Scala analysis: hanson11
11-tone hanson MOS (1/1 is A)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68.461 cents 68.461350 2: 248.654 cents 248.653990 3: 317.115 cents 317.115340 4: 385.577 cents 385.576690 5: 565.769 cents 565.769320 6: 634.231 cents 634.230680 7: 814.423 cents 814.423310 8: 882.885 cents 882.884660 9: 951.346 cents 951.346010 10: 1131.539 cents 1131.538650 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 68.4613 cents 68.4613 1: 68.4613 cents 68.4613 2: 180.1926 cents 180.1926 3: 68.4614 cents 68.4614 4: 68.4613 cents 68.4613 5: 180.1926 cents 180.1926 6: 68.4614 cents 68.4614 7: 180.1926 cents 180.1926 8: 68.4614 cents 68.4614 9: 68.4613 cents 68.4613 10: 180.1926 cents 180.1926 11: 68.4613 cents 68.4613
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 68.46135 cents 1: 4 180.19264 cents 2: 3 136.92270 cents 2: 8 248.65399 cents 3: 10 317.11534 cents 3: 1 428.84662 cents 4: 6 385.57669 cents 4: 5 497.30797 cents 5: 2 454.03804 cents 5: 9 565.76932 cents 6: 9 634.23068 cents 6: 2 745.96196 cents 7: 5 702.69202 cents 7: 6 814.42331 cents 8: 1 771.15338 cents 8: 10 882.88466 cents 9: 8 951.34601 cents 9: 3 1063.07730 cents 10: 4 1019.80736 cents 10: 7 1131.53865 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 68.5 248.7 317.1 385.6 565.8 634.2 814.4 882.9 951.3 1131.5 1200.0 68.5 : 180.2 248.7 317.1 497.3 565.8 746.0 814.4 882.9 1063.1 1131.5 1200.0 248.7 : 68.5 136.9 317.1 385.6 565.8 634.2 702.7 882.9 951.3 1019.8 1200.0 317.1 : 68.5 248.7 317.1 497.3 565.8 634.2 814.4 882.9 951.3 1131.5 1200.0 385.6 : 180.2 248.7 428.8 497.3 565.8 746.0 814.4 882.9 1063.1 1131.5 1200.0 565.8 : 68.5 248.7 317.1 385.6 565.8 634.2 702.7 882.9 951.3 1019.8 1200.0 634.2 : 180.2 248.7 317.1 497.3 565.8 634.2 814.4 882.9 951.3 1131.5 1200.0 814.4 : 68.5 136.9 317.1 385.6 454.0 634.2 702.7 771.2 951.3 1019.8 1200.0 882.9 : 68.5 248.7 317.1 385.6 565.8 634.2 702.7 882.9 951.3 1131.5 1200.0 951.3 : 180.2 248.7 317.1 497.3 565.8 634.2 814.4 882.9 1063.1 1131.5 1200.0 1131.5: 68.5 136.9 317.1 385.6 454.0 634.2 702.7 882.9 951.3 1019.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 68.4613 .. 180.1926 cents 111.73129 cents 68.46135 cents 2: 136.9227 .. 248.6540 cents 111.73129 cents -43.26994 cents 3: 317.1153 .. 428.8466 cents 111.73128 cents 68.46135 cents 4: 385.5767 .. 497.3080 cents 111.73128 cents -43.26993 cents 5: 454.0380 .. 565.7693 cents 111.73128 cents -43.26993 cents 6: 634.2307 .. 745.9620 cents 111.73128 cents 68.46136 cents 7: 702.6920 .. 814.4233 cents 111.73129 cents -43.26994 cents 8: 771.1534 .. 882.8847 cents 111.73128 cents -43.26993 cents 9: 951.3460 .. 1063.0773 cents 111.73129 cents 68.46135 cents 10: 1019.8074 .. 1131.5386 cents 111.73129 cents -43.26994 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 68.46135 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 180.19264 cents Average / Smallest step : 1.593467 Largest / Average step : 1.651766 Largest / Smallest step : 2.632035 Median interval of one step : 68.46135 cents, amount: 7 Most common interval of one step : 68.46135 cents, amount: 7 Least squares average step : 109.75335 cents, oct.: 1207.28682 cents Scale is not proper Scale has Myhill's property chromas: 111.73129 cents and 43.26994 cents, ratio: 2.582192 generators: 3 of 317.11534 cents and 8 of 882.88466 cents ET pair of linear temperament : 15&19 Scale is distributional even Scale is a mode of a 1525-tone equal temperament with octave 2/1 degrees: 87 316 403 490 719 806 1035 1122 1209 1438 1525 generators: 403 and 1122 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABABAABA Step pattern size order : SLSSLSLSSLS Scale is a Constant Structure, by a margin of 25.19142 cents Scale diversity : 1.241097 Lumma stability : 0.285256 Lumma impropriety factor : 0.216350 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 25.19142 cents Most common intervals : 317.11534 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 385.577 882.885 cents Most common triad is 0.0 317.115 882.885 cents, amount: 9 Number of recognisable fifths : 5, average 702.6920 cents Scale contains two identical conjunct hexachords Formal octave complements present : 11 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 32.1205 c. M:-50.7869 c. 13: 1 2 0 1 2 1 2 1 0 2 1 N T3 I SD: 24.8360 c. M: 40.1923 c. 15: 1 2 1 1 2 1 2 1 1 2 1 P M ME I SD: 9.1221 c. M:-14.4233 c. 19: 1 3 1 1 3 1 3 1 1 3 1 N M DE I SD: 4.1928 c. M:-6.6293 c. 34: 2 5 2 2 5 2 5 2 2 5 2 N M DE I SD: 1.6814 c. M:-2.6586 c. 53: 3 8 3 3 8 3 8 3 3 8 3 N M DE I SD: 0.4244 c. M:-0.6710 c. 87: 5 13 5 5 13 5 13 5 5 13 5 N M DE I SD: 0.3986 c. M:-0.6302 c. 140: 8 21 8 8 21 8 21 8 8 21 8 N M DE I SD: 0.0870 c. M:-0.1376 c. 193: 11 29 11 11 29 11 29 11 11 29 11 N M DE I SD: 0.0534 c. M:-0.0845 c. 333: 19 50 19 19 50 19 50 19 19 50 19 N M DE I SD: 0.0056 c. M:-0.0089 c. 1192: 68 179 68 68 179 68 179 68 68 179 68 N M DE I SD: 0.0039 c. M:-0.0062 c. 1525: 87 229 87 87 229 87 229 87 87 229 87 N M DE I SD: 0.0018 c. M:-0.0029 c. 1858: 106 279 106 106 279 106 279 106 106 279 106 N M DE I SD: 0.0005 c. M:-0.0008 c. 2191: 125 329 125 125 329 125 329 125 125 329 125 N M DE I SD: 0.0004 c. M:-0.0007 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: 33.8622 cents 3 x x x x 4 x x 5 x x 6 S SD: 22.5801 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 17.4869 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 13.6706 cents 6 x 7 x x 8:9 x 10 x x 12 S SD: 19.5010 cents 7 x 8 x 9 x 10:11 x 12:13:14 S SD: 12.7526 cents 8 x 9 x 10:11:12:13 x 14:15:16 S SD: 12.2839 cents 9 x 10:11 x 12:13:14:15:16:17:18 S SD: 13.7365 cents 10 x x 12:13:14 x 16 x 17:19:20 SD: 11.4974 cents 11:12 x 13:14:15:16 x 18:19:21:22 SD: 11.4830 cents 12:13:14 x 15 x 17:19:20:21:23:24 SD: 9.2391 cents 13:14:15 x 16:18:19:21:22:23:25:26 SD: 8.4503 cents 14:15:16:17 x 19:20:22:23:24:27:28 SD: 8.2780 cents 15:16:17:18:19:21:22:24:25:26:29:30 SD: 6.2101 cents 17:18:20 x 21:24:25:27:28:29:33:34 SD: 7.7608 cents 18:19:21:22 x 25:26:29:30:31:35:36 SD: 5.0168 cents 20:21:23:24:25:28:29:32:33:35:38:40 SD: 3.6804 cents 25:26:29:30:31:35:36:40:42:43:48:50 SD: 2.7685 cents 39:41:45:47:49:54:56:62:65:68:75:78 SD: 2.5570 cents 40:42:46:48:50:55:58:64:67:69:77:80 SD: 2.5018 cents 41:43:47:49:51:57:59:66:68:71:79:82 SD: 2.3645 cents 44:46:51:53:55:61:63:70:73:76:85:88 SD: 2.1544 cents 45:47:52:54:56:62:65:72:75:78:87:90 SD: 1.6385 cents 52:54:60:62:65:72:75:83:87:90:100:104 SD: 1.4905 cents 65:68:75:78:81:90:94:104:108:113:125:130 SD: 1.2688 cents 72:75:83:86:90:100:104:115:120:125:138:144 SD: 1.1977 cents 75:78:87:90:94:104:108:120:125:130:144:150 SD: 0.9836 cents 93:97:107:112:116:129:134:149:155:161:179:186 SD: 0.9099 cents 101:105:117:121:126:140:146:162:168:175:194:202 SD: 0.8877 cents 104:108:120:125:130:144:150:166:173:180:200:208 SD: 0.6369 cents 129:134:149:155:161:179:186:206:215:223:248:258 SD: 0.6250 cents 143:149:165:172:179:198:206:229:238:248:275:286 SD: 0.5799 cents 149:155:172:179:186:207:215:239:248:258:286:298 SD: 0.5499 cents 153:159:177:184:191:212:221:245:255:265:294:306 SD: 0.5339 cents 168:175:194:202:210:233:242:269:280:291:323:336 SD: 0.3848 cents 220:229:254:264:275:305:317:352:366:381:423:440 SD: 0.3001 cents 228:237:263:274:285:316:329:365:380:395:438:456 SD: 0.2938 cents 248:258:286:298:310:344:358:397:413:430:477:496 SD: 0.2836 cents 253:263:292:304:316:351:365:405:421:438:486:506 SD: 0.2743 cents 298:310:344:358:372:413:430:477:496:516:573:596 SD: 0.2098 cents 344:358:397:413:430:477:496:551:573:596:661:688 SD: 0.1916 cents 373:388:431:448:466:517:538:597:621:646:717:746 SD: 0.1662 cents 448:466:517:538:560:621:646:717:746:776:861:896 SD: 0.1301 cents 538:560:621:646:672:746:776:861:896:932:1034:1076 SD: 0.1214 cents 597:621:689:717:746:828:861:956:994:1034:1148:1194 SD: 0.1170 cents