Scala analysis: arch_enh_cheese
Archytas' enharmonic with just 5/4's 'round a circle of 5-ET
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44.916 cents 44.916000 2: 93.686 cents 93.686000 3: 240.000 cents 240.000000 4: 284.916 cents 284.916000 5: 333.686 cents 333.686000 6: 480.000 cents 480.000000 7: 524.916 cents 524.916000 8: 573.686 cents 573.686000 9: 720.000 cents 720.000000 10: 764.916 cents 764.916000 11: 813.686 cents 813.686000 12: 960.000 cents 960.000000 13: 1004.916 cents 1004.916000 14: 1053.686 cents 1053.686000 15: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 146.3140 cents 146.3140 1: 44.9160 cents 44.9160 2: 48.7700 cents 48.7700 3: 146.3140 cents 146.3140 4: 44.9160 cents 44.9160 5: 48.7700 cents 48.7700 6: 146.3140 cents 146.3140 7: 44.9160 cents 44.9160 8: 48.7700 cents 48.7700 9: 146.3140 cents 146.3140 10: 44.9160 cents 44.9160 11: 48.7700 cents 48.7700 12: 146.3140 cents 146.3140 13: 44.9160 cents 44.9160 14: 48.7700 cents 48.7700 15: 146.3140 cents 146.3140
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 44.91600 cents 1: 5 48.77000 cents 1: 5 146.31400 cents 2: 5 93.68600 cents 2: 5 191.23000 cents 2: 5 195.08400 cents 3: 15 240.00000 cents 4: 5 284.91600 cents 4: 5 288.77000 cents 4: 5 386.31400 cents 5: 5 333.68600 cents 5: 5 431.23000 cents 5: 5 435.08400 cents 6: 15 480.00000 cents 7: 5 524.91600 cents 7: 5 528.77000 cents 7: 5 626.31400 cents 8: 5 573.68600 cents 8: 5 671.23000 cents 8: 5 675.08400 cents 9: 15 720.00000 cents 10: 5 764.91600 cents 10: 5 768.77000 cents 10: 5 866.31400 cents 11: 5 813.68600 cents 11: 5 911.23000 cents 11: 5 915.08400 cents 12: 15 960.00000 cents 13: 5 1004.91600 cents 13: 5 1008.77000 cents 13: 5 1106.31400 cents 14: 5 1053.68600 cents 14: 5 1151.23000 cents 14: 5 1155.08400 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.42857 = 17/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 44.9 93.7 240.0 284.9 333.7 480.0 524.9 573.7 720.0 764.9 813.7 960.0 1004.9 1053.7 1200.0 44.9 : 48.8 195.1 240.0 288.8 435.1 480.0 528.8 675.1 720.0 768.8 915.1 960.0 1008.8 1155.1 1200.0 93.7 : 146.3 191.2 240.0 386.3 431.2 480.0 626.3 671.2 720.0 866.3 911.2 960.0 1106.3 1151.2 1200.0 240.0 : 44.9 93.7 240.0 284.9 333.7 480.0 524.9 573.7 720.0 764.9 813.7 960.0 1004.9 1053.7 1200.0 284.9 : 48.8 195.1 240.0 288.8 435.1 480.0 528.8 675.1 720.0 768.8 915.1 960.0 1008.8 1155.1 1200.0 333.7 : 146.3 191.2 240.0 386.3 431.2 480.0 626.3 671.2 720.0 866.3 911.2 960.0 1106.3 1151.2 1200.0 480.0 : 44.9 93.7 240.0 284.9 333.7 480.0 524.9 573.7 720.0 764.9 813.7 960.0 1004.9 1053.7 1200.0 524.9 : 48.8 195.1 240.0 288.8 435.1 480.0 528.8 675.1 720.0 768.8 915.1 960.0 1008.8 1155.1 1200.0 573.7 : 146.3 191.2 240.0 386.3 431.2 480.0 626.3 671.2 720.0 866.3 911.2 960.0 1106.3 1151.2 1200.0 720.0 : 44.9 93.7 240.0 284.9 333.7 480.0 524.9 573.7 720.0 764.9 813.7 960.0 1004.9 1053.7 1200.0 764.9 : 48.8 195.1 240.0 288.8 435.1 480.0 528.8 675.1 720.0 768.8 915.1 960.0 1008.8 1155.1 1200.0 813.7 : 146.3 191.2 240.0 386.3 431.2 480.0 626.3 671.2 720.0 866.3 911.2 960.0 1106.3 1151.2 1200.0 960.0 : 44.9 93.7 240.0 284.9 333.7 480.0 524.9 573.7 720.0 764.9 813.7 960.0 1004.9 1053.7 1200.0 1004.9: 48.8 195.1 240.0 288.8 435.1 480.0 528.8 675.1 720.0 768.8 915.1 960.0 1008.8 1155.1 1200.0 1053.7: 146.3 191.2 240.0 386.3 431.2 480.0 626.3 671.2 720.0 866.3 911.2 960.0 1106.3 1151.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.9160 .. 146.3140 cents 101.39800 cents 44.91600 cents 2: 93.6860 .. 195.0840 cents 101.39800 cents -52.62800 cents 3: 240.0000 .. 240.0000 cents 1/1, 0.0000 cents 44.91600 cents 4: 284.9160 .. 386.3140 cents 101.39800 cents 44.91600 cents 5: 333.6860 .. 435.0840 cents 101.39800 cents -52.62800 cents 6: 480.0000 .. 480.0000 cents 1/1, 0.0000 cents 44.91600 cents 7: 524.9160 .. 626.3140 cents 101.39800 cents 44.91600 cents 8: 573.6860 .. 675.0840 cents 101.39800 cents -52.62800 cents 9: 720.0000 .. 720.0000 cents 1/1, 0.0000 cents 44.91600 cents 10: 764.9160 .. 866.3140 cents 101.39800 cents 44.91600 cents 11: 813.6860 .. 915.0840 cents 101.39800 cents -52.62800 cents 12: 960.0000 .. 960.0000 cents 1/1, 0.0000 cents 44.91600 cents 13: 1004.9160 .. 1106.3140 cents 101.39800 cents 44.91600 cents 14: 1053.6860 .. 1155.0840 cents 101.39800 cents -52.62800 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 44.91600 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 146.31400 cents Average / Smallest step : 1.781103 Largest / Average step : 1.828925 Largest / Smallest step : 3.257503 Median interval of one step : 48.77000 cents, amount: 5 Least squares average step : 76.87056 cents, oct.: 1153.05847 cents Scale is not proper Scale has 5 repeating blocks of 3 notes Scale is 3-distributional even Scale is a mode of a 935-tone equal temperament with octave 2/1 degrees: 35 73 187 222 260 374 409 447 561 596 634 748 783 821 935 Least number of segments generator : 468 of 600.642 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 523 of 671.230 cents and inv. generated superset size: 753 = 738 more = 5020.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABCABCABCABC Step pattern size order : SMLSMLSMLSMLSML Scale is a Constant Structure, by a margin of 44.91600 cents Scale diversity : 1.210106 Lumma stability : 0.374300 Lumma impropriety factor : 0.219283 Number of different interval sizes : 34 = 2.42857 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.42857 = 17/7 Median interval variety : 3 Lowest interval variety : 1 Smallest interval difference : 3.85400 cents Most common triad is 0.0 240.000 480.000 cents, amount: 15 Number of recognisable fifths : 15, average 720.0000 cents Number of appreciable fifths : 0 Scale contains two identical disjunct heptachords Formal octave complements present : 5 = 33.3333% Limited transpositions : 3 6 9 12 Limited inverse transpositions with margin 101.3980 cents: 2 5 8 11 14 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
15: 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 N B D3 SD: 27.1094 c. M: 44.9160 c. 16: 0 1 2 1 0 2 1 0 2 1 1 2 0 1 2 N S SD: 26.7498 c. M: 48.6860 c. 17: 1 0 2 1 1 2 0 1 2 1 1 2 0 1 2 N SD: 20.2387 c. M:-33.3728 c. 18: 0 1 2 1 1 2 1 0 3 0 1 2 1 1 2 N SD: 24.2541 c. M: 44.9160 c. 20: 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 P B ME S SD: 17.5115 c. M:-26.3140 c. 22: 1 1 2 1 1 3 1 1 2 1 1 3 0 1 3 N SD: 15.6621 c. M:-26.3140 c. 25: 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 N B DE S SD: 2.2260 c. M:-3.0840 c. 80: 3 3 10 3 3 10 3 3 10 3 3 10 3 3 10 N B DE S SD: 2.1287 c. M: 3.6860 c. 105: 4 4 13 4 4 13 4 4 13 4 4 13 4 4 13 N B DE S SD: 1.3824 c. M: 2.2574 c. 130: 5 5 16 5 5 16 5 5 16 5 5 16 5 5 16 N B DE S SD: 1.0696 c. M: 1.3783 c. 155: 6 6 19 6 6 19 6 6 19 6 6 19 6 6 19 N B DE S SD: 0.9951 c. M:-1.5356 c. 165: 6 7 20 6 7 20 6 7 20 6 7 20 6 7 20 N B D3 SD: 0.8900 c. M: 1.2796 c. 190: 7 8 23 7 8 23 7 8 23 7 8 23 7 8 23 N B D3 SD: 0.7307 c. M:-1.0508 c. 215: 8 9 26 8 9 26 8 9 26 8 9 26 8 9 26 N B D3 SD: 0.7082 c. M:-1.1977 c. 245: 9 10 30 9 10 30 9 10 30 9 10 30 9 10 30 N B D3 SD: 0.6018 c. M: 0.8344 c. 270: 10 11 33 10 11 33 10 11 33 10 11 33 10 11 33 N B D3 SD: 0.3400 c. M: 0.4716 c. 295: 11 12 36 11 12 36 11 12 36 11 12 36 11 12 36 N B D3 SD: 0.1225 c. M: 0.1702 c. 320: 12 13 39 12 13 39 12 13 39 12 13 39 12 13 39 N B D3 SD: 0.0610 c. M:-0.0840 c. 615: 23 25 75 23 25 75 23 25 75 23 25 75 23 25 75 N B D3 SD: 0.0270 c. M: 0.0380 c. 935: 35 38 114 35 38 114 35 38 114 35 38 114 35 38 114 N B D3 SD: 0.0031 c. M:-0.0038 c.
FIT/HARMONIC
1 x x 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 x 3 x x x x x 4 S SD: 9.0225 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 24.3134 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 14.0828 cents 5 x x x x 6 x x 7 x x 8 x 9 x 10 S SD: 4.7510 cents 6 x x x 7 x 8 x x 9 x 10 x x 11:12 S SD: 12.8994 cents 7 x x 8 x x 9 x 10 x 11 x 12 x 13:14 S SD: 10.4681 cents 8 x x 9 x 10 x x 11:12 x 13:14 x 15:16 S SD: 10.3776 cents 9 x x 10 x 11:12 x 13 x 14 x x 16:17:18 S SD: 12.5701 cents 10 x 11 x x 12:13 x 14:15 x 16:17:18 x 20 S SD: 10.1541 cents 11 x 12 x 13 x x 15 x x 17:18:19 x 20:22 SD: 9.3437 cents 12 x 13 x 14:15:16 x 17:18 x 19:21 x 22:24 SD: 8.3940 cents 13 x 14:15 x 16:17 x 18 x 20:21 x 23:24:26 SD: 5.7155 cents 14 x 15:16 x 17:18:19:20:21:22 x 24:25:26:28 S SD: 6.6562 cents 15 x 16:17 x 18:20 x 21:23 x 24:26:27:28:30 SD: 4.9303 cents 16 x 17:18:19 x 21 x 22:24:25:26:28 x 29:32 SD: 5.7050 cents 17 x 18 x 20:21:22:23:24:26 x 27 x 30:31:34 SD: 5.6102 cents 18 x 19 x 21:22:24 x 25:27:28:29:31:32:33:36 SD: 3.5220 cents 19 x 20:22 x 23:25:26 x 29 x 30:33:34:35:38 SD: 3.2596 cents 20 x 21:23 x 24:26:27:28:30:31:32:35:36:37:40 SD: 3.3683 cents 21 x 22:24:25 x 28 x 29:32:33:34:37:38:39:42 SD: 4.6561 cents 22 x 23:25:26:27:29:30:31:33:34:35:38:39:40:44 SD: 3.8539 cents 23 x 24:26:27:28:30:31:32:35:36:37:40:41:42:46 SD: 3.3023 cents 24 x 25 x 28:29:32 x 33:36:37:38:42:43:44:48 SD: 4.3553 cents 25:26 x 29 x 30:33:34:35:38:39:40:44:45:46:50 SD: 3.2966 cents 26:27 x 30:31:32:34:35:36:39:40:42:45:46:48:52 S SD: 4.1696 cents 27:28:29:31:32:33:36:37:38:41:42:43:47:48:50:54 SD: 3.5877 cents 28:29:30:32:33:34:37:38:39:42:44:45:49:50:51:56 SD: 3.0077 cents 31:32:33:36:37:38:41:42:43:47:48:50:54:55:57:62 SD: 2.9508 cents 32:33:34:37:38:39:42:43:45:49:50:51:56:57:59:64 SD: 2.7115 cents 33:34:35:38:39:40:44:45:46:50:51:53:57:59:61:66 SD: 2.1932 cents 34:35:36:39:40:41:45:46:47:52:53:54:59:61:62:68 SD: 2.1660 cents 38:39:40:44:45:46:50:51:53:58:59:61:66:68:70:76 SD: 1.8645 cents 43:44:45:49:51:52:57:58:60:65:67:69:75:77:79:86 SD: 1.8536 cents 48:49:51:55:57:58:63:65:67:73:75:77:84:86:88:96 SD: 1.8337 cents 50:51:53:57:59:61:66:68:70:76:78:80:87:89:92:100 SD: 1.7427 cents 51:52:54:59:60:62:67:69:71:77:79:82:89:91:94:102 SD: 1.6545 cents 56:57:59:64:66:68:74:76:78:85:87:90:98:100:103:112 SD: 1.4463 cents 62:64:65:71:73:75:82:84:86:94:96:99:108:111:114:124 SD: 1.4143 cents 66:68:70:76:78:80:87:89:92:100:103:106:115:118:121:132 SD: 1.1621 cents 72:74:76:83:85:87:95:98:100:109:112:115:125:129:132:144 SD: 1.0908 cents 74:76:78:85:87:90:98:100:103:112:115:118:129:132:136:148 SD: 0.8662 cents 85:87:90:98:100:103:112:115:118:129:132:136:148:152:156:170 SD: 0.8624 cents 105:108:111:121:124:127:139:142:146:159:163:168:183:188:193:210 SD: 0.8342 cents 107:110:113:123:126:130:141:145:149:162:166:171:186:191:197:214 SD: 0.6048 cents 112:115:118:129:132:136:148:152:156:170:174:179:195:200:206:224 SD: 0.5877 cents 122:125:129:140:144:148:161:165:170:185:190:195:212:218:224:244 SD: 0.4828 cents 147:151:155:169:173:178:194:199:205:223:229:235:256:263:270:294 SD: 0.4450 cents 155:159:164:178:183:188:205:210:216:235:241:248:270:277:285:310 SD: 0.4406 cents 178:183:188:204:210:216:235:241:248:270:277:285:310:318:327:356 SD: 0.3949 cents 194:199:205:223:229:235:256:263:270:294:302:310:338:347:357:388 SD: 0.3928 cents 196:201:207:225:231:238:259:265:273:297:305:314:341:350:360:392 SD: 0.3854 cents 197:202:208:226:232:239:260:267:274:299:306:315:343:352:362:394 SD: 0.3843 cents 201:206:212:231:237:244:265:272:280:305:313:322:350:359:369:402 SD: 0.3784 cents 216:222:228:248:255:262:285:293:301:327:336:346:376:386:397:432 SD: 0.3715 cents 217:223:229:249:256:263:286:294:302:329:338:347:378:388:399:434 SD: 0.3465 cents 229:235:242:263:270:278:302:310:319:347:356:366:399:409:421:458 SD: 0.2714 cents 235:241:248:270:277:285:310:318:327:356:366:376:409:420:432:470 SD: 0.2400 cents 268:275:283:308:316:325:354:363:373:406:417:429:467:479:493:536 SD: 0.2387 cents 310:318:327:356:365:376:409:420:432:470:482:496:540:554:570:620 SD: 0.2203 cents 344:353:363:395:406:417:454:466:479:521:535:550:599:615:632:688 SD: 0.2169 cents 347:356:366:399:409:421:458:470:483:526:540:555:604:620:638:694 SD: 0.2080 cents 375:385:396:431:442:455:495:508:522:568:583:600:653:670:689:750 SD: 0.1866 cents 376:386:397:432:443:456:496:509:524:570:585:602:655:672:691:752 SD: 0.1578 cents 432:443:456:496:509:524:570:585:602:655:672:691:752:772:794:864 SD: 0.1519 cents 463:475:489:532:546:561:611:627:645:702:720:741:806:827:851:926 SD: 0.1472 cents 498:511:526:572:587:604:657:674:694:755:775:797:867:890:915:996 SD: 0.1410 cents 525:539:554:603:619:637:693:711:731:796:817:840:914:938:965:1050 SD: 0.1290 cents 537:551:567:617:633:651:709:727:748:814:835:859:935:960:987:1074 SD: 0.1214 cents 560:575:591:643:660:679:739:758:780:849:871:896:975:1001:1029:1120 SD: 0.1165 cents 598:614:631:687:705:725:789:810:833:906:930:957:1041:1069:1099:1196 SD: 0.1149 cents