Scala analysis: China_Sien_tsu
Sien tsu (Sanxian), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 189.000 cents 189.000000 2: 386.000 cents 386.000000 3: 702.000 cents 702.000000 4: 893.000 cents 893.000000 5: 1205.000 cents 1205.000000
SHOW/INTERVAL
0: 312.0000 cents 312.0000 1: 189.0000 cents 189.0000 2: 197.0000 cents 197.0000 3: 316.0000 cents 316.0000 4: 191.0000 cents 191.0000 5: 312.0000 cents 312.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 189.00000 cents 1: 1 191.00000 cents 1: 1 197.00000 cents 1: 1 312.00000 cents 1: 1 316.00000 cents 2: 1 386.00000 cents 2: 1 501.00000 cents 2: 1 503.00000 cents 2: 1 507.00000 cents 2: 1 513.00000 cents 3: 1 692.00000 cents 3: 1 698.00000 cents 3: 1 702.00000 cents 3: 1 704.00000 cents 3: 1 819.00000 cents 4: 1 889.00000 cents 4: 1 893.00000 cents 4: 1 1008.00000 cents 4: 1 1014.00000 cents 4: 1 1016.00000 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 : 189.0 386.0 702.0 893.0 1205.0 189.0 : 197.0 513.0 704.0 1016.0 1205.0 386.0 : 316.0 507.0 819.0 1008.0 1205.0 702.0 : 191.0 503.0 692.0 889.0 1205.0 893.0 : 312.0 501.0 698.0 1014.0 1205.0 1205.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 189.0000 .. 316.0000 cents 127.00000 cents 189.00000 cents 2: 386.0000 .. 513.0000 cents 127.00000 cents 70.00000 cents 3: 692.0000 .. 819.0000 cents 127.00000 cents 179.00000 cents 4: 889.0000 .. 1016.0000 cents 127.00000 cents 70.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 189.00000 cents, class 1 Average step (divided formal octave): 241.0000 cents Largest one step interval : 316.00000 cents Average / Smallest step : 1.275132 Largest / Average step : 1.311203 Largest / Smallest step : 1.671958 Median interval of one step : 197.00000 cents, amount: 1 Least squares average step : 230.25455 cents, oct.: 1151.27273 cents Scale is strictly proper Scale is a mode of a 1205-tone equal temperament with octave 1205.000 cents degrees: 189 386 702 893 1205 Least number of segments generator : 603 of 603.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 622 of 622.000 cents and inv. generated superset size: 120 = 115 more = 2400.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : ACEBD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 70.00000 cents Scale diversity : 1.338845 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.578423 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 : 2.00000 cents Number of recognisable fifths : 4, average 699.0000 cents Number of recognisable fourths : 4, average 506.0000 cents Number of appreciable fourths : 3, average 503.6667 cents Best fifths form a closed circle Formal octave complements present : 1 = 20.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 127.0000 cents: 2 -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 58.9949 c. M:-96.0000 c. 7: 1 1 2 1 2 P M ME S SD: 25.4831 c. M: 41.7143 c. Thai mode 1 12: 2 2 3 2 3 SP M ME S SD: 10.0187 c. M:-15.6667 c. Major Pentatonic, Ryosen, Yona Nuki Major: Japan, Man Jue, Gong: China, Raga Bhopali (Bhup), Bilahari, Deskar, Kokila, Jait Kalyan, Mohanam, Peruvian Pentatonic 1, Ghana Pentatonic 2, Tizita Major: Ethiopia 19: 3 3 5 3 5 SP M DE S SD: 3.9167 c. M: 5.4737 c. Nineteen-tone Major Pentatonic 31: 5 5 8 5 8 SP M DE S SD: 2.9147 c. M:-5.3548 c. 50: 8 8 13 8 13 SP M DE S SD: 2.2760 c. M:-3.8000 c. 65: 10 11 17 10 17 SP T3 SD: 2.8291 c. M: 3.6154 c. 69: 11 11 18 11 18 SP M DE S SD: 2.4600 c. M: 3.4493 c. 81: 13 13 21 13 21 SP M DE S SD: 2.3648 c. M:-4.3951 c. 84: 13 14 22 13 22 SP T3 SD: 2.0891 c. M: 3.5952 c. 96: 15 16 25 15 25 SP T3 SD: 1.6914 c. M:-3.1146 c. 103: 16 17 27 16 27 SP T3 SD: 1.9137 c. M: 3.8738 c. 113: 18 18 30 18 29 SP T3 SD: 2.1888 c. M:-2.9469 c. 115: 18 19 30 18 30 SP T3 SD: 1.3071 c. M: 2.3478 c. 134: 21 22 35 21 35 SP T3 SD: 1.2904 c. M: 2.7388 c. 146: 23 24 38 23 38 SP T3 SD: 1.2005 c. M:-1.9110 c. 159: 25 26 42 25 41 SP SD: 1.4149 c. M:-2.8113 c. 165: 26 27 43 26 43 SP T3 SD: 1.1701 c. M: 2.0303 c. 166: 26 27 44 26 43 SP SD: 1.1160 c. M:-2.1265 c. 178: 28 29 47 28 46 SP SD: 0.9855 c. M:-2.0449 c. 185: 29 30 49 29 48 SP SD: 1.0451 c. M: 1.7027 c. 190: 30 31 50 30 49 SP SD: 1.2470 c. M:-1.9737 c. 196: 31 32 51 31 51 SP T3 SD: 1.2599 c. M:-1.5867 c. 197: 31 32 52 31 51 SP SD: 0.7531 c. M:-1.4264 c. 209: 33 34 55 33 54 SP SD: 0.9021 c. M:-1.3971 c. 216: 34 35 57 34 56 SP SD: 0.7221 c. M: 1.0694 c. 228: 36 37 60 36 59 SP SD: 0.7076 c. M:-1.2632 c. 247: 39 40 65 39 64 SP SD: 0.6725 c. M:-1.2632 c. 275: 43 45 72 44 71 SP SD: 0.6509 c. M: 0.9091 c. 306: 48 50 80 49 79 SP SD: 0.6220 c. M: 1.0523 c. 312: 49 51 82 49 81 SP SD: 0.5742 c. M:-0.9167 c. 324: 51 53 85 51 84 SP SD: 0.6461 c. M:-0.9167 c. 325: 51 53 85 52 84 SP SD: 0.6369 c. M: 1.2462 c. 331: 52 54 87 52 86 SP SD: 0.5746 c. M: 1.0816 c. 340: 53 56 89 54 88 SP SD: 0.5530 c. M: 1.1618 c. 343: 54 56 90 54 89 SP SD: 0.5538 c. M:-0.7085 c. 352: 55 58 92 56 91 SP SD: 0.5460 c. M:-0.8324 c. 359: 56 59 94 57 93 SP SD: 0.5149 c. M: 1.0334 c. 371: 58 61 97 59 96 SP SD: 0.4169 c. M: 0.6173 c. 390: 61 64 102 62 101 SP SD: 0.3801 c. M: 0.6282 c. 409: 64 67 107 65 106 SP SD: 0.4313 c. M: 0.8020 c. 421: 66 69 110 67 109 SP SD: 0.3839 c. M: 0.7530 c. 472: 74 77 124 75 122 SP SD: 0.3324 c. M:-0.5381 c. 503: 79 82 132 80 130 SP SD: 0.3122 c. M:-0.5686 c. 522: 82 85 137 83 135 SP SD: 0.3208 c. M: 0.4923 c. 537: 84 88 141 85 139 SP SD: 0.2811 c. M: 0.5084 c. 549: 86 90 144 87 142 SP SD: 0.2789 c. M:-0.3679 c. 556: 87 91 146 88 144 SP SD: 0.2438 c. M: 0.4478 c. 568: 89 93 149 90 147 SP SD: 0.1494 c. M:-0.2095 c. 587: 92 96 154 93 152 SP SD: 0.0770 c. M: 0.1414 c. 618: 97 101 162 98 160 SP SD: 0.0731 c. M:-0.1343 c. 1186: 186 194 311 188 307 SP SD: 0.0627 c. M:-0.0877 c. 1205: 189 197 316 191 312 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 5.0000 cents 2 x x 3 x 4 S SD: 2.5001 cents 3 x 4 x 5:6 S SD: 37.4963 cents 4 x 5:6:7:8 S SD: 18.9978 cents 5 x 6 x 8:10 S SD: 35.3805 cents 6:7:8:9:10:12 S SD: 27.3625 cents 7:8:9:11:12:14 SD: 22.1831 cents 8:9:10:12:13:16 SD: 10.9558 cents 12:13:15:18:20:24 SD: 10.2814 cents 16:18:20:24:27:32 SD: 4.0641 cents 24:27:30:36:40:48 S SD: 3.5893 cents 28:31:35:42:47:56 SD: 2.8442 cents 36:40:45:54:60:72 S SD: 2.3940 cents 44:49:55:66:74:88 SD: 1.8064 cents 52:58:65:78:87:104 SD: 1.0786 cents 96:107:120:144:161:193 SD: 0.9397 cents 104:116:130:156:174:209 SD: 0.7745 cents 120:134:150:180:201:241 SD: 0.6029 cents 148:165:185:222:248:297 SD: 0.2725 cents 200:223:250:300:335:401 SD: 0.1854 cents 320:357:400:480:536:642 SD: 0.1327 cents 468:522:585:702:784:939 SD: 0.1327 cents 520:580:650:780:871:1043 SD: 0.0642 cents