Scala analysis: China_Flute_88
88 (Flute), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 203.000 cents 203.000000 2: 400.000 cents 400.000000 3: 704.000 cents 704.000000 4: 905.000 cents 905.000000 5: 1200.000 cents 1200.000000 6: 1605.000 cents 1605.000000
SHOW/INTERVAL
0: 405.0000 cents 405.0000 1: 203.0000 cents 203.0000 2: 197.0000 cents 197.0000 3: 304.0000 cents 304.0000 4: 201.0000 cents 201.0000 5: 295.0000 cents 295.0000 6: 405.0000 cents 405.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 197.00000 cents 1: 1 201.00000 cents 1: 1 203.00000 cents 1: 1 295.00000 cents 1: 1 304.00000 cents 1: 1 405.00000 cents 2: 1 400.00000 cents 2: 1 496.00000 cents 2: 1 501.00000 cents 2: 1 505.00000 cents 2: 1 608.00000 cents 2: 1 700.00000 cents 3: 1 702.00000 cents 3: 1 704.00000 cents 3: 1 800.00000 cents 3: 1 805.00000 cents 3: 1 901.00000 cents 3: 1 903.00000 cents 4: 1 905.00000 cents 4: 1 997.00000 cents 4: 1 1100.00000 cents 4: 1 1104.00000 cents 4: 1 1109.00000 cents 4: 1 1205.00000 cents 5: 1 1200.00000 cents 5: 1 1301.00000 cents 5: 1 1310.00000 cents 5: 1 1402.00000 cents 5: 1 1404.00000 cents 5: 1 1408.00000 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 203.0 400.0 704.0 905.0 1200.0 1605.0 203.0 : 197.0 501.0 702.0 997.0 1402.0 1605.0 400.0 : 304.0 505.0 800.0 1205.0 1408.0 1605.0 704.0 : 201.0 496.0 901.0 1104.0 1301.0 1605.0 905.0 : 295.0 700.0 903.0 1100.0 1404.0 1605.0 1200.0: 405.0 608.0 805.0 1109.0 1310.0 1605.0 1605.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 197.0000 .. 405.0000 cents 208.00000 cents 197.00000 cents 2: 400.0000 .. 700.0000 cents 300.00000 cents -5.00000 cents 3: 702.0000 .. 903.0000 cents 201.00000 cents 2.00000 cents 4: 905.0000 .. 1205.0000 cents 300.00000 cents 2.00000 cents 5: 1200.0000 .. 1408.0000 cents 208.00000 cents -5.00000 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 197.00000 cents, class 1 Average step (divided formal octave): 267.5000 cents Largest one step interval : 405.00000 cents Average / Smallest step : 1.357868 Largest / Average step : 1.514019 Largest / Smallest step : 2.055838 Median interval of one step : 249.00000 cents, amount: 0 Least squares average step : 245.76923 cents, oct.: 1474.61538 cents Scale is not proper Scale is a mode of a 1605-tone equal temperament with octave 1605.000 cents degrees: 203 400 704 905 1200 1605 Least number of segments generator : 803 of 803.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1304 of 1304.000 cents and inv. generated superset size: 99 = 93 more = 1650.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEF Step pattern size order : CAEBDF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.00000 cents Scale diversity : 0.732508 Lumma stability : 0.247975 Lumma impropriety factor : 0.006231 Rothenberg efficiency : 0.333333 redundancy: 0.666667 Efficiency x scale size : 2.000000 Number of different interval sizes : 30 = 6.00000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 6.00000 = 6 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 2.00000 cents Number of recognisable fifths : 3, average 702.0000 cents Number of recognisable fourths : 3, average 500.6667 cents Formal octave complements present : 1 = 16.6667% 2/1 octave complements present : 1 = 16.6667% -- Rational properties --
FIT/MODE
6: 0 1 1 1 1 2 N T3 SD: 138.2826 c. M: 203.0000 c. 7: 1 1 1 1 1 2 P M ME SD: 35.1176 c. M:-58.5714 c. 9: 1 1 2 1 2 2 P D3 SD: 29.1182 c. M:-48.3333 c. 16: 2 2 3 2 3 4 P SD: 2.2112 c. M:-3.7500 c. 135: 17 17 25 17 25 34 P SD: 2.1540 c. M:-4.2222 c. 151: 19 19 28 19 28 38 P SD: 2.0821 c. M:-3.9073 c. 165: 21 20 31 21 30 42 N SD: 2.1963 c. M: 3.6364 c. 167: 21 21 31 21 31 42 P SD: 2.0362 c. M:-3.6527 c. 169: 21 21 32 21 31 43 N SD: 2.3996 c. M: 3.5621 c. 173: 22 21 33 22 31 44 N SD: 2.2876 c. M:-4.1908 c. 174: 22 21 33 22 32 44 N SD: 1.9112 c. M: 3.3621 c. 182: 23 22 35 23 33 46 N SD: 1.9887 c. M:-3.3242 c. 185: 23 23 35 23 34 47 N SD: 2.2165 c. M: 3.4595 c. 189: 24 23 36 24 34 48 N SD: 1.9284 c. M:-3.6508 c. 190: 24 23 36 24 35 48 N SD: 1.7628 c. M: 2.9737 c. 197: 25 24 37 25 36 50 N SD: 1.7438 c. M: 3.3401 c. 198: 25 24 38 25 36 50 N SD: 1.7255 c. M:-2.8788 c. 205: 26 25 39 26 37 52 N SD: 1.6293 c. M:-3.1951 c. 206: 26 25 39 26 38 52 N SD: 1.6553 c. M: 2.7864 c. 213: 27 26 40 27 39 54 N SD: 1.5929 c. M: 3.2254 c. 214: 27 26 41 27 39 54 N SD: 1.5138 c. M: 2.5000 c. 221: 28 27 42 28 40 56 N SD: 1.3784 c. M:-2.8054 c. 222: 28 27 42 28 41 56 N SD: 1.5790 c. M: 2.7162 c. 229: 29 28 43 29 42 58 N SD: 1.4790 c. M: 3.1266 c. 230: 29 28 44 29 42 58 N SD: 1.3449 c. M: 2.2391 c. 237: 30 29 45 30 43 60 N SD: 1.1673 c. M:-2.4684 c. 245: 31 30 46 31 45 62 N SD: 1.3950 c. M: 3.0408 c. 246: 31 30 47 31 45 62 N SD: 1.2121 c. M: 2.0122 c. 253: 32 31 48 32 46 64 N SD: 0.9902 c. M:-2.1739 c. 262: 33 32 50 33 48 66 N SD: 1.1105 c. M: 1.8130 c. 269: 34 33 51 34 49 68 N SD: 0.8437 c. M:-1.9145 c. 278: 35 34 53 35 51 70 N SD: 1.0356 c. M: 1.6367 c. 285: 36 35 54 36 52 72 N SD: 0.7255 c. M:-1.6842 c. 294: 37 36 56 37 54 74 N SD: 0.9836 c. M: 1.4796 c. 301: 38 37 57 38 55 76 N SD: 0.6347 c. M:-1.4784 c. 310: 39 38 59 39 57 78 N SD: 0.9508 c. M: 1.3387 c. 317: 40 39 60 40 58 80 N SD: 0.5709 c. M:-1.2934 c. 326: 41 40 62 41 60 82 N SD: 0.9336 c. M:-1.2883 c. 333: 42 41 63 42 61 84 N SD: 0.5330 c. M:-1.1261 c. 349: 44 43 66 44 64 88 N SD: 0.5186 c. M:-0.9742 c. 365: 46 45 69 46 67 92 N SD: 0.5235 c. M:-0.8356 c. 381: 48 47 72 48 70 96 N SD: 0.5429 c. M: 0.7953 c. 401: 51 49 76 50 74 101 N SD: 0.6158 c. M:-1.1272 c. 413: 52 51 78 52 76 104 N SD: 0.6069 c. M: 0.9177 c. 417: 53 51 79 52 77 105 N SD: 0.6044 c. M:-0.9928 c. 506: 64 62 96 63 93 128 N SD: 0.5991 c. M: 1.0079 c. 522: 66 64 99 65 96 132 N SD: 0.5646 c. M: 1.0345 c. 538: 68 66 102 67 99 136 N SD: 0.5397 c. M: 1.0688 c. 554: 70 68 105 69 102 140 N SD: 0.5240 c. M: 1.1011 c. 570: 72 70 108 71 105 144 N SD: 0.5167 c. M: 1.1316 c. 591: 75 72 112 74 109 149 N SD: 0.5821 c. M: 0.7868 c. 594: 75 73 113 74 109 150 N SD: 0.5417 c. M:-1.2273 c. 599: 76 73 114 75 110 151 N SD: 0.5874 c. M: 0.7596 c. 602: 76 74 114 75 111 152 N SD: 0.5231 c. M: 1.1877 c. 607: 77 74 115 76 112 153 N SD: 0.5795 c. M: 0.7331 c. 610: 77 75 116 76 112 154 N SD: 0.5057 c. M:-1.1475 c. 615: 78 75 117 77 113 155 N SD: 0.5474 c. M: 0.7073 c. 618: 78 76 117 77 114 156 N SD: 0.5346 c. M: 1.2136 c. 622: 79 76 118 78 114 157 N SD: 0.4915 c. M:-0.8505 c. 626: 79 77 119 78 115 158 N SD: 0.4773 c. M:-1.0719 c. 631: 80 77 120 79 116 159 N SD: 0.5144 c. M: 0.6577 c. 638: 81 78 121 80 117 161 N SD: 0.4391 c. M:-0.7696 c. 647: 82 79 123 81 119 163 N SD: 0.4884 c. M:-0.6491 c. 654: 83 80 124 82 120 165 N SD: 0.3928 c. M:-0.6927 c. 670: 85 82 127 84 123 169 N SD: 0.3533 c. M:-0.6194 c. 686: 87 84 130 86 126 173 N SD: 0.3212 c. M:-0.5496 c. 702: 89 86 133 88 129 177 N SD: 0.2974 c. M:-0.4829 c. 718: 91 88 136 90 132 181 N SD: 0.2824 c. M:-0.4192 c. 734: 93 90 139 92 135 185 N SD: 0.2764 c. M:-0.4700 c. 839: 106 103 159 105 154 212 N SD: 0.2631 c. M: 0.5542 c. 855: 108 105 162 107 157 216 N SD: 0.2445 c. M: 0.4737 c. 871: 110 107 165 109 160 220 N SD: 0.2329 c. M: 0.3961 c. 887: 112 109 168 111 163 224 N SD: 0.2286 c. M: 0.3393 c. 1172: 148 144 222 147 215 296 N SD: 0.2234 c. M: 0.3584 c. 1188: 150 146 225 149 218 300 N SD: 0.2121 c. M: 0.3485 c. 1192: 151 146 226 149 219 301 N SD: 0.2103 c. M:-0.3180 c. 1204: 152 148 228 151 221 304 N SD: 0.2051 c. M: 0.3754 c. 1208: 153 148 229 151 222 305 N SD: 0.1879 c. M:-0.2823 c. 1224: 155 150 232 153 225 309 N SD: 0.1690 c. M:-0.2475 c. 1240: 157 152 235 155 228 313 N SD: 0.1541 c. M: 0.2460 c. 1256: 159 154 238 157 231 317 N SD: 0.1441 c. M: 0.2707 c. 1272: 161 156 241 159 234 321 N SD: 0.1395 c. M: 0.2948 c. 1509: 191 185 286 189 277 381 N SD: 0.1407 c. M: 0.2386 c. 1525: 193 187 289 191 280 385 N SD: 0.1160 c. M: 0.1967 c. 1541: 195 189 292 193 283 389 N SD: 0.0918 c. M: 0.1557 c. 1557: 197 191 295 195 286 393 N SD: 0.0682 c. M: 0.1156 c. 1573: 199 193 298 197 289 397 N SD: 0.0450 c. M: 0.0763 c. 1589: 201 195 301 199 292 401 N SD: 0.0223 c. M: 0.0378 c. 1605: 203 197 304 201 295 405 N SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x 2:3 S SD: 148.4775 cents 2 x x 3 x 4:5 S SD: 6.2660 cents 3 x 4 x 5:6:8 S SD: 34.1836 cents 4 x 5:6:7:8:10 S SD: 13.5859 cents 5 x 6 x 8:10:13 SD: 33.4259 cents 6:7:8:9:10:12:15 S SD: 20.0498 cents 7:8:9:11:12:14:18 SD: 16.5680 cents 8:9:10:12:14:16:20 S SD: 11.3226 cents 14:16:18:21:24:28:35 S SD: 9.3827 cents 15:17:19:23:25:30:38 SD: 7.4782 cents 16:18:20:24:27:32:40 SD: 3.8810 cents 26:29:33:39:44:52:66 SD: 3.5542 cents 32:36:40:48:54:64:81 SD: 2.3631 cents 38:43:48:57:64:76:96 SD: 2.0524 cents 42:47:53:63:71:84:106 SD: 1.6715 cents 57:64:72:86:96:114:144 SD: 1.6436 cents 58:65:73:87:98:116:147 SD: 1.4436 cents 64:72:81:96:108:128:162 SD: 1.4421 cents 66:74:83:99:111:132:167 SD: 1.3778 cents 70:79:88:105:118:140:177 SD: 1.3083 cents 73:82:92:110:123:146:184 SD: 1.3004 cents 74:83:93:111:125:148:187 SD: 1.1589 cents 80:90:101:120:135:160:202 SD: 0.7532 cents 96:108:121:144:162:192:243 SD: 0.6275 cents 112:126:141:168:189:224:283 SD: 0.4617 cents 169:190:213:254:285:338:427 SD: 0.2618 cents 265:298:334:398:447:530:670 SD: 0.1754 cents 281:316:354:422:474:562:710 SD: 0.0761 cents 546:614:688:820:921:1092:1380 SD: 0.0689 cents