Scala analysis: duo
72-et tempered version of the Ellis duodene
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: 316.667 cents 316.666667 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: 1016.667 cents 1016.666667 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: 116.6667 cents 116.6667 4: 66.6667 cents 66.6667 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: 133.3333 cents 133.3333 11: 66.6667 cents 66.6667 12: 116.6667 cents 116.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 66.66667 cents 1: 2 83.33333 cents 1: 6 116.66667 cents 1: 1 133.33333 cents 2: 4 183.33333 cents 2: 6 200.00000 cents 2: 2 233.33333 cents 3: 3 266.66667 cents 3: 3 300.00000 cents 3: 6 316.66667 cents 4: 8 383.33333 cents 4: 4 433.33333 cents 5: 1 466.66667 cents 5: 9 500.00000 cents 5: 2 516.66667 cents 6: 2 566.66667 cents 6: 4 583.33333 cents 6: 4 616.66667 cents 6: 2 633.33333 cents 7: 2 683.33333 cents 7: 9 700.00000 cents 7: 1 733.33333 cents 8: 4 766.66667 cents 8: 8 816.66667 cents 9: 6 883.33333 cents 9: 3 900.00000 cents 9: 3 933.33333 cents 10: 2 966.66667 cents 10: 6 1000.00000 cents 10: 4 1016.66667 cents 11: 1 1066.66667 cents 11: 6 1083.33333 cents 11: 2 1116.66667 cents 11: 3 1133.33333 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 116.7 200.0 316.7 383.3 500.0 583.3 700.0 816.7 883.3 1016.7 1083.3 1200.0 116.7 : 83.3 200.0 266.7 383.3 466.7 583.3 700.0 766.7 900.0 966.7 1083.3 1200.0 200.0 : 116.7 183.3 300.0 383.3 500.0 616.7 683.3 816.7 883.3 1000.0 1116.7 1200.0 316.7 : 66.7 183.3 266.7 383.3 500.0 566.7 700.0 766.7 883.3 1000.0 1083.3 1200.0 383.3 : 116.7 200.0 316.7 433.3 500.0 633.3 700.0 816.7 933.3 1016.7 1133.3 1200.0 500.0 : 83.3 200.0 316.7 383.3 516.7 583.3 700.0 816.7 900.0 1016.7 1083.3 1200.0 583.3 : 116.7 233.3 300.0 433.3 500.0 616.7 733.3 816.7 933.3 1000.0 1116.7 1200.0 700.0 : 116.7 183.3 316.7 383.3 500.0 616.7 700.0 816.7 883.3 1000.0 1083.3 1200.0 816.7 : 66.7 200.0 266.7 383.3 500.0 583.3 700.0 766.7 883.3 966.7 1083.3 1200.0 883.3 : 133.3 200.0 316.7 433.3 516.7 633.3 700.0 816.7 900.0 1016.7 1133.3 1200.0 1016.7: 66.7 183.3 300.0 383.3 500.0 566.7 683.3 766.7 883.3 1000.0 1066.7 1200.0 1083.3: 116.7 233.3 316.7 433.3 500.0 616.7 700.0 816.7 933.3 1000.0 1133.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6667 .. 133.3333 cents 66.66667 cents 66.66667 cents 2: 183.3333 .. 233.3333 cents 50.00000 cents 50.00000 cents 3: 266.6667 .. 316.6667 cents 50.00000 cents 33.33333 cents 4: 383.3333 .. 433.3333 cents 50.00000 cents 66.66667 cents 5: 466.6667 .. 516.6667 cents 50.00000 cents 33.33333 cents 6: 566.6667 .. 633.3333 cents 66.66667 cents 50.00000 cents 7: 683.3333 .. 733.3333 cents 50.00000 cents 50.00000 cents 8: 766.6667 .. 816.6667 cents 50.00000 cents 33.33333 cents 9: 883.3333 .. 933.3333 cents 50.00000 cents 66.66667 cents 10: 966.6667 .. 1016.6667 cents 50.00000 cents 33.33333 cents 11: 1066.6667 .. 1133.3333 cents 66.66667 cents 50.00000 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 : 133.33333 cents Average / Smallest step : 1.500000 Largest / Average step : 1.333333 Largest / Smallest step : 2.000000 Median interval of one step : 116.66667 cents, amount: 6 Most common interval of one step : 116.66667 cents, amount: 6 Least squares average step : 99.79487 cents, oct.: 1197.53846 cents Scale is strictly proper Scale is a mode of a 72-tone equal temperament with octave 2/1 degrees: 7 12 19 23 30 35 42 49 53 61 65 72 Least number of segments generator : 37 of 616.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 53 of 883.333 cents and inv. generated superset size: 29 = 17 more = 241.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABAACDCA Step pattern size order : CBCACBCCADAC Interval vector is [ 0 0 0 3 2 0 6 1 0 0 4 6 0 2 0 3 0 3 6 0 0 0 8 0 0 4 0 1 0 9 2 0 0 2 4 0 ] Scale is a Constant Structure, by a margin of 33.33333 cents Scale diversity : 1.347868 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.500000 Rothenberg efficiency : 0.439743 redundancy: 0.560257 Efficiency x scale size : 5.276912 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 16.66667 cents Most common intervals : 500.00000 cents & inv., amount: 9 Most common triad is 0.0 500.000 700.000 cents, amount: 6 Number of recognisable fifths : 9, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 9 = 75.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- 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: 13.6083 c. M: 16.6667 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 2 1 2 1 2 2 1 2 1 2 P M ME SD: 7.3740 c. M: 14.9123 c. Genus diatonico-chromaticum, Yasser's Supradiatonic inverse 31: 3 2 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 5.0051 c. M: 10.2151 c. Genus diatonico-chromaticum 41: 4 3 4 2 4 3 4 4 2 5 2 4 SP SD: 3.7843 c. M:-7.7236 c. 53: 5 4 5 3 5 4 5 5 3 6 3 5 SP SD: 2.6435 c. M:-5.3459 c. Genus diatonico-chromaticum 60: 6 4 6 3 6 4 6 6 3 7 3 6 SP SD: 2.7217 c. M:-3.3333 c. 72: 7 5 7 4 7 5 7 7 4 8 4 7 SP SD: 0.0000 c. M: 0.0000 c. Genus diatonico-chromaticum
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: 11.9933 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 0.6774 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.9406 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 13.2475 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.8416 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.6315 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.3209 cents 11:12 x 13:14:15 x 16 x 18:20:21:22 S SD: 10.9212 cents 12:13 x 14:15:16:17:18:19:20:22 x 24 S SD: 6.9846 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.5049 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 6.6748 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.0514 cents 18:19:20:22 x 24:25:27:29:30:32:34:36 SD: 4.8336 cents 20:21:22:24:25:27:28:30:32:33:36:37:40 SD: 4.7661 cents 23:25:26:28:29:31:32:34:37:38:41:43:46 SD: 4.7590 cents 24:26:27:29:30:32:34:36:38:40:43:45:48 SD: 3.2702 cents 30:32:34:36:37:40:42:45:48:50:54:56:60 SD: 2.2685 cents 40:43:45:48:50:53:56:60:64:67:72:75:80 SD: 1.6543 cents 56:60:63:67:70:75:78:84:90:93:101:105:112 SD: 1.4270 cents 60:64:67:72:75:80:84:90:96:100:108:112:120 SD: 0.9910 cents 84:90:94:101:105:112:118:126:135:140:151:157:168 SD: 0.8702 cents 90:96:101:108:112:120:126:135:144:150:162:168:180 SD: 0.7205 cents 105:112:118:126:131:140:147:157:168:175:189:196:210 SD: 0.6741 cents 113:121:127:136:141:151:158:169:181:188:203:211:226 SD: 0.6642 cents 114:122:128:137:142:152:160:171:183:190:205:213:228 SD: 0.5464 cents 129:138:145:155:161:172:181:193:207:215:232:241:258 SD: 0.4859 cents 170:182:191:204:212:227:238:255:272:283:306:318:340 SD: 0.4025 cents 189:202:212:227:236:252:265:283:303:315:340:353:378 SD: 0.3533 cents 215:230:241:258:268:287:301:322:345:358:387:402:430 SD: 0.3407 cents 229:245:257:275:286:306:321:343:367:381:412:428:458 SD: 0.2911 cents 230:246:258:276:287:307:322:345:369:383:414:430:460 SD: 0.2752 cents 245:262:275:294:306:327:343:367:393:408:441:458:490 SD: 0.2324 cents 269:288:302:323:336:359:377:403:431:448:484:503:538 SD: 0.2183 cents 299:320:336:359:373:399:419:448:479:498:538:559:598 SD: 0.2140 cents 343:367:385:412:428:458:480:514:550:571:617:641:686 SD: 0.1986 cents 359:384:403:431:448:479:503:538:575:598:646:671:718 SD: 0.1422 cents 484:518:543:581:604:646:678:725:776:806:871:905:968 SD: 0.1389 cents 514:550:577:617:641:686:720:770:824:856:925:961:1028 SD: 0.1290 cents 529:566:594:635:660:706:741:793:848:881:952:989:1058 SD: 0.1240 cents 532:569:597:639:664:710:745:797:853:886:957:995:1064 SD: 0.1164 cents