Scala analysis: Lumma_in_72
Carl Lumma's scale in 72-EDO
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.667 cents 116.666667 2: 200.000 cents 200.000000 3: 266.667 cents 266.666667 4: 383.333 cents 383.333333 5: 500.000 cents 500.000000 6: 583.333 cents 583.333333 7: 700.000 cents 700.000000 8: 816.667 cents 816.666667 9: 883.333 cents 883.333333 10: 966.667 cents 966.666667 11: 1083.333 cents 1083.333333 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.6667 cents 116.6667 1: 116.6667 cents 116.6667 2: 83.3333 cents 83.3333 3: 66.6667 cents 66.6667 4: 116.6667 cents 116.6667 5: 116.6667 cents 116.6667 6: 83.3333 cents 83.3333 7: 116.6667 cents 116.6667 8: 116.6667 cents 116.6667 9: 66.6667 cents 66.6667 10: 83.3333 cents 83.3333 11: 116.6667 cents 116.6667 12: 116.6667 cents 116.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 66.66667 cents 1: 3 83.33333 cents 1: 7 116.66667 cents 2: 2 150.00000 cents 2: 2 183.33333 cents 2: 4 200.00000 cents 2: 4 233.33333 cents 3: 4 266.66667 cents 3: 2 300.00000 cents 3: 5 316.66667 cents 3: 1 350.00000 cents 4: 8 383.33333 cents 4: 4 433.33333 cents 5: 2 466.66667 cents 5: 8 500.00000 cents 5: 1 516.66667 cents 5: 1 550.00000 cents 6: 6 583.33333 cents 6: 6 616.66667 cents 7: 1 650.00000 cents 7: 1 683.33333 cents 7: 8 700.00000 cents 7: 2 733.33333 cents 8: 4 766.66667 cents 8: 8 816.66667 cents 9: 1 850.00000 cents 9: 5 883.33333 cents 9: 2 900.00000 cents 9: 4 933.33333 cents 10: 4 966.66667 cents 10: 4 1000.00000 cents 10: 2 1016.66667 cents 10: 2 1050.00000 cents 11: 7 1083.33333 cents 11: 3 1116.66667 cents 11: 2 1133.33333 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 : 116.7 200.0 266.7 383.3 500.0 583.3 700.0 816.7 883.3 966.7 1083.3 1200.0 116.7 : 83.3 150.0 266.7 383.3 466.7 583.3 700.0 766.7 850.0 966.7 1083.3 1200.0 200.0 : 66.7 183.3 300.0 383.3 500.0 616.7 683.3 766.7 883.3 1000.0 1116.7 1200.0 266.7 : 116.7 233.3 316.7 433.3 550.0 616.7 700.0 816.7 933.3 1050.0 1133.3 1200.0 383.3 : 116.7 200.0 316.7 433.3 500.0 583.3 700.0 816.7 933.3 1016.7 1083.3 1200.0 500.0 : 83.3 200.0 316.7 383.3 466.7 583.3 700.0 816.7 900.0 966.7 1083.3 1200.0 583.3 : 116.7 233.3 300.0 383.3 500.0 616.7 733.3 816.7 883.3 1000.0 1116.7 1200.0 700.0 : 116.7 183.3 266.7 383.3 500.0 616.7 700.0 766.7 883.3 1000.0 1083.3 1200.0 816.7 : 66.7 150.0 266.7 383.3 500.0 583.3 650.0 766.7 883.3 966.7 1083.3 1200.0 883.3 : 83.3 200.0 316.7 433.3 516.7 583.3 700.0 816.7 900.0 1016.7 1133.3 1200.0 966.7 : 116.7 233.3 350.0 433.3 500.0 616.7 733.3 816.7 933.3 1050.0 1116.7 1200.0 1083.3: 116.7 233.3 316.7 383.3 500.0 616.7 700.0 816.7 933.3 1000.0 1083.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6667 .. 116.6667 cents 50.00000 cents 66.66667 cents 2: 150.0000 .. 233.3333 cents 83.33333 cents 33.33333 cents 3: 266.6667 .. 350.0000 cents 83.33333 cents 33.33333 cents 4: 383.3333 .. 433.3333 cents 50.00000 cents 33.33333 cents 5: 466.6667 .. 550.0000 cents 83.33333 cents 33.33333 cents 6: 583.3333 .. 616.6667 cents 33.33333 cents 33.33333 cents 7: 650.0000 .. 733.3333 cents 83.33333 cents 33.33333 cents 8: 766.6667 .. 816.6667 cents 50.00000 cents 33.33333 cents 9: 850.0000 .. 933.3333 cents 83.33333 cents 33.33333 cents 10: 966.6667 .. 1050.0000 cents 83.33333 cents 33.33333 cents 11: 1083.3333 .. 1133.3333 cents 50.00000 cents 33.33333 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 66.66667 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 116.66667 cents Average / Smallest step : 1.500000 Largest / Average step : 1.166667 Largest / Smallest step : 1.750000 Median interval of one step : 116.66667 cents, amount: 7 Most common interval of one step : 116.66667 cents, amount: 7 Least squares average step : 98.79487 cents, oct.: 1185.53846 cents Scale is strictly proper Scale is a mode of a 72-tone equal temperament with octave 2/1 degrees: 7 12 16 23 30 35 42 49 53 58 65 72 Least number of segments generator : 37 of 616.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 65 of 1083.333 cents and inv. generated superset size: 26 = 14 more = 216.667% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 72-tone equal temperament Step pattern alph. order: ABCAABAACBAA Step pattern size order : LMSLLMLLSMLL Interval vector is [ 0 0 0 2 3 0 7 0 2 0 2 4 0 4 0 4 0 2 5 0 1 0 8 0 0 4 0 2 0 8 1 0 1 0 6 0 ] Scale is a Constant Structure, by a margin of 33.33333 cents Scale diversity : 1.404776 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.388889 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 : 16.66667 cents Number of recognisable 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 -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.0021 c. M:-33.3333 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 1 2 2 1 2 2 1 1 2 2 P D3 SD: 9.9308 c. M: 19.2982 c. 22: 2 2 1 2 2 2 2 2 1 2 2 2 SP B ME SD: 10.2949 c. M:-18.1818 c. Jubilee-12 24: 2 2 1 3 2 2 2 2 2 1 3 2 P T3 SD: 13.6083 c. M:-16.6667 c. 26: 3 1 2 2 3 2 2 3 1 2 2 3 N SD: 13.3337 c. M:-21.7949 c. 29: 3 2 1 3 3 2 3 3 1 2 3 3 P SD: 10.0232 c. M: 18.3908 c. 31: 3 2 2 3 3 2 3 3 2 2 3 3 SP D3 SD: 3.7313 c. M:-6.9892 c. Fokker 12-tone 41: 4 3 2 4 4 3 4 4 2 3 4 4 SP SD: 2.8212 c. M: 5.2846 c. 72: 7 5 4 7 7 5 7 7 4 5 7 7 SP SD: 0.0000 c. M:-0.0000 c. Smith's Prism
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: 0.7359 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 1.0418 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 14.1448 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 5.6831 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 12.1592 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 5.0796 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 10.1239 cents 10 x 11:12 x 13:14:15:16:17 x 19:20 SD: 9.7854 cents 11:12 x 13:14:15 x 16 x 18:19:21:22 SD: 10.8289 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 4.5350 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 7.2950 cents 14:15:16 x 17:19:20:21:22:23:24:26:28 SD: 8.2319 cents 15:16:17:18:19:20:21:22:24:25:26:28:30 S SD: 5.8735 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 5.3369 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 5.0748 cents 18:19:20:21:22:24:25:27:29:30:31:34:36 SD: 4.8603 cents 23:25:26:27:29:31:32:34:37:38:40:43:46 SD: 4.2756 cents 24:26:27:28:30:32:34:36:38:40:42:45:48 S SD: 3.0891 cents 30:32:34:35:37:40:42:45:48:50:52:56:60 SD: 2.5641 cents 32:34:36:37:40:43:45:48:51:53:56:60:64 SD: 2.3583 cents 40:43:45:47:50:53:56:60:64:67:70:75:80 SD: 1.9610 cents 42:45:47:49:52:56:59:63:67:70:73:79:84 SD: 1.9051 cents 48:51:54:56:60:64:67:72:77:80:84:90:96 SD: 1.2834 cents 60:64:67:70:75:80:84:90:96:100:105:112:120 SD: 1.0007 cents 72:77:81:84:90:96:101:108:115:120:126:135:144 SD: 0.8531 cents 90:96:101:105:112:120:126:135:144:150:157:168:180 SD: 0.7641 cents 113:121:127:132:141:151:158:169:181:188:198:211:226 SD: 0.6739 cents 114:122:128:133:142:152:160:171:183:190:199:213:228 SD: 0.5589 cents 138:148:155:161:172:184:193:207:221:230:241:258:276 SD: 0.5580 cents 146:156:164:170:182:195:204:219:234:243:255:273:292 SD: 0.5575 cents 155:166:174:181:193:207:217:232:248:258:271:290:310 SD: 0.5135 cents 162:173:182:189:202:216:227:243:260:270:283:303:324 SD: 0.4461 cents 173:185:194:202:216:231:242:259:277:288:302:323:346 SD: 0.4435 cents 174:186:195:203:217:232:244:261:279:290:304:325:348 SD: 0.4308 cents 186:199:209:217:232:248:261:279:298:310:325:348:372 SD: 0.4160 cents 197:211:221:230:246:263:276:295:316:328:344:368:394 SD: 0.3536 cents 215:230:241:251:268:287:301:322:345:358:376:402:430 SD: 0.3501 cents 227:243:255:265:283:303:318:340:364:378:397:424:454 SD: 0.3006 cents 230:246:258:268:287:307:322:345:369:383:402:430:460 SD: 0.2980 cents 245:262:275:286:306:327:343:367:393:408:428:458:490 SD: 0.2371 cents 287:307:322:335:358:383:402:430:460:478:502:537:574 SD: 0.2010 cents 359:384:403:419:448:479:503:538:575:598:627:671:718 SD: 0.1894 cents 385:412:432:449:480:514:539:577:617:641:673:720:770 SD: 0.1892 cents 400:428:449:467:499:534:560:599:641:666:699:748:800 SD: 0.1843 cents 415:444:466:484:518:554:581:622:665:691:725:776:830 SD: 0.1485 cents 499:534:560:582:623:666:699:748:800:831:872:933:998 SD: 0.1363 cents 516:552:579:602:644:689:723:773:827:859:902:965:1032 SD: 0.1312 cents 529:566:594:617:660:706:741:793:848:881:925:989:1058 SD: 0.1265 cents 589:630:661:687:735:786:825:883:944:981:1029:1101:1178 SD: 0.1221 cents