Scala analysis: diadieorw1
84-et version of diadie1.scl (similar to lumma.scl)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 114.286 cents 114.285714 2: 200.000 cents 200.000000 3: 271.429 cents 271.428571 4: 385.714 cents 385.714286 5: 500.000 cents 500.000000 6: 585.714 cents 585.714286 7: 700.000 cents 700.000000 8: 814.286 cents 814.285714 9: 885.714 cents 885.714286 10: 971.429 cents 971.428571 11: 1085.714 cents 1085.714286 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 114.2857 cents 114.2857 1: 114.2857 cents 114.2857 2: 85.7143 cents 85.7143 3: 71.4286 cents 71.4286 4: 114.2857 cents 114.2857 5: 114.2857 cents 114.2857 6: 85.7143 cents 85.7143 7: 114.2857 cents 114.2857 8: 114.2857 cents 114.2857 9: 71.4286 cents 71.4286 10: 85.7143 cents 85.7143 11: 114.2857 cents 114.2857 12: 114.2857 cents 114.2857
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 71.42857 cents 1: 3 85.71429 cents 1: 7 114.28571 cents 2: 2 157.14286 cents 2: 2 185.71429 cents 2: 4 200.00000 cents 2: 4 228.57143 cents 3: 4 271.42857 cents 3: 2 300.00000 cents 3: 5 314.28571 cents 3: 1 342.85714 cents 4: 8 385.71429 cents 4: 4 428.57143 cents 5: 2 471.42857 cents 5: 8 500.00000 cents 5: 1 514.28571 cents 5: 1 542.85714 cents 6: 6 585.71429 cents 6: 6 614.28571 cents 7: 1 657.14286 cents 7: 1 685.71429 cents 7: 8 700.00000 cents 7: 2 728.57143 cents 8: 4 771.42857 cents 8: 8 814.28571 cents 9: 1 857.14286 cents 9: 5 885.71429 cents 9: 2 900.00000 cents 9: 4 928.57143 cents 10: 4 971.42857 cents 10: 4 1000.00000 cents 10: 2 1014.28571 cents 10: 2 1042.85714 cents 11: 7 1085.71429 cents 11: 3 1114.28571 cents 11: 2 1128.57143 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 114.3 200.0 271.4 385.7 500.0 585.7 700.0 814.3 885.7 971.4 1085.7 1200.0 114.3 : 85.7 157.1 271.4 385.7 471.4 585.7 700.0 771.4 857.1 971.4 1085.7 1200.0 200.0 : 71.4 185.7 300.0 385.7 500.0 614.3 685.7 771.4 885.7 1000.0 1114.3 1200.0 271.4 : 114.3 228.6 314.3 428.6 542.9 614.3 700.0 814.3 928.6 1042.9 1128.6 1200.0 385.7 : 114.3 200.0 314.3 428.6 500.0 585.7 700.0 814.3 928.6 1014.3 1085.7 1200.0 500.0 : 85.7 200.0 314.3 385.7 471.4 585.7 700.0 814.3 900.0 971.4 1085.7 1200.0 585.7 : 114.3 228.6 300.0 385.7 500.0 614.3 728.6 814.3 885.7 1000.0 1114.3 1200.0 700.0 : 114.3 185.7 271.4 385.7 500.0 614.3 700.0 771.4 885.7 1000.0 1085.7 1200.0 814.3 : 71.4 157.1 271.4 385.7 500.0 585.7 657.1 771.4 885.7 971.4 1085.7 1200.0 885.7 : 85.7 200.0 314.3 428.6 514.3 585.7 700.0 814.3 900.0 1014.3 1128.6 1200.0 971.4 : 114.3 228.6 342.9 428.6 500.0 614.3 728.6 814.3 928.6 1042.9 1114.3 1200.0 1085.7: 114.3 228.6 314.3 385.7 500.0 614.3 700.0 814.3 928.6 1000.0 1085.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 71.4286 .. 114.2857 cents 42.85714 cents 71.42857 cents 2: 157.1429 .. 228.5714 cents 71.42857 cents 42.85714 cents 3: 271.4286 .. 342.8571 cents 71.42857 cents 42.85714 cents 4: 385.7143 .. 428.5714 cents 42.85714 cents 42.85714 cents 5: 471.4286 .. 542.8571 cents 71.42857 cents 42.85714 cents 6: 585.7143 .. 614.2857 cents 28.57143 cents 42.85714 cents 7: 657.1429 .. 728.5714 cents 71.42857 cents 42.85714 cents 8: 771.4286 .. 814.2857 cents 42.85714 cents 42.85714 cents 9: 857.1429 .. 928.5714 cents 71.42857 cents 42.85714 cents 10: 971.4286 .. 1042.8571 cents 71.42857 cents 42.85714 cents 11: 1085.7143 .. 1128.5714 cents 42.85714 cents 42.85714 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 71.42857 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 114.28571 cents Average / Smallest step : 1.400000 Largest / Average step : 1.142857 Largest / Smallest step : 1.600000 Median interval of one step : 114.28571 cents, amount: 7 Most common interval of one step : 114.28571 cents, amount: 7 Least squares average step : 98.96703 cents, oct.: 1187.60440 cents Scale is strictly proper Scale is a mode of a 84-tone equal temperament with octave 1200.000 cents degrees: 8 14 19 27 35 41 49 57 62 68 76 84 Least number of segments generator : 43 of 614.286 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 65 of 928.571 cents and inv. generated superset size: 25 = 13 more = 208.333% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 84-tone equal temperament Step pattern alph. order: ABCAABAACBAA Step pattern size order : LMSLLMLLSMLL Interval vector is [ 0 0 0 0 2 3 0 7 0 0 2 0 2 4 0 4 0 0 4 0 2 5 0 1 0 0 8 0 0 4 0 0 2 0 8 1 0 1 0 0 6 0 ] Scale is a Constant Structure, by a margin of 42.85714 cents Scale diversity : 1.384800 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.476190 Rothenberg efficiency : 0.395893 redundancy: 0.604107 Efficiency x scale size : 4.750722 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 14.28571 cents Number of recognisable fifths : 9, average 698.4127 cents Number of appreciable fifths : 8, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 15.4303 c. M:-28.5714 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 1 2 2 1 2 2 1 1 2 2 P D3 SD: 12.1818 c. M: 24.0601 c. 22: 2 2 1 2 2 2 2 2 1 2 2 2 SP B ME SD: 9.4100 c. M:-18.1818 c. Jubilee-12 31: 3 2 2 3 3 2 3 3 2 2 3 3 SP D3 SD: 3.3390 c. M: 6.4516 c. Fokker 12-tone 53: 5 4 3 5 5 4 5 5 3 4 5 5 SP SD: 1.9530 c. M:-3.7736 c. 84: 8 6 5 8 8 6 8 8 5 6 8 8 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.9775 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.7930 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.8275 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 12.8013 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.1275 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 12.0312 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 5.4551 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 9.7211 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 9.5684 cents 11:12 x 13:14:15 x 16 x 18:19:21:22 SD: 10.8412 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 4.6339 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 7.4968 cents 14:15:16 x 18:19:20:21:22:23:25:26:28 SD: 8.2408 cents 15:16:17:18:19:20:21:22:24:25:26:28:30 S SD: 5.6329 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 5.2253 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.8485 cents 23:25:26:27:29:31:32:34:37:38:40:43:46 SD: 4.4795 cents 24:26:27:28:30:32:34:36:38:40:42:45:48 S SD: 3.0030 cents 30:32:34:35:37:40:42:45:48:50:53:56:60 SD: 2.7075 cents 32:34:36:37:40:43:45:48:51:53:56:60:64 SD: 2.4716 cents 40:43:45:47:50:53:56:60:64:67:70:75:80 SD: 1.7479 cents 48:51:54:56:60:64:67:72:77:80:84:90:96 SD: 1.2677 cents 57:61:64:67:71:76:80:85:91:95:100:107:114 SD: 1.2594 cents 60:64:67:70:75:80:84:90:96:100:105:112:120 SD: 1.0588 cents 72:77:81:84:90:96:101:108:115:120:126:135:144 SD: 0.7268 cents 105:112:118:123:131:140:147:157:168:175:184:197:210 SD: 0.6803 cents 117:125:131:137:146:156:164:175:187:195:205:219:234 SD: 0.5874 cents 132:141:148:154:165:176:185:198:211:220:231:247:264 SD: 0.5821 cents 147:157:165:172:184:196:206:220:235:245:258:275:294 SD: 0.4793 cents 165:176:185:193:206:220:231:247:264:275:289:309:330 SD: 0.4757 cents 177:189:199:207:221:236:248:265:283:295:310:331:354 SD: 0.4560 cents 188:201:211:220:235:251:264:282:301:314:329:352:376 SD: 0.4055 cents 189:202:212:221:236:252:265:283:303:315:331:354:378 SD: 0.3867 cents 205:219:230:240:256:274:288:307:328:342:359:384:410 SD: 0.3813 cents 221:236:248:259:276:295:310:331:354:369:387:414:442 SD: 0.3795 cents 235:251:264:275:294:314:330:352:376:392:412:440:470 SD: 0.3236 cents 236:252:265:276:295:315:331:354:378:394:414:442:472 SD: 0.2905 cents 253:270:284:296:316:338:355:379:405:422:443:474:506 SD: 0.2694 cents 293:313:329:343:366:391:411:439:469:489:514:549:586 SD: 0.2401 cents 295:315:331:345:369:394:414:442:472:492:517:552:590 SD: 0.2283 cents 325:347:365:380:406:434:456:487:520:542:570:608:650 SD: 0.2219 cents 335:358:376:392:419:447:470:502:536:559:587:627:670 SD: 0.1961 cents 353:377:396:413:441:471:495:529:565:589:619:661:706 SD: 0.1552 cents 424:453:476:496:530:566:595:635:679:707:743:794:848 SD: 0.1502 cents 425:454:477:497:531:567:596:637:680:709:745:796:850 SD: 0.1340 cents 588:628:660:688:735:785:825:881:941:981:1031:1101:1176 SD: 0.1163 cents