. 784 match: 16 SD: 0.1629 cents 457 .. 914 match: 16 SD: 0.1407 cents 499 .. 998 match: 16 SD: 0.1374 cents 537 .. 1074 match: 16 SD: 0.1316 cents 555 .. 1110 match: 16 SD: 0.1309 cents 572 .. 1144 match: 16 SD: 0.1243 cents 583 .. 1166 match: 16 SD: 0.1185 cents 595 .. 1190 match: 16 SD: 0.1048 cents