Scala analysis: hemi13
Hemiwuerschmidt[13] in pure 7s tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 37.409 cents 37.408912 2: 193.765 cents 193.765181 3: 231.174 cents 231.174094 4: 387.530 cents 387.530363 5: 424.939 cents 424.939275 6: 581.296 cents 581.295544 7: 618.704 cents 618.704456 8: 775.061 cents 775.060725 9: 812.470 cents 812.469637 10: 968.826 cents 968.825906 11: 1006.235 cents 1006.234819 12: 1162.591 cents 1162.591088 13: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 37.4089 cents 37.4089 1: 37.4089 cents 37.4089 2: 156.3563 cents 156.3563 3: 37.4089 cents 37.4089 4: 156.3563 cents 156.3563 5: 37.4089 cents 37.4089 6: 156.3563 cents 156.3563 7: 37.4089 cents 37.4089 8: 156.3563 cents 156.3563 9: 37.4089 cents 37.4089 10: 156.3563 cents 156.3563 11: 37.4089 cents 37.4089 12: 156.3563 cents 156.3563 13: 37.4089 cents 37.4089
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 37.40891 cents 1: 6 156.35627 cents 2: 1 74.81782 cents 2: 12 193.76518 cents 3: 8 231.17409 cents 3: 5 350.12145 cents 4: 2 268.58301 cents 4: 11 387.53036 cents 5: 9 424.93927 cents 5: 4 543.88663 cents 6: 3 462.34819 cents 6: 10 581.29554 cents 7: 10 618.70446 cents 7: 3 737.65181 cents 8: 4 656.11337 cents 8: 9 775.06073 cents 9: 11 812.46964 cents 9: 2 931.41699 cents 10: 5 849.87855 cents 10: 8 968.82591 cents 11: 12 1006.23482 cents 11: 1 1125.18218 cents 12: 6 1043.64373 cents 12: 7 1162.59109 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 12 13 0.0 : 37.4 193.8 231.2 387.5 424.9 581.3 618.7 775.1 812.5 968.8 1006.2 1162.6 1200.0 37.4 : 156.4 193.8 350.1 387.5 543.9 581.3 737.7 775.1 931.4 968.8 1125.2 1162.6 1200.0 193.8 : 37.4 193.8 231.2 387.5 424.9 581.3 618.7 775.1 812.5 968.8 1006.2 1043.6 1200.0 231.2 : 156.4 193.8 350.1 387.5 543.9 581.3 737.7 775.1 931.4 968.8 1006.2 1162.6 1200.0 387.5 : 37.4 193.8 231.2 387.5 424.9 581.3 618.7 775.1 812.5 849.9 1006.2 1043.6 1200.0 424.9 : 156.4 193.8 350.1 387.5 543.9 581.3 737.7 775.1 812.5 968.8 1006.2 1162.6 1200.0 581.3 : 37.4 193.8 231.2 387.5 424.9 581.3 618.7 656.1 812.5 849.9 1006.2 1043.6 1200.0 618.7 : 156.4 193.8 350.1 387.5 543.9 581.3 618.7 775.1 812.5 968.8 1006.2 1162.6 1200.0 775.1 : 37.4 193.8 231.2 387.5 424.9 462.3 618.7 656.1 812.5 849.9 1006.2 1043.6 1200.0 812.5 : 156.4 193.8 350.1 387.5 424.9 581.3 618.7 775.1 812.5 968.8 1006.2 1162.6 1200.0 968.8 : 37.4 193.8 231.2 268.6 424.9 462.3 618.7 656.1 812.5 849.9 1006.2 1043.6 1200.0 1006.2: 156.4 193.8 231.2 387.5 424.9 581.3 618.7 775.1 812.5 968.8 1006.2 1162.6 1200.0 1162.6: 37.4 74.8 231.2 268.6 424.9 462.3 618.7 656.1 812.5 849.9 1006.2 1043.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 37.4089 .. 156.3563 cents 118.94736 cents 37.40891 cents 2: 74.8178 .. 193.7652 cents 118.94736 cents -81.53844 cents 3: 231.1741 .. 350.1215 cents 118.94736 cents 37.40891 cents 4: 268.5830 .. 387.5304 cents 118.94736 cents -81.53844 cents 5: 424.9393 .. 543.8866 cents 118.94736 cents 37.40891 cents 6: 462.3482 .. 581.2955 cents 118.94736 cents -81.53844 cents 7: 618.7045 .. 737.6518 cents 118.94736 cents 37.40891 cents 8: 656.1134 .. 775.0607 cents 118.94736 cents -81.53844 cents 9: 812.4696 .. 931.4170 cents 118.94736 cents 37.40891 cents 10: 849.8785 .. 968.8259 cents 118.94736 cents -81.53844 cents 11: 1006.2348 .. 1125.1822 cents 118.94736 cents 37.40891 cents 12: 1043.6437 .. 1162.5911 cents 118.94736 cents -81.53844 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 37.40891 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 156.35627 cents Average / Smallest step : 2.467532 Largest / Average step : 1.693860 Largest / Smallest step : 4.179653 Median interval of one step : 37.40891 cents, amount: 7 Most common interval of one step : 37.40891 cents, amount: 7 Least squares average step : 93.32434 cents, oct.: 1213.21637 cents Scale is not proper Scale has Myhill's property chromas: 118.94736 cents and 81.53844 cents, ratio: 1.458789 generators: 2 of 193.76518 cents and 11 of 1006.23482 cents ET pair of linear temperament : 31&161 Scale is distributional even Scale is a mode of a 1251-tone equal temperament with octave 1200.000 cents degrees: 39 202 241 404 443 606 645 808 847 1010 1049 1212 1251 generators: 202 and 1049 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABABA Step pattern size order : SLSLSLSLSLSLS Scale is a Constant Structure, by a margin of 37.40891 cents Scale diversity : 1.199047 Lumma stability : 0.218219 Lumma impropriety factor : 0.407692 Rothenberg efficiency : 0.717949 redundancy: 0.282051 Efficiency x scale size : 9.333333 Number of different interval sizes : 24 = 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 : 37.40891 cents Most common intervals : 193.76518 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 193.765 387.530 cents Most common triad is 0.0 193.765 1006.235 cents, amount: 11 Number of recognisable fifths : 0 Scale contains two identical disjunct hexachords Formal octave complements present : 13 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 6-7 -- Rational properties --
FIT/MODE
13: 0 2 0 2 0 2 0 2 0 2 0 2 1 N T3 SD: 48.7442 c. M: 83.1579 c. 14: 0 2 0 2 0 2 1 2 0 2 0 2 1 N SD: 46.2130 c. M: 82.0821 c. 15: 0 2 0 2 1 2 0 2 1 2 0 2 1 N SD: 42.8809 c. M: 71.1741 c. 16: 0 2 1 2 0 2 1 2 0 2 1 2 1 N T3 SD: 40.3629 c. M: 68.8259 c. 17: 0 2 1 2 1 2 0 3 0 2 1 2 1 N SD: 33.1352 c. M: 53.9986 c. 18: 0 2 1 2 1 2 1 2 1 2 1 2 1 N T3 SD: 35.3924 c. M: 60.4318 c. 19: 1 2 1 2 1 2 1 2 1 2 1 2 1 P M ME I SD: 16.0573 c. M: 25.7490 c. 21: 1 2 1 3 0 3 1 3 0 3 1 2 1 N I SD: 16.5015 c. M: 24.9393 c. 25: 1 3 1 3 1 3 1 3 1 3 1 3 1 N M DE I SD: 6.6047 c. M:-10.5911 c. 31: 1 4 1 4 1 4 1 4 1 4 1 4 1 N M DE I SD: 0.8112 c. M:-1.3008 c. 99: 3 13 3 13 3 13 3 13 3 13 3 13 3 N M DE I SD: 0.6518 c. M:-1.0453 c. 130: 4 17 4 17 4 17 4 17 4 17 4 17 4 N M DE I SD: 0.3030 c. M:-0.4858 c. 161: 5 21 5 21 5 21 5 21 5 21 5 21 5 N M DE I SD: 0.0884 c. M: 0.1418 c. 192: 6 25 6 25 6 25 6 25 6 25 6 25 6 N M DE I SD: 0.0568 c. M:-0.0911 c. 353: 11 46 11 46 11 46 11 46 11 46 11 46 11 N M DE I SD: 0.0094 c. M:-0.0151 c. 898: 28 117 28 117 28 117 28 117 28 117 28 117 28 N M DE I SD: 0.0047 c. M:-0.0076 c. 1251: 39 163 39 163 39 163 39 163 39 163 39 163 39 N M DE I SD: 0.0007 c. M:-0.0012 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x 3 x x x x 4 S SD: 36.5529 cents 3 x x x x 4 x x x 5 x x x 6 S SD: 34.1768 cents 4 x x x 5 x x x 6 x 7 x x 8 S SD: 18.2790 cents 5 x x x 6 x 7 x x 8 x 9 x 10 S SD: 14.5603 cents 6 x x 7 x 8 x x 9:10 x 11 x 12 S SD: 22.9681 cents 7 x x 8 x 9 x 10:11 x 12:13 x 14 S SD: 10.8042 cents 8 x 9 x 10 x 11 x x 13:14 x x 16 SD: 7.0520 cents 9 x 10 x 11:12 x 13:14 x x 16 x 18 S SD: 12.4622 cents 10 x 11 x x 13:14 x x 16 x 18 x 20 SD: 7.1029 cents 11 x 12:13 x 14:15:16:17:18:19:20 x 22 S SD: 10.7502 cents 12 x 13:14:15 x x 17 x 19:21 x 23:24 SD: 9.8188 cents 13 x x 15:16:17:18:19:20:21 x 23:25:26 SD: 8.2778 cents 14 x x 16 x 18 x 20:22 x x 25:27:28 SD: 4.0869 cents 15:16 x 17 x 19:21 x 23:24:26:27:29:30 SD: 8.9824 cents 16:17:18 x 20 x 22:23:25:26:28:29:31:32 SD: 7.7691 cents 17:18:19 x 21:22:24 x x 27:30 x 33:34 SD: 8.2501 cents 18:19:20:21 x 23:25:26:28:29 x 32:35:36 SD: 6.7724 cents 19:20:21:22:24 x x 27:30 x 33:34:37:38 SD: 6.6797 cents 20:21:22:23:25:26:28:29:31:32:35:36:39:40 SD: 5.4718 cents 22:23 x 25 x 28:31 x 34:35 x 39:43:44 SD: 5.7062 cents 23:24:26 x 29 x 32:33:36:37:40:41:45:46 SD: 4.3002 cents 24:25:27 x 30:31 x 34 x 38:42:43:47:48 SD: 4.5657 cents 25:26:28:29:31:32:35:36:39:40:44:45:49:50 SD: 3.6530 cents 26:27:29:30 x 33:36:37:41:42 x 46:51:52 SD: 4.5112 cents 27:28:30:31:34:35:38:39:42:43:47:48:53:54 SD: 3.7385 cents 28:29:31:32:35:36:39:40:44:45:49:50:55:56 SD: 2.6611 cents 29:30:32:33:36:37:41 x 45:46:51:52:57:58 SD: 3.8317 cents 30:31 x 34 x 38:42:43:47:48:53:54:59:60 SD: 3.3113 cents 31:32:35 x 39:40:43:44:49:50:54:55:61:62 SD: 3.8969 cents 32:33:36:37:40:41:45:46:50:51:56:57:63:64 SD: 2.5935 cents 33:34:37:38:41:42:46:47:52:53:58:59:65:66 SD: 2.4962 cents 34:35:38:39 x 43:48:49:53:54:60:61:67:68 SD: 3.2721 cents 35:36:39:40:44:45:49:50:55:56:61:63:69:70 SD: 2.0970 cents 38:39 x 43:48:49:53:54:59:61:67:68:74:76 SD: 3.2036 cents 39:40:44:45:49:50:55:56:61:62:68:70:76:78 SD: 2.5698 cents 40:41:45:46:50:51:56:57:63:64:70:72:78:80 SD: 1.8863 cents 43:44:48:49:54:55:60:61:67:69:75:77:84:86 SD: 1.5959 cents 48:49:54:55:60:61:67:69:75:77:84:86:94:96 SD: 1.5104 cents 51:52:57:58:64:65:71:73:80:82:89:91:100:102 SD: 1.5028 cents 60:61:67:69:75:77:84:86:94:96:105:107:117:120 SD: 1.4242 cents 65:66:73:74:81:83:91:93:102:104:114:116:127:130 SD: 1.3940 cents 68:69:76:78:85:87:95:97:106:109:119:122:133:136 SD: 1.3520 cents 72:74:81:82:90:92:101:103:113:115:126:129:141:144 SD: 1.3483 cents 75:77:84:86:94:96:105:107:117:120:131:134:147:150 SD: 1.0451 cents 83:85:93:95:104:106:116:119:130:133:145:148:162:166 SD: 0.9258 cents 90:92:101:103:113:115:126:129:141:144:158:161:176:180 SD: 0.9223 cents 91:93:102:104:114:116:127:130:142:145:159:163:178:182 SD: 0.9004 cents 92:94:103:105:115:118:129:132:144:147:161:165:180:184 SD: 0.8714 cents 93:95:104:106:116:119:130:133:146:149:163:166:182:186 SD: 0.8255 cents 100:102:112:114:125:128:140:143:156:160:175:179:196:200 SD: 0.6926 cents 127:130:142:145:159:162:178:182:199:203:222:227:249:254 SD: 0.6644 cents 128:131:143:146:160:164:179:183:200:205:224:229:251:256 SD: 0.6301 cents 133:136:149:152:166:170:186:190:208:213:233:238:260:266 SD: 0.5130 cents 140:143:157:160:175:179:196:200:219:224:245:250:274:280 SD: 0.4507 cents 168:172:188:192:210:215:235:240:263:269:294:300:329:336 SD: 0.4441 cents 175:179:196:200:219:224:245:250:274:280:306:313:343:350 SD: 0.4150 cents 184:188:206:210:230:235:257:263:288:294:322:329:360:368 SD: 0.3624 cents 195:199:218:223:244:249:273:279:305:312:341:349:382:390 SD: 0.3589 cents 219:224:245:250:274:280:306:313:343:350:383:392:429:438 SD: 0.3588 cents 230:235:257:263:288:294:322:329:360:368:403:411:450:460 SD: 0.3229 cents 259:265:290:296:324:331:362:370:405:414:453:463:507:518 SD: 0.3062 cents 279:285:312:319:349:357:390:399:437:446:488:499:546:558 SD: 0.2565 cents 280:286:313:320:350:358:392:400:438:448:490:501:548:560 SD: 0.2270 cents 331:338:370:378:414:423:463:473:518:529:579:592:648:662 SD: 0.1903 cents 356:364:398:407:445:455:498:509:557:569:623:637:697:712 SD: 0.1786 cents 363:371:406:415:454:464:508:519:568:580:635:649:710:726 SD: 0.1575 cents 414:423:463:473:518:529:579:592:648:662:725:740:810:828 SD: 0.1571 cents 421:430:471:481:527:538:589:602:659:673:737:753:824:842 SD: 0.1561 cents 463:473:518:529:579:592:648:662:724:740:810:828:906:926 SD: 0.1509 cents 489:500:547:559:612:625:684:699:765:782:856:874:957:978 SD: 0.1480 cents 491:502:549:561:614:628:687:702:768:785:859:878:961:982 SD: 0.1442 cents 496:507:555:567:620:634:694:709:776:793:868:887:971:992 SD: 0.1314 cents 547:559:612:625:684:699:765:782:856:875:957:978:1071:1094 SD: 0.1300 cents 589:602:659:673:737:753:824:842:922:942:1031:1053:1153:1178 SD: 0.1173 cents