Scala analysis: plum
686/675 comma pump scale in 46et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 130.435 cents 130.434780 2: 260.870 cents 260.869570 3: 391.304 cents 391.304350 4: 443.478 cents 443.478260 5: 521.739 cents 521.739130 6: 573.913 cents 573.913040 7: 704.348 cents 704.347830 8: 834.783 cents 834.782610 9: 965.217 cents 965.217390 10: 1069.565 cents 1069.565220 11: 1095.652 cents 1095.652170 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 104.3478 cents 104.3478 1: 130.4348 cents 130.4348 2: 130.4348 cents 130.4348 3: 130.4348 cents 130.4348 4: 52.1739 cents 52.1739 5: 78.2609 cents 78.2609 6: 52.1739 cents 52.1739 7: 130.4348 cents 130.4348 8: 130.4348 cents 130.4348 9: 130.4348 cents 130.4348 10: 104.3478 cents 104.3478 11: 26.0869 cents 26.0869 12: 104.3478 cents 104.3478
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 26.08695 cents 1: 2 52.17391 cents 1: 1 78.26087 cents 1: 2 104.34783 cents 1: 6 130.43478 cents 2: 4 130.43478 cents 2: 2 182.60869 cents 2: 2 234.78261 cents 2: 4 260.86957 cents 3: 1 182.60869 cents 3: 1 234.78261 cents 3: 4 260.86956 cents 3: 2 313.04348 cents 3: 2 365.21739 cents 3: 2 391.30435 cents 4: 2 313.04347 cents 4: 2 365.21739 cents 4: 4 391.30435 cents 4: 2 443.47826 cents 4: 2 495.65218 cents 5: 3 443.47826 cents 5: 3 495.65217 cents 5: 4 521.73913 cents 5: 2 547.82609 cents 6: 6 573.91304 cents 6: 6 626.08696 cents 7: 2 652.17391 cents 7: 4 678.26087 cents 7: 3 704.34783 cents 7: 3 756.52174 cents 8: 2 704.34782 cents 8: 2 756.52174 cents 8: 4 808.69565 cents 8: 2 834.78261 cents 8: 2 886.95653 cents 9: 2 808.69565 cents 9: 2 834.78260 cents 9: 2 886.95652 cents 9: 4 939.13044 cents 9: 1 965.21739 cents 9: 1 1017.39131 cents 10: 4 939.13043 cents 10: 2 965.21739 cents 10: 2 1017.39131 cents 10: 4 1069.56522 cents 11: 6 1069.56522 cents 11: 2 1095.65217 cents 11: 1 1121.73913 cents 11: 2 1147.82609 cents 11: 1 1173.91305 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.54545 = 50/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 130.4 260.9 391.3 443.5 521.7 573.9 704.3 834.8 965.2 1069.6 1095.7 1200.0 130.4 : 130.4 260.9 313.0 391.3 443.5 573.9 704.3 834.8 939.1 965.2 1069.6 1200.0 260.9 : 130.4 182.6 260.9 313.0 443.5 573.9 704.3 808.7 834.8 939.1 1069.6 1200.0 391.3 : 52.2 130.4 182.6 313.0 443.5 573.9 678.3 704.3 808.7 939.1 1069.6 1200.0 443.5 : 78.3 130.4 260.9 391.3 521.7 626.1 652.2 756.5 887.0 1017.4 1147.8 1200.0 521.7 : 52.2 182.6 313.0 443.5 547.8 573.9 678.3 808.7 939.1 1069.6 1121.7 1200.0 573.9 : 130.4 260.9 391.3 495.7 521.7 626.1 756.5 887.0 1017.4 1069.6 1147.8 1200.0 704.3 : 130.4 260.9 365.2 391.3 495.7 626.1 756.5 887.0 939.1 1017.4 1069.6 1200.0 834.8 : 130.4 234.8 260.9 365.2 495.7 626.1 756.5 808.7 887.0 939.1 1069.6 1200.0 965.2 : 104.3 130.4 234.8 365.2 495.7 626.1 678.3 756.5 808.7 939.1 1069.6 1200.0 1069.6: 26.1 130.4 260.9 391.3 521.7 573.9 652.2 704.3 834.8 965.2 1095.7 1200.0 1095.7: 104.3 234.8 365.2 495.7 547.8 626.1 678.3 808.7 939.1 1069.6 1173.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.0869 .. 130.4348 cents 104.34783 cents 26.08695 cents 2: 130.4348 .. 260.8696 cents 130.43479 cents 1/1, 0.0000 cents 3: 182.6087 .. 391.3044 cents 208.69566 cents -78.26088 cents 4: 313.0435 .. 495.6522 cents 182.60871 cents -78.26088 cents 5: 443.4783 .. 547.8261 cents 104.34783 cents -52.17392 cents 6: 573.9130 .. 626.0870 cents 52.17392 cents 26.08695 cents 7: 652.1739 .. 756.5217 cents 104.34783 cents 26.08695 cents 8: 704.3478 .. 886.9565 cents 182.60871 cents -52.17392 cents 9: 808.6957 .. 1017.3913 cents 208.69566 cents -78.26088 cents 10: 939.1304 .. 1069.5652 cents 130.43479 cents -78.26088 cents 11: 1069.5652 .. 1173.9131 cents 104.34783 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 26.08695 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 130.43478 cents Average / Smallest step : 3.833334 Largest / Average step : 1.304348 Largest / Smallest step : 5.000001 Median interval of one step : 117.39130 cents, amount: 0 Most common interval of one step : 130.43478 cents, amount: 6 Least squares average step : 103.22408 cents, oct.: 1238.68896 cents Scale is not proper Scale is a mode of a 46-tone equal temperament with octave 1200.000 cents degrees: 5 10 15 17 20 22 27 32 37 41 42 46 Least number of segments generator : 41 of 1069.565 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 29 of 756.522 cents and inv. generated superset size: 20 = 8 more = 166.667% Number of contiguous 1-step segments: 1 Step pattern alph. order: AAABCBAAADED Step pattern size order : EEEBCBEEEDAD Interval vector is [ 1 2 1 2 10 0 3 0 3 8 0 4 0 4 6 0 5 0 5 4 2 6 0 ] Scale is not a Constant Structure Scale diversity : 1.360460 Lumma stability : 0.086956 Lumma impropriety factor : 0.347826 Rothenberg efficiency : 0.514153 redundancy: 0.485847 Efficiency x scale size : 6.169841 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 4.54545 = 50/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 26.08695 cents Most common intervals : 130.43478 cents & inv., amount: 10 Most common triad is 0.0 130.435 1069.565 cents, amount: 8 Number of recognisable fifths : 5, average 704.3478 cents Formal octave complements present : 3 = 25.0000% Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 10-11 -- Rational properties --
FIT/MODE
12: 1 2 1 0 1 1 1 1 2 1 0 1 N T3 SD: 27.3257 c. M: 43.4783 c. 16: 2 1 2 1 1 1 1 2 2 1 1 1 N D3 SD: 20.3424 c. M: 35.8696 c. 17: 2 2 2 0 1 1 2 2 2 1 1 1 N SD: 19.9980 c. M:-33.7596 c. 19: 2 2 2 1 1 1 2 2 2 2 0 2 N SD: 11.6907 c. M: 21.9680 c. 25: 3 2 3 1 2 1 3 2 3 2 1 2 N SD: 11.9962 c. M: 20.8696 c. 27: 3 3 3 1 2 1 3 3 3 2 1 2 N SD: 8.2268 c. M:-15.4589 c. 34: 4 3 4 2 2 1 4 4 3 3 1 3 N SD: 9.6444 c. M:-15.3453 c. 35: 4 4 3 2 2 2 4 3 4 3 1 3 N SD: 9.2544 c. M:-15.6522 c. 36: 4 4 4 1 3 1 4 4 4 3 1 3 N SD: 6.1772 c. M:-11.5942 c. 37: 4 4 4 2 2 2 4 4 4 3 1 3 N SD: 6.3910 c. M:-10.5758 c. 46: 5 5 5 2 3 2 5 5 5 4 1 4 N SD: 0.0000 c. M: 0.0000 c. Plum
FIT/HARMONIC
1 x 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 x 4 S SD: 1.1964 cents 3 x x x x 4 x x 5 x x x 6 S SD: 18.3158 cents 4 x x 5 x x x 6 x 7 x x 8 S SD: 1.6518 cents 5 x 6 x x x 7 x 8 x 9 x 10 S SD: 15.7730 cents 6 x 7 x x 8 x 9:10 x 11 x 12 S SD: 9.8165 cents 7 x 8 x 9 x 10 x 11:12:13 x 14 S SD: 11.6230 cents 8 x 9:10 x x 11:12:13:14 x 15:16 S SD: 7.7923 cents 9:10 x 11 x 12:13:14:15:16 x 17:18 S SD: 14.1550 cents 10:11:12 x 13 x 14:15:16:17 x 19:20 SD: 9.4581 cents 11:12:13 x 14:15 x 17:18:19:20:21:22 SD: 8.3592 cents 12:13:14:15 x 16:17:18:19:21:22:23:24 SD: 6.0580 cents 13:14:15:16:17 x 18:20:21:23:24 x 26 SD: 6.3651 cents 14:15:16 x 18:19:20:21:23:24:26 x 28 SD: 6.8326 cents 15:16:17:19 x 20:21:23:24:26:28 x 30 SD: 7.2556 cents 16:17:19:20:21 x 22:24:26:28 x 30:32 SD: 5.8130 cents 17:18:20:21:22:23:24:26:28:30 x 32:34 S SD: 6.2672 cents 18:19:21 x 23:24:25:27:29:31:33:34:36 SD: 5.3419 cents 19:20:22:24:25:26 x 29:31:33:35:36:38 SD: 6.2240 cents 20:22:23:25:26:27:28:30:32:35:37:38:40 SD: 4.1646 cents 22:24:26 x 28:30:31:33:36:38:41 x 44 SD: 5.7105 cents 23:25:27:29:30:31:32:35:37:40 x 43:46 SD: 3.7761 cents 24:26:28:30:31:32:33:36:39:42 x 45:48 S SD: 3.2847 cents 28:30:33:35:36:38:39:42:45:49:52:53:56 SD: 2.7693 cents 30:32:35:38:39:41:42:45:49:52:56 x 60 SD: 3.8221 cents 31:33:36:39:40:42:43:47:50:54 x 58:62 SD: 2.9666 cents 34:37:40:43:44:46:47:51:55:59:63:64:68 SD: 2.9241 cents 35:38:41:44:45:47:49:53:57:61:65:66:70 SD: 2.5287 cents 36:39:42:45:47:49:50:54:58:63:67:68:72 SD: 2.3443 cents 40:43:47:50:52:54:56:60:65:70:74:75:80 SD: 2.2187 cents 42:45:49:53:54:57:59:63:68:73:78:79:84 SD: 2.2004 cents 43:46:50:54:56:58:60:65:70:75:80:81:86 SD: 2.1087 cents 48:52:56:60:62:65:67:72:78:84:89:90:96 SD: 1.3326 cents 62:67:72:78:80:84:86:93:100:108:115:117:124 SD: 1.2452 cents 63:68:73:79:81:85:88:95:102:110:117:119:126 SD: 1.2343 cents 66:71:77:83:85:89:92:99:107:115:122:124:132 SD: 1.1925 cents 68:73:79:85:88:92:95:102:110:119:126:128:136 SD: 1.0086 cents 74:80:86:93:96:100:103:111:120:129:137:139:148 SD: 0.9926 cents 76:82:88:95:98:103:106:114:123:133:141:143:152 SD: 0.9664 cents 79:85:92:99:102:107:110:119:128:138:147:149:158 SD: 0.8301 cents 99:107:115:124:128:134:138:149:160:173:184:186:198 SD: 0.7616 cents 102:110:119:128:132:138:142:153:165:178:189:192:204 SD: 0.6803 cents 117:126:136:147:151:158:163:176:189:204:217:220:234 SD: 0.6780 cents 127:137:148:159:164:172:177:191:206:222:236:239:254 SD: 0.6459 cents 129:139:150:162:167:174:180:194:209:225:239:243:258 SD: 0.6357 cents 130:140:151:163:168:176:181:195:211:227:241:245:260 SD: 0.5162 cents 153:165:178:192:198:207:213:230:248:267:284:288:306 SD: 0.4083 cents 165:178:192:207:213:223:230:248:267:288:306:311:330 SD: 0.3248 cents 216:233:251:271:279:292:301:324:350:377:401:407:432 SD: 0.3201 cents 229:247:266:287:296:310:319:344:371:400:425:431:458 SD: 0.2926 cents 257:277:299:322:332:347:358:386:416:449:477:484:514 SD: 0.2555 cents 295:318:343:370:381:399:411:443:478:515:547:555:590 SD: 0.2091 cents 308:332:358:386:398:416:429:463:499:538:571:580:616 SD: 0.2010 cents 370:399:430:464:478:500:515:556:599:646:686:697:740 SD: 0.1962 cents 386:416:449:484:499:522:538:580:625:674:716:727:772 SD: 0.1854 cents 387:417:450:485:500:523:539:581:627:676:718:729:774 SD: 0.1646 cents 394:425:458:494:509:533:549:592:638:688:731:742:788 SD: 0.1542 cents 418:451:486:524:540:565:582:628:677:730:775:787:836 SD: 0.1392 cents 486:524:565:609:628:657:677:730:787:849:901:915:972 SD: 0.1152 cents 524:565:609:657:677:708:730:787:849:915:972:987:1048 SD: 0.1111 cents 552:595:642:692:713:746:769:829:894:964:1024:1039:1104 SD: 0.1058 cents 572:617:665:717:739:773:797:859:926:999:1061:1077:1144 SD: 0.1044 cents