Scala analysis: coll7
Seven note Collatz cycle scale, -17 starting point
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 37/34 146.388629 2: 41/34 324.106996 3: 91/68 504.398159 4: 25/17 667.672018 5: 55/34 832.676247 6: 61/34 1011.929396 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 68/61 188.0706 1: 37/34 146.3886 2: 41/37 177.7184 3: 91/82 180.2912 4: 100/91 163.2739 5: 11/10 165.0042 Ptolemy's second, 4/5-tone 6: 61/55 179.2531 7: 68/61 188.0706
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 37/34 146.389 cents 1: 1 100/91 163.274 cents 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 41/37 177.718 cents 1: 1 61/55 179.253 cents 1: 1 91/82 180.291 cents 1: 1 68/61 188.071 cents 2: 1 41/34 324.107 cents 2: 1 110/91 328.278 cents 2: 1 74/61 334.459 cents 2: 1 50/41 343.565 cents 2: 1 61/50 344.257 cents 2: 1 91/74 358.010 cents 2: 1 68/55 367.324 cents 3: 1 91/68 504.398 cents 3: 1 122/91 507.531 cents 3: 1 55/41 508.569 cents 3: 1 82/61 512.178 cents 3: 1 74/55 513.712 cents 3: 1 50/37 521.283 cents 3: 1 34/25 532.328 cents 4: 1 25/17 667.672 cents 4: 1 37/25 678.717 cents 4: 1 55/37 686.288 cents 4: 1 61/41 687.822 cents 4: 1 82/55 691.431 cents 4: 1 91/61 692.469 cents 4: 1 136/91 695.602 cents 5: 1 55/34 832.676 cents 5: 1 148/91 841.990 cents 5: 1 100/61 855.743 cents 5: 1 41/25 856.435 cents 5: 1 61/37 865.541 cents 5: 1 91/55 871.722 cents 5: 1 68/41 875.893 cents 6: 1 61/34 1011.929 cents 6: 1 164/91 1019.709 cents 6: 1 110/61 1020.747 cents 6: 1 74/41 1022.282 cents 6: 1 20/11 1034.996 cents large minor seventh 6: 1 91/50 1036.726 cents 6: 1 68/37 1053.611 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 146.4 324.1 504.4 667.7 832.7 1011.9 1200.0 146.4 : 177.7 358.0 521.3 686.3 865.5 1053.6 1200.0 324.1 : 180.3 343.6 508.6 687.8 875.9 1022.3 1200.0 504.4 : 163.3 328.3 507.5 695.6 842.0 1019.7 1200.0 667.7 : 165.0 344.3 532.3 678.7 856.4 1036.7 1200.0 832.7 : 179.3 367.3 513.7 691.4 871.7 1035.0 1200.0 1011.9: 188.1 334.5 512.2 692.5 855.7 1020.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 146.3886 .. 188.0706 cents 2312/2257, 41.6820 cents 37/34, 146.3886 cents 2: 324.1070 .. 367.3238 cents 2312/2255, 43.2168 cents 2501/2312, 136.0364 cents 3: 504.3982 .. 532.3280 cents 2312/2275, 27.9298 cents 5005/4624, 137.0744 cents 4: 667.6720 .. 695.6018 cents 2312/2275, 27.9298 cents 625/578, 135.3440 cents 5: 832.6762 .. 875.8930 cents 2312/2255, 43.2168 cents 5005/4624, 137.0744 cents 6: 1011.9294 .. 1053.6114 cents 2312/2257, 41.6820 cents 2501/2312, 136.0364 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 37/34, 146.3886 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 68/61, 188.0706 cents Average / Smallest step : 1.171051 Largest / Average step : 1.097079 Largest / Smallest step : 1.284735 Median interval of one step : 41/37, 177.7184 cents, amount: 1 Least squares average step : 168.66745 cents, oct.: 1180.67214 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : ADFBCEG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 135.34404 cents Scale diversity : 1.205031 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.811952 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 2501/2500, 0.6924 cents Number of recognisable fifths : 5, average 690.7223 cents Number of appreciable fifths : 3, average 693.1671 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited transpositions with margin 43.2168 cents: 3 4 Limited inverse transpositions with margin 39.0457 cents: 1 4 5 -- Rational properties -- Prime limit : 61 Odd number limit : 91 (O: 91 U: 91) Highest odd numerator or denominator: 91 Scale harmonicity : 0.010359 Fundamental : 1/68, -6.0875 octaves, 3.8474 Hz. Guide tone : too high to compute Exponens Consonantiae : 3.149404E+11, 38.19629 octaves Euler's gradus suavitatis : 192 Sum of Mann's harmonic distance : 267.0, average 38.14286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.06366, average 1.43767 Sum of Tenney's harmonic distance : 19.55356, average 2.79337 Vogel's harmonic complexity : 30.14286 Wille's k value : 45 Wilson's harmonic complexity : 197 Rectangular lattice diameter : 9 Triangular lattice diameter : 2 Lattice compactness : 50.66940, average 1.80962 Lattice compactness (without 2's) : 37.74932, average 1.34819 Number of different primes : 9 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.71429 7 1 5: 0 .. 2 0.42857 3 7: 0 .. 1 0.14286 1 11: 0 .. 1 0.14286 1 13: 0 .. 1 0.14286 1 17: -1 .. 0 -0.85714 6 3 37: 0 .. 1 0.14286 1 1 41: 0 .. 1 0.14286 1 1 61: 0 .. 1 0.14286 1 1 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is JI-epimorphic with val: <7 16 20 24 25 28 36 37 41| Scale is weakly epimorphic with val: <7 16 20 24 25 29 35 37 41| Scale is weakly epimorphic with val: <7 16 20 25 27 28 37 38 43| Scale is weakly epimorphic with val: <7 16 20 25 27 29 37 38 42| Scale is weakly epimorphic with val: <7 16 20 25 27 30 35 38 43| Scale is weakly epimorphic with val: <7 16 20 25 27 30 36 38 42|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 18.0374 c. M:-25.0399 c. Lebeng 19: 2 3 3 2 3 3 3 SP M ME S SD: 16.5298 c. M: 36.0931 c. Nineteen-tone Locrian 23: 3 3 4 3 3 3 4 SP M ME S SD: 12.3505 c. M: 20.6250 c. 25: 3 4 4 3 3 4 4 SP D3 S SD: 12.0503 c. M:-23.6018 c. 26: 3 4 4 3 4 4 4 SP M ME S SD: 8.8911 c. M: 21.5182 c. 27: 3 4 4 4 4 4 4 SP M ME S SD: 10.8583 c. M: 15.5093 c. 30: 4 4 5 4 4 4 5 SP M ME S SD: 10.6468 c. M:-15.6018 c. 32: 4 5 4 5 4 5 5 SP M ME S SD: 9.1878 c. M: 16.8982 c. 33: 4 5 5 4 5 5 5 SP M ME S SD: 6.0700 c. M: 13.1266 c. 36: 4 6 5 5 5 5 6 SP D3 S SD: 7.7336 c. M: 13.0553 c. 40: 5 6 6 5 6 6 6 SP M ME S SD: 6.0567 c. M:-8.0706 c. 43: 5 7 6 6 6 6 7 SP D3 S SD: 5.9199 c. M:-10.7767 c. 45: 5 7 7 6 6 7 7 SP D3 S SD: 5.7514 c. M: 13.0553 c. 52: 6 8 8 7 7 8 8 SP D3 S SD: 3.6402 c. M: 7.9271 c. 58: 7 9 8 8 8 9 9 SP T3 SD: 4.9680 c. M: 7.8464 c. 59: 7 9 9 8 8 9 9 SP D3 S SD: 3.2408 c. M:-5.0198 c. 81: 10 12 12 11 11 12 13 SP SD: 2.3185 c. M: 4.5220 c. 84: 10 13 12 12 11 13 13 SP SD: 3.5509 c. M:-4.4644 c. 85: 10 13 13 11 12 13 13 SP SD: 3.3828 c. M: 5.2122 c. 88: 11 13 13 12 12 13 14 SP SD: 2.1427 c. M:-3.6114 c. 108: 13 16 16 15 15 16 17 SP SD: 2.0280 c. M: 4.3982 c. 115: 14 17 17 16 16 17 18 SP SD: 1.5792 c. M: 3.5286 c. 121: 15 18 18 16 17 18 19 SP SD: 2.0051 c. M: 3.2092 c. 122: 15 18 18 17 17 18 19 SP SD: 1.8306 c. M:-3.3893 c. 133: 16 20 20 18 18 20 21 SP SD: 1.4188 c. M: 2.6011 c. 140: 17 21 21 19 19 21 22 SP SD: 1.0273 c. M:-1.6073 c. 212: 26 31 32 29 29 32 33 SP SD: 0.8624 c. M: 1.4655 c. 223: 27 33 34 30 31 33 35 SP SD: 0.9996 c. M:-1.4314 c. 241: 29 36 36 33 33 36 38 SP SD: 1.1469 c. M: 1.9903 c. 245: 30 36 37 33 34 37 38 SP SD: 1.0153 c. M:-1.9482 c. 248: 30 37 37 34 34 37 39 SP SD: 0.7047 c. M: 1.2273 c. 255: 31 38 38 35 35 38 40 SP SD: 0.5049 c. M: 0.8687 c. 352: 43 52 53 48 48 53 55 SP SD: 0.4541 c. M: 0.8581 c. 460: 56 68 69 63 63 69 72 SP SD: 0.4882 c. M: 0.9199 c. 467: 57 69 70 64 64 70 73 SP SD: 0.4018 c. M: 0.7579 c. 473: 58 70 71 64 65 71 74 SP SD: 0.5047 c. M:-0.7572 c. 474: 58 70 71 65 65 71 74 SP SD: 0.4804 c. M:-0.7288 c. 478: 58 71 72 65 66 71 75 SP SD: 0.4491 c. M:-0.7966 c. 500: 61 74 75 68 69 75 78 SP SD: 0.4082 c. M:-0.8706 c. 516: 63 76 78 70 71 77 81 SP SD: 0.3706 c. M: 0.8512 c. 523: 64 77 79 71 72 78 82 SP SD: 0.3276 c. M: 0.5888 c. 581: 71 86 87 79 80 87 91 SP SD: 0.3158 c. M: 0.5464 c. 607: 74 90 91 83 83 91 95 SP SD: 0.2929 c. M:-0.5323 c. 633: 77 94 95 86 87 95 99 SP SD: 0.3141 c. M: 0.4488 c. 640: 78 95 96 87 88 96 100 SP SD: 0.2613 c. M:-0.5706 c. 663: 81 98 100 90 91 99 104 SP SD: 0.2607 c. M:-0.5792 c. 764: 93 113 115 104 105 114 120 SP SD: 0.3106 c. M: 0.5468 c. 771: 94 114 116 105 106 115 121 SP SD: 0.1797 c. M: 0.3716 c. 778: 95 115 117 106 107 116 122 SP SD: 0.1518 c. M:-0.2286 c. 918: 112 136 138 125 126 137 144 SP SD: 0.1491 c. M:-0.3018 c. 1163: 142 172 175 158 160 174 182 SP SD: 0.1425 c. M:-0.2804 c. 1199: 146 178 180 163 165 179 188 SP SD: 0.1306 c. M: 0.2669 c. 1206: 147 179 181 164 166 180 189 SP SD: 0.1309 c. M:-0.2711 c. 1352: 165 200 203 184 186 202 212 SP SD: 0.1526 c. M: 0.2561 c. 1359: 166 201 204 185 187 203 213 SP SD: 0.1163 c. M: 0.2039 c. 1411: 172 209 212 192 194 211 221 SP SD: 0.0825 c. M:-0.1188 c. 1418: 173 210 213 193 195 212 222 SP SD: 0.0794 c. M:-0.2004 c. 1722: 210 255 259 234 237 257 270 SP SD: 0.0777 c. M:-0.1315 c. 1977: 241 293 297 269 272 295 310 SP SD: 0.0661 c. M: 0.1064 c. 2189: 267 324 329 298 301 327 343 SP SD: 0.0568 c. M: 0.1234 c. 2270: 277 336 341 309 312 339 356 SP SD: 0.0682 c. M: 0.1232 c. 2277: 278 337 342 310 313 340 357 SP SD: 0.0591 c. M:-0.1199 c. 2329: 284 345 350 317 320 348 365 SP SD: 0.0436 c. M:-0.0824 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 17.1415 cents 3 x x 4 x 5 x 6 S SD: 17.3572 cents 4 x 5 x 6 x 7:8 S SD: 20.7709 cents 5 x 6:7 x 8:9:10 S SD: 16.2064 cents 6 x 7:8:9:10:11:12 S SD: 15.4237 cents 7:8 x 9:10:11:13:14 SD: 23.9227 cents 8:9:10:11:12:13:14:16 S SD: 15.9558 cents 9:10:11:12:13:15:16:18 SD: 10.8484 cents 10:11:12:13:15:16:18:20 SD: 9.5882 cents 11:12:13:15:16:18:20:22 SD: 8.5534 cents 14:15:17:19:21:23:25:28 SD: 8.3528 cents 15:16:18:20:22:24:27:30 S SD: 5.9372 cents 20:22:24:27:29:32:36:40 SD: 5.7788 cents 21:23:25:28:31:34:38:42 SD: 4.3423 cents 23:25:28:31:34:37:41:46 SD: 3.8465 cents 24:26:29:32:35:39:43:48 SD: 2.8246 cents 34:37:41:46:50:55:61:68 SD: 2.7030 cents 44:48:53:59:65:71:79:88 SD: 1.5350 cents 68:74:82:91:100:110:122:136 SD: 0.0000 cents