Scala analysis: modmos13a
13 note modmos of hemiwuerschmidt in 229-et poptimal
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 47.162 cents 47.161572 2: 83.843 cents 83.842795 3: 157.205 cents 157.205240 4: 314.410 cents 314.410480 5: 387.773 cents 387.772926 6: 471.616 cents 471.615721 7: 544.978 cents 544.978166 8: 702.183 cents 702.183406 9: 738.865 cents 738.864629 10: 932.751 cents 932.751092 11: 969.432 cents 969.432314 12: 1016.594 cents 1016.593886 13: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 183.4061 cents 183.4061 1: 47.1616 cents 47.1616 2: 36.6812 cents 36.6812 3: 73.3624 cents 73.3624 4: 157.2052 cents 157.2052 5: 73.3624 cents 73.3624 6: 83.8428 cents 83.8428 7: 73.3624 cents 73.3624 8: 157.2052 cents 157.2052 9: 36.6812 cents 36.6812 10: 193.8865 cents 193.8865 11: 36.6812 cents 36.6812 12: 47.1616 cents 47.1616 13: 183.4061 cents 183.4061
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 36.68122 cents 1: 2 47.16157 cents 1: 3 73.36245 cents 1: 1 83.84279 cents 1: 2 157.20524 cents 1: 1 183.40611 cents 1: 1 193.88646 cents 2: 2 83.84279 cents 2: 1 110.04367 cents 2: 2 157.20524 cents 2: 1 193.88646 cents 2: 7 230.56769 cents 3: 1 157.20524 cents 3: 1 230.56769 cents 3: 5 267.24891 cents 3: 2 277.72926 cents 3: 1 303.93013 cents 3: 2 314.41048 cents 3: 1 387.77293 cents 4: 4 314.41048 cents 4: 2 340.61135 cents 4: 1 351.09170 cents 4: 3 387.77293 cents 4: 1 424.45415 cents 4: 2 461.13537 cents 5: 1 351.09170 cents 5: 2 387.77293 cents 5: 2 424.45415 cents 5: 1 461.13537 cents 5: 1 471.61572 cents 5: 3 497.81659 cents 5: 1 508.29694 cents 5: 2 544.97817 cents 6: 1 424.45415 cents 6: 1 471.61572 cents 6: 1 497.81659 cents 6: 4 544.97816 cents 6: 1 571.17904 cents 6: 2 581.65939 cents 6: 2 618.34061 cents 6: 1 655.02183 cents 7: 1 544.97817 cents 7: 2 581.65939 cents 7: 2 618.34061 cents 7: 1 628.82096 cents 7: 4 655.02183 cents 7: 1 702.18341 cents 7: 1 728.38428 cents 7: 1 775.54585 cents 8: 2 655.02183 cents 8: 1 691.70306 cents 8: 3 702.18341 cents 8: 1 728.38428 cents 8: 1 738.86463 cents 8: 2 775.54585 cents 8: 2 812.22707 cents 8: 1 848.90830 cents 9: 2 738.86463 cents 9: 1 775.54585 cents 9: 3 812.22707 cents 9: 1 848.90830 cents 9: 2 859.38865 cents 9: 4 885.58952 cents 10: 1 812.22707 cents 10: 2 885.58952 cents 10: 1 896.06987 cents 10: 2 922.27074 cents 10: 5 932.75109 cents 10: 1 969.43231 cents 10: 1 1042.79476 cents 11: 7 969.43231 cents 11: 1 1006.11354 cents 11: 2 1042.79476 cents 11: 1 1089.95633 cents 11: 2 1116.15721 cents 12: 1 1006.11354 cents 12: 1 1016.59389 cents 12: 2 1042.79476 cents 12: 1 1116.15720 cents 12: 3 1126.63755 cents 12: 2 1152.83843 cents 12: 3 1163.31878 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.83333 = 41/6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 0.0 : 47.2 83.8 157.2 314.4 387.8 471.6 545.0 702.2 738.9 932.8 969.4 1016.6 1200.0 47.2 : 36.7 110.0 267.2 340.6 424.5 497.8 655.0 691.7 885.6 922.3 969.4 1152.8 1200.0 83.8 : 73.4 230.6 303.9 387.8 461.1 618.3 655.0 848.9 885.6 932.8 1116.2 1163.3 1200.0 157.2 : 157.2 230.6 314.4 387.8 545.0 581.7 775.5 812.2 859.4 1042.8 1090.0 1126.6 1200.0 314.4 : 73.4 157.2 230.6 387.8 424.5 618.3 655.0 702.2 885.6 932.8 969.4 1042.8 1200.0 387.8 : 83.8 157.2 314.4 351.1 545.0 581.7 628.8 812.2 859.4 896.1 969.4 1126.6 1200.0 471.6 : 73.4 230.6 267.2 461.1 497.8 545.0 728.4 775.5 812.2 885.6 1042.8 1116.2 1200.0 545.0 : 157.2 193.9 387.8 424.5 471.6 655.0 702.2 738.9 812.2 969.4 1042.8 1126.6 1200.0 702.2 : 36.7 230.6 267.2 314.4 497.8 545.0 581.7 655.0 812.2 885.6 969.4 1042.8 1200.0 738.9 : 193.9 230.6 277.7 461.1 508.3 545.0 618.3 775.5 848.9 932.8 1006.1 1163.3 1200.0 932.8 : 36.7 83.8 267.2 314.4 351.1 424.5 581.7 655.0 738.9 812.2 969.4 1006.1 1200.0 969.4 : 47.2 230.6 277.7 314.4 387.8 545.0 618.3 702.2 775.5 932.8 969.4 1163.3 1200.0 1016.6: 183.4 230.6 267.2 340.6 497.8 571.2 655.0 728.4 885.6 922.3 1116.2 1152.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.6812 .. 193.8865 cents 157.20524 cents 36.68122 cents 2: 83.8428 .. 230.5677 cents 146.72489 cents -110.04367 cents 3: 157.2052 .. 387.7729 cents 230.56769 cents -73.36244 cents 4: 314.4105 .. 461.1354 cents 146.72489 cents -73.36245 cents 5: 351.0917 .. 544.9782 cents 193.88646 cents -110.04367 cents 6: 424.4541 .. 655.0218 cents 230.56769 cents -120.52402 cents 7: 544.9782 .. 775.5459 cents 230.56769 cents -110.04367 cents 8: 655.0218 .. 848.9083 cents 193.88646 cents -120.52402 cents 9: 738.8646 .. 885.5895 cents 146.72489 cents -110.04367 cents 10: 812.2271 .. 1042.7948 cents 230.56769 cents -73.36245 cents 11: 969.4323 .. 1116.1572 cents 146.72489 cents -73.36245 cents 12: 1006.1135 .. 1163.3188 cents 157.20524 cents -110.04367 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 36.68122 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 193.88646 cents Average / Smallest step : 2.516484 Largest / Average step : 2.100437 Largest / Smallest step : 5.285714 Median interval of one step : 73.36245 cents, amount: 3 Least squares average step : 86.18456 cents, oct.: 1120.39925 cents Scale is not proper Scale is a mode of a 229-tone equal temperament with octave 1200.000 cents degrees: 9 16 30 60 74 90 104 134 141 178 185 194 229 Least number of segments generator : 115 of 602.620 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 192 of 1006.114 cents and inv. generated superset size: 31 = 18 more = 238.462% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCECDBFBAG Step pattern size order : BACECDCEAGABF Scale is not a Constant Structure Scale diversity : 1.435824 Lumma stability : 0.061135 Lumma impropriety factor : 0.720524 Number of different interval sizes : 48 = 4.00000 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 6.83333 = 41/6 Median interval variety : 5.5 Lowest interval variety : 5 Smallest interval difference : 10.48035 cents Most common intervals : 230.56769 cents & inv., amount: 8 Number of recognisable fifths : 5, average 700.0873 cents Formal octave complements present : 1 = 7.6923% -- Rational properties --
FIT/MODE
13: 1 0 1 1 1 1 1 2 0 2 1 0 2 N T3 SD: 25.2882 c. M:-45.9523 c. 15: 1 0 1 2 1 1 1 2 0 3 0 1 2 N SD: 16.7108 c. M:-32.8384 c. 18: 1 0 1 3 1 1 1 3 0 3 1 0 3 N SD: 17.8110 c. M:-31.1499 c. 19: 1 0 1 3 1 1 2 2 1 3 0 1 3 N SD: 18.1723 c. M: 30.8895 c. 21: 1 1 1 3 1 1 2 2 1 3 1 1 3 N SD: 17.2584 c. M:-30.4429 c. 22: 1 1 1 3 1 2 1 3 1 3 1 1 3 N SD: 13.9844 c. M:-25.2481 c. 24: 1 1 1 3 2 1 2 3 1 4 0 1 4 N SD: 13.1556 c. M: 21.6157 c. 26: 1 1 1 4 1 2 2 3 1 4 1 1 4 N SD: 9.6711 c. M: 18.7437 c. 27: 1 1 2 3 2 2 1 4 1 4 1 1 4 N SD: 10.7788 c. M:-20.5725 c. 28: 1 1 2 3 2 2 2 3 1 5 1 1 4 N SD: 10.6415 c. M: 16.4691 c. 31: 1 1 2 4 2 2 2 4 1 5 1 1 5 N SD: 5.2701 c. M: 10.1423 c. 46: 2 1 3 6 3 3 3 6 1 8 1 2 7 N SD: 4.0974 c. M: 8.4298 c. 53: 2 2 3 7 3 4 3 7 2 8 2 2 8 N SD: 3.8616 c. M:-8.3052 c. 68: 3 2 4 9 4 5 4 9 2 11 2 3 10 N SD: 3.6038 c. M:-6.9355 c. 77: 3 2 5 10 5 5 5 10 2 13 2 3 12 N SD: 3.2232 c. M: 6.3971 c. 84: 3 3 5 11 5 6 5 11 3 13 3 3 13 N SD: 2.4544 c. M: 4.3044 c. 99: 4 3 6 13 6 7 6 13 3 16 3 4 15 N SD: 0.8251 c. M:-1.5879 c. 130: 5 4 8 17 8 9 8 17 4 21 4 5 20 N SD: 0.6284 c. M: 1.2093 c. 229: 9 7 14 30 14 16 14 30 7 37 7 9 35 N SD: 0.0000 c. M: 0.0000 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: 0.1142 cents 3 x x x x x 4 x x x 5 x x 6 S SD: 18.3797 cents 4 x x x x 5 x x 6 x x 7 x 8 S SD: 0.3992 cents 5 x x x 6 x x 7 x 8 x x 9:10 S SD: 16.7447 cents 6 x x x 7 x 8 x 9 x 10 x 11:12 S SD: 13.3064 cents 7 x x 8 x x 9:10 x 11:12 x 13:14 S SD: 18.6285 cents 8 x x 9 x 10 x 11:12 x x 14 x 16 S SD: 7.8600 cents 9 x x 10:11 x 12 x x 14:15 x 16:18 S SD: 10.9388 cents 10 x x 11:12 x 13:14:15 x 17 x 18:20 SD: 5.5539 cents 11 x x 12:13:14 x 15 x 17:19 x 20:22 SD: 6.0782 cents 12 x x 13:14:15:16 x 18 x x 21:22:24 S SD: 8.2746 cents 13 x x 14 x 16:17:18 x 20:22:23 x 26 SD: 6.7228 cents 14 x 15 x 17 x 18:19:21 x 24 x 25:28 SD: 7.3981 cents 15 x 16 x 18:19:20:21 x 23 x 26:27:30 SD: 6.7081 cents 16 x 17:18:19:20:21:22:24:25:27:28:29:32 SD: 5.8851 cents 17 x 18:19:20:21:22:23 x 26:29:30:31:34 SD: 6.4156 cents 18 x 19:20:22:23:24:25:27:28:31 x 32:36 SD: 6.7965 cents 19 x 20:21:23:24:25:26 x 29 x 33:34:38 SD: 3.4071 cents 20 x 21:22:24:25:26:27:30:31:34:35:36:40 SD: 3.3427 cents 21 x 22:23:25:26:28:29 x 32:36:37:38:42 SD: 3.7517 cents 22 x 23:24:26:28:29:30:33:34:38:39:40:44 SD: 4.5095 cents 23 x 24:25:28:29:30:32 x 35:39:40:41:46 SD: 4.8556 cents 24 x 25:26:29:30:32:33:36:37:41:42:43:48 SD: 3.3629 cents 25 x 26:27:30:31:33:34 x 38:43:44:45:50 SD: 3.6676 cents 26:27 x 28:31:33:34:36:39:40:45:46:47:52 SD: 4.5787 cents 27:28 x 30:32:34:35:37 x 41:46:47:49:54 SD: 4.6375 cents 28:29 x 31:34:35:37:38:42:43:48:49:50:56 SD: 3.3154 cents 29:30 x 32:35:36:38:40 x 44:50:51:52:58 SD: 3.2244 cents 30:31 x 33:36:38:39:41:45:46:51:53:54:60 SD: 3.1037 cents 32:33:34:35:38:40:42:44:48:49:55:56:58:64 SD: 2.4449 cents 35:36:37:38:42:44:46:48:53:54:60:61:63:70 SD: 2.3281 cents 36:37:38:39:43:45:47:49:54:55:62:63:65:72 SD: 2.2489 cents 40:41:42:44:48:50:53:55:60:61:69:70:72:80 SD: 1.8235 cents 41:42:43:45:49:51:54:56:62:63:70:72:74:82 SD: 1.8092 cents 44:45:46:48:53:55:58:60:66:67:75:77:79:88 SD: 1.8040 cents 56:58:59:61:67:70:74:77:84:86:96:98:101:112 SD: 1.7577 cents 60:62:63:66:72:75:79:82:90:92:103:105:108:120 SD: 1.1060 cents 64:66:67:70:77:80:84:88:96:98:110:112:115:128 SD: 0.9965 cents 76:78:80:83:91:95:100:104:114:116:130:133:137:152 SD: 0.9323 cents 84:86:88:92:101:105:110:115:126:129:144:147:151:168 SD: 0.8324 cents 105:108:110:115:126:131:138:144:158:161:180:184:189:210 SD: 0.6733 cents 116:119:122:127:139:145:152:159:174:178:199:203:209:232 SD: 0.5706 cents 140:144:147:153:168:175:184:192:210:215:240:245:252:280 SD: 0.4903 cents 160:164:168:175:192:200:210:219:240:245:274:280:288:320 SD: 0.4602 cents 176:181:185:193:211:220:231:241:264:270:302:308:317:352 SD: 0.4244 cents 179:184:188:196:215:224:235:245:269:274:307:313:322:358 SD: 0.4215 cents 210:216:220:230:252:263:276:288:315:322:360:368:378:420 SD: 0.4194 cents 216:222:227:237:259:270:284:296:324:331:370:378:389:432 SD: 0.4116 cents 220:226:231:241:264:275:289:301:330:337:377:385:396:440 SD: 0.2683 cents 284:292:298:311:341:355:373:389:426:435:487:497:511:568 SD: 0.2477 cents 322:331:338:353:386:403:423:441:483:493:552:564:579:644 SD: 0.2348 cents 338:347:355:370:405:423:444:463:507:518:579:592:608:676 SD: 0.2257 cents 357:367:375:391:428:447:469:489:536:547:612:625:642:714 SD: 0.2130 cents 367:377:385:402:440:459:482:503:551:562:629:642:660:734 SD: 0.2118 cents 368:378:386:403:441:460:483:504:552:564:631:644:662:736 SD: 0.2093 cents 398:409:418:436:477:498:523:545:597:610:682:697:716:796 SD: 0.1784 cents 402:413:422:440:482:503:528:551:603:616:689:704:723:804 SD: 0.1227 cents 462:475:485:506:554:578:607:633:693:708:792:809:831:924 SD: 0.1184 cents 546:561:573:598:655:683:717:748:819:837:936:956:982:1092 SD: 0.1013 cents