Scala analysis: 11-17
11 out of 17-tet
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 70.588 cents 70.588240 2: 211.765 cents 211.764710 3: 282.353 cents 282.352940 4: 423.529 cents 423.529410 5: 494.118 cents 494.117650 6: 635.294 cents 635.294120 7: 705.882 cents 705.882350 8: 847.059 cents 847.058820 9: 917.647 cents 917.647060 10: 1058.824 cents 1058.823530 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 141.1765 cents 141.1765 1: 70.5882 cents 70.5882 2: 141.1765 cents 141.1765 3: 70.5882 cents 70.5882 4: 141.1765 cents 141.1765 5: 70.5882 cents 70.5882 6: 141.1765 cents 141.1765 7: 70.5882 cents 70.5882 8: 141.1765 cents 141.1765 9: 70.5882 cents 70.5882 10: 141.1765 cents 141.1765 11: 141.1765 cents 141.1765
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 70.58824 cents 1: 6 141.17647 cents 2: 10 211.76471 cents 2: 1 282.35294 cents 3: 4 282.35294 cents 3: 7 352.94117 cents 4: 9 423.52941 cents 4: 2 494.11765 cents 5: 3 494.11765 cents 5: 8 564.70588 cents 6: 8 635.29412 cents 6: 3 705.88235 cents 7: 2 705.88235 cents 7: 9 776.47058 cents 8: 7 847.05882 cents 8: 4 917.64706 cents 9: 1 917.64706 cents 9: 10 988.23529 cents 10: 6 1058.82353 cents 10: 5 1129.41176 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 : 70.6 211.8 282.4 423.5 494.1 635.3 705.9 847.1 917.6 1058.8 1200.0 70.6 : 141.2 211.8 352.9 423.5 564.7 635.3 776.5 847.1 988.2 1129.4 1200.0 211.8 : 70.6 211.8 282.4 423.5 494.1 635.3 705.9 847.1 988.2 1058.8 1200.0 282.4 : 141.2 211.8 352.9 423.5 564.7 635.3 776.5 917.6 988.2 1129.4 1200.0 423.5 : 70.6 211.8 282.4 423.5 494.1 635.3 776.5 847.1 988.2 1058.8 1200.0 494.1 : 141.2 211.8 352.9 423.5 564.7 705.9 776.5 917.6 988.2 1129.4 1200.0 635.3 : 70.6 211.8 282.4 423.5 564.7 635.3 776.5 847.1 988.2 1058.8 1200.0 705.9 : 141.2 211.8 352.9 494.1 564.7 705.9 776.5 917.6 988.2 1129.4 1200.0 847.1 : 70.6 211.8 352.9 423.5 564.7 635.3 776.5 847.1 988.2 1058.8 1200.0 917.6 : 141.2 282.4 352.9 494.1 564.7 705.9 776.5 917.6 988.2 1129.4 1200.0 1058.8: 141.2 211.8 352.9 423.5 564.7 635.3 776.5 847.1 988.2 1058.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.5882 .. 141.1765 cents 70.58823 cents 70.58824 cents 2: 211.7647 .. 282.3529 cents 70.58823 cents 70.58824 cents 3: 282.3529 .. 352.9412 cents 70.58823 cents 1/1, 0.0000 cents 4: 423.5294 .. 494.1176 cents 70.58824 cents 70.58824 cents 5: 494.1176 .. 564.7059 cents 70.58823 cents 1/1, 0.0000 cents 6: 635.2941 .. 705.8823 cents 70.58823 cents 70.58824 cents 7: 705.8823 .. 776.4706 cents 70.58823 cents 1/1, 0.0000 cents 8: 847.0588 .. 917.6471 cents 70.58824 cents 70.58824 cents 9: 917.6471 .. 988.2353 cents 70.58823 cents 1/1, 0.0000 cents 10: 1058.8235 .. 1129.4118 cents 70.58823 cents 70.58824 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 70.58823 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 141.17647 cents Average / Smallest step : 1.545455 Largest / Average step : 1.294118 Largest / Smallest step : 2.000000 Median interval of one step : 141.17647 cents, amount: 6 Most common interval of one step : 141.17647 cents, amount: 6 Least squares average step : 104.90584 cents, oct.: 1153.96419 cents Scale is proper Scale has Myhill's property chromas: 70.58823 cents and 0.00001 cents, ratio: 7058823.436642 generators: 2 of 211.76471 cents and 988.23529 cents Scale is maximally even in 17-tone equal temperament ET pair of linear temperament : 11&17 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 17-tone equal temperament with octave 2/1 degrees: 1 3 4 6 7 9 10 12 13 15 17 generators: 3 and 14 Number of contiguous 1-step segments: 5 Step pattern alph. order: ABABABABABB Step pattern size order : SLSLSLSLSLL Interval vector is [ 5 6 10 5 7 9 5 8 ] Scale is not a Constant Structure Scale diversity : 1.181542 Rothenberg stability : 0.818182 = 9/11 Lumma stability : 0.411765 Rothenberg efficiency : 0.735498 redundancy: 0.264502 Efficiency x scale size : 8.090476 Number of different interval sizes : 16 = 1.60000 / 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 : 70.58823 cents Most common intervals : 211.76471 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 211.765 423.529 cents Most common triad is 0.0 211.765 988.235 cents, amount: 9 Number of recognisable fifths : 5, average 705.8823 cents Formal octave complements present : 5 = 45.4545% Limited inverse transpositions : 9 Inversional symmetry on degrees : 10 Inversional symmetry on intervals : 4-5 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
11: 0 1 1 1 1 1 1 1 1 1 2 N T3 SD: 72.5240 c. M: 102.6738 c. 12: 1 1 1 1 1 1 1 1 1 2 1 P M ME S SD: 25.9455 c. M: 47.0588 c. 13: 1 1 1 2 0 2 1 1 1 1 2 N D3 SD: 25.4156 c. M: 43.4389 c. 14: 1 1 1 2 1 1 1 2 1 1 2 P M ME S SD: 23.7953 c. M: 40.3361 c. 15: 1 2 1 1 1 2 1 2 1 1 2 P D3 S SD: 24.3287 c. M:-42.3529 c. 16: 1 2 1 2 1 1 1 2 1 2 2 N D3 SD: 21.8169 c. M: 35.2941 c. 17: 1 2 1 2 1 2 1 2 1 2 2 P M ME S SD: 0.0000 c. M: 0.0000 c. Machine-11
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 x 3 x x x 4 S SD: 1.9637 cents 3 x x x x 4 x x x 5 x 6 S SD: 11.1731 cents 4 x x x 5 x x 6 x 7 x 8 S SD: 15.8503 cents 5 x x 6 x x 7 x 8 x 9:10 S SD: 16.3798 cents 6 x x 7 x 8 x 9 x 10:11:12 S SD: 6.3861 cents 7 x 8 x 9 x 10 x 11:12:13:14 S SD: 10.4995 cents 8 x 9 x 10:11 x 12:13:14:15:16 S SD: 11.3626 cents 9 x 10:11 x 12:13:14 x 15:17:18 SD: 13.3973 cents 10 x 11:12:13 x 14:15:16:17:18:20 S SD: 11.0286 cents 11 x 12:13:14:15:16:17:18:19:20:22 S SD: 9.7610 cents 12:13 x 14:15:16:17:18 x 20:22:24 S SD: 10.2547 cents 13:14 x 15 x 17:19:20:21:22:24:26 SD: 9.8187 cents 14:15:16 x 18:19:20:21:23:24:26:28 SD: 7.0595 cents 16:17:18:19:20:21:23:24:26:27:29:32 SD: 6.1009 cents 18:19:20:21:23:24:26:27:29:31:33:36 SD: 4.7786 cents 21:22:24:25:27:28:30:32:34:36:39:42 SD: 4.4886 cents 22:23:25:26:28:29:32:33:36:37:41:44 SD: 3.3528 cents 24:25:27:28:31:32:35:36:39:41:44:48 SD: 3.2221 cents 30:31:34:35:38:40:43:45:49:51:55:60 SD: 2.7736 cents 39:41:44:46:50:52:56:59:64:66:72:78 SD: 2.3973 cents 40:42:45:47:51:53:58:60:65:68:74:80 SD: 1.9959 cents 46:48:52:54:59:61:66:69:75:78:85:92 SD: 1.4891 cents 68:71:77:80:87:90:98:102:111:116:125:136 SD: 1.3281 cents 69:72:78:81:88:92:100:104:113:117:127:138 SD: 1.2549 cents 70:73:79:82:89:93:101:105:114:119:129:140 SD: 1.1894 cents 76:79:86:89:97:101:110:114:124:129:140:152 SD: 1.0990 cents 79:82:89:93:101:105:114:119:129:134:146:158 SD: 0.9734 cents 90:94:102:106:115:120:130:135:147:153:166:180 SD: 0.8519 cents 97:101:110:114:124:129:140:146:158:165:179:194 SD: 0.7284 cents 115:120:130:135:147:153:166:173:188:195:212:230 SD: 0.7196 cents 122:127:138:144:156:162:176:183:199:207:225:244 SD: 0.7170 cents 123:128:139:145:157:164:178:185:201:209:227:246 SD: 0.7103 cents 140:146:158:165:179:186:202:210:228:238:258:280 SD: 0.6264 cents 145:151:164:171:185:193:209:218:237:246:267:290 SD: 0.6044 cents 147:153:166:173:188:196:212:221:240:250:271:294 SD: 0.5152 cents 163:170:184:192:208:217:235:245:266:277:300:326 SD: 0.4626 cents 169:176:191:199:216:225:244:254:276:287:312:338 SD: 0.3679 cents 209:218:236:246:267:278:302:314:341:355:385:418 SD: 0.3541 cents 239:249:270:281:305:318:345:359:390:406:441:478 SD: 0.3230 cents 260:271:294:306:332:346:375:391:424:442:479:520 SD: 0.2378 cents 338:352:382:398:432:450:488:508:551:574:623:676 SD: 0.2264 cents 339:353:383:399:433:451:489:510:553:576:625:678 SD: 0.1614 cents 429:447:485:505:548:571:619:645:700:729:791:858 SD: 0.1451 cents 485:505:548:571:619:645:700:729:791:824:894:970 SD: 0.1426 cents 530:552:599:624:677:705:765:797:865:900:977:1060 SD: 0.1368 cents 548:571:619:645:700:729:791:824:894:931:1010:1096 SD: 0.1095 cents