Scala analysis: or9
Orwell[9] in 1728/1715 (0,-1) tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 156.144 cents 156.143810 2: 271.229 cents 271.228762 3: 427.373 cents 427.372572 4: 542.458 cents 542.457524 5: 698.601 cents 698.601334 6: 813.686 cents 813.686286 7: 928.771 cents 928.771238 8: 1084.915 cents 1084.915048 9: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 115.0850 cents 115.0850 1: 156.1438 cents 156.1438 2: 115.0850 cents 115.0850 3: 156.1438 cents 156.1438 4: 115.0850 cents 115.0850 5: 156.1438 cents 156.1438 6: 115.0850 cents 115.0850 7: 115.0850 cents 115.0850 8: 156.1438 cents 156.1438 9: 115.0850 cents 115.0850
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 115.08495 cents 1: 4 156.14381 cents 2: 1 230.16990 cents 2: 8 271.22876 cents 3: 6 386.31371 cents 3: 3 427.37257 cents 4: 2 501.39867 cents 4: 7 542.45752 cents 5: 7 657.54248 cents 5: 2 698.60133 cents 6: 3 772.62743 cents 6: 6 813.68629 cents 7: 8 928.77124 cents 7: 1 969.83010 cents 8: 4 1043.85619 cents 8: 5 1084.91505 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 156.1 271.2 427.4 542.5 698.6 813.7 928.8 1084.9 1200.0 156.1 : 115.1 271.2 386.3 542.5 657.5 772.6 928.8 1043.9 1200.0 271.2 : 156.1 271.2 427.4 542.5 657.5 813.7 928.8 1084.9 1200.0 427.4 : 115.1 271.2 386.3 501.4 657.5 772.6 928.8 1043.9 1200.0 542.5 : 156.1 271.2 386.3 542.5 657.5 813.7 928.8 1084.9 1200.0 698.6 : 115.1 230.2 386.3 501.4 657.5 772.6 928.8 1043.9 1200.0 813.7 : 115.1 271.2 386.3 542.5 657.5 813.7 928.8 1084.9 1200.0 928.8 : 156.1 271.2 427.4 542.5 698.6 813.7 969.8 1084.9 1200.0 1084.9: 115.1 271.2 386.3 542.5 657.5 813.7 928.8 1043.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 115.0850 .. 156.1438 cents 41.05886 cents 115.08495 cents 2: 230.1699 .. 271.2288 cents 41.05886 cents 74.02609 cents 3: 386.3137 .. 427.3726 cents 41.05886 cents 115.08495 cents 4: 501.3987 .. 542.4575 cents 41.05886 cents 74.02609 cents 5: 657.5425 .. 698.6013 cents 41.05886 cents 115.08495 cents 6: 772.6274 .. 813.6863 cents 41.05886 cents 74.02609 cents 7: 928.7712 .. 969.8301 cents 41.05886 cents 115.08495 cents 8: 1043.8562 .. 1084.9150 cents 41.05886 cents 74.02609 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 115.08495 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 156.14381 cents Average / Smallest step : 1.158564 Largest / Average step : 1.171079 Largest / Smallest step : 1.356770 Median interval of one step : 115.08495 cents, amount: 5 Most common interval of one step : 115.08495 cents, amount: 5 Least squares average step : 135.11015 cents, oct.: 1215.99134 cents Scale is strictly proper Scale has Myhill's property chromas: 41.05886 cents and 74.02609 cents, ratio: 1.802926 generators: 2 of 271.22876 cents and 7 of 928.77124 cents ET pair of linear temperament : 22&31 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1783-tone equal temperament with octave 1200.000 cents degrees: 232 403 635 806 1038 1209 1380 1612 1783 generators: 403 and 1380 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABBAB Step pattern size order : LSLSLSSLS Scale is a Constant Structure, by a margin of 74.02609 cents Scale diversity : 1.206555 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.726274 Rothenberg efficiency : 0.740741 redundancy: 0.259259 Efficiency x scale size : 6.666667 Number of different interval sizes : 16 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 41.05886 cents Most common intervals : 271.22876 cents & inv., amount: 8 Scale is a chain of 4 triads 0.0 271.229 542.458 cents Most common triad is 0.0 271.229 928.771 cents, amount: 7 Number of recognisable fifths : 2, average 698.6013 cents Best fifths form a closed circle Formal octave complements present : 3 = 33.3333% Limited inverse transpositions : 3 Inversional symmetry on degrees : 6 Inversional symmetry on intervals : 1-2 -- Rational properties --
FIT/MODE
9: 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.0573 c. M: 31.9347 c. Pelog Nawanada: Sunda 17: 2 2 2 2 2 2 1 2 2 SP M ME S SD: 17.7288 c. M:-33.3725 c. 19: 2 2 3 2 2 2 2 2 2 SP M ME S SD: 17.2173 c. M: 29.8280 c. Mandelbaum Nine out of 19 22: 3 2 3 2 3 2 2 3 2 SP M ME S SD: 5.9313 c. M:-10.4896 c. 31: 4 3 4 3 4 3 3 4 3 SP M ME S SD: 1.0331 c. M: 1.8271 c. 84: 11 8 11 8 11 8 8 11 8 SP M DE S SD: 0.7909 c. M:-1.3987 c. 115: 15 11 15 11 15 11 11 15 11 SP M DE S SD: 0.2992 c. M:-0.5291 c. 146: 19 14 19 14 19 14 14 19 14 SP M DE S SD: 0.0163 c. M:-0.0288 c. 1053: 137 101 137 101 137 101 101 137 101 SP M DE S SD: 0.0146 c. M: 0.0258 c. 1199: 156 115 156 115 156 115 115 156 115 SP M DE S SD: 0.0108 c. M: 0.0192 c. 1345: 175 129 175 129 175 129 129 175 129 SP M DE S SD: 0.0079 c. M: 0.0140 c. 1491: 194 143 194 143 194 143 143 194 143 SP M DE S SD: 0.0055 c. M: 0.0098 c. 1637: 213 157 213 157 213 157 157 213 157 SP M DE S SD: 0.0036 c. M: 0.0063 c. 1783: 232 171 232 171 232 171 171 232 171 SP M DE S SD: 0.0020 c. M: 0.0035 c. 1929: 251 185 251 185 251 185 185 251 185 SP M DE S SD: 0.0006 c. M: 0.0010 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x 4 S SD: 1.6768 cents 3 x x x 4 x x 5 x 6 S SD: 20.9363 cents 4 x x 5 x 6 x 7 x 8 S SD: 14.3646 cents 5 x 6 x 7 x 8 x 9:10 S SD: 18.0096 cents 6 x 7 x 8:9 x 10:11:12 S SD: 12.0636 cents 7 x 8:9:10 x 11:12:13:14 S SD: 13.1398 cents 8:9 x 10:11:12:13:14:15:16 S SD: 9.9947 cents 9:10:11 x 12:13:14:15:17:18 SD: 16.2589 cents 10:11:12:13:14:15:16:17:19:20 SD: 7.9973 cents 14:15:16:18:19:21:22:24:26:28 SD: 7.3521 cents 17:19:20:22:23:25:27:29:32:34 SD: 6.4742 cents 18:20:21:23:25:27:29:31:34:36 SD: 4.9377 cents 22:24:26:28:30:33:35:38:41:44 SD: 3.4154 cents 30:33:35:38:41:45:48:51:56:60 SD: 2.6335 cents 40:44:47:51:55:60:64:68:75:80 SD: 2.1984 cents 46:50:54:59:63:69:74:79:86:92 SD: 2.0910 cents 52:57:61:67:71:78:83:89:97:104 SD: 1.7103 cents 54:59:63:69:74:81:86:92:101:108 SD: 1.4157 cents 65:71:76:83:89:97:104:111:122:130 SD: 1.0739 cents 82:90:96:105:112:123:131:140:153:164 SD: 1.0379 cents 93:102:109:119:127:139:149:159:174:186 SD: 0.7901 cents 107:117:125:137:146:160:171:183:200:214 SD: 0.6920 cents 117:128:137:150:160:175:187:200:219:234 SD: 0.4802 cents 125:137:146:160:171:187:200:214:234:250 SD: 0.4757 cents 147:161:172:188:201:220:235:251:275:294 SD: 0.4204 cents 193:211:226:247:264:289:309:330:361:386 SD: 0.3424 cents 225:246:263:288:308:337:360:385:421:450 SD: 0.2985 cents 242:265:283:310:331:362:387:414:453:484 SD: 0.2874 cents 272:298:318:348:372:407:435:465:509:544 SD: 0.2849 cents 296:324:346:379:405:443:474:506:554:592 SD: 0.2311 cents 318:348:372:407:435:476:509:544:595:636 SD: 0.1254 cents 465:509:544:595:636:696:744:795:870:930 SD: 0.1177 cents