Scala analysis: China_Ti-tsu
Ti-tsu (Ti-tzu), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 178.000 cents 178.000000 2: 339.000 cents 339.000000 3: 448.000 cents 448.000000 4: 662.000 cents 662.000000 5: 888.000 cents 888.000000 6: 1103.000 cents 1103.000000 7: 1196.000 cents 1196.000000
SHOW/INTERVAL
0: 93.0000 cents 93.0000 1: 178.0000 cents 178.0000 2: 161.0000 cents 161.0000 3: 109.0000 cents 109.0000 4: 214.0000 cents 214.0000 5: 226.0000 cents 226.0000 6: 215.0000 cents 215.0000 7: 93.0000 cents 93.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 93.00000 cents 1: 1 109.00000 cents 1: 1 161.00000 cents 1: 1 178.00000 cents 1: 1 214.00000 cents 1: 1 215.00000 cents 1: 1 226.00000 cents 2: 1 270.00000 cents 2: 1 271.00000 cents 2: 1 308.00000 cents 2: 1 323.00000 cents 2: 1 339.00000 cents 2: 1 440.00000 cents 2: 1 441.00000 cents 3: 1 432.00000 cents 3: 1 448.00000 cents 3: 1 484.00000 cents 3: 1 486.00000 cents 3: 1 534.00000 cents 3: 1 549.00000 cents 3: 1 655.00000 cents 4: 1 541.00000 cents 4: 1 647.00000 cents 4: 1 662.00000 cents 4: 1 710.00000 cents 4: 1 712.00000 cents 4: 1 748.00000 cents 4: 1 764.00000 cents 5: 1 755.00000 cents 5: 1 756.00000 cents 5: 1 857.00000 cents 5: 1 873.00000 cents 5: 1 888.00000 cents 5: 1 925.00000 cents 5: 1 926.00000 cents 6: 1 970.00000 cents 6: 1 981.00000 cents 6: 1 982.00000 cents 6: 1 1018.00000 cents 6: 1 1035.00000 cents 6: 1 1087.00000 cents 6: 1 1103.00000 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 : 178.0 339.0 448.0 662.0 888.0 1103.0 1196.0 178.0 : 161.0 270.0 484.0 710.0 925.0 1018.0 1196.0 339.0 : 109.0 323.0 549.0 764.0 857.0 1035.0 1196.0 448.0 : 214.0 440.0 655.0 748.0 926.0 1087.0 1196.0 662.0 : 226.0 441.0 534.0 712.0 873.0 982.0 1196.0 888.0 : 215.0 308.0 486.0 647.0 756.0 970.0 1196.0 1103.0: 93.0 271.0 432.0 541.0 755.0 981.0 1196.0 1196.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.0000 .. 226.0000 cents 133.00000 cents 93.00000 cents 2: 270.0000 .. 441.0000 cents 171.00000 cents 44.00000 cents 3: 432.0000 .. 655.0000 cents 223.00000 cents -9.00000 cents 4: 541.0000 .. 764.0000 cents 223.00000 cents -114.00000 cents 5: 755.0000 .. 926.0000 cents 171.00000 cents -9.00000 cents 6: 970.0000 .. 1103.0000 cents 133.00000 cents 44.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 93.00000 cents, class 1 Average step (divided formal octave): 170.8571 cents Largest one step interval : 226.00000 cents Average / Smallest step : 1.837174 Largest / Average step : 1.322742 Largest / Smallest step : 2.430108 Median interval of one step : 178.00000 cents, amount: 1 Least squares average step : 173.41429 cents, oct.: 1213.90000 cents Scale is not proper Scale is a mode of a 1196-tone equal temperament with octave 1196.000 cents degrees: 178 339 448 662 888 1103 1196 Least number of segments generator : 599 of 599.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 625 of 625.000 cents and inv. generated superset size: 347 = 340 more = 4957.143% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : DCBEGFA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.00000 cents Scale diversity : 1.565109 Lumma stability : 0.229097 Lumma impropriety factor : 0.110368 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 : 1.00000 cents Number of recognisable fifths : 2, average 711.0000 cents Number of recognisable fourths : 2, average 485.0000 cents Number of appreciable fourths : 1, average 486.0000 cents Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 207.0000 cents: 2 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 41.2058 c. M: 77.8571 c. Lebeng 8: 1 1 1 1 2 1 1 P M ME S SD: 37.3817 c. M: 64.0000 c. 11: 2 1 1 2 2 2 1 N D3 SD: 19.1353 c. M:-39.4545 c. 13: 2 2 1 2 3 2 1 N G T3 S SD: 18.4003 c. M:-32.0000 c. 14: 2 2 1 3 2 3 1 N T3 S SD: 17.5115 c. M: 33.7143 c. 18: 3 2 2 3 3 4 1 N SD: 17.2864 c. M:-26.5556 c. 20: 3 3 1 4 4 3 2 N SD: 17.1737 c. M: 29.4000 c. 21: 3 3 2 4 4 3 2 N SD: 14.8931 c. M:-23.2381 c. 22: 3 3 2 4 4 4 2 N S SD: 13.2490 c. M: 18.1818 c. 24: 4 3 2 4 5 4 2 N SD: 11.2007 c. M:-21.3333 c. 26: 4 3 3 4 5 5 2 N SD: 11.8924 c. M: 18.0000 c. 27: 4 4 2 5 5 5 2 N S SD: 6.4585 c. M:-15.3704 c. 34: 5 5 3 6 6 6 3 N S SD: 8.6595 c. M:-12.7647 c. 35: 5 5 3 6 7 6 3 N S SD: 6.8214 c. M: 12.7429 c. 38: 6 5 3 7 7 7 3 N SD: 6.2375 c. M:-10.8421 c. 40: 6 5 4 7 8 7 3 N SD: 5.5259 c. M: 10.1000 c. 42: 6 6 4 7 8 8 3 N SD: 5.9865 c. M:-7.6190 c. 49: 7 7 4 9 9 9 4 N S SD: 5.9786 c. M: 9.3061 c. 50: 7 7 5 9 9 9 4 N SD: 5.9358 c. M: 10.5600 c. 52: 8 7 5 9 10 9 4 N SD: 6.7929 c. M:-12.0000 c. 53: 8 7 5 9 10 10 4 N SD: 4.5590 c. M: 7.9245 c. 54: 8 7 5 10 10 10 4 N SD: 3.8112 c. M: 6.7778 c. 61: 9 8 6 11 11 11 5 N SD: 4.1865 c. M: 5.7049 c. 66: 10 9 6 12 12 12 5 N SD: 4.4956 c. M:-8.4848 c. 67: 10 9 6 12 13 12 5 N SD: 2.3971 c. M:-4.5373 c. 74: 11 10 7 13 14 13 6 N SD: 2.3262 c. M:-4.5405 c. 94: 14 13 8 17 18 17 7 N SD: 2.6817 c. M:-4.5319 c. 101: 15 14 9 18 19 18 8 N SD: 1.9916 c. M:-4.4059 c. 105: 16 14 9 19 20 19 8 N SD: 2.5408 c. M:-4.2476 c. 106: 16 14 10 19 20 19 8 N SD: 2.6758 c. M:-3.6981 c. 112: 17 15 10 20 21 20 9 N SD: 2.1579 c. M:-3.5357 c. 117: 17 16 11 21 22 21 9 N SD: 2.1553 c. M: 4.2222 c. 120: 18 16 11 21 23 22 9 N SD: 2.1278 c. M: 4.2000 c. 128: 19 17 12 23 24 23 10 N SD: 1.1740 c. M: 2.6250 c. 141: 21 19 13 25 27 25 11 N SD: 1.1793 c. M:-2.6383 c. 155: 23 21 14 28 29 28 12 N SD: 0.7422 c. M:-1.5871 c. 222: 33 30 20 40 42 40 17 N SD: 0.7740 c. M:-1.4144 c. 229: 34 31 21 41 43 41 18 N SD: 0.7950 c. M:-1.2838 c. 257: 38 35 23 46 49 46 20 N SD: 0.8890 c. M: 1.2451 c. 269: 40 36 25 48 51 48 21 N SD: 0.7731 c. M:-1.2193 c. 283: 42 38 26 51 53 51 22 N SD: 0.7174 c. M:-1.5053 c. 296: 44 40 27 53 56 53 23 N SD: 0.4973 c. M:-0.9189 c. 424: 63 57 39 76 80 76 33 N SD: 0.4871 c. M:-0.8774 c. 435: 65 58 40 78 82 78 34 N SD: 0.5092 c. M: 0.8207 c. 451: 67 61 41 81 85 81 35 N SD: 0.4552 c. M:-0.9712 c. 459: 68 62 42 82 87 82 36 N SD: 0.4955 c. M: 0.8148 c. 462: 69 62 42 83 87 83 36 N SD: 0.3749 c. M:-0.7186 c. 502: 75 67 46 90 95 90 39 N SD: 0.4637 c. M: 0.6892 c. 504: 75 68 46 90 95 91 39 N SD: 0.3420 c. M:-0.5000 c. 529: 79 71 48 95 100 95 41 N SD: 0.3896 c. M:-0.6087 c. 544: 81 73 50 97 103 98 42 N SD: 0.3737 c. M:-0.6618 c. 551: 82 74 50 99 104 99 43 N SD: 0.3869 c. M: 0.8566 c. 564: 84 76 51 101 107 101 44 N SD: 0.3630 c. M: 0.5603 c. 571: 85 77 52 102 108 103 44 N SD: 0.3561 c. M:-0.8389 c. 593: 88 80 54 106 112 107 46 N SD: 0.3716 c. M: 0.5801 c. 603: 90 81 55 108 114 108 47 N SD: 0.3654 c. M:-0.5705 c. 625: 93 84 57 112 118 112 49 N SD: 0.3253 c. M: 0.7664 c. 632: 94 85 58 113 119 114 49 N SD: 0.3240 c. M:-0.5000 c. 645: 96 87 59 115 122 116 50 N SD: 0.3305 c. M:-0.7318 c. 652: 97 88 59 117 123 117 51 N SD: 0.3118 c. M: 0.5521 c. 667: 99 90 61 119 126 120 52 N SD: 0.3090 c. M: 0.4828 c. 692: 103 93 63 124 131 124 54 N SD: 0.2491 c. M: 0.3642 c. 734: 109 99 67 131 139 132 57 N SD: 0.2360 c. M: 0.4523 c. 811: 121 109 74 145 153 146 63 N SD: 0.2413 c. M:-0.4414 c. 846: 126 114 77 151 160 152 66 N SD: 0.2384 c. M: 0.3830 c. 847: 126 114 77 152 160 152 66 N SD: 0.2053 c. M: 0.3825 c. 865: 129 116 79 155 163 156 67 N SD: 0.2731 c. M:-0.3630 c. 878: 131 118 80 157 166 158 68 N SD: 0.2445 c. M:-0.4465 c. 889: 132 120 81 159 168 160 69 N SD: 0.1770 c. M: 0.4162 c. 900: 134 121 82 161 170 162 70 N SD: 0.1635 c. M: 0.3022 c. 1041: 155 140 95 186 197 187 81 N SD: 0.1105 c. M: 0.2363 c. 1196: 178 161 109 214 226 215 93 N SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 4.0000 cents 2 x x x 3 x x 4 S SD: 20.0774 cents 3 x x 4 x 5 x 6 S SD: 16.7788 cents 4 x 5 x 6:7 x 8 S SD: 25.4753 cents 5 x 6 x 7:8:9:10 S SD: 28.0687 cents 6 x 7:8:9:10:11:12 S SD: 18.4163 cents 7:8 x 9:10:12:13:14 S SD: 14.9144 cents 8:9:10 x 12:13:15:16 SD: 13.9373 cents 9:10:11:12:13:15:17:18 SD: 8.1715 cents 17:19:21:22:25:28:32:34 SD: 5.7639 cents 18:20:22:23:26:30:34:36 SD: 5.2022 cents 19:21:23:25:28:32:36:38 SD: 4.8437 cents 24:27:29:31:35:40:45:48 SD: 4.8423 cents 27:30:33:35:40:45:51:54 SD: 3.0810 cents 28:31:34:36:41:47:53:56 SD: 2.3714 cents 37:41:45:48:54:62:70:74 SD: 1.5110 cents 64:71:78:83:94:107:121:128 SD: 1.0175 cents 92:102:112:119:135:154:174:184 SD: 0.9443 cents 101:112:123:131:148:169:191:202 SD: 0.8715 cents 112:124:136:145:164:187:212:223 SD: 0.8155 cents 129:143:157:167:189:215:244:257 SD: 0.6969 cents 139:154:169:180:204:232:263:277 SD: 0.5170 cents 148:164:180:192:217:247:280:295 SD: 0.5144 cents 166:184:202:215:243:277:314:331 SD: 0.4535 cents 176:195:214:228:258:294:333:351 SD: 0.2234 cents 369:409:449:478:541:616:698:736 SD: 0.2102 cents 397:440:483:514:582:663:751:792 SD: 0.1763 cents 406:450:494:526:595:678:768:810 SD: 0.1457 cents 582:645:708:754:853:972:1101:1161 SD: 0.1313 cents