Scala analysis: China_Pi-Pa
Pi-Pa (Pipa), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 145.000 cents 145.000000 2: 351.000 cents 351.000000 3: 547.000 cents 547.000000 4: 774.000 cents 774.000000 5: 1095.000 cents 1095.000000
SHOW/INTERVAL
0: 321.0000 cents 321.0000 1: 145.0000 cents 145.0000 2: 206.0000 cents 206.0000 3: 196.0000 cents 196.0000 4: 227.0000 cents 227.0000 5: 321.0000 cents 321.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 145.00000 cents 1: 1 196.00000 cents 1: 1 206.00000 cents 1: 1 227.00000 cents 1: 1 321.00000 cents 2: 1 351.00000 cents 2: 1 402.00000 cents 2: 1 423.00000 cents 2: 1 466.00000 cents 2: 1 548.00000 cents 3: 1 547.00000 cents 3: 1 629.00000 cents 3: 1 672.00000 cents 3: 1 693.00000 cents 3: 1 744.00000 cents 4: 1 774.00000 cents 4: 1 868.00000 cents 4: 1 889.00000 cents 4: 1 899.00000 cents 4: 1 950.00000 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 : 145.0 351.0 547.0 774.0 1095.0 145.0 : 206.0 402.0 629.0 950.0 1095.0 351.0 : 196.0 423.0 744.0 889.0 1095.0 547.0 : 227.0 548.0 693.0 899.0 1095.0 774.0 : 321.0 466.0 672.0 868.0 1095.0 1095.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 145.0000 .. 321.0000 cents 176.00000 cents 145.00000 cents 2: 351.0000 .. 548.0000 cents 197.00000 cents 30.00000 cents 3: 547.0000 .. 744.0000 cents 197.00000 cents -1.00000 cents 4: 774.0000 .. 950.0000 cents 176.00000 cents 30.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 145.00000 cents, class 1 Average step (divided formal octave): 219.0000 cents Largest one step interval : 321.00000 cents Average / Smallest step : 1.510345 Largest / Average step : 1.465753 Largest / Smallest step : 2.213793 Median interval of one step : 206.00000 cents, amount: 1 Least squares average step : 201.07273 cents, oct.: 1005.36364 cents Scale is not proper Scale is a mode of a 1095-tone equal temperament with octave 1095.000 cents degrees: 145 351 547 774 1095 Least number of segments generator : 548 of 548.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1064 of 1064.000 cents and inv. generated superset size: 122 = 117 more = 2440.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : ACBDE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 1.00000 cents Scale diversity : 1.746656 Lumma stability : 0.319635 Lumma impropriety factor : 0.000913 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 : 1.00000 cents Number of recognisable fifths : 1, average 693.0000 cents Number of recognisable fourths : 0 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: 113.1539 c. M: 145.0000 c. 6: 1 1 1 1 2 P M ME S SD: 26.6026 c. M: 44.0000 c. 10: 1 2 2 2 3 P T3 SD: 19.0945 c. M: 35.5000 c. 14: 2 2 3 3 4 P SD: 18.1772 c. M: 38.1429 c. 16: 2 3 3 3 5 P SD: 10.8889 c. M: 21.1875 c. 22: 3 4 4 5 6 P SD: 10.2542 c. M:-22.3636 c. 24: 3 5 4 5 7 P SD: 7.2788 c. M:-14.0000 c. 28: 4 5 5 6 8 P SD: 6.2944 c. M:-11.4286 c. 38: 5 7 7 8 11 P SD: 2.9819 c. M: 5.2105 c. 44: 6 8 8 9 13 P SD: 2.5288 c. M:-4.3182 c. 62: 8 12 11 13 18 P SD: 2.3898 c. M: 3.7097 c. 68: 9 13 12 14 20 P SD: 1.5514 c. M:-3.2647 c. 106: 14 20 19 22 31 P SD: 0.4533 c. M:-0.7642 c. 218: 29 41 39 45 64 P SD: 0.5056 c. M:-0.6651 c. 256: 34 48 46 53 75 P SD: 0.3289 c. M:-0.5000 c. 324: 43 61 58 67 95 P SD: 0.3438 c. M:-0.5000 c. 362: 48 68 65 75 106 P SD: 0.2946 c. M:-0.5000 c. 430: 57 81 77 89 126 P SD: 0.3058 c. M:-0.5000 c. 468: 62 88 84 97 137 P SD: 0.3042 c. M:-0.5000 c. 543: 72 102 97 113 159 N SD: 0.2974 c. M: 0.5083 c. 552: 73 104 99 114 162 P SD: 0.2925 c. M:-0.5000 c. 559: 74 105 100 116 164 N SD: 0.2928 c. M: 0.4794 c. 580: 77 109 104 120 170 P SD: 0.2878 c. M:-0.5000 c. 583: 77 110 104 121 171 N SD: 0.2888 c. M: 0.4391 c. 590: 78 111 106 122 173 P SD: 0.2700 c. M:-0.5000 c. 611: 81 115 109 127 179 N SD: 0.2424 c. M: 0.3961 c. 627: 83 118 112 130 184 N SD: 0.2271 c. M: 0.3732 c. 665: 88 125 119 138 195 N SD: 0.1977 c. M: 0.3233 c. 717: 95 135 128 149 210 N SD: 0.2121 c. M:-0.2887 c. 733: 97 138 131 152 215 N SD: 0.1455 c. M: 0.2469 c. 771: 102 145 138 160 226 N SD: 0.1445 c. M: 0.2101 c. 839: 111 158 150 174 246 N SD: 0.1003 c. M: 0.1526 c. 945: 125 178 169 196 277 N SD: 0.0912 c. M: 0.1587 c. 989: 131 186 177 205 290 N SD: 0.0486 c. M: 0.0819 c. 1095: 145 206 196 227 321 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 105.0000 cents 2 x x x 3:4 S SD: 63.6700 cents 3 x x 4:5:6 S SD: 53.3340 cents 4 x 5 x 6:8 S SD: 44.0486 cents 5 x 6:7:8:9 S SD: 25.0969 cents 6 x 7:8:9:11 SD: 32.3531 cents 7:8:9:10:11:13 SD: 28.3405 cents 8:9:10:11:13:15 SD: 19.1910 cents 9:10:11:12:14:17 SD: 12.5341 cents 13:14:16:18:20:24 S SD: 10.0842 cents 14:15:17:19:22:26 SD: 8.5430 cents 19:21:23:26:30:36 SD: 8.0875 cents 21:23:26:29:33:40 SD: 6.7539 cents 22:24:27:30:34:41 SD: 5.8574 cents 25:27:31:34:39:47 SD: 5.7745 cents 27:29:33:37:42:51 SD: 4.8475 cents 32:35:39:44:50:60 SD: 3.1061 cents 35:38:43:48:55:66 SD: 2.1706 cents 57:62:70:78:89:107 SD: 1.6357 cents 67:73:82:92:105:126 SD: 1.1724 cents 94:102:115:129:147:177 SD: 0.8471 cents 103:112:126:141:161:194 SD: 0.8271 cents 137:149:168:188:214:258 SD: 0.6229 cents 151:164:185:207:236:284 SD: 0.5656 cents 161:175:197:221:252:303 SD: 0.5576 cents 170:185:208:233:266:320 SD: 0.5535 cents 183:199:224:251:286:344 SD: 0.5448 cents 204:222:250:280:319:384 SD: 0.4244 cents 218:237:267:299:341:410 SD: 0.3150 cents 298:324:365:409:466:561 SD: 0.2374 cents 307:334:376:421:480:578 SD: 0.2169 cents 401:436:491:550:627:755 SD: 0.1345 cents 525:571:643:720:821:988 SD: 0.1169 cents