Scala analysis: China_Sheng
Sheng (Sheng), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 210.000 cents 210.000000 2: 338.000 cents 338.000000 3: 498.000 cents 498.000000 4: 715.000 cents 715.000000 5: 908.000 cents 908.000000 6: 1040.000 cents 1040.000000 7: 1199.000 cents 1199.000000 8: 1413.000 cents 1413.000000 9: 1564.000 cents 1564.000000 10: 1746.000 cents 1746.000000
SHOW/INTERVAL
0: 182.0000 cents 182.0000 1: 210.0000 cents 210.0000 2: 128.0000 cents 128.0000 3: 160.0000 cents 160.0000 4: 217.0000 cents 217.0000 5: 193.0000 cents 193.0000 6: 132.0000 cents 132.0000 7: 159.0000 cents 159.0000 8: 214.0000 cents 214.0000 9: 151.0000 cents 151.0000 10: 182.0000 cents 182.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128.00000 cents 1: 1 132.00000 cents 1: 1 151.00000 cents 1: 1 159.00000 cents 1: 1 160.00000 cents 1: 1 182.00000 cents 1: 1 193.00000 cents 1: 1 210.00000 cents 1: 1 214.00000 cents 1: 1 217.00000 cents 2: 1 288.00000 cents 2: 1 291.00000 cents 2: 1 325.00000 cents 2: 1 333.00000 cents 2: 1 338.00000 cents 2: 1 365.00000 cents 2: 1 373.00000 cents 2: 1 377.00000 cents 2: 1 392.00000 cents 2: 1 410.00000 cents 3: 1 484.00000 cents 3: 1 498.00000 cents 3: 2 505.00000 cents 3: 1 520.00000 cents 3: 1 524.00000 cents 3: 1 542.00000 cents 3: 1 543.00000 cents 3: 1 547.00000 cents 3: 1 570.00000 cents 4: 1 656.00000 cents 4: 1 671.00000 cents 4: 1 680.00000 cents 4: 2 698.00000 cents 4: 1 701.00000 cents 4: 1 702.00000 cents 4: 1 706.00000 cents 4: 1 715.00000 cents 4: 1 757.00000 cents 5: 1 830.00000 cents 5: 1 831.00000 cents 5: 1 838.00000 cents 5: 1 849.00000 cents 5: 1 861.00000 cents 5: 1 885.00000 cents 5: 1 897.00000 cents 5: 1 908.00000 cents 5: 1 915.00000 cents 5: 1 916.00000 cents 6: 1 989.00000 cents 6: 1 1031.00000 cents 6: 1 1040.00000 cents 6: 1 1044.00000 cents 6: 1 1045.00000 cents 6: 2 1048.00000 cents 6: 1 1066.00000 cents 6: 1 1075.00000 cents 6: 1 1090.00000 cents 7: 1 1176.00000 cents 7: 1 1199.00000 cents 7: 1 1203.00000 cents 7: 1 1204.00000 cents 7: 1 1222.00000 cents 7: 1 1226.00000 cents 7: 2 1241.00000 cents 7: 1 1248.00000 cents 7: 1 1262.00000 cents 8: 1 1336.00000 cents 8: 1 1354.00000 cents 8: 1 1369.00000 cents 8: 1 1373.00000 cents 8: 1 1381.00000 cents 8: 1 1408.00000 cents 8: 1 1413.00000 cents 8: 1 1421.00000 cents 8: 1 1455.00000 cents 8: 1 1458.00000 cents 9: 1 1529.00000 cents 9: 1 1532.00000 cents 9: 1 1536.00000 cents 9: 1 1553.00000 cents 9: 1 1564.00000 cents 9: 1 1586.00000 cents 9: 1 1587.00000 cents 9: 1 1595.00000 cents 9: 1 1614.00000 cents 9: 1 1618.00000 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 9.55556 = 86/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 210.0 338.0 498.0 715.0 908.0 1040.0 1199.0 1413.0 1564.0 1746.0 210.0 : 128.0 288.0 505.0 698.0 830.0 989.0 1203.0 1354.0 1536.0 1746.0 338.0 : 160.0 377.0 570.0 702.0 861.0 1075.0 1226.0 1408.0 1618.0 1746.0 498.0 : 217.0 410.0 542.0 701.0 915.0 1066.0 1248.0 1458.0 1586.0 1746.0 715.0 : 193.0 325.0 484.0 698.0 849.0 1031.0 1241.0 1369.0 1529.0 1746.0 908.0 : 132.0 291.0 505.0 656.0 838.0 1048.0 1176.0 1336.0 1553.0 1746.0 1040.0: 159.0 373.0 524.0 706.0 916.0 1044.0 1204.0 1421.0 1614.0 1746.0 1199.0: 214.0 365.0 547.0 757.0 885.0 1045.0 1262.0 1455.0 1587.0 1746.0 1413.0: 151.0 333.0 543.0 671.0 831.0 1048.0 1241.0 1373.0 1532.0 1746.0 1564.0: 182.0 392.0 520.0 680.0 897.0 1090.0 1222.0 1381.0 1595.0 1746.0 1746.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.0000 .. 217.0000 cents 89.00000 cents 128.00000 cents 2: 288.0000 .. 410.0000 cents 122.00000 cents 71.00000 cents 3: 484.0000 .. 570.0000 cents 86.00000 cents 74.00000 cents 4: 656.0000 .. 757.0000 cents 101.00000 cents 86.00000 cents 5: 830.0000 .. 916.0000 cents 86.00000 cents 73.00000 cents 6: 989.0000 .. 1090.0000 cents 101.00000 cents 73.00000 cents 7: 1176.0000 .. 1262.0000 cents 86.00000 cents 86.00000 cents 8: 1336.0000 .. 1458.0000 cents 122.00000 cents 74.00000 cents 9: 1529.0000 .. 1618.0000 cents 89.00000 cents 71.00000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 128.00000 cents, class 1 Average step (divided formal octave): 174.6000 cents Largest one step interval : 217.00000 cents Average / Smallest step : 1.364062 Largest / Average step : 1.242841 Largest / Smallest step : 1.695313 Median interval of one step : 171.00000 cents, amount: 0 Least squares average step : 174.68312 cents, oct.: 1746.83117 cents Scale is strictly proper Scale is a mode of a 1746-tone equal temperament with octave 1746.000 cents degrees: 210 338 498 715 908 1040 1199 1413 1564 1746 Least number of segments generator : 875 of 875.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1591 of 1591.000 cents and inv. generated superset size: 698 = 688 more = 6980.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFGHIJ Step pattern size order : HAEJGBDICF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 71.00000 cents Scale diversity : 0.515320 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.494845 Rothenberg efficiency : 0.208889 redundancy: 0.791111 Efficiency x scale size : 2.088889 Number of different interval sizes : 86 = 9.55556 / class Number of one step interval sizes : 10 Highest interval variety : 10 Mean interval variety : 9.55556 = 86/9 Median interval variety : 9 Lowest interval variety : 9 Smallest interval difference : 1.00000 cents Number of recognisable fifths : 6, average 703.3333 cents Number of appreciable fifths : 5, average 701.0000 cents Number of recognisable fourths : 4, average 498.0000 cents Number of appreciable fourths : 3, average 502.6667 cents Formal octave complements present : 1 = 10.0000% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 21.1140 c. M: 35.4000 c. 17: 2 1 2 2 2 1 2 2 1 2 P M ME SD: 19.7310 c. M:-33.4706 c. 22: 3 1 2 3 2 2 2 3 2 2 P D3 SD: 19.5896 c. M: 35.0000 c. 25: 3 2 2 3 3 2 2 3 2 3 SP D3 SD: 13.0358 c. M: 27.5200 c. 31: 4 2 3 4 3 2 3 4 3 3 P SD: 13.4128 c. M: 26.1935 c. 32: 4 2 3 4 4 2 3 4 3 3 SP SD: 10.1192 c. M:-19.5625 c. 35: 4 3 3 4 4 3 3 4 3 4 SP D3 SD: 11.1500 c. M: 17.5429 c. 41: 5 3 4 5 4 3 4 5 4 4 SP SD: 10.0712 c. M: 17.9512 c. 42: 5 3 4 5 5 3 4 5 4 4 SP SD: 6.6140 c. M:-15.7143 c. 48: 6 3 5 6 5 4 4 6 4 5 SP SD: 8.4880 c. M:-14.8750 c. 52: 6 4 5 6 6 4 5 6 5 5 SP SD: 7.1604 c. M:-14.1154 c. 57: 7 4 5 7 7 4 5 7 5 6 SP SD: 5.9377 c. M:-10.9474 c. 64: 8 4 6 8 7 5 6 8 5 7 SP SD: 6.6780 c. M: 10.6250 c. 66: 8 5 6 8 7 5 6 8 6 7 SP SD: 6.3501 c. M: 10.9091 c. 67: 8 5 6 8 8 5 6 8 6 7 SP SD: 4.4368 c. M: 11.3881 c. 69: 8 5 7 8 8 5 6 9 6 7 SP SD: 6.2893 c. M: 9.6957 c. 73: 9 5 7 9 8 5 7 9 6 8 SP SD: 5.4449 c. M: 11.5342 c. 77: 9 6 7 10 8 6 7 9 7 8 SP SD: 4.7146 c. M:-10.6104 c. 82: 10 6 7 11 9 6 7 10 7 9 SP SD: 6.5459 c. M: 9.6341 c. 83: 10 6 8 10 9 6 8 10 7 9 SP SD: 4.6139 c. M: 9.2289 c. 84: 10 6 8 10 10 6 8 10 7 9 SP SD: 4.6500 c. M: 8.2857 c. 93: 11 7 8 12 10 7 9 11 8 10 SP SD: 5.2699 c. M: 9.8710 c. 94: 11 7 9 11 11 7 8 12 8 10 SP SD: 5.1700 c. M: 10.2340 c. 96: 12 7 8 12 11 7 9 12 8 10 SP SD: 5.0214 c. M:-8.2500 c. 98: 12 7 9 12 11 7 9 12 9 10 SP SD: 3.7258 c. M: 6.6531 c. 108: 13 8 10 13 12 8 10 13 10 11 SP SD: 3.5781 c. M: 6.5000 c. 109: 13 8 10 14 12 8 10 13 10 11 SP SD: 3.4541 c. M:-5.8257 c. 115: 14 8 11 14 13 8 11 14 10 12 SP SD: 3.1789 c. M: 7.5826 c. 117: 14 9 10 15 13 9 10 15 10 12 SP SD: 3.8034 c. M: 5.5385 c. 119: 14 9 11 15 13 9 11 14 11 12 SP SD: 3.3995 c. M:-5.9328 c. 125: 15 9 12 15 14 9 12 15 11 13 SP SD: 2.9848 c. M: 6.3680 c. 131: 16 9 12 17 14 10 12 16 11 14 SP SD: 3.2231 c. M: 4.8550 c. 134: 16 10 12 17 15 10 12 16 12 14 SP SD: 2.6431 c. M: 5.7761 c. 141: 17 10 13 18 15 11 13 17 12 15 SP SD: 2.6071 c. M: 4.0426 c. 144: 17 11 13 18 16 11 13 18 12 15 SP SD: 2.4733 c. M:-5.6250 c. 164: 20 12 15 20 18 13 15 20 14 17 SP SD: 2.6632 c. M:-4.0366 c. 166: 20 12 15 21 18 13 15 20 15 17 SP SD: 2.2818 c. M: 3.6506 c. 173: 21 12 16 22 19 13 16 21 15 18 SP SD: 2.1727 c. M: 4.9480 c. 175: 21 13 16 22 19 13 16 22 15 18 SP SD: 2.0571 c. M:-3.7543 c. 183: 22 13 17 23 20 14 17 22 16 19 SP SD: 1.8533 c. M: 4.0656 c. 185: 22 14 17 23 20 14 17 23 16 19 SP SD: 2.0126 c. M:-2.6811 c. 200: 24 15 18 25 22 15 18 25 17 21 SP SD: 1.4423 c. M: 2.9900 c. 210: 25 16 19 26 23 16 19 26 18 22 SP SD: 1.4581 c. M:-2.8857 c. 227: 27 17 21 28 25 17 21 28 19 24 SP SD: 1.5810 c. M: 2.5991 c. 231: 28 17 21 29 25 18 21 28 20 24 SP SD: 1.8965 c. M:-3.0649 c. 232: 28 17 21 29 26 17 21 29 20 24 SP SD: 1.5057 c. M:-2.6293 c. 242: 29 18 22 30 27 18 22 30 21 25 SP SD: 1.0148 c. M:-1.6281 c. 325: 39 24 30 40 36 25 29 40 28 34 SP SD: 0.9834 c. M:-2.2277 c. 346: 42 25 32 43 38 26 32 42 30 36 SP SD: 1.1486 c. M:-2.0058 c. 357: 43 26 33 44 40 27 32 44 31 37 SP SD: 0.9845 c. M:-1.7311 c. 371: 45 27 34 46 41 28 34 45 32 39 SP SD: 0.9834 c. M:-1.7790 c. 373: 45 27 34 47 41 28 34 46 32 39 SP SD: 0.8917 c. M: 1.8177 c. 383: 46 28 35 48 42 29 35 47 33 40 SP SD: 0.5858 c. M: 1.0966 c. 450: 54 33 41 56 50 34 41 55 39 47 SP SD: 0.6380 c. M: 1.3600 c. 498: 60 36 46 62 55 38 45 61 43 52 SP SD: 0.6323 c. M: 1.4217 c. 582: 70 43 53 72 65 44 53 71 50 61 SP SD: 0.7746 c. M: 1.0000 c. 583: 70 43 53 73 64 44 53 72 50 61 SP SD: 0.6689 c. M: 1.0583 c. 588: 71 43 54 73 65 44 54 72 51 61 SP SD: 0.6567 c. M:-0.8673 c. 593: 71 44 54 74 65 45 54 73 51 62 SP SD: 0.6464 c. M: 1.1400 c. 596: 72 43 55 74 66 45 54 73 52 62 SP SD: 0.6233 c. M: 1.1040 c. 606: 73 44 56 75 67 46 55 74 53 63 SP SD: 0.5854 c. M: 1.2178 c. 613: 74 45 56 76 68 46 56 75 53 64 SP SD: 0.4869 c. M:-0.9462 c. 625: 75 46 57 78 69 47 57 77 54 65 SP SD: 0.4697 c. M: 0.7808 c. 698: 84 51 64 87 77 53 63 86 60 73 SP SD: 0.4245 c. M: 0.8138 c. 708: 85 52 65 88 78 54 64 87 61 74 SP SD: 0.3740 c. M:-0.6949 c. 740: 89 54 68 92 82 56 67 91 64 77 SP SD: 0.3424 c. M: 0.5973 c. 750: 90 55 69 93 83 57 68 92 65 78 SP SD: 0.3358 c. M:-0.6160 c. 823: 99 60 76 102 91 62 75 101 71 86 SP SD: 0.3628 c. M: 0.6804 c. 923: 111 68 84 115 102 70 84 113 80 96 SP SD: 0.3235 c. M:-0.6067 c. 950: 114 70 87 118 105 72 86 117 82 99 SP SD: 0.3058 c. M: 0.6926 c. 981: 118 72 90 122 108 74 90 120 85 102 SP SD: 0.3759 c. M:-0.5963 c. 992: 119 73 91 123 110 75 90 122 86 103 SP SD: 0.3662 c. M:-0.7117 c. 996: 120 73 91 124 110 75 91 122 86 104 SP SD: 0.2529 c. M: 0.4639 c. 1006: 121 74 92 125 111 76 92 123 87 105 SP SD: 0.2519 c. M:-0.4394 c. 1038: 125 76 95 129 115 78 95 127 90 108 SP SD: 0.2551 c. M: 0.4740 c. 1121: 135 82 103 139 124 85 102 137 97 117 SP SD: 0.2619 c. M:-0.4353 c. 1133: 136 83 104 141 125 86 103 139 98 118 SP SD: 0.2634 c. M: 0.5119 c. 1248: 150 92 114 155 138 94 114 153 108 130 SP SD: 0.2523 c. M:-0.5673 c. 1296: 156 95 119 161 143 98 118 159 112 135 SP SD: 0.2215 c. M:-0.4722 c. 1321: 159 97 121 164 146 100 120 162 114 138 SP SD: 0.2200 c. M: 0.3982 c. 1353: 163 99 124 168 150 102 123 166 117 141 SP SD: 0.2080 c. M:-0.4878 c. 1363: 164 100 125 169 151 103 124 167 118 142 SP SD: 0.1646 c. M:-0.3081 c. 1504: 181 110 138 187 166 114 137 184 130 157 SP SD: 0.1633 c. M: 0.2620 c. 1704: 205 125 156 212 188 129 155 209 147 178 SP SD: 0.1630 c. M: 0.3873 c. 1736: 209 127 159 216 192 131 158 213 150 181 SP SD: 0.1216 c. M:-0.2039 c. 1746: 210 128 160 217 193 132 159 214 151 182 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 x x 3 S SD: 77.9791 cents 2 x x x 3 x x 4 x 5 x S SD: 8.6222 cents 3 x x 4 x 5 x 6:7 x 8 S SD: 15.1811 cents 4 x 5 x 6:7 x 8:9:10:11 S SD: 11.7924 cents 5 x 6:7 x 8:9:10:11:12:14 S SD: 18.9636 cents 6:7 x 8:9:10:11:12:14:15:16 S SD: 10.9723 cents 7:8 x 9:11:12:13:14:16:17:19 SD: 12.1748 cents 8:9:10:11:12:14:15:16:18:20:22 S SD: 10.9653 cents 9:10:11:12:14:15:16:18:20:22:25 SD: 8.6932 cents 10:11:12:13:15:17:18:20:23:25:27 SD: 8.5231 cents 12:14:15:16:18:20:22:24:27:30:33 S SD: 8.3637 cents 13:15:16:17:20:22:24:26:29:32:36 SD: 7.2969 cents 14:16:17:19:21:24:26:28:32:35:38 SD: 6.5796 cents 15:17:18:20:23:25:27:30:34:37:41 SD: 4.7679 cents 18:20:22:24:27:30:33:36:41:44:49 SD: 4.7340 cents 22:25:27:29:33:37:40:44:50:54:60 SD: 3.5937 cents 23:26:28:31:35:39:42:46:52:57:63 SD: 2.4594 cents 33:37:40:44:50:56:60:66:75:81:90 SD: 2.2566 cents 38:43:46:51:57:64:69:76:86:94:104 SD: 2.1882 cents 39:44:47:52:59:66:71:78:88:96:107 SD: 1.6868 cents 45:51:55:60:68:76:82:90:102:111:123 SD: 1.3330 cents 55:62:67:73:83:93:100:110:124:136:151 SD: 1.2834 cents 61:69:74:81:92:103:111:122:138:151:167 SD: 1.1611 cents 69:78:84:92:104:117:126:138:156:170:189 SD: 0.9550 cents 78:88:95:104:118:132:142:156:176:193:214 SD: 0.8418 cents 84:95:102:112:127:142:153:168:190:207:230 SD: 0.5500 cents 139:157:169:185:210:235:253:278:314:343:381 SD: 0.5253 cents 147:166:179:196:222:248:268:294:332:363:403 SD: 0.5095 cents 148:167:180:197:224:250:270:296:335:365:406 SD: 0.4711 cents 162:183:197:216:245:274:295:324:366:400:444 SD: 0.4168 cents 171:193:208:228:258:289:312:342:387:422:469 SD: 0.3747 cents 180:203:219:240:272:304:328:360:407:444:493 SD: 0.3548 cents 186:210:226:248:281:314:339:372:421:459:510 SD: 0.2533 cents 255:288:310:340:385:431:465:510:577:629:699 SD: 0.2530 cents 264:298:321:352:399:446:481:528:597:652:724 SD: 0.2268 cents 325:367:395:433:491:549:593:650:735:802:891 SD: 0.2194 cents 333:376:405:444:503:563:607:666:753:822:913 SD: 0.2172 cents 348:393:423:464:526:588:635:696:787:859:954 SD: 0.1716 cents 465:525:565:620:703:786:848:929:1052:1148:1275 SD: 0.1683 cents 481:543:585:641:727:813:877:961:1088:1187:1319 SD: 0.1679 cents 483:545:587:644:730:816:881:965:1092:1192:1324 SD: 0.1602 cents 487:550:592:649:736:823:888:973:1102:1202:1335 SD: 0.1567 cents 510:576:620:680:771:862:930:1019:1154:1259:1398 SD: 0.1532 cents 519:586:631:692:784:877:946:1037:1174:1281:1423 SD: 0.1369 cents 528:596:642:704:798:892:963:1055:1194:1303:1448 SD: 0.1150 cents 534:603:649:712:807:902:974:1067:1208:1318:1464 SD: 0.1097 cents