Scala analysis: China_Flute_01B
Flute 1B (Flute), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 170.000 cents 170.000000 2: 318.000 cents 318.000000 3: 472.000 cents 472.000000 4: 667.000 cents 667.000000 5: 854.000 cents 854.000000 6: 990.000 cents 990.000000 7: 1194.000 cents 1194.000000
SHOW/INTERVAL
0: 204.0000 cents 204.0000 1: 170.0000 cents 170.0000 2: 148.0000 cents 148.0000 3: 154.0000 cents 154.0000 4: 195.0000 cents 195.0000 5: 187.0000 cents 187.0000 6: 136.0000 cents 136.0000 7: 204.0000 cents 204.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 136.00000 cents 1: 1 148.00000 cents 1: 1 154.00000 cents 1: 1 170.00000 cents 1: 1 187.00000 cents 1: 1 195.00000 cents 1: 1 204.00000 cents 2: 1 302.00000 cents 2: 1 318.00000 cents 2: 1 323.00000 cents 2: 1 340.00000 cents 2: 1 349.00000 cents 2: 1 374.00000 cents 2: 1 382.00000 cents 3: 1 472.00000 cents 3: 1 497.00000 cents 3: 1 510.00000 cents 3: 1 518.00000 cents 3: 1 522.00000 cents 3: 1 527.00000 cents 3: 1 536.00000 cents 4: 1 658.00000 cents 4: 1 667.00000 cents 4: 1 672.00000 cents 4: 1 676.00000 cents 4: 1 684.00000 cents 4: 1 697.00000 cents 4: 1 722.00000 cents 5: 1 812.00000 cents 5: 1 820.00000 cents 5: 1 845.00000 cents 5: 1 854.00000 cents 5: 1 871.00000 cents 5: 1 876.00000 cents 5: 1 892.00000 cents 6: 1 990.00000 cents 6: 1 999.00000 cents 6: 1 1007.00000 cents 6: 1 1024.00000 cents 6: 1 1040.00000 cents 6: 1 1046.00000 cents 6: 1 1058.00000 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 : 170.0 318.0 472.0 667.0 854.0 990.0 1194.0 170.0 : 148.0 302.0 497.0 684.0 820.0 1024.0 1194.0 318.0 : 154.0 349.0 536.0 672.0 876.0 1046.0 1194.0 472.0 : 195.0 382.0 518.0 722.0 892.0 1040.0 1194.0 667.0 : 187.0 323.0 527.0 697.0 845.0 999.0 1194.0 854.0 : 136.0 340.0 510.0 658.0 812.0 1007.0 1194.0 990.0 : 204.0 374.0 522.0 676.0 871.0 1058.0 1194.0 1194.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 136.0000 .. 204.0000 cents 68.00000 cents 136.00000 cents 2: 302.0000 .. 382.0000 cents 80.00000 cents 98.00000 cents 3: 472.0000 .. 536.0000 cents 64.00000 cents 90.00000 cents 4: 658.0000 .. 722.0000 cents 64.00000 cents 122.00000 cents 5: 812.0000 .. 892.0000 cents 80.00000 cents 90.00000 cents 6: 990.0000 .. 1058.0000 cents 68.00000 cents 98.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 136.00000 cents, class 1 Average step (divided formal octave): 170.5714 cents Largest one step interval : 204.00000 cents Average / Smallest step : 1.254202 Largest / Average step : 1.195980 Largest / Smallest step : 1.500000 Median interval of one step : 170.00000 cents, amount: 1 Least squares average step : 167.55714 cents, oct.: 1172.90000 cents Scale is strictly proper Scale is a mode of a 1194-tone equal temperament with octave 1194.000 cents degrees: 170 318 472 667 854 990 1194 Least number of segments generator : 599 of 599.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 853 of 853.000 cents and inv. generated superset size: 287 = 280 more = 4100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : DBCFEAG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.00000 cents Scale diversity : 1.407959 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.644891 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 : 4.00000 cents Number of recognisable fifths : 1, average 697.0000 cents Number of recognisable fourths : 2, average 503.5000 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% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 22.2504 c. M:-39.7143 c. Lebeng 15: 2 2 2 2 3 1 3 SP D3 S SD: 19.7766 c. M: 34.8000 c. 16: 2 2 2 3 2 2 3 SP M ME S SD: 20.3980 c. M: 33.1250 c. Antilydian 18: 3 2 2 3 3 2 3 SP D3 S SD: 13.0627 c. M:-29.0000 c. 20: 3 2 3 3 3 3 3 SP M ME S SD: 14.8889 c. M:-24.9000 c. Minor quasi-equal Heptatonic 21: 3 3 2 4 3 2 4 SP T3 SD: 15.1829 c. M: 23.4286 c. 22: 3 3 3 3 4 2 4 SP D3 S SD: 11.9862 c. M:-16.4545 c. 23: 3 3 3 4 3 3 4 SP M ME S SD: 11.2834 c. M: 23.3913 c. Pelogic-7, Antilydian 25: 4 3 3 4 4 3 4 SP D3 S SD: 11.6085 c. M:-21.0400 c. 27: 4 3 4 4 4 3 5 SP D3 SD: 10.8461 c. M: 17.1111 c. 28: 4 3 4 5 4 3 5 SP T3 SD: 10.0642 c. M: 19.5000 c. 29: 4 4 3 5 5 3 5 SP SD: 10.0486 c. M: 19.1034 c. 30: 4 4 4 5 4 4 5 SP M ME S SD: 9.2316 c. M: 18.2000 c. Pelogic-7, Antilydian 34: 5 4 4 6 5 4 6 SP SD: 7.9667 c. M: 15.4706 c. 35: 5 4 5 6 5 4 6 SP T3 SD: 7.4401 c. M:-15.2857 c. 36: 5 5 4 6 6 4 6 SP SD: 7.2782 c. M:-13.6667 c. 38: 5 5 5 6 6 4 7 SP SD: 8.6054 c. M: 15.9474 c. 40: 6 5 5 6 7 4 7 SP S SD: 8.3461 c. M:-11.6500 c. 41: 6 5 5 7 6 5 7 SP SD: 4.8093 c. M: 9.4634 c. 48: 7 6 6 8 7 6 8 SP SD: 4.7921 c. M: 8.2500 c. 53: 8 6 7 9 8 6 9 SP SD: 5.3012 c. M:-10.2264 c. 56: 8 7 7 9 9 6 10 SP SD: 4.3893 c. M: 9.2143 c. 59: 8 8 7 10 9 7 10 SP SD: 4.8055 c. M: 8.1017 c. 63: 9 8 8 10 10 7 11 SP SD: 2.8271 c. M: 4.4762 c. 71: 10 9 9 12 11 8 12 SP SD: 2.8633 c. M:-5.6761 c. 91: 13 11 12 15 14 10 16 SP SD: 2.7061 c. M: 5.9341 c. 98: 14 12 13 16 15 11 17 SP SD: 2.1551 c. M:-3.1633 c. 99: 14 12 13 16 16 11 17 SP SD: 2.4896 c. M: 4.4242 c. 106: 15 13 14 17 17 12 18 SP SD: 1.7215 c. M: 2.6038 c. 127: 18 16 16 21 20 14 22 SP SD: 1.5901 c. M: 2.8346 c. 134: 19 17 17 22 21 15 23 SP SD: 1.3503 c. M:-2.7761 c. 147: 21 18 19 24 23 17 25 SP SD: 0.9055 c. M: 1.2245 c. 210: 30 26 27 34 33 24 36 SP SD: 0.8790 c. M: 1.7714 c. 217: 31 27 28 35 34 25 37 SP SD: 0.9271 c. M: 1.2212 c. 218: 31 27 28 36 34 25 37 SP SD: 0.8054 c. M:-1.3486 c. 240: 34 30 31 39 38 27 41 SP SD: 0.7825 c. M:-1.7000 c. 274: 39 34 35 45 43 31 47 SP SD: 0.6143 c. M: 1.3723 c. 281: 40 35 36 46 44 32 48 SP SD: 0.2949 c. M:-0.6833 c. 387: 55 48 50 63 61 44 66 SP SD: 0.3792 c. M:-0.6202 c. 428: 61 53 55 70 67 49 73 SP SD: 0.2995 c. M: 0.5374 c. 526: 75 65 68 86 82 60 90 SP SD: 0.2915 c. M: 0.4943 c. 632: 90 78 82 103 99 72 108 SP SD: 0.2622 c. M: 0.6076 c. 668: 95 83 86 109 105 76 114 SP SD: 0.2295 c. M:-0.3892 c. 759: 108 94 98 124 119 86 130 SP SD: 0.2285 c. M: 0.5059 c. 766: 109 95 99 125 120 87 131 SP SD: 0.1673 c. M:-0.3003 c. 807: 115 100 104 132 126 92 138 SP SD: 0.1818 c. M: 0.2974 c. 906: 129 112 117 148 142 103 155 SP SD: 0.2033 c. M: 0.3907 c. 913: 130 113 118 149 143 104 156 SP SD: 0.0908 c. M: 0.2103 c. 1047: 149 130 135 171 164 119 179 SP SD: 0.1271 c. M:-0.1719 c. 1194: 170 148 154 195 187 136 204 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 6.0000 cents 2 x x x 3 x x 4 S SD: 17.7331 cents 3 x x 4 x 5 x 6 S SD: 13.4825 cents 4 x 5 x 6 x 7:8 S SD: 19.9577 cents 5 x 6 x 7:8:9:10 S SD: 19.5617 cents 6 x 7:8:9:10:11:12 S SD: 15.8079 cents 7:8 x 9:10:11:12:14 S SD: 21.0424 cents 8:9:10:11:12:13:14:16 S SD: 16.9005 cents 9:10:11:12:13:15:16:18 SD: 8.5891 cents 16:18:19:21:24:26:28:32 SD: 8.4016 cents 17:19:20:22:25:28:30:34 SD: 7.4056 cents 19:21:23:25:28:31:34:38 SD: 3.4524 cents 30:33:36:39:44:49:53:60 SD: 3.0051 cents 38:42:46:50:56:62:67:76 SD: 2.6616 cents 39:43:47:51:57:64:69:78 SD: 2.2004 cents 49:54:59:64:72:80:87:98 SD: 1.9631 cents 58:64:70:76:85:95:103:116 SD: 1.7841 cents 60:66:72:79:88:98:106:120 SD: 1.7164 cents 70:77:84:92:103:115:124:140 SD: 1.4305 cents 79:87:95:104:116:129:140:157 SD: 1.2888 cents 89:98:107:117:131:146:158:177 SD: 1.0547 cents 96:106:115:126:141:157:170:191 SD: 1.0146 cents 105:116:126:138:154:172:186:209 SD: 0.8322 cents 115:127:138:151:169:188:204:229 SD: 0.7386 cents 124:137:149:163:182:203:220:247 SD: 0.7023 cents 143:158:172:188:210:234:253:285 SD: 0.6840 cents 144:159:173:189:212:236:255:287 SD: 0.5113 cents 185:204:222:243:272:303:328:369 SD: 0.4506 cents 204:225:245:268:300:334:361:407 SD: 0.4159 cents 223:246:268:293:328:365:395:444 SD: 0.3379 cents 262:289:315:344:385:429:464:522 SD: 0.2239 cents 398:439:478:523:585:652:705:793 SD: 0.2143 cents 406:448:488:533:597:665:719:809 SD: 0.1967 cents 417:460:501:548:613:683:739:831 SD: 0.1750 cents 447:493:537:587:657:732:792:891 SD: 0.1137 cents 600:662:721:788:882:983:1063:1196 SD: 0.1102 cents