Scala analysis: China_Flute_01A
Flute 1A (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: 1055.000 cents 1055.000000 7: 1195.000 cents 1195.000000
SHOW/INTERVAL
0: 140.0000 cents 140.0000 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: 201.0000 cents 201.0000 7: 140.0000 cents 140.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 140.00000 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: 1 201.00000 cents 2: 1 302.00000 cents 2: 1 310.00000 cents 2: 1 318.00000 cents 2: 1 341.00000 cents 2: 1 349.00000 cents 2: 1 382.00000 cents 2: 1 388.00000 cents 3: 1 458.00000 cents 3: 1 472.00000 cents 3: 1 497.00000 cents 3: 1 511.00000 cents 3: 1 528.00000 cents 3: 1 536.00000 cents 3: 1 583.00000 cents 4: 1 612.00000 cents 4: 1 659.00000 cents 4: 1 667.00000 cents 4: 1 684.00000 cents 4: 1 698.00000 cents 4: 1 723.00000 cents 4: 1 737.00000 cents 5: 1 807.00000 cents 5: 1 813.00000 cents 5: 1 846.00000 cents 5: 1 854.00000 cents 5: 1 877.00000 cents 5: 1 885.00000 cents 5: 1 893.00000 cents 6: 1 994.00000 cents 6: 1 1000.00000 cents 6: 1 1008.00000 cents 6: 1 1025.00000 cents 6: 1 1041.00000 cents 6: 1 1047.00000 cents 6: 1 1055.00000 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 1055.0 1195.0 170.0 : 148.0 302.0 497.0 684.0 885.0 1025.0 1195.0 318.0 : 154.0 349.0 536.0 737.0 877.0 1047.0 1195.0 472.0 : 195.0 382.0 583.0 723.0 893.0 1041.0 1195.0 667.0 : 187.0 388.0 528.0 698.0 846.0 1000.0 1195.0 854.0 : 201.0 341.0 511.0 659.0 813.0 1008.0 1195.0 1055.0: 140.0 310.0 458.0 612.0 807.0 994.0 1195.0 1195.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 140.0000 .. 201.0000 cents 61.00000 cents 140.00000 cents 2: 302.0000 .. 388.0000 cents 86.00000 cents 101.00000 cents 3: 458.0000 .. 583.0000 cents 125.00000 cents 70.00000 cents 4: 612.0000 .. 737.0000 cents 125.00000 cents 29.00000 cents 5: 807.0000 .. 893.0000 cents 86.00000 cents 70.00000 cents 6: 994.0000 .. 1055.0000 cents 61.00000 cents 101.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 140.00000 cents, class 1 Average step (divided formal octave): 170.7143 cents Largest one step interval : 201.00000 cents Average / Smallest step : 1.219388 Largest / Average step : 1.177406 Largest / Smallest step : 1.435714 Median interval of one step : 170.00000 cents, amount: 1 Least squares average step : 170.39286 cents, oct.: 1192.75000 cents Scale is strictly proper Scale is a mode of a 1195-tone equal temperament with octave 1195.000 cents degrees: 170 318 472 667 854 1055 1195 Least number of segments generator : 598 of 598.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 913 of 913.000 cents and inv. generated superset size: 232 = 225 more = 3314.286% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : DBCFEGA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 29.00000 cents Scale diversity : 1.473328 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.544770 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 : 6.00000 cents Number of recognisable fifths : 1, average 698.0000 cents Number of recognisable fourths : 2, average 504.0000 cents Best fifths 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% Limited inverse transpositions with margin 111.0000 cents: 2 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 21.8954 c. M:-40.1429 c. Lebeng 15: 2 2 2 2 3 2 2 SP M ME S SD: 16.4876 c. M: 29.6667 c. 16: 2 2 2 3 2 3 2 P D3 S SD: 19.0224 c. M: 32.4375 c. 18: 3 2 2 3 3 3 2 P D3 SD: 13.3200 c. M:-29.1667 c. 20: 3 2 3 3 3 4 2 P SD: 13.6993 c. M:-20.5000 c. 23: 3 3 3 4 3 4 3 SP D3 S SD: 12.5142 c. M: 22.6957 c. 25: 4 3 3 4 4 4 3 SP D3 SD: 10.8124 c. M:-21.2000 c. 27: 4 3 4 4 4 5 3 SP SD: 9.0227 c. M:-14.8519 c. 31: 4 4 4 5 5 5 4 SP S SD: 10.7173 c. M: 15.8065 c. 33: 5 4 4 5 6 5 4 SP SD: 9.7700 c. M: 15.1818 c. 34: 5 4 4 6 5 6 4 P SD: 7.3092 c. M: 15.0882 c. 36: 5 5 4 6 6 6 4 P S SD: 7.6296 c. M:-13.9444 c. 41: 6 5 5 7 6 7 5 SP SD: 5.1197 c. M: 8.7561 c. 49: 7 6 6 8 8 8 6 SP SD: 5.1952 c. M: 8.6327 c. 50: 7 6 7 8 8 8 6 SP SD: 4.6895 c. M: 7.3000 c. 56: 8 7 7 9 9 9 7 SP SD: 4.3001 c. M: 9.3750 c. 63: 9 8 8 10 10 11 7 SP SD: 3.5314 c. M:-7.2222 c. 68: 10 8 9 11 11 11 8 SP SD: 3.6510 c. M:-7.1029 c. 70: 10 9 9 11 11 12 8 SP SD: 3.5924 c. M:-6.3571 c. 71: 10 9 9 12 11 12 8 SP SD: 3.6519 c. M:-6.2394 c. 76: 11 9 10 12 12 13 9 SP SD: 3.6138 c. M: 6.6053 c. 78: 11 10 10 13 12 13 9 SP SD: 3.6883 c. M:-7.1026 c. 79: 11 10 10 13 12 14 9 SP SD: 3.5317 c. M: 6.9114 c. 83: 12 10 11 13 13 14 10 SP SD: 3.3299 c. M: 4.7108 c. 84: 12 10 11 14 13 14 10 SP SD: 2.3946 c. M: 5.0238 c. 91: 13 11 12 15 14 15 11 SP SD: 2.2843 c. M: 4.4505 c. 101: 14 13 13 16 16 17 12 SP SD: 2.6913 c. M: 4.4257 c. 102: 15 12 13 17 16 17 12 SP SD: 2.6620 c. M:-5.7353 c. 104: 15 13 13 17 16 18 12 SP SD: 2.3552 c. M:-3.7308 c. 113: 16 14 15 18 18 19 13 SP SD: 2.0682 c. M:-3.8850 c. 120: 17 15 15 20 19 20 14 SP SD: 1.8063 c. M: 3.9583 c. 125: 18 15 16 21 19 21 15 SP SD: 2.6655 c. M: 3.5600 c. 126: 18 16 16 20 20 21 15 SP SD: 2.3980 c. M:-4.4603 c. 127: 18 16 16 21 20 21 15 SP SD: 1.4131 c. M:-2.2598 c. 147: 21 18 19 24 23 25 17 SP SD: 0.8683 c. M:-1.8027 c. 154: 22 19 20 25 24 26 18 SP SD: 0.6259 c. M:-1.3442 c. 274: 39 34 35 45 43 46 32 SP SD: 0.5406 c. M: 0.9781 c. 281: 40 35 36 46 44 47 33 SP SD: 0.5473 c. M:-0.9502 c. 357: 51 44 46 58 56 60 42 SP SD: 0.5091 c. M: 0.8796 c. 410: 58 51 53 67 64 69 48 SP SD: 0.4209 c. M: 0.9512 c. 428: 61 53 55 70 67 72 50 SP SD: 0.2907 c. M:-0.3972 c. 582: 83 72 75 95 91 98 68 SP SD: 0.2854 c. M:-0.4210 c. 613: 87 76 79 100 96 103 72 SP SD: 0.2710 c. M: 0.3997 c. 760: 108 94 98 124 119 128 89 SP SD: 0.2415 c. M: 0.3816 c. 767: 109 95 99 125 120 129 90 SP SD: 0.1622 c. M: 0.2216 c. 921: 131 114 119 150 144 155 108 SP SD: 0.1608 c. M:-0.2910 c. 1041: 148 129 134 170 163 175 122 SP SD: 0.0926 c. M: 0.1988 c. 1195: 170 148 154 195 187 201 140 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 5.0000 cents 2 x x x 3 x x 4 S SD: 17.6554 cents 3 x x 4 x 5 x 6 S SD: 13.4371 cents 4 x 5 x 6 x 7:8 S SD: 28.8743 cents 5 x 6 x 7:8:9:10 S SD: 20.1921 cents 6 x 7:8:9:10:11:12 S SD: 12.3522 cents 7:8 x 9:10:11:13:14 SD: 18.9838 cents 8:9:10:11:12:13:15:16 SD: 17.2870 cents 9:10:11:12:13:15:17:18 SD: 10.7731 cents 10:11:12:13:15:16:18:20 SD: 9.7079 cents 13:14:16:17:19:21:24:26 SD: 9.3097 cents 16:18:19:21:24:26:29:32 SD: 8.6257 cents 17:19:20:22:25:28:31:34 SD: 7.6321 cents 19:21:23:25:28:31:35:38 SD: 2.3720 cents 39:43:47:51:57:64:72:78 SD: 2.3145 cents 49:54:59:64:72:80:90:98 SD: 1.8554 cents 58:64:70:76:85:95:107:116 SD: 1.7728 cents 60:66:72:79:88:98:110:120 SD: 1.7050 cents 68:75:82:89:100:111:125:136 SD: 1.6464 cents 70:77:84:92:103:115:129:140 SD: 1.4312 cents 79:87:95:104:116:129:145:158 SD: 1.3880 cents 80:88:96:105:118:131:147:160 SD: 1.3871 cents 89:98:107:117:131:146:164:177 SD: 1.1045 cents 105:116:126:138:154:172:193:209 SD: 0.9121 cents 115:127:138:151:169:188:212:229 SD: 0.9121 cents 119:131:143:156:175:195:219:237 SD: 0.8085 cents 124:137:149:163:182:203:228:247 SD: 0.6506 cents 143:158:172:188:210:234:263:285 SD: 0.6227 cents 144:159:173:189:212:236:265:287 SD: 0.5384 cents 185:204:222:243:272:303:340:369 SD: 0.4109 cents 194:214:233:255:285:318:357:387 SD: 0.3839 cents 204:225:245:268:300:334:375:407 SD: 0.2654 cents 328:362:394:431:482:537:603:654 SD: 0.2467 cents 347:383:417:456:510:568:638:692 SD: 0.2440 cents 387:427:465:508:569:634:712:772 SD: 0.2029 cents 417:460:501:548:613:683:767:832 SD: 0.1892 cents 447:493:537:587:657:732:822:891 SD: 0.1648 cents 466:514:560:612:685:763:857:929 SD: 0.1158 cents