Scala analysis: orwellian9
A distributionally even scale in orwellian temperament, ababababc
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 43.330 cents 43.330000 2: 270.470 cents 270.470000 3: 387.990 cents 387.990000 4: 431.320 cents 431.320000 5: 658.460 cents 658.460000 6: 701.790 cents 701.790000 7: 928.930 cents 928.930000 8: 972.260 cents 972.260000 9: 1199.400 cents 1199.400000
SHOW/INTERVAL
0: 227.1400 cents 227.1400 1: 43.3300 cents 43.3300 2: 227.1400 cents 227.1400 3: 117.5200 cents 117.5200 4: 43.3300 cents 43.3300 5: 227.1400 cents 227.1400 6: 43.3300 cents 43.3300 7: 227.1400 cents 227.1400 8: 43.3300 cents 43.3300 9: 227.1400 cents 227.1400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 43.33000 cents 1: 1 117.52000 cents 1: 4 227.14000 cents 2: 1 160.85000 cents 2: 7 270.47000 cents 2: 1 344.66000 cents 3: 3 313.80000 cents 3: 3 387.99000 cents 3: 3 497.61000 cents 4: 2 431.32000 cents 4: 5 540.94000 cents 4: 2 615.13000 cents 5: 2 584.27000 cents 5: 5 658.46000 cents 5: 2 768.08000 cents 6: 3 701.79000 cents 6: 3 811.41000 cents 6: 3 885.60000 cents 7: 1 854.74000 cents 7: 7 928.93000 cents 7: 1 1038.55000 cents 8: 4 972.26000 cents 8: 1 1081.88000 cents 8: 4 1156.07000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 43.3 270.5 388.0 431.3 658.5 701.8 928.9 972.3 1199.4 43.3 : 227.1 344.7 388.0 615.1 658.5 885.6 928.9 1156.1 1199.4 270.5 : 117.5 160.8 388.0 431.3 658.5 701.8 928.9 972.3 1199.4 388.0 : 43.3 270.5 313.8 540.9 584.3 811.4 854.7 1081.9 1199.4 431.3 : 227.1 270.5 497.6 540.9 768.1 811.4 1038.6 1156.1 1199.4 658.5 : 43.3 270.5 313.8 540.9 584.3 811.4 928.9 972.3 1199.4 701.8 : 227.1 270.5 497.6 540.9 768.1 885.6 928.9 1156.1 1199.4 928.9 : 43.3 270.5 313.8 540.9 658.5 701.8 928.9 972.3 1199.4 972.3 : 227.1 270.5 497.6 615.1 658.5 885.6 928.9 1156.1 1199.4 1199.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.3300 .. 227.1400 cents 183.81000 cents 43.33000 cents 2: 160.8500 .. 344.6600 cents 183.81000 cents -66.29000 cents 3: 313.8000 .. 497.6100 cents 183.81000 cents -30.86000 cents 4: 431.3200 .. 615.1300 cents 183.81000 cents -66.29000 cents 5: 584.2700 .. 768.0800 cents 183.81000 cents -30.86000 cents 6: 701.7900 .. 885.6000 cents 183.81000 cents -66.29000 cents 7: 854.7400 .. 1038.5500 cents 183.81000 cents -30.86000 cents 8: 972.2600 .. 1156.0700 cents 183.81000 cents -66.29000 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 43.33000 cents, class 1 Average step (divided formal octave): 133.2667 cents Largest one step interval : 227.14000 cents Average / Smallest step : 3.075621 Largest / Average step : 1.704402 Largest / Smallest step : 5.242096 Median interval of one step : 117.52000 cents, amount: 1 Least squares average step : 126.49737 cents, oct.: 1138.47632 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABABAB Step pattern size order : SLMSLSLSL Scale is a Constant Structure, by a margin of 30.86000 cents Scale diversity : 1.435212 Lumma stability : 0.072253 Lumma impropriety factor : 0.298266 Rothenberg efficiency : 0.525132 redundancy: 0.474868 Efficiency x scale size : 4.726190 Number of different interval sizes : 24 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 30.86000 cents Most common intervals : 270.47000 cents & inv., amount: 7 Scale is a chain of 4 triads 0.0 43.330 270.470 cents Most common triad is 0.0 270.470 928.930 cents, amount: 5 Number of recognisable fifths : 3, average 701.7900 cents Number of recognisable fourths : 3, average 497.6100 cents Formal octave complements present : 3 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
9: 0 2 1 0 2 0 2 0 2 N T3 SD: 25.6309 c. M: 43.3300 c. 16: 1 3 1 1 3 0 3 1 3 N SD: 21.7172 c. M:-31.6325 c. 17: 1 3 1 1 3 1 3 1 3 N M DE S SD: 18.6393 c. M: 35.2253 c. 18: 1 3 2 1 3 1 3 1 3 P T3 SD: 20.3373 c. M:-35.1133 c. 19: 1 3 2 1 3 1 4 0 4 N SD: 17.2305 c. M: 27.1968 c. 21: 1 4 2 1 4 0 4 1 4 N SD: 16.4526 c. M:-26.9114 c. 22: 1 4 2 1 4 1 4 1 4 N T3 SD: 6.2040 c. M:-11.1882 c. 31: 1 6 3 1 6 1 6 1 6 N T3 SD: 3.4973 c. M: 5.7265 c. 53: 2 10 5 2 10 2 10 2 10 N T3 SD: 1.6398 c. M: 3.2768 c. 80: 3 15 8 3 15 3 15 3 15 N T3 SD: 1.9274 c. M:-3.4625 c. 84: 3 16 8 3 16 3 16 3 16 N T3 SD: 1.6830 c. M: 2.9629 c. 89: 3 17 9 3 17 3 17 3 17 N T3 SD: 1.7192 c. M: 2.9008 c. 111: 4 21 11 4 21 4 21 4 21 N T3 SD: 0.5641 c. M:-1.0046 c. 164: 6 31 16 6 31 6 31 6 31 N T3 SD: 0.3056 c. M:-0.5505 c. 275: 10 52 27 10 52 10 52 10 52 N T3 SD: 0.2650 c. M:-0.4640 c. 306: 11 58 30 11 58 11 58 11 58 N T3 SD: 0.1284 c. M: 0.2143 c. 470: 17 89 46 17 89 17 89 17 89 N T3 SD: 0.0492 c. M: 0.0989 c. 776: 28 147 76 28 147 28 147 28 147 N T3 SD: 0.0522 c. M: 0.0924 c. 887: 32 168 87 32 168 32 168 32 168 N T3 SD: 0.0462 c. M:-0.0909 c. 1051: 38 199 103 38 199 38 199 38 199 N T3 SD: 0.0308 c. M:-0.0532 c. 1357: 49 257 133 49 257 49 257 49 257 N T3 SD: 0.0137 c. M:-0.0252 c. 1827: 66 346 179 66 346 66 346 66 346 N T3 SD: 0.0049 c. M: 0.0087 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.6000 cents 2 x x x x x 3 x x 4 S SD: 0.3111 cents 3 x x x 4 x x 5 x 6 S SD: 26.7482 cents 4 x x 5 x x 6 x 7:8 S SD: 0.9679 cents 5 x 6 x x 7:8 x 9:10 S SD: 29.9233 cents 6 x 7 x 8 x 9:10:11:12 S SD: 18.5570 cents 7 x 8 x 9:10:11:12 x 14 S SD: 16.4721 cents 8 x 9:10 x x 12 x 14:16 S SD: 13.3345 cents 9 x x 11:12:13:14:15:16:18 SD: 16.3607 cents 10 x 12 x 13 x 15:17:18:20 SD: 11.4579 cents 11:12:13 x 14:16:17:19 x 22 SD: 17.5772 cents 12:13:14:15 x x 18 x 21:24 S SD: 15.8982 cents 13:14:15:16:17:19:20:22:23:26 SD: 12.2488 cents 14:15:16 x 18:20:21:24:25:28 SD: 12.5269 cents 15:16:18:19 x 22:23 x 26:30 SD: 13.5923 cents 16:17:19:20:21:23:24:27:28:32 SD: 9.6509 cents 17:18:20:21:22:25:26:29:30:34 SD: 8.0870 cents 18:19:21 x 23:26:27:31:32:36 SD: 7.6880 cents 19:20:22:24 x 28:29:32:33:38 SD: 8.5418 cents 20:21:23:25:26:29:30:34:35:40 SD: 6.4607 cents 22:23:26 x 28:32:33:38:39:44 SD: 6.1545 cents 24:25:28:30:31:35:36:41:42:48 SD: 3.4157 cents 25:26:29:31:32:37 x 43:44:50 SD: 4.9939 cents 26:27:30 x 33:38:39:44:46:52 SD: 5.4735 cents 28:29:33:35:36:41:42:48:49:56 SD: 2.6030 cents 30:31:35:38 x 44:45:51:53:60 SD: 3.8343 cents 31:32:36:39:40:45:46:53:54:62 SD: 3.7017 cents 32:33:37:40:41:47:48:55:56:64 SD: 2.7445 cents 35:36:41:44:45:51:52:60:61:70 SD: 2.6412 cents 36:37:42:45:46:53:54:62:63:72 SD: 2.1253 cents 48:49:56:60:62:70:72:82:84:96 SD: 1.7766 cents 52:53:61:65:67:76:78:89:91:104 SD: 1.6355 cents 70:72:82:88:90:102:105:120:123:140 SD: 1.5658 cents 71:73:83:89:91:104:106:121:124:142 SD: 1.5281 cents 72:74:84:90:92:105:108:123:126:144 SD: 1.2389 cents 76:78:89:95:98:111:114:130:133:152 SD: 1.1714 cents 78:80:91:98:100:114:117:133:137:156 SD: 1.1266 cents 82:84:96:103:105:120:123:140:144:164 SD: 0.9975 cents 84:86:98:105:108:123:126:144:147:168 SD: 0.9271 cents 106:109:124:133:136:155:159:181:186:212 SD: 0.8506 cents 112:115:131:140:144:164:168:192:196:224 SD: 0.8353 cents 114:117:133:143:146:167:171:195:200:228 SD: 0.7980 cents 123:126:144:154:158:180:184:210:216:246 SD: 0.7927 cents 124:127:145:155:159:181:186:212:217:248 SD: 0.6429 cents 152:156:178:190:195:222:228:260:267:304 SD: 0.6183 cents 155:159:181:194:199:227:232:265:272:310 SD: 0.5649 cents 158:162:185:198:203:231:237:270:277:316 SD: 0.5415 cents 160:164:187:200:205:234:240:274:281:320 SD: 0.5239 cents 166:170:194:208:213:243:249:284:291:332 SD: 0.4133 cents 190:195:222:238:244:278:285:325:333:380 SD: 0.3849 cents 194:199:227:243:249:284:291:332:340:388 SD: 0.3753 cents 236:242:276:295:303:345:354:404:414:472 SD: 0.3534 cents 244:250:285:305:313:357:366:417:428:488 SD: 0.3359 cents 266:273:311:333:341:389:399:455:466:532 SD: 0.3238 cents 272:279:318:340:349:398:408:465:477:544 SD: 0.2317 cents 318:326:372:398:408:465:477:544:558:636 SD: 0.2245 cents 350:359:409:438:449:512:525:599:614:700 SD: 0.2178 cents 354:363:414:443:454:518:531:605:621:708 SD: 0.2021 cents 434:445:507:543:557:635:651:742:761:868 SD: 0.1911 cents 438:449:512:548:562:641:657:749:768:876 SD: 0.1279 cents