Scala analysis: China_Flute_04
Flute 4 (Flute), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 200.000 cents 200.000000 2: 375.000 cents 375.000000 3: 485.000 cents 485.000000 4: 680.000 cents 680.000000 5: 875.000 cents 875.000000 6: 985.000 cents 985.000000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 215.0000 cents 215.0000 1: 200.0000 cents 200.0000 2: 175.0000 cents 175.0000 3: 110.0000 cents 110.0000 4: 195.0000 cents 195.0000 5: 195.0000 cents 195.0000 6: 110.0000 cents 110.0000 7: 215.0000 cents 215.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 110.00000 cents 1: 1 175.00000 cents 1: 2 195.00000 cents 1: 1 200.00000 cents 1: 1 215.00000 cents 2: 1 285.00000 cents 2: 2 305.00000 cents 2: 1 325.00000 cents 2: 1 375.00000 cents 2: 1 390.00000 cents 2: 1 415.00000 cents 3: 1 480.00000 cents 3: 1 485.00000 cents 3: 2 500.00000 cents 3: 1 520.00000 cents 3: 1 525.00000 cents 3: 1 590.00000 cents 4: 1 610.00000 cents 4: 1 675.00000 cents 4: 1 680.00000 cents 4: 2 700.00000 cents 4: 1 715.00000 cents 4: 1 720.00000 cents 5: 1 785.00000 cents 5: 1 810.00000 cents 5: 1 825.00000 cents 5: 1 875.00000 cents 5: 2 895.00000 cents 5: 1 915.00000 cents 6: 1 985.00000 cents 6: 1 1000.00000 cents 6: 2 1005.00000 cents 6: 1 1025.00000 cents 6: 2 1090.00000 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.66667 = 17/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 200.0 375.0 485.0 680.0 875.0 985.0 1200.0 200.0 : 175.0 285.0 480.0 675.0 785.0 1000.0 1200.0 375.0 : 110.0 305.0 500.0 610.0 825.0 1025.0 1200.0 485.0 : 195.0 390.0 500.0 715.0 915.0 1090.0 1200.0 680.0 : 195.0 305.0 520.0 720.0 895.0 1005.0 1200.0 875.0 : 110.0 325.0 525.0 700.0 810.0 1005.0 1200.0 985.0 : 215.0 415.0 590.0 700.0 895.0 1090.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 110.0000 .. 215.0000 cents 105.00000 cents 110.00000 cents 2: 285.0000 .. 415.0000 cents 130.00000 cents 70.00000 cents 3: 480.0000 .. 590.0000 cents 110.00000 cents 65.00000 cents 4: 610.0000 .. 720.0000 cents 110.00000 cents 20.00000 cents 5: 785.0000 .. 915.0000 cents 130.00000 cents 65.00000 cents 6: 985.0000 .. 1090.0000 cents 105.00000 cents 70.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 110.00000 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 215.00000 cents Average / Smallest step : 1.558442 Largest / Average step : 1.254167 Largest / Smallest step : 1.954545 Median interval of one step : 195.00000 cents, amount: 2 Least squares average step : 170.07143 cents, oct.: 1190.50000 cents Scale is strictly proper Scale is a mode of a 240-tone equal temperament with octave 1200.000 cents degrees: 40 75 97 136 175 197 240 Least number of segments generator : 121 of 605.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 197 of 985.000 cents and inv. generated superset size: 76 = 69 more = 1085.714% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDDCE Step pattern size order : DBACCAE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 20.00000 cents Scale diversity : 1.548865 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.425000 Rothenberg efficiency : 0.340136 redundancy: 0.659864 Efficiency x scale size : 2.380952 Number of different interval sizes : 34 = 5.66667 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.66667 = 17/3 Median interval variety : 5.5 Lowest interval variety : 5 Smallest interval difference : 5.00000 cents Number of recognisable fifths : 4, average 708.7500 cents Number of appreciable fifths : 2, average 700.0000 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 26.6113 c. M:-43.5714 c. Lebeng 10: 2 1 1 2 1 1 2 P D3 I SD: 27.5162 c. M:-40.0000 c. 11: 2 1 1 2 2 1 2 P D3 S SD: 28.3780 c. M: 48.6364 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 17.3205 c. M:-25.0000 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 18: 3 3 1 3 3 2 3 P T3 SD: 14.3095 c. M:-25.0000 c. 22: 4 3 2 3 4 2 4 P SD: 12.3936 c. M: 25.4545 c. 23: 4 3 2 4 4 2 4 SP SD: 9.2217 c. M: 15.4348 c. 30: 5 4 3 5 5 3 5 SP SD: 8.4515 c. M: 15.0000 c. 32: 5 5 3 5 5 3 6 P SD: 7.9620 c. M: 12.5000 c. 37: 6 6 3 6 6 3 7 N SD: 7.3585 c. M:-14.1892 c. 41: 7 6 4 6 7 4 7 SP SD: 7.2711 c. M:-12.5610 c. 42: 7 6 4 7 7 3 8 P SD: 7.0193 c. M: 13.5714 c. 43: 7 6 4 7 7 4 8 SP SD: 8.8899 c. M: 12.2093 c. 44: 7 7 4 7 7 4 8 P SD: 5.1080 c. M: 9.0909 c. 49: 8 7 5 8 8 4 9 SP SD: 5.4000 c. M: 7.6531 c. 55: 9 8 5 9 9 5 10 SP SD: 3.4532 c. M: 5.0000 c. 67: 11 10 6 11 11 6 12 SP SD: 1.6630 c. M: 2.9851 c. 118: 20 17 11 19 19 11 21 SP SD: 1.9651 c. M:-3.3898 c. 122: 20 18 11 20 20 11 22 SP SD: 1.9007 c. M: 3.2787 c. 138: 23 20 13 22 23 12 25 SP SD: 1.8665 c. M:-3.2609 c. 144: 24 21 13 24 23 13 26 SP SD: 1.5430 c. M:-3.3333 c. 160: 27 23 15 26 26 14 29 SP SD: 2.1129 c. M:-2.5000 c. 161: 27 23 15 26 26 15 29 SP SD: 1.7028 c. M: 2.9503 c. 163: 27 24 15 26 27 15 29 SP SD: 1.3736 c. M: 2.6994 c. 166: 28 24 15 27 27 15 30 SP SD: 1.2463 c. M:-2.4096 c. 169: 28 25 15 28 27 16 30 SP SD: 1.5657 c. M: 2.1598 c. 173: 29 25 16 28 28 16 31 SP SD: 0.6440 c. M:-1.1561 c. 240: 40 35 22 39 39 22 43 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 10.9775 cents 3 x x 4 x 5 x 6 S SD: 5.3516 cents 4 x 5 x 6 x 7:8 S SD: 7.3808 cents 5 x 6 x 7:8:9:10 S SD: 26.7202 cents 6:7 x 8:9:10:11:12 S SD: 16.1194 cents 7:8 x 9:10 x 12:14 S SD: 20.0617 cents 8:9:10:11:12:13:14:16 S SD: 11.4939 cents 9:10:11:12:13:15:16:18 SD: 8.2483 cents 15:17:19:20:22:25:27:30 SD: 7.9008 cents 16:18:20:21:24:27:28:32 S SD: 6.4551 cents 17:19:21:23:25:28:30:34 SD: 6.2050 cents 21:24:26:28:31:35:37:42 SD: 5.1703 cents 24:27:30:32:36:40:42:48 S SD: 4.8333 cents 25:28:31:33:37:41:44:50 SD: 2.9494 cents 33:37:41:44:49:55:58:66 SD: 2.6988 cents 40:45:50:53:59:66:71:80 SD: 2.6109 cents 41:46:51:54:61:68:72:82 SD: 2.2177 cents 49:55:61:65:73:81:87:98 SD: 2.2152 cents 50:56:62:66:74:83:88:100 SD: 1.3359 cents 65:73:81:86:96:108:115:130 SD: 1.3121 cents 74:83:92:98:110:123:131:148 SD: 1.2988 cents 81:91:101:107:120:134:143:162 SD: 1.2345 cents 83:93:103:110:123:138:147:166 SD: 1.1620 cents 87:98:108:115:129:144:154:174 SD: 1.1549 cents 90:101:112:119:133:149:159:180 SD: 0.8485 cents 99:111:123:131:147:164:175:198 SD: 0.7339 cents 108:121:134:143:160:179:191:216 SD: 0.6111 cents 137:154:170:181:203:227:242:274 SD: 0.5945 cents 149:167:185:197:221:247:263:298 SD: 0.5868 cents 154:173:191:204:228:255:272:308 SD: 0.5394 cents 164:184:204:217:243:272:290:328 SD: 0.5234 cents 170:191:211:225:252:282:300:340 SD: 0.4540 cents 189:212:235:250:280:313:334:378 SD: 0.4531 cents 198:222:246:262:293:328:350:396 SD: 0.4410 cents 210:236:261:278:311:348:371:420 SD: 0.3795 cents 245:275:304:324:363:406:433:490 SD: 0.3176 cents 260:292:323:344:385:431:459:520 SD: 0.2298 cents 318:357:395:421:471:527:562:636 SD: 0.1886 cents 359:403:446:475:532:595:634:718 SD: 0.1848 cents 368:413:457:487:545:610:650:736 SD: 0.0494 cents