Scala analysis: hirajoshi
Observed Japanese pentatonic koto scale. Helmholtz/Ellis p.519, nr.112
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 185.000 cents 185.000000 2: 337.000 cents 337.000000 3: 683.000 cents 683.000000 4: 790.000 cents 790.000000 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 410.0000 cents 410.0000 1: 185.0000 cents 185.0000 2: 152.0000 cents 152.0000 3: 346.0000 cents 346.0000 4: 107.0000 cents 107.0000 5: 410.0000 cents 410.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 107.00000 cents 1: 1 152.00000 cents 1: 1 185.00000 cents 1: 1 346.00000 cents 1: 1 410.00000 cents 2: 1 337.00000 cents 2: 1 453.00000 cents 2: 1 498.00000 cents 2: 1 517.00000 cents 2: 1 595.00000 cents 3: 1 605.00000 cents 3: 1 683.00000 cents 3: 1 702.00000 cents 3: 1 747.00000 cents 3: 1 863.00000 cents 4: 1 790.00000 cents 4: 1 854.00000 cents 4: 1 1015.00000 cents 4: 1 1048.00000 cents 4: 1 1093.00000 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 : 185.0 337.0 683.0 790.0 1200.0 185.0 : 152.0 498.0 605.0 1015.0 1200.0 337.0 : 346.0 453.0 863.0 1048.0 1200.0 683.0 : 107.0 517.0 702.0 854.0 1200.0 790.0 : 410.0 595.0 747.0 1093.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 107.0000 .. 410.0000 cents 303.00000 cents 107.00000 cents 2: 337.0000 .. 595.0000 cents 258.00000 cents -73.00000 cents 3: 605.0000 .. 863.0000 cents 258.00000 cents 10.00000 cents 4: 790.0000 .. 1093.0000 cents 303.00000 cents -73.00000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 107.00000 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 410.00000 cents Average / Smallest step : 2.242991 Largest / Average step : 1.708333 Largest / Smallest step : 3.831776 Median interval of one step : 185.00000 cents, amount: 1 Least squares average step : 219.41818 cents, oct.: 1097.09091 cents Scale is not proper Scale is a mode of a 1200-tone equal temperament with octave 2/1 degrees: 185 337 683 790 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1039 of 1039.000 cents and inv. generated superset size: 233 = 228 more = 4660.000% 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 9.00000 cents Scale diversity : 1.630333 Lumma stability : 0.186667 Lumma impropriety factor : 0.121667 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 : 9.00000 cents Number of recognisable fifths : 1, average 702.0000 cents Best fifths form a closed circle Formal octave complements present : 1 = 20.0000% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
5: 1 0 2 0 2 N T3 SD: 61.1604 c. M: 97.0000 c. 6: 1 1 1 1 2 P M ME S SD: 47.2927 c. M: 83.0000 c. 7: 1 1 2 1 2 P M ME S SD: 30.7702 c. M:-67.1429 c. Thai mode 1 11: 2 1 3 1 4 N SD: 23.2394 c. M:-33.1818 c. 12: 2 1 4 1 4 N T3 SD: 19.9148 c. M: 37.0000 c. Aeolian Pentatonic, Hira-joshi, Kata-kumoi, Yona Nuki Minor: Japan, Tizita Minor (Half tizita): Ethiopia 14: 2 2 4 1 5 N SD: 10.6841 c. M: 18.5714 c. 18: 3 2 5 2 6 N SD: 11.0020 c. M: 16.3333 c. 21: 3 3 6 2 7 N SD: 8.0729 c. M: 13.5714 c. 26: 4 3 8 2 9 N SD: 7.8693 c. M: 13.9231 c. 32: 5 4 9 3 11 N SD: 3.9179 c. M: 8.0000 c. 46: 7 6 13 4 16 N SD: 4.1797 c. M: 7.3913 c. 47: 7 6 14 4 16 N SD: 4.6464 c. M:-6.3617 c. 53: 8 7 15 5 18 N SD: 2.8967 c. M: 3.8679 c. 58: 9 7 17 5 20 N SD: 3.2090 c. M: 5.9655 c. 65: 10 8 19 6 22 N SD: 2.7190 c. M: 4.6923 c. 79: 12 10 23 7 27 N SD: 1.7713 c. M: 2.8228 c. 111: 17 14 32 10 38 N SD: 1.3636 c. M: 1.9189 c. 135: 21 17 39 12 46 N SD: 1.1579 c. M:-1.6667 c. 149: 23 19 43 13 51 N SD: 0.9613 c. M:-1.5638 c. 167: 26 21 48 15 57 N SD: 0.9132 c. M:-1.8263 c. 181: 28 23 52 16 62 N SD: 0.7456 c. M:-1.1215 c. 214: 33 27 62 19 73 N SD: 0.6279 c. M:-1.1121 c. 246: 38 31 71 22 84 N SD: 0.2723 c. M: 0.4146 c. 395: 61 50 114 35 135 N SD: 0.3029 c. M:-0.5443 c. 427: 66 54 123 38 146 N SD: 0.2787 c. M:-0.4801 c. 448: 69 57 129 40 153 N SD: 0.2510 c. M:-0.5000 c. 506: 78 64 146 45 173 N SD: 0.1644 c. M: 0.2767 c. 694: 107 88 200 62 237 N SD: 0.1198 c. M:-0.2017 c. 940: 145 119 271 84 321 N SD: 0.1072 c. M:-0.2128 c. 954: 147 121 275 85 326 N SD: 0.0702 c. M:-0.1069 c. 1200: 185 152 346 107 410 N SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 9.4775 cents 3 x 4 x 5:6 S SD: 62.2174 cents 4 x 5:6 x 8 S SD: 17.6104 cents 5 x 6:7:8:10 S SD: 26.3570 cents 6 x 7:9 x 12 SD: 24.2152 cents 8:9:10:12:13:16 SD: 15.1020 cents 9:10:11:13:14:18 SD: 10.7622 cents 10:11:12:15:16:20 S SD: 8.4294 cents 17:19:21:25:27:34 SD: 7.0484 cents 18:20:22:27:28:36 SD: 6.6440 cents 19:21:23:28:30:38 SD: 3.5424 cents 33:37:40:49:52:66 SD: 2.7998 cents 43:48:52:64:68:86 SD: 2.3262 cents 52:58:63:77:82:104 SD: 1.4554 cents 79:88:96:117:125:158 SD: 1.1375 cents 97:108:118:144:153:194 SD: 0.5731 cents 116:129:141:172:183:232 SD: 0.3831 cents 159:177:193:236:251:318 SD: 0.3682 cents 213:237:259:316:336:426 SD: 0.3523 cents 223:248:271:331:352:446 SD: 0.2794 cents 256:285:311:380:404:512 SD: 0.2299 cents 275:306:334:408:434:550 SD: 0.1029 cents 372:414:452:552:587:744 SD: 0.1008 cents