Scala analysis: hirajoshi3
Observed Japanese pentatonic koto scale. Helmholtz/Ellis p.519, nr.111
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 193.000 cents 193.000000 2: 357.000 cents 357.000000 3: 719.000 cents 719.000000 4: 801.000 cents 801.000000 5: 1199.000 cents 1199.000000
SHOW/INTERVAL
0: 398.0000 cents 398.0000 1: 193.0000 cents 193.0000 2: 164.0000 cents 164.0000 3: 362.0000 cents 362.0000 4: 82.0000 cents 82.0000 5: 398.0000 cents 398.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 82.00000 cents 1: 1 164.00000 cents 1: 1 193.00000 cents 1: 1 362.00000 cents 1: 1 398.00000 cents 2: 1 357.00000 cents 2: 1 444.00000 cents 2: 1 480.00000 cents 2: 1 526.00000 cents 2: 1 591.00000 cents 3: 1 608.00000 cents 3: 1 673.00000 cents 3: 1 719.00000 cents 3: 1 755.00000 cents 3: 1 842.00000 cents 4: 1 801.00000 cents 4: 1 837.00000 cents 4: 1 1006.00000 cents 4: 1 1035.00000 cents 4: 1 1117.00000 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 : 193.0 357.0 719.0 801.0 1199.0 193.0 : 164.0 526.0 608.0 1006.0 1199.0 357.0 : 362.0 444.0 842.0 1035.0 1199.0 719.0 : 82.0 480.0 673.0 837.0 1199.0 801.0 : 398.0 591.0 755.0 1117.0 1199.0 1199.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.0000 .. 398.0000 cents 316.00000 cents 82.00000 cents 2: 357.0000 .. 591.0000 cents 234.00000 cents -41.00000 cents 3: 608.0000 .. 842.0000 cents 234.00000 cents 17.00000 cents 4: 801.0000 .. 1117.0000 cents 316.00000 cents -41.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 82.00000 cents, class 1 Average step (divided formal octave): 239.8000 cents Largest one step interval : 398.00000 cents Average / Smallest step : 2.924390 Largest / Average step : 1.659716 Largest / Smallest step : 4.853659 Median interval of one step : 193.00000 cents, amount: 1 Least squares average step : 222.96364 cents, oct.: 1114.81818 cents Scale is not proper Scale is a mode of a 1199-tone equal temperament with octave 1199.000 cents degrees: 193 357 719 801 1199 Least number of segments generator : 600 of 600.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1006 of 1006.000 cents and inv. generated superset size: 65 = 60 more = 1300.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : CBDAE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 5.00000 cents Scale diversity : 1.628000 Lumma stability : 0.150959 Lumma impropriety factor : 0.068390 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 : 5.00000 cents Number of recognisable fifths : 1, average 719.0000 cents Number of appreciable fifths : 0 Number of recognisable fourths : 0 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 316.0000 cents: 2 -- Rational properties --
FIT/MODE
5: 1 0 2 0 2 N T3 SD: 67.2083 c. M: 117.2000 c. 6: 1 1 2 0 2 P D3 S SD: 40.8004 c. M:-80.3333 c. 7: 1 1 2 1 2 P M ME S SD: 31.2996 c. M:-55.4286 c. Thai mode 1 10: 2 1 3 1 3 P T3 SD: 27.0724 c. M:-46.8000 c. 12: 2 2 3 1 4 P SD: 21.2293 c. M:-42.6667 c. Raga Bhupeshwari, Janasammodini 13: 2 2 4 1 4 P T3 S SD: 16.8268 c. M:-29.0769 c. 17: 3 2 5 1 6 N SD: 15.4024 c. M: 25.1765 c. 18: 3 2 6 1 6 N SD: 12.7366 c. M: 23.9444 c. 20: 3 3 6 1 7 N SD: 11.3938 c. M: 21.6500 c. 23: 4 3 7 1 8 N SD: 12.5172 c. M: 19.0435 c. 24: 4 3 7 2 8 N SD: 9.8605 c. M: 19.5833 c. 27: 4 4 8 2 9 N SD: 7.9245 c. M: 15.3704 c. 30: 5 4 9 2 10 N SD: 3.3741 c. M:-6.8333 c. 57: 9 8 17 4 19 N SD: 2.4980 c. M: 3.8070 c. 87: 14 12 26 6 29 N SD: 1.4199 c. M: 2.3563 c. 117: 19 16 35 8 39 N SD: 1.4985 c. M:-1.7094 c. 118: 19 16 36 8 39 N SD: 1.4656 c. M:-2.4322 c. 130: 21 18 39 9 43 N SD: 1.4071 c. M:-2.7000 c. 148: 24 20 45 10 49 N SD: 1.2243 c. M:-2.0203 c. 162: 26 22 49 11 54 N SD: 1.2081 c. M: 1.7407 c. 168: 27 23 51 11 56 N SD: 1.1165 c. M:-1.8274 c. 175: 28 24 53 12 58 N SD: 0.6947 c. M: 1.1600 c. 205: 33 28 62 14 68 N SD: 0.2410 c. M:-0.4000 c. 440: 71 60 133 30 146 N SD: 0.2859 c. M:-0.4750 c. 467: 75 64 141 32 155 N SD: 0.2121 c. M: 0.4411 c. 497: 80 68 150 34 165 N SD: 0.0497 c. M: 0.0825 c. 702: 113 96 212 48 233 N SD: 0.0352 c. M:-0.0584 c. 1199: 193 164 362 82 398 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 1.0000 cents 2 x x 3 x 4 S SD: 8.5372 cents 3 x 4 x 5:6 S SD: 54.6132 cents 4 x 5:6 x 8 S SD: 11.3079 cents 5 x 6 x 8:10 S SD: 14.4241 cents 6:7 x 9:10:12 SD: 28.1704 cents 7:8:9 x 11:14 SD: 22.2176 cents 8:9:10:12:13:16 SD: 10.6439 cents 9:10:11 x 14:18 SD: 9.7062 cents 11:12:14:17 x 22 SD: 20.3970 cents 12:13:15:18:19:24 SD: 12.8729 cents 14:16:17:21:22:28 SD: 10.0537 cents 16:18:20:24:25:32 SD: 9.1101 cents 17:19:21:26:27:34 SD: 3.7616 cents 27:30:33:41:43:54 SD: 3.1276 cents 35:39:43:53:56:70 SD: 2.7909 cents 43:48:53:65:68:86 SD: 2.0312 cents 58:65:71:88:92:116 SD: 1.7815 cents 60:67:74:91:95:120 SD: 1.7403 cents 66:74:81:100:105:132 SD: 1.2778 cents 78:87:96:118:124:156 SD: 1.1040 cents 95:106:117:144:151:190 SD: 1.0552 cents 101:113:124:153:160:202 SD: 1.0348 cents 109:122:134:165:173:218 SD: 0.5874 cents 136:152:167:206:216:272 SD: 0.3746 cents 245:274:301:371:389:490 SD: 0.3237 cents 262:293:322:397:416:524 SD: 0.2781 cents 340:380:418:515:540:680 SD: 0.2485 cents 406:454:499:615:645:812 SD: 0.2336 cents 476:532:585:721:756:951 SD: 0.1898 cents 542:606:666:821:861:1083 SD: 0.1542 cents 559:625:687:847:888:1117 SD: 0.1530 cents 585:654:719:886:929:1169 SD: 0.1354 cents