Scala analysis: diadieorw2
84-et version of diadie2.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: 314.286 cents 314.285714 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: 928.571 cents 928.571429 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: 114.2857 cents 114.2857 4: 71.4286 cents 71.4286 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: 114.2857 cents 114.2857 10: 42.8571 cents 42.8571 11: 114.2857 cents 114.2857 12: 114.2857 cents 114.2857
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 42.85714 cents 1: 1 71.42857 cents 1: 2 85.71429 cents 1: 8 114.28571 cents 2: 2 157.14286 cents 2: 2 185.71429 cents 2: 4 200.00000 cents 2: 4 228.57143 cents 3: 5 271.42857 cents 3: 1 300.00000 cents 3: 4 314.28571 cents 3: 2 342.85714 cents 4: 8 385.71429 cents 4: 4 428.57143 cents 5: 3 471.42857 cents 5: 7 500.00000 cents 5: 2 542.85714 cents 6: 6 585.71429 cents 6: 6 614.28571 cents 7: 2 657.14286 cents 7: 7 700.00000 cents 7: 3 728.57143 cents 8: 4 771.42857 cents 8: 8 814.28571 cents 9: 2 857.14286 cents 9: 4 885.71429 cents 9: 1 900.00000 cents 9: 5 928.57143 cents 10: 4 971.42857 cents 10: 4 1000.00000 cents 10: 2 1014.28571 cents 10: 2 1042.85714 cents 11: 8 1085.71429 cents 11: 2 1114.28571 cents 11: 1 1128.57143 cents 11: 1 1157.14286 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 : 114.3 200.0 314.3 385.7 500.0 585.7 700.0 814.3 928.6 971.4 1085.7 1200.0 114.3 : 85.7 200.0 271.4 385.7 471.4 585.7 700.0 814.3 857.1 971.4 1085.7 1200.0 200.0 : 114.3 185.7 300.0 385.7 500.0 614.3 728.6 771.4 885.7 1000.0 1114.3 1200.0 314.3 : 71.4 185.7 271.4 385.7 500.0 614.3 657.1 771.4 885.7 1000.0 1085.7 1200.0 385.7 : 114.3 200.0 314.3 428.6 542.9 585.7 700.0 814.3 928.6 1014.3 1128.6 1200.0 500.0 : 85.7 200.0 314.3 428.6 471.4 585.7 700.0 814.3 900.0 1014.3 1085.7 1200.0 585.7 : 114.3 228.6 342.9 385.7 500.0 614.3 728.6 814.3 928.6 1000.0 1114.3 1200.0 700.0 : 114.3 228.6 271.4 385.7 500.0 614.3 700.0 814.3 885.7 1000.0 1085.7 1200.0 814.3 : 114.3 157.1 271.4 385.7 500.0 585.7 700.0 771.4 885.7 971.4 1085.7 1200.0 928.6 : 42.9 157.1 271.4 385.7 471.4 585.7 657.1 771.4 857.1 971.4 1085.7 1200.0 971.4 : 114.3 228.6 342.9 428.6 542.9 614.3 728.6 814.3 928.6 1042.9 1157.1 1200.0 1085.7: 114.3 228.6 314.3 428.6 500.0 614.3 700.0 814.3 928.6 1042.9 1085.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 42.8571 .. 114.2857 cents 71.42857 cents 42.85714 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 .. 1157.1429 cents 71.42857 cents 42.85714 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 42.85714 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 114.28571 cents Average / Smallest step : 2.333333 Largest / Average step : 1.142857 Largest / Smallest step : 2.666667 Median interval of one step : 114.28571 cents, amount: 8 Most common interval of one step : 114.28571 cents, amount: 8 Least squares average step : 99.75824 cents, oct.: 1197.09890 cents Scale is strictly proper Scale is a mode of a 84-tone equal temperament with octave 1200.000 cents degrees: 8 14 22 27 35 41 49 57 65 68 76 84 Least number of segments generator : 71 of 1014.286 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 65 of 928.571 cents and inv. generated superset size: 22 = 10 more = 183.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABAAADAA Step pattern size order : DCDBDCDDDADD Interval vector is [ 0 0 1 0 1 2 0 8 0 0 2 0 2 4 0 4 0 0 5 0 1 4 0 2 0 0 8 0 0 4 0 0 3 0 7 0 0 2 0 0 6 0 ] Scale is a Constant Structure, by a margin of 42.85714 cents Scale diversity : 1.414349 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.428571 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 : 4 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 : 7, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- 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 2 1 2 1 2 2 2 0 2 2 P D3 SD: 12.1818 c. M: 24.0601 c. 22: 2 2 2 1 2 2 2 2 2 1 2 2 SP B ME SD: 9.4100 c. M:-18.1818 c. Pajara-12 31: 3 2 3 2 3 2 3 3 3 1 3 3 SP D3 SD: 3.3390 c. M: 6.4516 c. Marvel-12 53: 5 4 5 3 5 4 5 5 5 2 5 5 SP SD: 1.9530 c. M:-3.7736 c. Marvel-12 84: 8 6 8 5 8 6 8 8 8 3 8 8 SP SD: 0.0000 c. M:-0.0000 c. Marvel-12
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: 14.7520 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: 9.2605 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 12.3962 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.7350 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 5.4551 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 10.6788 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.8847 cents 11:12 x 13:14:15 x 16:18:19 x 21:22 SD: 11.0425 cents 12:13 x 14:15:16:17:18:19 x 21:22:24 SD: 6.9453 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.2351 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.4653 cents 15:16:17:18:19:20:21:22:24 x 26:28:30 S SD: 4.6482 cents 18:19:20:22 x 24:25:27:29:31:32:34:36 SD: 5.1917 cents 20:21:22:24:25:27:28:30:32:34:35:37:40 SD: 4.5992 cents 24:26:27:29:30:32:34:36:38:41:42:45:48 SD: 3.1798 cents 30:32:34:36:37:40:42:45:48:51:53:56:60 SD: 2.8055 cents 32:34:36:38:40:43:45:48:51:55:56:60:64 SD: 2.1900 cents 40:43:45:48:50:53:56:60:64:68:70:75:80 SD: 1.7222 cents 48:51:54:58:60:64:67:72:77:82:84:90:96 SD: 1.6432 cents 55:59:62:66:69:73:77:82:88:94:96:103:110 SD: 1.6431 cents 56:60:63:67:70:75:79:84:90:96:98:105:112 SD: 1.3901 cents 60:64:67:72:75:80:84:90:96:103:105:112:120 SD: 1.1460 cents 72:77:81:86:90:96:101:108:115:123:126:135:144 SD: 0.8341 cents 100:107:112:120:125:133:140:150:160:171:175:187:200 SD: 0.7899 cents 104:111:117:125:130:139:146:156:166:178:182:195:208 SD: 0.7693 cents 105:112:118:126:131:140:147:157:168:180:184:197:210 SD: 0.7509 cents 116:124:130:139:145:155:163:174:186:198:203:217:232 SD: 0.6165 cents 131:140:147:157:164:175:184:196:210:224:230:245:262 SD: 0.5650 cents 132:141:148:158:165:176:185:198:211:226:231:247:264 SD: 0.5332 cents 156:167:175:187:195:208:219:234:250:267:273:292:312 SD: 0.5274 cents 161:172:181:193:201:215:226:241:258:275:282:301:322 SD: 0.4544 cents 189:202:212:227:236:252:265:283:303:323:331:354:378 SD: 0.4428 cents 203:217:228:243:254:271:285:304:325:347:356:380:406 SD: 0.3863 cents 206:220:231:247:257:275:289:309:330:352:361:386:412 SD: 0.3746 cents 221:236:248:265:276:295:310:331:354:378:387:414:442 SD: 0.2263 cents 335:358:376:402:419:447:470:502:536:573:587:627:670 SD: 0.2200 cents 337:360:378:404:421:450:473:505:539:576:591:631:674 SD: 0.2163 cents 352:376:395:422:440:470:494:527:563:602:617:659:704 SD: 0.1941 cents 368:393:413:441:460:491:516:551:589:629:645:689:736 SD: 0.1721 cents 457:488:513:548:571:610:641:685:731:781:801:856:914 SD: 0.1540 cents 472:504:530:566:590:630:662:707:755:807:827:884:944 SD: 0.1516 cents 514:549:577:616:642:686:721:770:823:879:901:962:1028 SD: 0.1347 cents 541:578:607:649:676:722:759:811:866:925:948:1013:1082 SD: 0.1332 cents 558:596:626:669:697:745:783:836:893:954:978:1045:1116 SD: 0.1294 cents 573:612:643:687:716:765:804:859:917:980:1004:1073:1146 SD: 0.1294 cents 586:626:658:703:732:782:822:878:938:1002:1027:1097:1172 SD: 0.1123 cents