Scala analysis: starling11
Starling[11] hobbit <11 18 26 31| in <135 214 314 379| tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 80.000 cents 80.000000 2: 231.111 cents 231.111110 3: 311.111 cents 311.111110 4: 391.111 cents 391.111110 5: 577.778 cents 577.777780 6: 622.222 cents 622.222220 7: 808.889 cents 808.888890 8: 888.889 cents 888.888890 9: 968.889 cents 968.888890 10: 1120.000 cents 1120.000000 11: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 80.0000 cents 80.0000 1: 80.0000 cents 80.0000 2: 151.1111 cents 151.1111 3: 80.0000 cents 80.0000 4: 80.0000 cents 80.0000 5: 186.6667 cents 186.6667 6: 44.4444 cents 44.4444 7: 186.6667 cents 186.6667 8: 80.0000 cents 80.0000 9: 80.0000 cents 80.0000 10: 151.1111 cents 151.1111 11: 80.0000 cents 80.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 44.44444 cents 1: 6 80.00000 cents 1: 2 151.11111 cents 1: 2 186.66667 cents 2: 3 160.00000 cents 2: 6 231.11111 cents 2: 2 266.66667 cents 3: 8 311.11111 cents 3: 2 346.66667 cents 3: 1 417.77778 cents 4: 6 391.11111 cents 4: 1 462.22222 cents 4: 4 497.77778 cents 5: 2 471.11111 cents 5: 4 542.22222 cents 5: 5 577.77778 cents 6: 5 622.22222 cents 6: 4 657.77778 cents 6: 2 728.88889 cents 7: 4 702.22222 cents 7: 1 737.77778 cents 7: 6 808.88889 cents 8: 1 782.22222 cents 8: 2 853.33333 cents 8: 8 888.88889 cents 9: 2 933.33333 cents 9: 6 968.88889 cents 9: 3 1040.00000 cents 10: 2 1013.33333 cents 10: 2 1048.88889 cents 10: 6 1120.00000 cents 10: 1 1155.55556 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.20000 = 16/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 80.0 231.1 311.1 391.1 577.8 622.2 808.9 888.9 968.9 1120.0 1200.0 80.0 : 151.1 231.1 311.1 497.8 542.2 728.9 808.9 888.9 1040.0 1120.0 1200.0 231.1 : 80.0 160.0 346.7 391.1 577.8 657.8 737.8 888.9 968.9 1048.9 1200.0 311.1 : 80.0 266.7 311.1 497.8 577.8 657.8 808.9 888.9 968.9 1120.0 1200.0 391.1 : 186.7 231.1 417.8 497.8 577.8 728.9 808.9 888.9 1040.0 1120.0 1200.0 577.8 : 44.4 231.1 311.1 391.1 542.2 622.2 702.2 853.3 933.3 1013.3 1200.0 622.2 : 186.7 266.7 346.7 497.8 577.8 657.8 808.9 888.9 968.9 1155.6 1200.0 808.9 : 80.0 160.0 311.1 391.1 471.1 622.2 702.2 782.2 968.9 1013.3 1200.0 888.9 : 80.0 231.1 311.1 391.1 542.2 622.2 702.2 888.9 933.3 1120.0 1200.0 968.9 : 151.1 231.1 311.1 462.2 542.2 622.2 808.9 853.3 1040.0 1120.0 1200.0 1120.0: 80.0 160.0 311.1 391.1 471.1 657.8 702.2 888.9 968.9 1048.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.4444 .. 186.6667 cents 142.22223 cents 44.44444 cents 2: 160.0000 .. 266.6667 cents 106.66667 cents -26.66667 cents 3: 311.1111 .. 417.7778 cents 106.66667 cents 44.44444 cents 4: 391.1111 .. 497.7778 cents 106.66667 cents -26.66667 cents 5: 471.1111 .. 577.7778 cents 106.66667 cents -26.66667 cents 6: 622.2222 .. 728.8889 cents 106.66667 cents 44.44444 cents 7: 702.2222 .. 808.8889 cents 106.66667 cents -26.66667 cents 8: 782.2222 .. 888.8889 cents 106.66667 cents -26.66667 cents 9: 933.3333 .. 1040.0000 cents 106.66667 cents 44.44444 cents 10: 1013.3333 .. 1155.5556 cents 142.22223 cents -26.66667 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 44.44444 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 186.66667 cents Average / Smallest step : 2.454546 Largest / Average step : 1.711111 Largest / Smallest step : 4.200000 Median interval of one step : 80.00000 cents, amount: 6 Most common interval of one step : 80.00000 cents, amount: 6 Least squares average step : 109.79359 cents, oct.: 1207.72947 cents Scale is not proper Scale is a mode of a 135-tone equal temperament with octave 1200.000 cents degrees: 9 26 35 44 65 70 91 100 109 126 135 Least number of segments generator : 77 of 684.444 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 74 of 657.778 cents and inv. generated superset size: 29 = 18 more = 263.636% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAACDCAABA Step pattern size order : BCBBDADBBCB Interval vector is [ 0 0 0 0 1 0 0 0 6 0 0 0 0 0 0 0 2 3 0 0 2 0 0 0 0 6 0 0 0 2 0 0 0 0 8 0 0 0 2 0 0 0 0 6 0 0 1 0 0 0 0 1 2 0 0 4 0 0 0 0 4 0 0 0 5 0 0 ] Scale is a Constant Structure, by a margin of 8.88889 cents Scale diversity : 1.397328 Lumma stability : 0.185185 Lumma impropriety factor : 0.133333 Rothenberg efficiency : 0.428571 redundancy: 0.571429 Efficiency x scale size : 4.714286 Number of different interval sizes : 32 = 3.20000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.20000 = 16/5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 8.88889 cents Most common intervals : 311.11111 cents & inv., amount: 8 Most common triad is 0.0 311.111 888.889 cents, amount: 5 Number of recognisable fifths : 4, average 702.2222 cents Formal octave complements present : 11 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties --
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 28.1787 c. M: 45.2525 c. 12: 1 1 1 1 2 0 2 1 1 1 1 P D3 I SD: 19.3729 c. M: 31.1111 c. 15: 1 2 1 1 2 1 2 1 1 2 1 P M ME I SD: 10.0280 c. M: 17.7778 c. 27: 2 3 2 2 4 1 4 2 2 3 2 P I SD: 6.5649 c. M: 8.8889 c. 31: 2 4 2 2 5 1 5 2 2 4 2 N I SD: 2.4997 c. M: 4.0143 c. 46: 3 6 3 3 7 2 7 3 3 6 3 N I SD: 2.5303 c. M: 3.8647 c. 58: 4 7 4 4 9 2 9 4 4 7 4 N I SD: 2.2132 c. M:-3.5249 c. 73: 5 9 5 5 11 3 11 5 5 9 5 N I SD: 2.1231 c. M: 3.4094 c. 77: 5 10 5 5 12 3 12 5 5 10 5 N I SD: 1.6671 c. M:-2.6551 c. 89: 6 11 6 6 14 3 14 6 6 11 6 N I SD: 1.3078 c. M: 1.9975 c. 104: 7 13 7 7 16 4 16 7 7 13 7 N I SD: 0.7451 c. M: 1.1966 c. 135: 9 17 9 9 21 5 21 9 9 17 9 N I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x x 4 S SD: 39.8664 cents 3 x x x x 4 x x 5 x x 6 S SD: 26.6205 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 19.9693 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 9.8760 cents 6 x 7 x x 8:9 x 10 x 11:12 S SD: 22.9755 cents 7 x 8 x 9 x 10:11 x 12:13:14 S SD: 11.3068 cents 8 x 9 x 10:11 x 13 x 14:15:16 SD: 8.4164 cents 9 x 10:11 x x 13:14:15:16:17:18 SD: 10.4211 cents 10 x 11:12:13:14 x 16:17:18:19:20 S SD: 12.0458 cents 11:12 x 13:14:15:16 x 18:19:21:22 SD: 11.3125 cents 12:13:14 x 15 x 17:19:20:21:23:24 SD: 8.1196 cents 13:14:15 x 16:18:19:21:22:23:25:26 SD: 8.0400 cents 14:15:16:17:18 x 20:22:23:25:27:28 SD: 8.4914 cents 15:16:17:18:19:21 x 24:25:26:29:30 SD: 4.8588 cents 17:18:19:20:21:24 x 27:28:30:32:34 S SD: 7.2527 cents 18:19:21:22:23:25:26:29:30:32:34:36 SD: 6.7894 cents 19:20:22:23:24 x 27:30:32:33:36:38 S SD: 4.7115 cents 20:21:23:24:25:28:29:32:33:35:38:40 SD: 3.1854 cents 24:25:27:29:30 x 34:38:40:42:46:48 SD: 4.1596 cents 25:26:29:30:31:35:36:40:42:44:48:50 SD: 3.6145 cents 27:28:31:32:34:38:39:43:45:47:52:54 SD: 3.4477 cents 35:37:40:42:44:49:50:56:58:61:67:70 SD: 2.3246 cents 40:42:46:48:50:56:57:64:67:70:76:80 SD: 1.8254 cents 55:58:63:66:69:77:79:88:92:96:105:110 SD: 1.5019 cents 63:66:72:75:79:88:90:101:105:110:120:126 SD: 1.3901 cents 64:67:73:77:80:89:92:102:107:112:122:128 SD: 1.3321 cents 71:74:81:85:89:99:102:113:119:124:136:142 SD: 1.2702 cents 76:80:87:91:95:106:109:121:127:133:145:152 SD: 1.0516 cents 86:90:98:103:108:120:123:137:144:151:164:172 SD: 0.9314 cents 91:95:104:109:114:127:130:145:152:159:174:182 SD: 0.7865 cents 106:111:121:127:133:148:152:169:177:186:202:212 SD: 0.6508 cents 127:133:145:152:159:177:182:203:212:222:243:254 SD: 0.6103 cents 131:137:150:157:164:183:188:209:219:229:250:262 SD: 0.6046 cents 146:153:167:175:183:204:209:233:244:256:279:292 SD: 0.4617 cents 169:177:193:202:212:236:242:270:282:296:323:338 SD: 0.4478 cents 188:197:215:225:236:262:269:300:314:329:359:376 SD: 0.4423 cents 189:198:216:226:237:264:271:302:316:331:361:378 SD: 0.3587 cents 232:243:265:278:291:324:332:370:388:406:443:464 SD: 0.3192 cents 252:264:288:302:316:352:361:402:421:441:481:504 SD: 0.2487 cents 280:293:320:335:351:391:401:447:468:490:535:560 SD: 0.1959 cents 356:373:407:426:446:497:510:568:595:623:680:712 SD: 0.1370 cents 462:484:528:553:579:645:662:737:772:809:882:924 SD: 0.1320 cents 532:557:608:637:667:743:762:849:889:931:1016:1064 SD: 0.1071 cents 553:579:632:662:693:772:792:882:924:968:1056:1106 SD: 0.1050 cents