Scala analysis: xen18-erlich-garibaldi-12
5L 7s MOS for Garibaldi, L=115.44, s=89.08
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 89.080 cents 89.080000 2: 204.520 cents 204.520000 3: 293.600 cents 293.600000 4: 409.040 cents 409.040000 5: 498.120 cents 498.120000 6: 587.200 cents 587.200000 7: 702.640 cents 702.640000 8: 791.720 cents 791.720000 9: 907.160 cents 907.160000 10: 996.240 cents 996.240000 11: 1111.680 cents 1111.680000 12: 1200.760 cents 1200.760000
SHOW/INTERVAL
0: 89.0800 cents 89.0800 1: 89.0800 cents 89.0800 2: 115.4400 cents 115.4400 3: 89.0800 cents 89.0800 4: 115.4400 cents 115.4400 5: 89.0800 cents 89.0800 6: 89.0800 cents 89.0800 7: 115.4400 cents 115.4400 8: 89.0800 cents 89.0800 9: 115.4400 cents 115.4400 10: 89.0800 cents 89.0800 11: 115.4400 cents 115.4400 12: 89.0800 cents 89.0800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 89.08000 cents 1: 5 115.44000 cents 2: 2 178.16000 cents 2: 10 204.52000 cents 3: 9 293.60000 cents 3: 3 319.96000 cents 4: 4 382.68000 cents 4: 8 409.04000 cents 5: 11 498.12000 cents 5: 1 524.48000 cents 6: 6 587.20000 cents 6: 6 613.56000 cents 7: 1 676.28000 cents 7: 11 702.64000 cents 8: 8 791.72000 cents 8: 4 818.08000 cents 9: 3 880.80000 cents 9: 9 907.16000 cents 10: 10 996.24000 cents 10: 2 1022.60000 cents 11: 5 1085.32000 cents 11: 7 1111.68000 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 0.0 : 89.1 204.5 293.6 409.0 498.1 587.2 702.6 791.7 907.2 996.2 1111.7 1200.8 89.1 : 115.4 204.5 320.0 409.0 498.1 613.6 702.6 818.1 907.2 1022.6 1111.7 1200.8 204.5 : 89.1 204.5 293.6 382.7 498.1 587.2 702.6 791.7 907.2 996.2 1085.3 1200.8 293.6 : 115.4 204.5 293.6 409.0 498.1 613.6 702.6 818.1 907.2 996.2 1111.7 1200.8 409.0 : 89.1 178.2 293.6 382.7 498.1 587.2 702.6 791.7 880.8 996.2 1085.3 1200.8 498.1 : 89.1 204.5 293.6 409.0 498.1 613.6 702.6 791.7 907.2 996.2 1111.7 1200.8 587.2 : 115.4 204.5 320.0 409.0 524.5 613.6 702.6 818.1 907.2 1022.6 1111.7 1200.8 702.6 : 89.1 204.5 293.6 409.0 498.1 587.2 702.6 791.7 907.2 996.2 1085.3 1200.8 791.7 : 115.4 204.5 320.0 409.0 498.1 613.6 702.6 818.1 907.2 996.2 1111.7 1200.8 907.2 : 89.1 204.5 293.6 382.7 498.1 587.2 702.6 791.7 880.8 996.2 1085.3 1200.8 996.2 : 115.4 204.5 293.6 409.0 498.1 613.6 702.6 791.7 907.2 996.2 1111.7 1200.8 1111.7: 89.1 178.2 293.6 382.7 498.1 587.2 676.3 791.7 880.8 996.2 1085.3 1200.8 1200.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.0800 .. 115.4400 cents 26.36000 cents 89.08000 cents 2: 178.1600 .. 204.5200 cents 26.36000 cents 62.72000 cents 3: 293.6000 .. 319.9600 cents 26.36000 cents 89.08000 cents 4: 382.6800 .. 409.0400 cents 26.36000 cents 62.72000 cents 5: 498.1200 .. 524.4800 cents 26.36000 cents 89.08000 cents 6: 587.2000 .. 613.5600 cents 26.36000 cents 62.72000 cents 7: 676.2800 .. 702.6400 cents 26.36000 cents 62.72000 cents 8: 791.7200 .. 818.0800 cents 26.36000 cents 89.08000 cents 9: 880.8000 .. 907.1600 cents 26.36000 cents 62.72000 cents 10: 996.2400 .. 1022.6000 cents 26.36000 cents 89.08000 cents 11: 1085.3200 .. 1111.6800 cents 26.36000 cents 62.72000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 89.08000 cents, class 1 Average step (divided formal octave): 100.0633 cents Largest one step interval : 115.44000 cents Average / Smallest step : 1.123297 Largest / Average step : 1.153669 Largest / Smallest step : 1.295914 Median interval of one step : 89.08000 cents, amount: 7 Most common interval of one step : 89.08000 cents, amount: 7 Least squares average step : 100.07009 cents, oct.: 1200.84111 cents Scale is strictly proper Scale has Myhill's property chromas: 26.36000 cents and 62.72000 cents, ratio: 2.379363 generators: 5 of 498.12000 cents and 7 of 702.64000 cents ET pair of linear temperament : 12&41 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 957-tone equal temperament with octave 1200.760 cents degrees: 71 163 234 326 397 468 560 631 723 794 886 957 generators: 397 and 560 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABABABA Step pattern size order : SLSLSSLSLSLS Scale is a Constant Structure, by a margin of 62.72000 cents Scale diversity : 1.168775 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.758520 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 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 : 26.36000 cents Most common intervals : 498.12000 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 89.080 702.640 cents Most common triad is 0.0 498.120 702.640 cents, amount: 10 Number of recognisable fifths : 11, average 702.6400 cents Number of recognisable fourths : 11, average 498.1200 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.6621 c. M:-13.1800 c. Twelve-tone Chromatic (1/11-comma) 29: 2 3 2 3 2 2 3 2 3 2 3 2 SP M ME SD: 4.3733 c. M: 7.5228 c. 41: 3 4 3 4 3 3 4 3 4 3 4 3 SP M ME SD: 0.8507 c. M: 1.4634 c. 94: 7 9 7 9 7 7 9 7 9 7 9 7 SP M DE SD: 0.2360 c. M:-0.4060 c. 135: 10 13 10 13 10 10 13 10 13 10 13 10 SP M DE SD: 0.0940 c. M: 0.1618 c. 229: 17 22 17 22 17 17 22 17 22 17 22 17 SP M DE SD: 0.0414 c. M:-0.0713 c. 364: 27 35 27 35 27 27 35 27 35 27 35 27 SP M DE SD: 0.0088 c. M: 0.0152 c. 957: 71 92 71 92 71 71 92 71 92 71 92 71 SP M DE SD: 0.0032 c. M:-0.0055 c. 1321: 98 127 98 127 98 98 127 98 127 98 127 98 SP M DE SD: 0.0001 c. M: 0.0002 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.7600 cents 2 x x x x x x 3 x x x x 4 S SD: 0.5116 cents 3 x x x x 4 x x x 5 x x 6 S SD: 7.6047 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.9060 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.6078 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.6163 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.7567 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.2595 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.4141 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.1195 cents 11 x 12:13:14:15 x x 17:19:20:21:22 SD: 10.5639 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.7000 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.7127 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 7.1841 cents 15:16:17:18:19:20:21:23:24:25:27:29:30 SD: 5.8346 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.5815 cents 17:18:19:20:22:23:24:26:27:29:30:32:34 SD: 5.5483 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 4.6793 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 2.9362 cents 32:34:36:38:41:43:45:48:51:54:57:61:64 SD: 2.7991 cents 33:35:37:39:42:44:46:50:52:56:59:63:66 SD: 2.5942 cents 38:40:43:45:48:51:53:57:60:64:68:72:76 SD: 1.9401 cents 42:44:47:50:53:56:59:63:66:71:75:80:84 SD: 1.7471 cents 54:57:61:64:68:72:76:81:85:91:96:103:108 SD: 1.3828 cents 60:63:68:71:76:80:84:90:95:101:107:114:120 SD: 1.3711 cents 64:67:72:76:81:85:90:96:101:108:114:122:128 SD: 1.2147 cents 71:75:80:84:90:95:100:107:112:120:126:135:142 SD: 1.1514 cents 72:76:81:85:91:96:101:108:114:122:128:137:144 SD: 0.9432 cents 90:95:101:107:114:120:126:135:142:152:160:171:180 SD: 0.8660 cents 96:101:108:114:122:128:135:144:152:162:171:182:192 SD: 0.8625 cents 102:107:115:121:129:136:143:153:161:172:181:194:204 SD: 0.7787 cents 112:118:126:133:142:149:157:168:177:189:199:213:224 SD: 0.5771 cents 136:143:153:161:172:181:191:204:215:230:242:258:272 SD: 0.5603 cents 150:158:169:178:190:200:211:225:237:253:267:285:300 SD: 0.4888 cents 168:177:189:199:213:224:236:252:265:284:299:319:336 SD: 0.4073 cents 190:200:214:225:241:253:267:285:300:321:338:361:380 SD: 0.3923 cents 206:217:232:244:261:275:289:309:325:348:366:392:412 SD: 0.3876 cents 210:221:236:249:266:280:295:315:332:355:373:399:420 SD: 0.3573 cents 222:234:250:263:281:296:312:333:351:375:395:422:444 SD: 0.3280 cents 240:253:270:284:304:320:337:360:379:405:427:456:480 SD: 0.3260 cents 248:261:279:294:314:331:348:372:392:419:441:471:496 SD: 0.2538 cents 270:284:304:320:342:360:379:405:427:456:480:513:540 SD: 0.2364 cents 319:336:359:378:404:425:448:479:504:539:567:606:638 SD: 0.2172 cents 342:360:385:405:433:456:480:513:540:578:608:650:684 SD: 0.1934 cents 431:454:485:511:546:575:605:647:681:728:766:819:862 SD: 0.1855 cents 438:461:493:519:555:584:615:657:692:740:779:832:876 SD: 0.1655 cents 492:518:554:583:623:656:691:738:777:831:875:935:984 SD: 0.1569 cents 495:521:557:586:627:660:695:743:782:836:880:941:990 SD: 0.1557 cents 510:537:574:604:646:680:716:765:806:861:907:969:1020 SD: 0.1414 cents 552:581:621:654:699:736:775:828:872:932:981:1049:1104 SD: 0.1311 cents 585:616:658:693:741:780:821:878:924:988:1040:1112:1171 SD: 0.1238 cents