Scala analysis: duo101
Ellis duodene tempered in 101-et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 106.931 cents 106.930693 2: 201.980 cents 201.980198 3: 308.911 cents 308.910891 4: 392.079 cents 392.079208 5: 499.010 cents 499.009901 6: 594.059 cents 594.059406 7: 700.990 cents 700.990099 8: 807.921 cents 807.920792 9: 891.089 cents 891.089109 10: 1009.901 cents 1009.900990 11: 1093.069 cents 1093.069307 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 106.9307 cents 106.9307 1: 106.9307 cents 106.9307 2: 95.0495 cents 95.0495 3: 106.9307 cents 106.9307 4: 83.1683 cents 83.1683 5: 106.9307 cents 106.9307 6: 95.0495 cents 95.0495 7: 106.9307 cents 106.9307 8: 106.9307 cents 106.9307 9: 83.1683 cents 83.1683 10: 118.8119 cents 118.8119 11: 83.1683 cents 83.1683 12: 106.9307 cents 106.9307
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 83.16832 cents 1: 2 95.04950 cents 1: 6 106.93069 cents 1: 1 118.81188 cents 2: 4 190.09901 cents 2: 6 201.98020 cents 2: 2 213.86139 cents 3: 3 285.14852 cents 3: 3 297.02970 cents 3: 6 308.91089 cents 4: 8 392.07921 cents 4: 4 415.84158 cents 5: 1 487.12871 cents 5: 9 499.00990 cents 5: 2 510.89109 cents 6: 2 582.17822 cents 6: 4 594.05941 cents 6: 4 605.94059 cents 6: 2 617.82178 cents 7: 2 689.10891 cents 7: 9 700.99010 cents 7: 1 712.87129 cents 8: 4 784.15842 cents 8: 8 807.92079 cents 9: 6 891.08911 cents 9: 3 902.97030 cents 9: 3 914.85149 cents 10: 2 986.13861 cents 10: 6 998.01980 cents 10: 4 1009.90099 cents 11: 1 1081.18812 cents 11: 6 1093.06931 cents 11: 2 1104.95050 cents 11: 3 1116.83168 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 : 106.9 202.0 308.9 392.1 499.0 594.1 701.0 807.9 891.1 1009.9 1093.1 1200.0 106.9 : 95.0 202.0 285.1 392.1 487.1 594.1 701.0 784.2 903.0 986.1 1093.1 1200.0 202.0 : 106.9 190.1 297.0 392.1 499.0 605.9 689.1 807.9 891.1 998.0 1105.0 1200.0 308.9 : 83.2 190.1 285.1 392.1 499.0 582.2 701.0 784.2 891.1 998.0 1093.1 1200.0 392.1 : 106.9 202.0 308.9 415.8 499.0 617.8 701.0 807.9 914.9 1009.9 1116.8 1200.0 499.0 : 95.0 202.0 308.9 392.1 510.9 594.1 701.0 807.9 903.0 1009.9 1093.1 1200.0 594.1 : 106.9 213.9 297.0 415.8 499.0 605.9 712.9 807.9 914.9 998.0 1105.0 1200.0 701.0 : 106.9 190.1 308.9 392.1 499.0 605.9 701.0 807.9 891.1 998.0 1093.1 1200.0 807.9 : 83.2 202.0 285.1 392.1 499.0 594.1 701.0 784.2 891.1 986.1 1093.1 1200.0 891.1 : 118.8 202.0 308.9 415.8 510.9 617.8 701.0 807.9 903.0 1009.9 1116.8 1200.0 1009.9: 83.2 190.1 297.0 392.1 499.0 582.2 689.1 784.2 891.1 998.0 1081.2 1200.0 1093.1: 106.9 213.9 308.9 415.8 499.0 605.9 701.0 807.9 914.9 998.0 1116.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.1683 .. 118.8119 cents 35.64356 cents 83.16832 cents 2: 190.0990 .. 213.8614 cents 23.76238 cents 71.28713 cents 3: 285.1485 .. 308.9109 cents 23.76238 cents 71.28713 cents 4: 392.0792 .. 415.8416 cents 23.76238 cents 83.16832 cents 5: 487.1287 .. 510.8911 cents 23.76238 cents 71.28713 cents 6: 582.1782 .. 617.8218 cents 35.64356 cents 71.28713 cents 7: 689.1089 .. 712.8713 cents 23.76238 cents 71.28713 cents 8: 784.1584 .. 807.9208 cents 23.76238 cents 71.28713 cents 9: 891.0891 .. 914.8515 cents 23.76238 cents 83.16832 cents 10: 986.1386 .. 1009.9010 cents 23.76238 cents 71.28713 cents 11: 1081.1881 .. 1116.8317 cents 35.64356 cents 71.28713 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 83.16832 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 118.81188 cents Average / Smallest step : 1.202381 Largest / Average step : 1.188119 Largest / Smallest step : 1.428571 Median interval of one step : 106.93069 cents, amount: 6 Most common interval of one step : 106.93069 cents, amount: 6 Least squares average step : 99.96649 cents, oct.: 1199.59787 cents Scale is strictly proper Scale is a mode of a 101-tone equal temperament with octave 1200.000 cents degrees: 9 17 26 33 42 50 59 68 75 85 92 101 Least number of segments generator : 51 of 605.941 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 59 of 700.990 cents and inv. generated superset size: 20 = 8 more = 166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABAACDCA Step pattern size order : CBCACBCCADAC Interval vector is [ 0 0 0 0 0 0 3 2 6 1 0 0 0 0 0 4 6 2 0 0 0 0 0 3 3 6 0 0 0 0 0 0 8 0 4 0 0 0 0 0 1 9 2 0 0 0 0 0 2 4 ] Scale is a Constant Structure, by a margin of 71.28713 cents Scale diversity : 1.203251 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.752475 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 : 11.88119 cents Most common intervals : 499.00990 cents & inv., amount: 9 Most common triad is 0.0 499.010 700.990 cents, amount: 6 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 9 = 75.0000% Limited transpositions with margin 23.7624 cents: 2 5 7 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: 6.5800 c. M: 9.9010 c. Twelve-tone Chromatic (1/11-comma) 31: 3 2 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 6.5735 c. M: 13.4142 c. Genus diatonico-chromaticum 43: 4 3 4 3 4 3 4 4 3 4 3 4 SP M ME SD: 4.2146 c. M: 8.0129 c. Genus diatonico-chromaticum 46: 4 4 4 3 4 4 4 4 3 5 3 4 SP D3 SD: 4.1607 c. M:-7.4903 c. 55: 5 4 5 4 5 4 5 5 4 5 4 5 SP M ME SD: 3.4799 c. M: 6.2646 c. Genus diatonico-chromaticum 58: 5 5 5 4 5 5 5 5 4 6 4 5 SP D3 SD: 3.1246 c. M:-5.9406 c. 65: 6 5 6 4 6 5 6 6 4 7 4 6 SP SD: 3.6443 c. M:-5.4836 c. 67: 6 5 6 5 6 5 6 6 5 6 5 6 SP M ME SD: 3.4325 c. M: 6.9159 c. 70: 6 6 6 5 6 6 6 6 5 7 5 6 SP D3 SD: 2.9111 c. M:-5.9406 c. 77: 7 6 7 5 7 6 7 7 5 8 5 7 SP SD: 2.0509 c. M:-3.0860 c. 89: 8 7 8 6 8 7 8 8 6 9 6 8 SP SD: 0.8872 c. M:-1.3350 c. 101: 9 8 9 7 9 8 9 9 7 10 7 9 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: 0.4825 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.2664 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.3722 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 3.2930 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.6778 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.1768 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.5130 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.4813 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.8802 cents 11:12 x 13:14:15 x 16 x 18:20:21:22 S SD: 11.0716 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 6.8903 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 9.1209 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.0569 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.1226 cents 24:26:27:29:30:32:34:36:38:40:43:45:48 SD: 3.4272 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.4012 cents 30:32:34:36:38:40:42:45:48:50:54:56:60 SD: 2.6468 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1955 cents 42:45:47:50:53:56:59:63:67:70:75:79:84 SD: 1.8441 cents 47:50:53:56:59:63:66:70:75:79:84:88:94 SD: 1.7572 cents 48:51:54:57:60:64:68:72:77:80:86:90:96 SD: 1.7209 cents 51:54:57:61:64:68:72:76:81:85:91:96:102 SD: 1.7200 cents 56:60:63:67:70:75:79:84:89:94:100:105:112 SD: 1.6053 cents 62:66:70:74:78:83:87:93:99:104:111:117:124 SD: 1.3560 cents 66:70:74:79:83:88:93:99:105:110:118:124:132 SD: 1.0217 cents 82:87:92:98:103:109:116:123:131:137:147:154:164 SD: 0.9749 cents 91:97:102:109:114:121:128:136:145:152:163:171:182 SD: 0.9672 cents 92:98:103:110:115:123:130:138:147:154:165:173:184 SD: 0.9522 cents 96:102:108:115:120:128:135:144:153:161:172:181:192 SD: 0.8813 cents 98:104:110:117:123:131:138:147:156:164:176:184:196 SD: 0.7043 cents 114:121:128:136:143:152:161:171:182:191:204:214:228 SD: 0.6763 cents 122:130:137:146:153:163:172:183:195:204:219:229:244 SD: 0.6282 cents 129:137:145:154:162:172:182:193:206:216:231:243:258 SD: 0.6133 cents 138:147:155:165:173:184:194:207:220:231:247:259:276 SD: 0.5508 cents 144:153:162:172:181:192:203:216:230:241:258:271:288 SD: 0.5035 cents 153:163:172:183:192:204:216:229:244:256:274:288:306 SD: 0.4746 cents 168:179:189:201:211:224:237:252:268:281:301:316:336 SD: 0.4275 cents 200:213:225:239:251:267:282:300:319:335:358:376:400 SD: 0.3747 cents 220:234:247:263:276:293:310:330:351:368:394:414:440 SD: 0.3404 cents 235:250:264:281:295:314:331:352:375:393:421:442:470 SD: 0.3389 cents 236:251:265:282:296:315:333:354:376:395:423:444:472 SD: 0.2900 cents 251:267:282:300:315:335:354:376:400:420:450:472:502 SD: 0.2247 cents 347:369:390:415:435:463:489:520:553:581:622:652:694 SD: 0.2148 cents 362:385:407:433:454:483:510:543:577:606:649:681:724 SD: 0.2125 cents 374:398:420:447:469:499:527:561:596:626:670:703:748 SD: 0.1951 cents 389:414:437:465:488:519:548:583:620:651:697:731:778 SD: 0.1698 cents 410:436:461:490:514:547:578:615:654:686:735:771:820 SD: 0.1602 cents 437:465:491:522:548:583:616:655:697:731:783:822:874 SD: 0.1447 cents 501:533:563:599:628:668:706:751:799:838:898:942:1002 SD: 0.1330 cents 533:567:599:637:668:711:751:799:850:892:955:1002:1066 SD: 0.1228 cents 599:637:673:716:751:799:844:898:955:1002:1073:1126:1198 SD: 0.1108 cents