Scala analysis: ForCarl1
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: 19/16 297.513016 19th harmonic 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: 203/128 798.403101 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: 19/18 93.6030 undevicesimal semitone 4: 81/76 110.3070 5: 19/18 93.6030 undevicesimal semitone 6: 182/171 107.9306 7: 96/91 92.6014 8: 203/192 96.4481 9: 216/203 107.4619 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: 3 19/18 93.603 cents undevicesimal semitone 1: 1 203/192 96.448 cents 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 17/16 104.955 cents 17th harmonic 1: 1 216/203 107.462 cents 1: 1 182/171 107.931 cents 1: 2 81/76 110.307 cents 2: 1 29/26 189.050 cents 2: 1 19/17 192.558 cents quasi-meantone 2: 1 272/243 195.180 cents Persian whole tone 2: 2 64/57 200.532 cents 2: 1 228/203 201.065 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: 1 203/171 296.980 cents 3: 3 19/16 297.513 cents 19th harmonic 3: 1 81/68 302.865 cents Persian wosta 3: 1 68/57 305.487 cents 3: 1 243/203 311.372 cents 3: 1 91/76 311.841 cents 4: 1 304/243 387.738 cents 4: 1 114/91 390.114 cents 4: 1 203/162 390.583 cents 4: 1 171/136 396.468 cents 4: 1 34/27 399.090 cents septendecimal major third 4: 1 256/203 401.597 cents 4: 3 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: 7 4/3 498.045 cents perfect fourth 5: 1 243/182 500.421 cents 5: 1 203/152 500.890 cents 5: 1 171/128 501.423 cents 5: 1 91/68 504.398 cents 5: 1 272/203 506.552 cents 6: 1 128/91 590.646 cents 6: 3 38/27 591.648 cents 6: 1 203/144 594.493 cents 6: 1 24/17 597.000 cents 1st septendecimal tritone 6: 1 17/12 603.000 cents 2nd septendecimal tritone 6: 1 288/203 605.507 cents 6: 3 27/19 608.352 cents 6: 1 91/64 609.354 cents 7: 1 203/136 693.448 cents 7: 1 136/91 695.602 cents 7: 1 256/171 698.577 cents 7: 1 304/203 699.110 cents 7: 1 364/243 699.579 cents 7: 7 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: 3 19/12 795.558 cents undevicesimal minor sixth 8: 1 203/128 798.403 cents 8: 1 27/17 800.910 cents septendecimal minor sixth 8: 1 272/171 803.532 cents 8: 1 324/203 809.417 cents 8: 1 91/57 809.886 cents 8: 1 243/152 812.262 cents 9: 1 152/91 888.159 cents 9: 1 406/243 888.628 cents 9: 1 57/34 894.513 cents 9: 1 136/81 897.135 cents 9: 3 32/19 902.487 cents 19th subharmonic 9: 1 342/203 903.020 cents 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: 1 203/114 998.935 cents 10: 2 57/32 999.468 cents undevicesimal minor seventh 10: 1 243/136 1004.820 cents 10: 1 34/19 1007.442 cents quasi-mean seventh 10: 1 52/29 1010.950 cents 11: 2 152/81 1089.693 cents 11: 1 171/91 1092.069 cents 11: 1 203/108 1092.538 cents 11: 1 32/17 1095.045 cents 17th subharmonic 11: 1 17/9 1101.045 cents septendecimal major seventh 11: 1 384/203 1103.552 cents 11: 3 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: 9 Average number of different intervals per interval class: 7.81818 = 86/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 105.0 203.9 297.5 407.8 501.4 609.4 702.0 798.4 905.9 999.5 1109.8 1200.0 105.0 : 99.0 192.6 302.9 396.5 504.4 597.0 693.4 800.9 894.5 1004.8 1095.0 1200.0 203.9 : 93.6 203.9 297.5 405.4 498.0 594.5 702.0 795.6 905.9 996.1 1101.0 1200.0 297.5 : 110.3 203.9 311.8 404.4 500.9 608.4 702.0 812.3 902.5 1007.4 1106.4 1200.0 407.8 : 93.6 201.5 294.1 390.6 498.0 591.6 702.0 792.2 897.1 996.1 1089.7 1200.0 501.4 : 107.9 200.5 297.0 404.4 498.0 608.4 698.6 803.5 902.5 996.1 1106.4 1200.0 609.4 : 92.6 189.0 296.5 390.1 500.4 590.6 695.6 794.6 888.2 998.5 1092.1 1200.0 702.0 : 96.4 203.9 297.5 407.8 498.0 603.0 702.0 795.6 905.9 999.5 1107.4 1200.0 798.4 : 107.5 201.1 311.4 401.6 506.6 605.5 699.1 809.4 903.0 1011.0 1103.6 1200.0 905.9 : 93.6 203.9 294.1 399.1 498.0 591.6 702.0 795.6 903.5 996.1 1092.5 1200.0 999.5 : 110.3 200.5 305.5 404.4 498.0 608.4 702.0 809.9 902.5 998.9 1106.4 1200.0 1109.8: 90.2 195.2 294.1 387.7 498.0 591.6 699.6 792.2 888.6 996.1 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: 189.0495 .. 203.9100 cents 117/116, 14.8605 cents 1102/1053, 78.7425 cents 3: 294.1350 .. 311.8406 cents 2457/2432, 17.7056 cents 256/243, 90.2250 cents 4: 387.7380 .. 407.8200 cents 19683/19456, 20.0820 cents 23104/22113, 75.8975 cents 5: 498.0450 .. 506.5523 cents 204/203, 8.5073 cents 256/243, 90.2250 cents 6: 590.6464 .. 609.3536 cents 8281/8192, 18.7071 cents 232/221, 84.0941 cents 7: 693.4477 .. 701.9550 cents 204/203, 8.5073 cents 232/221, 84.0941 cents 8: 792.1800 .. 812.2620 cents 19683/19456, 20.0820 cents 256/243, 90.2250 cents 9: 888.1594 .. 905.8650 cents 2457/2432, 17.7056 cents 23104/22113, 75.8975 cents 10: 996.0900 .. 1010.9505 cents 117/116, 14.8605 cents 256/243, 90.2250 cents 11: 1089.6930 .. 1109.7750 cents 19683/19456, 20.0820 cents 1102/1053, 78.7425 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 : 97.70135 cents, amount: 0 Most common interval of one step : 19/18, 93.6030 cents, amount: 3 Least squares average step : 100.39343 cents, oct.: 1204.72119 cents Scale is strictly proper Step pattern alph. order: ABCDCEFGHCDI Step pattern size order : FECICHBDGCIA Scale is a Constant Structure, by a margin of 75.89746 cents Scale diversity : 1.126875 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.849015 Rothenberg efficiency : 0.248169 redundancy: 0.751831 Efficiency x scale size : 2.978030 Number of different interval sizes : 86 = 7.81818 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 7.81818 = 86/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 18473/18468, 0.4686 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 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 6 different sizes of fifth Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Length of longest harmonic part : 3 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 20.0820 cents: 1 2 3 5 7 8 10 Limited inverse transpositions with margin 20.0820 cents: 1 2 4 6 7 9 11 -- Rational properties -- Prime limit : 29 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.005812 Average absolute harmonicity : 0.143858 Specific harmonicity : 0.053534 Fundamental : 1/128, -7.0000 octaves, 2.0439 Hz. Guide tone : 414264942, 28.6260 octaves, 108382299635.136 Hz. Exponens Consonantiae : 5.302591E+10, 35.62598 octaves Euler's gradus suavitatis : 99 Sum of Mann's harmonic distance : 763.0, average 63.58333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.92143, average 1.49345 Sum of Tenney's harmonic distance : 34.47808, average 2.87317 Vogel's harmonic complexity : 17.91667 Wille's k value : 121 Wilson's harmonic complexity : 100 Rectangular lattice diameter : 10 Triangular lattice diameter : 5 Lattice compactness : 328.61804, average 4.21305 Lattice compactness (without 2's) : 181.29281, average 2.32427 Number of different primes : 7 Prime exponents' range, average, count, tones@limit: 2: -7 .. 1 -4.41667 55 1 3: 0 .. 5 1.50000 18 5 7: 0 .. 1 0.16667 2 13: 0 .. 1 0.08333 1 1 17: 0 .. 1 0.08333 1 1 19: 0 .. 1 0.25000 3 3 29: 0 .. 1 0.08333 1 1 Average exponent except 2's : 26 / 12 = 2.16667 Average absolute exponent except 2's: 26 / 12 = 2.16667 Scale is JI-epimorphic with val: <12 19 32 46 49 51 60| Scale is JI-epimorphic with val: <12 19 33 45 49 51 59| Scale is JI-epimorphic with val: <12 19 34 44 49 51 58| = patent Scale is weakly epimorphic with val: <12 19 34 46 49 51 56| Scale is JI-epimorphic with val: <12 19 35 43 49 51 57| Scale is weakly epimorphic with val: <12 19 35 45 49 51 55| Scale is JI-epimorphic with val: <12 19 36 42 49 51 56|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.2702 c. M: 9.7750 c. Twelve-tone Chromatic (1/11-comma) 41: 4 3 3 4 3 4 3 3 4 3 4 3 SP M ME SD: 5.0934 c. M:-12.1178 c. 53: 5 4 4 5 4 5 4 4 5 4 5 4 SP M ME SD: 3.4054 c. M:-8.2521 c. 65: 6 5 5 6 5 6 5 5 6 5 6 5 SP M ME SD: 2.6442 c. M:-5.8138 c. 77: 7 6 6 7 6 7 6 6 7 6 7 6 SP M ME SD: 2.4124 c. M:-4.1355 c. 89: 8 7 7 8 7 8 7 7 8 7 8 7 SP M ME SD: 2.4480 c. M: 4.1570 c. 118: 10 10 9 11 9 11 9 9 11 9 11 9 SP D3 S SD: 2.3543 c. M: 5.1828 c. 130: 11 11 10 12 10 12 10 10 12 10 12 10 SP D3 S SD: 2.2689 c. M: 4.5569 c. 132: 12 10 11 12 10 12 10 11 12 10 12 10 SP T3 SD: 2.2326 c. M:-4.1355 c. 134: 12 11 10 13 10 12 10 11 12 11 12 10 SP SD: 2.2397 c. M:-4.1203 c. 137: 12 11 11 13 10 13 10 11 12 11 13 10 SP SD: 2.3188 c. M:-3.8588 c. 138: 12 11 11 13 11 12 11 11 12 11 13 10 SP SD: 2.0497 c. M: 3.9100 c. 142: 12 12 11 13 11 13 11 11 13 11 13 11 SP D3 S SD: 2.2800 c. M: 4.0369 c. 144: 13 11 12 13 11 13 11 12 13 11 13 11 SP T3 SD: 2.0623 c. M: 3.9100 c. 146: 13 12 11 14 11 13 11 12 13 12 13 11 SP SD: 1.9580 c. M: 3.3249 c. 150: 13 12 12 14 12 13 12 12 13 12 14 11 SP SD: 1.8806 c. M: 3.9100 c. 158: 14 13 12 15 12 14 12 13 14 13 14 12 SP SD: 1.8055 c. M: 3.2208 c. 159: 14 13 12 15 12 15 12 13 14 12 15 12 SP SD: 1.7960 c. M: 3.3098 c. 161: 14 13 13 15 12 15 12 13 15 12 15 12 SP SD: 1.7194 c. M:-3.4518 c. 167: 15 13 13 16 13 15 13 13 15 13 15 13 SP SD: 1.9970 c. M: 3.1882 c. 168: 15 14 13 15 13 15 13 14 15 13 15 13 SP D3 SD: 1.9150 c. M:-3.2329 c. 171: 15 14 13 16 13 16 13 14 15 13 16 13 SP SD: 1.6557 c. M: 3.1774 c. 173: 15 14 14 16 13 16 13 14 16 13 16 13 SP SD: 1.4944 c. M:-2.8055 c. 185: 16 15 15 17 14 17 14 15 17 14 17 14 SP SD: 1.3785 c. M: 2.8289 c. 197: 17 16 16 18 15 18 15 16 18 15 18 15 SP SD: 1.3549 c. M: 2.8948 c. 201: 18 16 16 18 16 18 16 16 18 15 19 15 SP SD: 1.5720 c. M:-2.5226 c. 203: 18 16 16 19 16 18 16 16 18 16 19 15 SP SD: 1.3786 c. M: 2.9248 c. 204: 18 17 16 18 16 19 15 17 18 16 19 15 SP SD: 1.6619 c. M:-2.4870 c. 205: 18 17 16 19 16 18 16 17 18 16 19 15 SP SD: 1.6648 c. M:-3.5481 c. 209: 18 17 17 19 16 19 16 17 19 16 19 16 SP SD: 1.3986 c. M: 2.9531 c. 213: 19 17 17 19 17 19 17 17 19 16 20 16 SP SD: 1.4896 c. M: 2.2849 c. 215: 19 18 16 20 17 19 17 17 19 17 20 16 SP SD: 1.2368 c. M:-2.6016 c. 217: 19 18 17 20 17 19 17 17 20 17 20 16 SP SD: 1.2513 c. M: 2.0897 c. 227: 20 19 17 21 18 20 18 18 20 18 21 17 SP SD: 1.1643 c. M:-2.2574 c. 229: 20 19 18 21 18 20 18 18 21 18 21 17 SP SD: 1.1086 c. M: 1.8966 c. 241: 21 20 19 22 19 21 19 19 22 19 22 18 SP SD: 1.0429 c. M: 1.8847 c. 258: 23 21 20 24 20 23 20 21 23 20 24 19 SP SD: 1.1297 c. M:-2.0213 c. 265: 23 22 21 24 21 24 20 21 24 21 24 20 SP SD: 0.9904 c. M:-1.9672 c. 270: 24 22 21 25 21 24 21 22 24 21 25 20 SP SD: 0.9405 c. M:-1.7113 c. 277: 24 23 22 25 22 25 21 22 25 22 25 21 SP SD: 0.9494 c. M:-1.4768 c. 282: 25 23 22 26 22 25 22 23 25 22 26 21 SP SD: 0.8086 c. M:-1.5969 c. 289: 25 24 23 26 23 26 22 23 26 23 26 22 SP SD: 0.9629 c. M:-1.4489 c. 294: 26 24 23 27 23 26 23 24 26 23 27 22 SP SD: 0.7415 c. M:-1.5969 c. 306: 27 25 24 28 24 27 24 25 27 24 28 23 SP SD: 0.7383 c. M:-1.5969 c. 311: 27 26 24 29 24 28 24 25 28 24 29 23 SP SD: 0.6957 c. M:-1.4790 c. 323: 28 27 25 30 25 29 25 26 29 25 30 24 SP SD: 0.5468 c. M:-1.0609 c. 335: 29 28 26 31 26 30 26 27 30 26 31 25 SP SD: 0.4583 c. M: 1.0748 c. 347: 30 29 27 32 27 31 27 28 31 27 32 26 SP SD: 0.4460 c. M: 1.2090 c. 376: 33 31 29 35 29 34 29 30 34 29 35 28 SP SD: 0.5009 c. M:-0.8633 c. 388: 34 32 30 36 30 35 30 31 35 30 36 29 SP SD: 0.3718 c. M: 0.6058 c. 400: 35 33 31 37 31 36 31 32 36 31 37 30 SP SD: 0.2975 c. M: 0.5130 c. 412: 36 34 32 38 32 37 32 33 37 32 38 31 SP SD: 0.3022 c. M: 0.6157 c. 718: 63 59 56 66 56 65 55 58 64 56 66 54 SP SD: 0.2590 c. M:-0.6743 c. 730: 64 60 57 67 57 66 56 59 65 57 67 55 SP SD: 0.2332 c. M:-0.5094 c. 735: 64 61 57 68 57 66 57 59 66 57 68 55 SP SD: 0.2916 c. M: 0.4656 c. 742: 65 61 58 68 58 67 57 60 66 58 68 56 SP SD: 0.2388 c. M:-0.5187 c. 935: 82 77 73 86 73 84 72 75 84 73 86 70 SP SD: 0.2599 c. M:-0.3952 c. 947: 83 78 74 87 74 85 73 76 85 74 87 71 SP SD: 0.2117 c. M:-0.3721 c. 959: 84 79 75 88 75 86 74 77 86 75 88 72 SP SD: 0.1786 c. M:-0.3497 c. 971: 85 80 76 89 76 87 75 78 87 76 89 73 SP SD: 0.1676 c. M:-0.3278 c. 1065: 93 88 83 98 83 96 82 86 95 83 98 80 SP SD: 0.1628 c. M:-0.4701 c. 1077: 94 89 84 99 84 97 83 87 96 84 99 81 SP SD: 0.1577 c. M:-0.4827 c. 1118: 98 92 87 103 87 101 86 90 100 87 103 84 SP SD: 0.1544 c. M:-0.3065 c. 1130: 99 93 88 104 88 102 87 91 101 88 104 85 SP SD: 0.1299 c. M:-0.2040 c. 1142: 100 94 89 105 89 103 88 92 102 89 105 86 SP SD: 0.1278 c. M: 0.1971 c. 1347: 118 111 105 124 105 121 104 108 121 105 124 101 SP SD: 0.1366 c. M:-0.2473 c. 1359: 119 112 106 125 106 122 105 109 122 106 125 102 SP SD: 0.1050 c. M: 0.1691 c. 1371: 120 113 107 126 107 123 106 110 123 107 126 103 SP SD: 0.0888 c. M: 0.1632 c. 2077: 182 171 162 191 162 187 160 167 186 162 191 156 SP SD: 0.0922 c. M:-0.1963 c. 2089: 183 172 163 192 163 188 161 168 187 163 192 157 SP SD: 0.0704 c. M:-0.1667 c. 2101: 184 173 164 193 164 189 162 169 188 164 193 158 SP SD: 0.0573 c. M:-0.1374 c. 2113: 185 174 165 194 165 190 163 170 189 165 194 159 SP SD: 0.0587 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: 8.0282 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.4115 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.0338 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.7852 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.1485 cents 10 x 11:12:13 x 14:15:16:17:18:19:20 S SD: 7.3774 cents 11:12 x 13:14:15:16 x 17:19:20:21:22 SD: 10.0225 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.9381 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.9092 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.3223 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.6507 cents 16:17:18:19:20:21:23:24:25:27:29:30:32 SD: 5.1322 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.9588 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.1558 cents 30:32:34:36:38:40:43:45:48:51:53:57:60 SD: 3.0570 cents 31:33:35:37:39:41:44:47:49:52:55:59:62 SD: 2.7592 cents 32:34:36:38:41:43:46:48:51:54:57:61:64 SD: 2.6797 cents 33:35:37:39:42:44:47:50:52:56:59:63:66 SD: 2.4752 cents 38:40:43:45:48:51:54:57:60:64:68:72:76 SD: 2.0528 cents 42:45:47:50:53:56:60:63:67:71:75:80:84 SD: 2.0074 cents 48:51:54:57:61:64:68:72:76:81:86:91:96 SD: 1.2303 cents 78:83:88:93:99:104:111:117:124:132:139:148:156 SD: 1.0565 cents 80:85:90:95:101:107:114:120:127:135:143:152:160 SD: 0.7386 cents 112:119:126:133:142:150:159:168:178:189:200:213:224 SD: 0.7308 cents 128:136:144:152:162:171:182:192:203:216:228:243:256 SD: 0.0000 cents