Scala analysis: chain_of_minor_thirds
19-note chain of minor thirds
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 648/625 62.565148 major diesis 2: 419904/390625 125.130296 two (major diesis) 3: 78125/69984 190.510991 4: 125/108 253.076139 semi-augmented whole tone 5: 6/5 315.641287 minor third 6: 3888/3125 378.206435 7: 2519424/1953125 440.771583 8: 15625/11664 506.152278 two (semi-augmented whole tone) 9: 25/18 568.717426 classic augmented fourth 10: 36/25 631.282574 classic diminished fifth 11: 23328/15625 693.847722 12: 1953125/1259712 759.228417 13: 3125/1944 821.793565 14: 5/3 884.358713 major sixth, BP sixth 15: 216/125 946.923861 semi-augmented sixth 16: 139968/78125 1009.489009 17: 390625/209952 1074.869704 18: 625/324 1137.434852 octave - major diesis 19: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 648/625 62.5651 major diesis 1: 648/625 62.5651 major diesis 2: 648/625 62.5651 major diesis 3: 65.3807 cents 65.3807 4: 648/625 62.5651 major diesis 5: 648/625 62.5651 major diesis 6: 648/625 62.5651 major diesis 7: 648/625 62.5651 major diesis 8: 65.3807 cents 65.3807 9: 648/625 62.5651 major diesis 10: 648/625 62.5651 major diesis 11: 648/625 62.5651 major diesis 12: 65.3807 cents 65.3807 13: 648/625 62.5651 major diesis 14: 648/625 62.5651 major diesis 15: 648/625 62.5651 major diesis 16: 648/625 62.5651 major diesis 17: 65.3807 cents 65.3807 18: 648/625 62.5651 major diesis 19: 648/625 62.5651 major diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 15 648/625 62.565 cents major diesis 1: 4 65.38069 cents 2: 11 419904/390625 125.130 cents two (major diesis) 2: 8 48828125/45349632 127.946 cents 3: 7 272097792/244140625 187.695 cents 3: 12 78125/69984 190.511 cents 4: 3 250.26059 cents 4: 16 125/108 253.076 cents semi-augmented whole tone 5: 18 6/5 315.641 cents minor third 5: 1 318.45683 cents 6: 14 3888/3125 378.206 cents 6: 5 381.02198 cents 7: 10 2519424/1953125 440.772 cents 7: 9 9765625/7558272 443.587 cents 8: 6 1632586752/12207031 503.337 cents 8: 13 15625/11664 506.152 cents two (semi-augmented whole tone) 9: 2 565.90188 cents 9: 17 25/18 568.717 cents classic augmented fourth 10: 17 36/25 631.283 cents classic diminished fifth 10: 2 634.09812 cents 11: 13 23328/15625 693.848 cents 11: 6 1220703125/81629337 696.663 cents 12: 9 15116544/9765625 756.413 cents 12: 10 1953125/1259712 759.228 cents 13: 5 818.97802 cents 13: 14 3125/1944 821.794 cents 14: 1 881.54317 cents 14: 18 5/3 884.359 cents major sixth, BP sixth 15: 16 216/125 946.924 cents semi-augmented sixth 15: 3 949.73941 cents 16: 12 139968/78125 1009.489 cents 16: 7 244140625/136048896 1012.305 cents 17: 8 90699264/48828125 1072.054 cents 17: 11 390625/209952 1074.870 cents 18: 4 1134.61931 cents 18: 15 625/324 1137.435 cents octave - major diesis Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 62.6 125.1 190.5 253.1 315.6 378.2 440.8 506.2 568.7 631.3 693.8 759.2 821.8 884.4 946.9 1009.5 1074.9 1137.4 1200.0 62.6 : 62.6 127.9 190.5 253.1 315.6 378.2 443.6 506.2 568.7 631.3 696.7 759.2 821.8 884.4 946.9 1012.3 1074.9 1137.4 1200.0 125.1 : 65.4 127.9 190.5 253.1 315.6 381.0 443.6 506.2 568.7 634.1 696.7 759.2 821.8 884.4 949.7 1012.3 1074.9 1137.4 1200.0 190.5 : 62.6 125.1 187.7 250.3 315.6 378.2 440.8 503.3 568.7 631.3 693.8 756.4 819.0 884.4 946.9 1009.5 1072.1 1134.6 1200.0 253.1 : 62.6 125.1 187.7 253.1 315.6 378.2 440.8 506.2 568.7 631.3 693.8 756.4 821.8 884.4 946.9 1009.5 1072.1 1137.4 1200.0 315.6 : 62.6 125.1 190.5 253.1 315.6 378.2 443.6 506.2 568.7 631.3 693.8 759.2 821.8 884.4 946.9 1009.5 1074.9 1137.4 1200.0 378.2 : 62.6 127.9 190.5 253.1 315.6 381.0 443.6 506.2 568.7 631.3 696.7 759.2 821.8 884.4 946.9 1012.3 1074.9 1137.4 1200.0 440.8 : 65.4 127.9 190.5 253.1 318.5 381.0 443.6 506.2 568.7 634.1 696.7 759.2 821.8 884.4 949.7 1012.3 1074.9 1137.4 1200.0 506.2 : 62.6 125.1 187.7 253.1 315.6 378.2 440.8 503.3 568.7 631.3 693.8 756.4 819.0 884.4 946.9 1009.5 1072.1 1134.6 1200.0 568.7 : 62.6 125.1 190.5 253.1 315.6 378.2 440.8 506.2 568.7 631.3 693.8 756.4 821.8 884.4 946.9 1009.5 1072.1 1137.4 1200.0 631.3 : 62.6 127.9 190.5 253.1 315.6 378.2 443.6 506.2 568.7 631.3 693.8 759.2 821.8 884.4 946.9 1009.5 1074.9 1137.4 1200.0 693.8 : 65.4 127.9 190.5 253.1 315.6 381.0 443.6 506.2 568.7 631.3 696.7 759.2 821.8 884.4 946.9 1012.3 1074.9 1137.4 1200.0 759.2 : 62.6 125.1 187.7 250.3 315.6 378.2 440.8 503.3 565.9 631.3 693.8 756.4 819.0 881.5 946.9 1009.5 1072.1 1134.6 1200.0 821.8 : 62.6 125.1 187.7 253.1 315.6 378.2 440.8 503.3 568.7 631.3 693.8 756.4 819.0 884.4 946.9 1009.5 1072.1 1137.4 1200.0 884.4 : 62.6 125.1 190.5 253.1 315.6 378.2 440.8 506.2 568.7 631.3 693.8 756.4 821.8 884.4 946.9 1009.5 1074.9 1137.4 1200.0 946.9 : 62.6 127.9 190.5 253.1 315.6 378.2 443.6 506.2 568.7 631.3 693.8 759.2 821.8 884.4 946.9 1012.3 1074.9 1137.4 1200.0 1009.5: 65.4 127.9 190.5 253.1 315.6 381.0 443.6 506.2 568.7 631.3 696.7 759.2 821.8 884.4 949.7 1012.3 1074.9 1137.4 1200.0 1074.9: 62.6 125.1 187.7 250.3 315.6 378.2 440.8 503.3 565.9 631.3 693.8 756.4 819.0 884.4 946.9 1009.5 1072.1 1134.6 1200.0 1137.4: 62.6 125.1 187.7 253.1 315.6 378.2 440.8 503.3 568.7 631.3 693.8 756.4 821.8 884.4 946.9 1009.5 1072.1 1137.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.5651 .. 65.3807 cents 2.81555 cents 648/625, 62.5651 cents 2: 125.1303 .. 127.9458 cents 2.81555 cents 59.74960 cents 3: 187.6954 .. 190.5110 cents 2.81555 cents 59.74960 cents 4: 250.2606 .. 253.0761 cents 2.81555 cents 59.74960 cents 5: 315.6413 .. 318.4568 cents 2.81555 cents 648/625, 62.5651 cents 6: 378.2064 .. 381.0220 cents 2.81555 cents 59.74960 cents 7: 440.7716 .. 443.5871 cents 2.81555 cents 59.74960 cents 8: 503.3367 .. 506.1523 cents 2.81555 cents 59.74960 cents 9: 565.9019 .. 568.7174 cents 2.81555 cents 59.74960 cents 10: 631.2826 .. 634.0981 cents 2.81555 cents 648/625, 62.5651 cents 11: 693.8477 .. 696.6633 cents 2.81555 cents 59.74960 cents 12: 756.4129 .. 759.2284 cents 2.81555 cents 59.74960 cents 13: 818.9780 .. 821.7936 cents 2.81555 cents 59.74960 cents 14: 881.5432 .. 884.3587 cents 2.81555 cents 59.74960 cents 15: 946.9239 .. 949.7394 cents 2.81555 cents 648/625, 62.5651 cents 16: 1009.4890 .. 1012.3046 cents 2.81555 cents 59.74960 cents 17: 1072.0542 .. 1074.8697 cents 2.81555 cents 59.74960 cents 18: 1134.6193 .. 1137.4349 cents 2.81555 cents 59.74960 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 648/625, 62.5651 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 65.38069 cents Average / Smallest step : 1.009474 Largest / Average step : 1.035194 Largest / Smallest step : 1.045002 Median interval of one step : 648/625, 62.5651 cents, amount: 15 Most common interval of one step : 648/625, 62.5651 cents, amount: 15 Least squares average step : 63.16587 cents, oct.: 1200.15161 cents Scale is strictly proper Scale has Myhill's property chromas: 2.81555 cents and 59.74960 cents, ratio: 21.221312 generators: 5 of 315.64129 cents and 14 of 884.35871 cents ET pair of linear temperament : 19&422 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1707-tone equal temperament with octave 2/1 degrees: 89 178 271 360 449 538 627 720 809 898 987 1080 1169 1258 1347 1436 1529 1618 1707 generators: 449 and 1258 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAAABAAABAAAABAA Step pattern size order : SSLSSSSLSSSLSSSSLSS Scale is a Constant Structure, by a margin of 59.74960 cents Scale diversity : 1.028471 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.957767 Rothenberg efficiency : 0.701754 redundancy: 0.298246 Efficiency x scale size : 13.333333 Number of different interval sizes : 36 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 2.81555 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 440.772 884.359 cents Most common triad is 0.0 315.641 884.359 cents, amount: 17 Number of recognisable fifths : 19, average 694.7368 cents Scale contains two identical disjunct "tetrachords" of 9 notes Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 3 5 Formal octave complements present : 19 = 100.0000% Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval class 5 Limited transpositions with margin 2.8155 cents: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Limited inverse transpositions with margin 2.8155 cents: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties -- Prime limit : 5 Odd number limit : too high to compute Highest odd numerator or denominator: 1953125 Scale harmonicity : 0.005675 Average absolute harmonicity : 0.083304 Fundamental : too low to compute Guide tone : too high to compute Exponens Consonantiae : 1.210689E+25, 83.32403 octaves Euler's gradus suavitatis : 122 Sum of Mann's harmonic distance : 4771970.0, average 251156.31579 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 62.90730, average 3.31091 Sum of Tenney's harmonic distance : 125.71619, average 6.61664 Vogel's harmonic complexity : too high to compute Wille's k value : too high to compute Wilson's harmonic complexity : 144 Rectangular lattice diameter : 36 Triangular lattice diameter : 18 Lattice compactness : 1958.18124, average 10.30622 Lattice compactness (without 2's) : 1739.48268, average 9.15517 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 7 0.52632 66 1 3: -9 .. 9 0.00000 90 5: -9 .. 9 0.00000 90 18 Average exponent except 2's : 0 / 19 = 0.00000 Average absolute exponent except 2's: 180 / 19 = 9.47368 Scale is JI-epimorphic with val: <19 27 41| Scale is weakly epimorphic with val: <19 27 42| Scale is weakly epimorphic with val: <19 27 43| Scale is weakly epimorphic with val: <19 27 44| Scale is weakly epimorphic with val: <19 27 45| Scale is weakly epimorphic with val: <19 27 47| Scale is weakly epimorphic with val: <19 28 41| Scale is JI-epimorphic with val: <19 28 42| Scale is weakly epimorphic with val: <19 28 43| Scale is weakly epimorphic with val: <19 28 44| Scale is weakly epimorphic with val: <19 28 45| Scale is weakly epimorphic with val: <19 28 46| Scale is weakly epimorphic with val: <19 29 41| Scale is weakly epimorphic with val: <19 29 42| Scale is JI-epimorphic with val: <19 29 43| Scale is weakly epimorphic with val: <19 29 44| Scale is weakly epimorphic with val: <19 29 45| Scale is weakly epimorphic with val: <19 29 46| Scale is weakly epimorphic with val: <19 29 47| Scale is weakly epimorphic with val: <19 30 41| Scale is weakly epimorphic with val: <19 30 42| Scale is weakly epimorphic with val: <19 30 43| Scale is JI-epimorphic with val: <19 30 44| = patent Scale is weakly epimorphic with val: <19 30 45| Scale is weakly epimorphic with val: <19 30 46| Scale is weakly epimorphic with val: <19 30 47| Scale is weakly epimorphic with val: <19 31 41| Scale is weakly epimorphic with val: <19 31 42| Scale is weakly epimorphic with val: <19 31 43| Scale is weakly epimorphic with val: <19 31 44| Scale is JI-epimorphic with val: <19 31 45| Scale is weakly epimorphic with val: <19 31 46| Scale is weakly epimorphic with val: <19 31 47| Scale is weakly epimorphic with val: <19 32 41| Scale is weakly epimorphic with val: <19 32 42| Scale is weakly epimorphic with val: <19 32 43| Scale is weakly epimorphic with val: <19 32 44| Scale is weakly epimorphic with val: <19 32 45| Scale is JI-epimorphic with val: <19 32 46| Scale is weakly epimorphic with val: <19 32 47| Scale is weakly epimorphic with val: <19 33 41| Scale is weakly epimorphic with val: <19 33 42| Scale is weakly epimorphic with val: <19 33 43| Scale is weakly epimorphic with val: <19 33 44| Scale is weakly epimorphic with val: <19 33 45| Scale is weakly epimorphic with val: <19 33 46| Scale is JI-epimorphic with val: <19 33 47|
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.8117 c. M: 1.3337 c. 232: 12 12 13 12 12 12 12 13 12 12 12 13 12 12 12 12 13 12 12 SP M ME I SD: 0.6794 c. M: 1.1164 c. 251: 13 13 14 13 13 13 13 14 13 13 13 14 13 13 13 13 14 13 13 SP M ME I SD: 0.5666 c. M: 0.9309 c. 270: 14 14 15 14 14 14 14 15 14 14 14 15 14 14 14 14 15 14 14 SP M ME I SD: 0.4696 c. M: 0.7716 c. 289: 15 15 16 15 15 15 15 16 15 15 15 16 15 15 15 15 16 15 15 SP M ME I SD: 0.3853 c. M: 0.6332 c. 308: 16 16 17 16 16 16 16 17 16 16 16 17 16 16 16 16 17 16 16 SP M ME I SD: 0.3115 c. M: 0.5118 c. 327: 17 17 18 17 17 17 17 18 17 17 17 18 17 17 17 17 18 17 17 SP M ME I SD: 0.2462 c. M: 0.4046 c. 346: 18 18 19 18 18 18 18 19 18 18 18 19 18 18 18 18 19 18 18 SP M ME I SD: 0.1881 c. M: 0.3092 c. 365: 19 19 20 19 19 19 19 20 19 19 19 20 19 19 19 19 20 19 19 SP M ME I SD: 0.1361 c. M: 0.2236 c. 384: 20 20 21 20 20 20 20 21 20 20 20 21 20 20 20 20 21 20 20 SP M ME I SD: 0.0892 c. M: 0.1466 c. 403: 21 21 22 21 21 21 21 22 21 21 21 22 21 21 21 21 22 21 21 SP M ME I SD: 0.0467 c. M: 0.0768 c. 422: 22 22 23 22 22 22 22 23 22 22 22 23 22 22 22 22 23 22 22 SP M ME I SD: 0.0081 c. M: 0.0133 c. 1285: 67 67 70 67 67 67 67 70 67 67 67 70 67 67 67 67 70 67 67 SP M DE I SD: 0.0040 c. M:-0.0066 c. 1707: 89 89 93 89 89 89 89 93 89 89 89 93 89 89 89 89 93 89 89 SP M DE I SD: 0.0010 c. M: 0.0017 c. 2129: 111 111 116 111 111 111 111 116 111 111 111 116 111 111 111 111 116 111 111 SP M DE I SD: 0.0008 c. M: 0.0013 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 4.0536 cents 3 .. 6 match: 3 H SD: 2.7024 cents 4 .. 8 match: 4 H SD: 6.1804 cents 5 .. 10 match: 5 H SD: 3.5875 cents 6 .. 12 match: 6 H SD: 5.1971 cents 7 .. 14 match: 7 H SD: 5.4283 cents 8 .. 16 match: 8 H SD: 5.0373 cents 9 .. 18 match: 9 H SD: 4.9759 cents 10 .. 20 match: 10 H SD: 5.2028 cents 11 .. 22 match: 11 H SD: 6.4894 cents 12 .. 24 match: 12 H SD: 4.7945 cents 13 .. 26 match: 13 H SD: 4.3994 cents 14 .. 28 match: 14 H SD: 3.9914 cents 15 .. 30 match: 15 H SD: 4.0052 cents 16 .. 32 match: 16 H SD: 4.1328 cents 17 .. 34 match: 16 S SD: 5.0687 cents 18 .. 36 match: 17 SD: 3.5773 cents 19 .. 38 match: 17 SD: 4.8996 cents 20 .. 40 match: 18 SD: 3.2590 cents 21 .. 42 match: 18 SD: 3.7306 cents 22 .. 44 match: 18 SD: 4.5286 cents 23 .. 46 match: 19 SD: 3.5392 cents 24 .. 48 match: 19 SD: 2.8286 cents 25 .. 50 match: 19 SD: 2.5317 cents 29 .. 58 match: 19 SD: 2.5138 cents 33 .. 66 match: 19 SD: 2.4498 cents 34 .. 68 match: 19 SD: 2.3962 cents 36 .. 72 match: 19 SD: 2.1114 cents 38 .. 76 match: 19 SD: 2.0189 cents 41 .. 82 match: 19 SD: 1.8646 cents 44 .. 88 match: 19 SD: 1.5393 cents 49 .. 98 match: 19 SD: 1.5252 cents 51 .. 102 match: 19 SD: 1.2650 cents 59 .. 118 match: 19 SD: 1.2007 cents 69 .. 138 match: 19 SD: 0.9979 cents 77 .. 154 match: 19 SD: 0.8423 cents 85 .. 170 match: 19 SD: 0.8347 cents 94 .. 188 match: 19 SD: 0.8345 cents 95 .. 190 match: 19 SD: 0.7616 cents 102 .. 204 match: 19 SD: 0.7276 cents 103 .. 206 match: 19 SD: 0.7034 cents 106 .. 212 match: 19 SD: 0.6705 cents 107 .. 214 match: 19 SD: 0.6593 cents 109 .. 218 match: 19 SD: 0.6527 cents 110 .. 220 match: 19 SD: 0.6207 cents 114 .. 228 match: 19 SD: 0.5802 cents 120 .. 240 match: 19 SD: 0.5420 cents 135 .. 270 match: 19 SD: 0.5141 cents 136 .. 272 match: 19 SD: 0.5022 cents 138 .. 276 match: 19 SD: 0.5006 cents 144 .. 288 match: 19 SD: 0.4674 cents 159 .. 318 match: 19 SD: 0.4354 cents 164 .. 328 match: 19 SD: 0.4233 cents 165 .. 330 match: 19 SD: 0.3805 cents 189 .. 378 match: 19 SD: 0.3449 cents 209 .. 418 match: 19 SD: 0.3267 cents 214 .. 428 match: 19 SD: 0.3060 cents 216 .. 432 match: 19 SD: 0.2848 cents 241 .. 482 match: 19 SD: 0.2483 cents 265 .. 530 match: 19 SD: 0.2291 cents 280 .. 560 match: 19 SD: 0.2249 cents 294 .. 588 match: 19 SD: 0.2080 cents 324 .. 648 match: 19 SD: 0.1914 cents 345 .. 690 match: 19 SD: 0.1716 cents 389 .. 778 match: 19 SD: 0.1654 cents 414 .. 828 match: 19 SD: 0.1512 cents 430 .. 860 match: 19 SD: 0.1443 cents 438 .. 876 match: 19 SD: 0.1200 cents 489 .. 978 match: 19 SD: 0.1107 cents 507 .. 1014 match: 19 SD: 0.1107 cents 545 .. 1090 match: 19 SD: 0.1057 cents