Scala analysis: China_Flute_87
87 (Flute), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 315.000 cents 315.000000 2: 525.000 cents 525.000000 3: 822.000 cents 822.000000 4: 1217.000 cents 1217.000000 5: 1700.000 cents 1700.000000
SHOW/INTERVAL
0: 483.0000 cents 483.0000 1: 315.0000 cents 315.0000 2: 210.0000 cents 210.0000 3: 297.0000 cents 297.0000 4: 395.0000 cents 395.0000 5: 483.0000 cents 483.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 210.00000 cents 1: 1 297.00000 cents 1: 1 315.00000 cents 1: 1 395.00000 cents 1: 1 483.00000 cents 2: 1 507.00000 cents 2: 1 525.00000 cents 2: 1 692.00000 cents 2: 1 798.00000 cents 2: 1 878.00000 cents 3: 1 822.00000 cents 3: 1 902.00000 cents 3: 1 1008.00000 cents 3: 1 1175.00000 cents 3: 1 1193.00000 cents 4: 1 1217.00000 cents 4: 1 1305.00000 cents 4: 1 1385.00000 cents 4: 1 1403.00000 cents 4: 1 1490.00000 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 315.0 525.0 822.0 1217.0 1700.0 315.0 : 210.0 507.0 902.0 1385.0 1700.0 525.0 : 297.0 692.0 1175.0 1490.0 1700.0 822.0 : 395.0 878.0 1193.0 1403.0 1700.0 1217.0: 483.0 798.0 1008.0 1305.0 1700.0 1700.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 210.0000 .. 483.0000 cents 273.00000 cents 210.00000 cents 2: 507.0000 .. 878.0000 cents 371.00000 cents 24.00000 cents 3: 822.0000 .. 1193.0000 cents 371.00000 cents -56.00000 cents 4: 1217.0000 .. 1490.0000 cents 273.00000 cents 24.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 210.00000 cents, class 1 Average step (divided formal octave): 340.0000 cents Largest one step interval : 483.00000 cents Average / Smallest step : 1.619048 Largest / Average step : 1.420588 Largest / Smallest step : 2.300000 Median interval of one step : 315.00000 cents, amount: 1 Least squares average step : 312.70909 cents, oct.: 1563.54545 cents Scale is not proper Scale is a mode of a 1700-tone equal temperament with octave 1700.000 cents degrees: 315 525 822 1217 1700 Least number of segments generator : 851 of 851.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 991 of 991.000 cents and inv. generated superset size: 276 = 271 more = 5520.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : CABDE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 24.00000 cents Scale diversity : 0.649626 Lumma stability : 0.275294 Lumma impropriety factor : 0.032941 Rothenberg efficiency : 0.400000 redundancy: 0.600000 Efficiency x scale size : 2.000000 Number of different interval sizes : 20 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 5.00000 = 5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 18.00000 cents Number of recognisable fifths : 1, average 692.0000 cents Number of recognisable fourths : 2, average 495.0000 cents Number of appreciable fourths : 1, average 507.0000 cents Best minor thirds form a closed circle Formal octave complements present : 1 = 20.0000% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
5: 0 1 1 1 2 N T3 SD: 196.1749 c. M: 315.0000 c. 6: 1 1 1 1 2 P M ME S SD: 45.8759 c. M: 83.6667 c. 10: 2 1 2 2 3 P T3 SD: 21.7394 c. M:-28.0000 c. 17: 3 2 3 4 5 N SD: 18.0167 c. M: 25.0000 c. 22: 4 3 4 5 6 P SD: 17.0116 c. M:-28.0000 c. 25: 5 3 4 6 7 N SD: 14.6356 c. M:-25.0000 c. 27: 5 3 5 6 8 N SD: 13.3741 c. M: 21.2963 c. 29: 5 4 5 7 8 N SD: 11.7033 c. M: 21.8966 c. 33: 6 4 6 8 9 N SD: 10.1182 c. M:-19.3636 c. 36: 7 4 6 9 10 N SD: 12.3166 c. M: 19.2222 c. 38: 7 5 6 9 11 N SD: 10.0663 c. M: 16.7368 c. 39: 7 5 7 9 11 N SD: 5.5135 c. M: 9.8718 c. 49: 9 6 9 11 14 N SD: 5.4686 c. M:-10.6531 c. 64: 12 8 11 15 18 N SD: 3.9738 c. M:-6.2500 c. 77: 14 10 13 18 22 N SD: 4.2938 c. M: 5.9091 c. 81: 15 10 14 19 23 N SD: 1.5704 c. M: 3.4815 c. 91: 17 11 16 21 26 N SD: 1.8833 c. M: 2.7143 c. 120: 22 15 21 28 34 N SD: 1.6550 c. M: 3.3333 c. 130: 24 16 23 30 37 N SD: 1.3531 c. M: 1.9231 c. 155: 29 19 27 36 44 N SD: 1.5499 c. M:-3.0645 c. 172: 32 21 30 40 49 N SD: 1.2174 c. M: 1.6512 c. 194: 36 24 34 45 55 N SD: 0.9824 c. M:-1.7113 c. 211: 39 26 37 49 60 N SD: 0.7099 c. M: 1.3033 c. 275: 51 34 48 64 78 N SD: 0.4435 c. M:-0.8182 c. 356: 66 44 62 83 101 N SD: 0.4511 c. M:-0.6966 c. 366: 68 45 64 85 104 N SD: 0.3891 c. M:-0.8470 c. 405: 75 50 71 94 115 N SD: 0.3802 c. M:-0.7160 c. 447: 83 55 78 104 127 N SD: 0.3841 c. M:-0.6600 c. 486: 90 60 85 113 138 N SD: 0.2052 c. M: 0.3086 c. 761: 141 94 133 177 216 N SD: 0.2167 c. M:-0.4770 c. 767: 142 95 134 178 218 N SD: 0.2354 c. M:-0.2947 c. 848: 157 105 148 197 241 N SD: 0.1709 c. M: 0.2594 c. 852: 158 105 149 198 242 N SD: 0.1701 c. M:-0.2582 c. 933: 173 115 163 217 265 N SD: 0.1935 c. M: 0.2422 c. 939: 174 116 164 218 267 N SD: 0.1756 c. M: 0.3866 c. 1059: 196 131 185 246 301 N SD: 0.1910 c. M: 0.3636 c. 1123: 208 139 196 261 319 N SD: 0.1482 c. M:-0.2894 c. 1133: 210 140 198 263 322 N SD: 0.1491 c. M:-0.2418 c. 1214: 225 150 212 282 345 N SD: 0.0821 c. M:-0.1236 c. 1425: 264 176 249 331 405 N SD: 0.0856 c. M: 0.1579 c. 1619: 300 200 283 376 460 N SD: 0.0786 c. M:-0.1742 c. 1700: 315 210 297 395 483 N SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x 2:3 S SD: 101.3346 cents 2 x x 3:4:5 S SD: 55.4019 cents 3 x 4:5:6:8 S SD: 17.5143 cents 4:5 x 6:8:11 SD: 37.4324 cents 5:6:7:8:10:13 SD: 15.1823 cents 9:11:12:14:18:24 SD: 14.5990 cents 10:12:14:16:20:27 SD: 12.7255 cents 11:13:15:18:22:29 SD: 10.0110 cents 14:17:19:23:28:37 SD: 9.9137 cents 15:18:20:24:30:40 S SD: 6.5998 cents 20:24:27:32:40:53 SD: 4.7002 cents 25:30:34:40:50:67 SD: 4.2748 cents 31:37:42:50:63:83 SD: 3.1431 cents 36:43:49:58:73:96 SD: 2.7976 cents 40:48:54:64:81:107 SD: 2.2926 cents 45:54:61:72:91:120 SD: 1.7961 cents 51:61:69:82:103:136 SD: 1.1303 cents 90:108:122:145:182:240 SD: 0.9995 cents 96:115:130:154:194:256 SD: 0.9969 cents 99:119:134:159:200:264 SD: 0.9074 cents 105:126:142:169:212:280 SD: 0.7530 cents 110:132:149:177:222:294 SD: 0.5817 cents 150:180:203:241:303:400 SD: 0.5261 cents 155:186:210:249:313:414 SD: 0.3787 cents 206:247:279:331:416:550 SD: 0.2566 cents 260:312:352:418:525:694 SD: 0.1957 cents 406:487:550:653:820:1084 SD: 0.1849 cents 415:498:562:667:838:1108 SD: 0.1838 cents 421:505:570:677:850:1124 SD: 0.1737 cents 446:535:604:717:901:1191 SD: 0.1220 cents 551:661:746:886:1113:1471 SD: 0.1182 cents 556:667:753:894:1123:1484 SD: 0.0967 cents