Scala analysis: ForCarl3
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 9/8 203.910002 major whole tone 3: 153/128 308.865411 4: 81/64 407.820003 Pythagorean major third 5: 171/128 501.423018 6: 91/64 609.353568 7: 3/2 701.955001 perfect fifth 8: 51/32 806.910410 9: 27/16 905.865003 Pythagorean major sixth 10: 57/32 999.468017 undevicesimal minor seventh 11: 243/128 1109.775004 Pythagorean major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 17/16 104.9554 17th harmonic 2: 18/17 98.9546 Arabic lute index finger 3: 17/16 104.9554 17th harmonic 4: 18/17 98.9546 Arabic lute index finger 5: 19/18 93.6030 undevicesimal semitone 6: 182/171 107.9306 7: 96/91 92.6014 8: 17/16 104.9554 17th harmonic 9: 18/17 98.9546 Arabic lute index finger 10: 19/18 93.6030 undevicesimal semitone 11: 81/76 110.3070 12: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 96/91 92.601 cents 1: 2 19/18 93.603 cents undevicesimal semitone 1: 3 18/17 98.955 cents Arabic lute index finger 1: 3 17/16 104.955 cents 17th harmonic 1: 1 182/171 107.931 cents 1: 1 81/76 110.307 cents 2: 2 19/17 192.558 cents quasi-meantone 2: 1 272/243 195.180 cents Persian whole tone 2: 1 102/91 197.557 cents 2: 2 64/57 200.532 cents 2: 1 91/81 201.534 cents 2: 5 9/8 203.910 cents major whole tone 3: 3 32/27 294.135 cents Pythagorean minor third 3: 1 108/91 296.511 cents 3: 2 19/16 297.513 cents 19th harmonic 3: 1 182/153 300.488 cents 3: 2 81/68 302.865 cents Persian wosta 3: 2 68/57 305.487 cents 3: 1 153/128 308.865 cents 4: 1 114/91 390.114 cents 4: 2 64/51 393.090 cents 4: 1 171/136 396.468 cents 4: 3 34/27 399.090 cents septendecimal major third 4: 2 24/19 404.442 cents smaller undevicesimal major third 4: 1 91/72 405.444 cents 4: 2 81/64 407.820 cents Pythagorean major third 5: 8 4/3 498.045 cents perfect fourth 5: 1 243/182 500.421 cents 5: 1 171/128 501.423 cents 5: 1 91/68 504.398 cents 5: 1 51/38 509.397 cents 6: 1 128/91 590.646 cents 6: 2 38/27 591.648 cents 6: 3 24/17 597.000 cents 1st septendecimal tritone 6: 3 17/12 603.000 cents 2nd septendecimal tritone 6: 2 27/19 608.352 cents 6: 1 91/64 609.354 cents 7: 1 76/51 690.603 cents 7: 1 136/91 695.602 cents 7: 1 256/171 698.577 cents 7: 1 364/243 699.579 cents 7: 8 3/2 701.955 cents perfect fifth 8: 2 128/81 792.180 cents Pythagorean minor sixth 8: 1 144/91 794.556 cents 8: 2 19/12 795.558 cents undevicesimal minor sixth 8: 3 27/17 800.910 cents septendecimal minor sixth 8: 1 272/171 803.532 cents 8: 2 51/32 806.910 cents 8: 1 91/57 809.886 cents 9: 1 256/153 891.135 cents 9: 2 57/34 894.513 cents 9: 2 136/81 897.135 cents 9: 1 153/91 899.512 cents 9: 2 32/19 902.487 cents 19th subharmonic 9: 1 91/54 903.489 cents 9: 3 27/16 905.865 cents Pythagorean major sixth 10: 5 16/9 996.090 cents Pythagorean minor seventh 10: 1 162/91 998.466 cents 10: 2 57/32 999.468 cents undevicesimal minor seventh 10: 1 91/51 1002.443 cents 10: 1 243/136 1004.820 cents 10: 2 34/19 1007.442 cents quasi-mean seventh 11: 1 152/81 1089.693 cents 11: 1 171/91 1092.069 cents 11: 3 32/17 1095.045 cents 17th subharmonic 11: 3 17/9 1101.045 cents septendecimal major seventh 11: 2 36/19 1106.397 cents smaller undevicesimal major seventh 11: 1 91/48 1107.399 cents 11: 1 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.36364 = 70/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 105.0 203.9 308.9 407.8 501.4 609.4 702.0 806.9 905.9 999.5 1109.8 1200.0 105.0 : 99.0 203.9 302.9 396.5 504.4 597.0 702.0 800.9 894.5 1004.8 1095.0 1200.0 203.9 : 105.0 203.9 297.5 405.4 498.0 603.0 702.0 795.6 905.9 996.1 1101.0 1200.0 308.9 : 99.0 192.6 300.5 393.1 498.0 597.0 690.6 800.9 891.1 996.1 1095.0 1200.0 407.8 : 93.6 201.5 294.1 399.1 498.0 591.6 702.0 792.2 897.1 996.1 1101.0 1200.0 501.4 : 107.9 200.5 305.5 404.4 498.0 608.4 698.6 803.5 902.5 1007.4 1106.4 1200.0 609.4 : 92.6 197.6 296.5 390.1 500.4 590.6 695.6 794.6 899.5 998.5 1092.1 1200.0 702.0 : 105.0 203.9 297.5 407.8 498.0 603.0 702.0 806.9 905.9 999.5 1107.4 1200.0 806.9 : 99.0 192.6 302.9 393.1 498.0 597.0 702.0 800.9 894.5 1002.4 1095.0 1200.0 905.9 : 93.6 203.9 294.1 399.1 498.0 603.0 702.0 795.6 903.5 996.1 1101.0 1200.0 999.5 : 110.3 200.5 305.5 404.4 509.4 608.4 702.0 809.9 902.5 1007.4 1106.4 1200.0 1109.8: 90.2 195.2 294.1 399.1 498.0 591.6 699.6 792.2 897.1 996.1 1089.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 110.3070 cents 19683/19456, 20.0820 cents 256/243, 90.2250 cents 2: 192.5576 .. 203.9100 cents 153/152, 11.3524 cents 1444/1377, 82.2506 cents 3: 294.1350 .. 308.8654 cents 4131/4096, 14.7304 cents 256/243, 90.2250 cents 4: 390.1144 .. 407.8200 cents 2457/2432, 17.7056 cents 4864/4641, 81.2490 cents 5: 498.0450 .. 509.3974 cents 153/152, 11.3524 cents 256/243, 90.2250 cents 6: 590.6464 .. 609.3536 cents 8281/8192, 18.7071 cents 4864/4641, 81.2490 cents 7: 690.6026 .. 701.9550 cents 153/152, 11.3524 cents 4864/4641, 81.2490 cents 8: 792.1800 .. 809.8856 cents 2457/2432, 17.7056 cents 256/243, 90.2250 cents 9: 891.1346 .. 905.8650 cents 4131/4096, 14.7304 cents 4864/4641, 81.2490 cents 10: 996.0900 .. 1007.4424 cents 153/152, 11.3524 cents 256/243, 90.2250 cents 11: 1089.6930 .. 1109.7750 cents 19683/19456, 20.0820 cents 1444/1377, 82.2506 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 81/76, 110.3070 cents Average / Smallest step : 1.108340 Largest / Average step : 1.103070 Largest / Smallest step : 1.222577 Median interval of one step : 18/17, 98.9546 cents, amount: 3 Least squares average step : 100.55053 cents, oct.: 1206.60640 cents Scale is strictly proper Step pattern alph. order: ABABCDEABCFG Step pattern size order : EDEDCFBEDCGA Scale is a Constant Structure, by a margin of 81.24904 cents Scale diversity : 1.118522 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.859039 Rothenberg efficiency : 0.307765 redundancy: 0.692235 Efficiency x scale size : 3.693182 Number of different interval sizes : 70 = 6.36364 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.36364 = 70/11 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 1729/1728, 1.0016 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 8 Most common triad is 0.0 498.045 701.955 cents, amount: 5 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 5 different sizes of fifth Best fifths form a closed circle Length of longest harmonic part : 3 at degree 2 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 20.0820 cents: 1 2 3 5 7 8 9 10 Limited inverse transpositions with margin 20.0820 cents: 1 2 3 4 6 7 8 9 11 -- Rational properties -- Prime limit : 19 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.008475 Average absolute harmonicity : 0.144671 Specific harmonicity : 0.063443 Fundamental : 1/128, -7.0000 octaves, 2.0439 Hz. Guide tone : 14284998, 23.7680 octaves, 3737320677.074 Hz. Exponens Consonantiae : 1.828480E+09, 30.76800 octaves Euler's gradus suavitatis : 71 Sum of Mann's harmonic distance : 762.0, average 63.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 18.22744, average 1.51895 Sum of Tenney's harmonic distance : 35.08512, average 2.92376 Vogel's harmonic complexity : 16.83333 Wille's k value : 121 Wilson's harmonic complexity : 71 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 320.11976, average 4.10410 Lattice compactness (without 2's) : 171.22369, average 2.19518 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -7 .. 1 -4.50000 56 1 3: 0 .. 5 1.75000 21 5 7: 0 .. 1 0.08333 1 13: 0 .. 1 0.08333 1 1 17: 0 .. 1 0.25000 3 3 19: 0 .. 1 0.16667 2 2 Average exponent except 2's : 28 / 12 = 2.33333 Average absolute exponent except 2's: 28 / 12 = 2.33333 Scale is JI-epimorphic with val: <12 19 32 46 49 51| Scale is JI-epimorphic with val: <12 19 33 45 49 51| Scale is JI-epimorphic with val: <12 19 34 44 49 51| = patent Scale is JI-epimorphic with val: <12 19 35 43 49 51| Scale is JI-epimorphic with val: <12 19 36 42 49 51|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.1299 c. M: 9.7750 c. Twelve-tone Chromatic (1/11-comma) 53: 5 4 5 4 4 5 4 5 4 4 5 4 SP M ME SD: 4.3448 c. M:-8.2521 c. 65: 6 5 6 5 5 6 5 6 5 5 6 5 SP M ME SD: 3.0625 c. M:-5.8138 c. 77: 7 6 7 6 6 7 6 7 6 6 7 6 SP M ME SD: 2.4996 c. M:-4.1355 c. 89: 8 7 8 7 7 8 7 8 7 7 8 7 SP M ME SD: 2.3911 c. M: 4.1570 c. 94: 8 8 8 8 7 9 7 8 8 7 9 7 SP D3 S SD: 2.2539 c. M: 3.7233 c. 101: 9 8 9 8 8 9 8 9 8 8 9 8 SP M ME SD: 2.5116 c. M: 4.8245 c. 106: 9 9 9 9 8 10 8 9 9 8 10 8 SP D3 S SD: 2.1431 c. M: 3.3098 c. 118: 10 10 10 10 9 11 9 10 10 9 11 9 SP D3 S SD: 2.2285 c. M: 3.7807 c. 130: 11 11 11 11 10 12 10 11 11 10 12 10 SP D3 S SD: 2.4021 c. M: 4.2500 c. 132: 12 10 12 11 10 12 10 12 11 10 12 10 SP T3 SD: 2.1580 c. M:-4.1355 c. 144: 13 11 13 12 11 13 11 13 12 11 13 11 SP T3 SD: 1.9281 c. M: 3.9100 c. 147: 13 12 13 12 11 14 11 13 12 11 14 11 SP SD: 1.7815 c. M: 3.5496 c. 158: 14 13 14 13 12 14 12 14 13 13 14 12 SP SD: 1.9647 c. M: 3.2208 c. 159: 14 13 14 13 12 15 12 14 13 12 15 12 SP SD: 1.4948 c. M: 3.3098 c. 160: 14 13 14 13 13 14 13 14 13 12 15 12 SP SD: 1.8667 c. M:-3.0896 c. 162: 14 14 14 13 13 14 13 14 13 13 15 12 SP SD: 1.7806 c. M:-3.4974 c. 163: 14 14 14 13 13 15 12 15 13 13 15 12 SP SD: 1.8799 c. M: 2.9120 c. 171: 15 14 15 14 13 16 13 15 14 13 16 13 SP SD: 1.3742 c. M: 3.1774 c. 183: 16 15 16 15 14 17 14 16 15 14 17 14 SP SD: 1.3907 c. M: 3.0624 c. 186: 16 16 16 15 15 16 15 16 15 15 17 14 SP SD: 1.6517 c. M: 2.9020 c. 187: 16 16 16 16 14 17 14 17 15 15 17 14 SP SD: 1.5770 c. M:-2.8752 c. 191: 17 15 17 16 15 17 15 16 16 15 18 14 SP SD: 1.6190 c. M: 2.8629 c. 195: 17 16 17 16 15 18 15 17 16 15 18 15 SP SD: 1.4964 c. M: 2.9615 c. 198: 17 17 17 16 16 18 15 17 16 16 18 15 SP SD: 1.6428 c. M: 2.8347 c. 199: 17 17 17 17 15 18 15 18 16 16 18 15 SP SD: 1.4839 c. M: 2.4575 c. 205: 18 17 18 17 16 18 16 18 17 16 19 15 SP SD: 1.3639 c. M:-2.4201 c. 213: 19 17 19 17 17 19 17 18 18 16 20 16 SP SD: 1.4586 c. M: 2.2849 c. 215: 19 18 18 18 17 19 17 19 17 17 20 16 SP SD: 1.4344 c. M:-2.6016 c. 216: 19 18 19 17 17 20 16 19 18 17 20 16 SP SD: 1.4769 c. M: 2.2644 c. 217: 19 18 19 18 17 19 17 19 18 17 20 16 SP SD: 1.0830 c. M:-1.8028 c. 229: 20 19 20 19 18 20 18 20 19 18 21 17 SP SD: 0.9067 c. M:-1.6338 c. 241: 21 20 21 20 19 21 19 21 20 19 22 18 SP SD: 0.8485 c. M: 1.8847 c. 277: 24 23 24 23 22 25 21 24 23 22 25 21 SP SD: 0.9180 c. M:-1.4768 c. 282: 25 23 25 23 22 25 22 25 23 22 26 21 SP SD: 0.9518 c. M:-1.7729 c. 294: 26 24 26 24 23 26 23 26 24 23 27 22 SP SD: 0.7751 c. M:-1.3387 c. 306: 27 25 27 25 24 27 24 27 25 24 28 23 SP SD: 0.6749 c. M: 1.5104 c. 311: 27 26 27 26 24 28 24 27 26 24 29 23 SP SD: 0.6958 c. M:-1.4790 c. 318: 28 26 28 26 25 28 25 28 26 25 29 24 SP SD: 0.6610 c. M: 1.8064 c. 323: 28 27 28 27 25 29 25 28 27 25 30 24 SP SD: 0.5875 c. M:-1.0609 c. 335: 29 28 29 28 26 30 26 29 28 26 31 25 SP SD: 0.5666 c. M: 1.0748 c. 376: 33 31 33 31 29 34 29 33 31 29 35 28 SP SD: 0.5019 c. M:-0.8633 c. 388: 34 32 34 32 30 35 30 34 32 30 36 29 SP SD: 0.3342 c. M:-0.5343 c. 400: 35 33 35 33 31 36 31 35 33 31 37 30 SP SD: 0.2350 c. M: 0.4680 c. 412: 36 34 36 34 32 37 32 36 34 32 38 31 SP SD: 0.2623 c. M: 0.6157 c. 665: 58 55 58 55 52 60 51 58 55 52 61 50 SP SD: 0.2402 c. M:-0.5712 c. 677: 59 56 59 56 53 61 52 59 56 53 62 51 SP SD: 0.2628 c. M: 0.4459 c. 718: 63 59 63 59 56 65 55 63 59 56 66 54 SP SD: 0.2563 c. M:-0.6743 c. 730: 64 60 64 60 57 66 56 64 60 57 67 55 SP SD: 0.1995 c. M:-0.5094 c. 742: 65 61 65 61 58 67 57 65 61 58 68 56 SP SD: 0.1875 c. M:-0.3499 c. 959: 84 79 84 79 75 86 74 84 79 75 88 72 SP SD: 0.1743 c. M:-0.3497 c. 971: 85 80 85 80 76 87 75 85 80 76 89 73 SP SD: 0.1434 c. M:-0.3278 c. 1053: 92 87 92 87 82 95 81 92 87 82 97 79 SP SD: 0.1343 c. M:-0.3330 c. 1065: 93 88 93 88 83 96 82 93 88 83 98 80 SP SD: 0.1060 c. M:-0.2239 c. 1077: 94 89 94 89 84 97 83 94 89 84 99 81 SP SD: 0.1186 c. M: 0.2303 c. 1130: 99 93 99 93 88 102 87 99 93 88 104 85 SP SD: 0.1278 c. M:-0.2040 c. 1142: 100 94 100 94 89 103 88 100 94 89 105 86 SP SD: 0.1123 c. M: 0.1971 c. 1154: 101 95 101 95 90 104 89 101 95 90 106 87 SP SD: 0.1310 c. M: 0.2429 c. 1359: 119 112 119 112 106 122 105 119 112 106 125 102 SP SD: 0.1148 c. M:-0.1854 c. 1371: 120 113 120 113 107 123 106 120 113 107 126 103 SP SD: 0.0839 c. M: 0.1632 c. 1383: 121 114 121 114 108 124 107 121 114 108 127 104 SP SD: 0.0822 c. M: 0.2429 c. 1465: 128 121 128 121 114 132 113 128 121 114 135 110 SP SD: 0.0907 c. M: 0.1506 c. 1477: 129 122 129 122 115 133 114 129 122 115 136 111 SP SD: 0.0925 c. M: 0.1484 c. 1771: 155 146 155 146 138 159 137 155 146 138 163 133 SP SD: 0.0888 c. M: 0.2062 c. 1783: 156 147 156 147 139 160 138 156 147 139 164 134 SP SD: 0.0829 c. M: 0.2678 c. 2024: 177 167 177 167 158 182 156 177 167 158 186 152 SP SD: 0.0852 c. M:-0.1580 c. 2036: 178 168 178 168 159 183 157 178 168 159 187 153 SP SD: 0.0684 c. M:-0.1487 c. 2048: 179 169 179 169 160 184 158 179 169 160 188 154 SP SD: 0.0688 c. M:-0.1414 c. 2101: 184 173 184 173 164 189 162 184 173 164 193 158 SP SD: 0.0738 c. M:-0.1374 c. 2113: 185 174 185 174 165 190 163 185 174 165 194 159 SP SD: 0.0608 c. M:-0.1085 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: 7.2567 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.3590 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.7555 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 11.4588 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.4134 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.2564 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.8697 cents 10 x 11:12:13 x 14:15:16:17:18:19:20 S SD: 7.0514 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 10.4116 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.5631 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.7114 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.0959 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.3538 cents 18:19:20:22:23:24:26:27:29:30:32:34:36 SD: 5.2753 cents 19:20:21:23:24:25:27:29:30:32:34:36:38 SD: 5.0262 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 4.2117 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.3793 cents 30:32:34:36:38:40:43:45:48:51:53:57:60 SD: 2.4655 cents 41:44:46:49:52:55:58:62:65:69:73:78:82 SD: 2.3270 cents 42:45:47:50:53:56:60:63:67:71:75:80:84 SD: 1.8836 cents 48:51:54:57:61:64:68:72:77:81:86:91:96 SD: 1.7988 cents 50:53:56:60:63:67:71:75:80:84:89:95:100 SD: 1.4982 cents 62:66:70:74:78:83:88:93:99:105:110:118:124 SD: 1.4457 cents 64:68:72:77:81:86:91:96:102:108:114:122:128 SD: 1.3936 cents 66:70:74:79:84:88:94:99:105:111:118:125:132 SD: 1.3561 cents 71:75:80:85:90:95:101:107:113:120:126:135:142 SD: 1.3406 cents 78:83:88:93:99:104:111:117:124:132:139:148:156 SD: 0.9594 cents 86:91:97:103:109:115:122:129:137:145:153:163:172 SD: 0.9219 cents 96:102:108:115:122:128:137:144:153:162:171:182:192 SD: 0.9200 cents 97:103:109:116:123:130:138:146:155:164:173:184:194 SD: 0.9191 cents 98:104:110:117:124:131:139:147:156:165:175:186:196 SD: 0.7564 cents 113:120:127:135:143:151:161:170:180:191:201:215:226 SD: 0.7106 cents 128:136:144:153:162:171:182:192:204:216:228:243:256 SD: 0.0000 cents