Scala analysis: Keenan4
Chain of quarter-4ths MOS, 6 tetrads, max abs err 18c
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 124.511 cents 124.511250 2: 249.023 cents 249.022500 3: 373.534 cents 373.533750 4: 4/3 498.044999 perfect fourth 5: 622.556 cents 622.556250 6: 3/2 701.955001 perfect fifth 7: 826.466 cents 826.466250 8: 950.977 cents 950.977500 9: 1075.489 cents 1075.488750 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 124.5112 cents 124.5112 1: 124.5112 cents 124.5112 2: 124.5113 cents 124.5113 3: 124.5112 cents 124.5112 4: 124.5112 cents 124.5112 5: 124.5113 cents 124.5113 6: 79.3988 cents 79.3988 7: 124.5112 cents 124.5112 8: 124.5112 cents 124.5112 9: 124.5113 cents 124.5113 10: 124.5112 cents 124.5112
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 79.39875 cents 1: 9 124.51125 cents 2: 2 9/8 203.910 cents major whole tone 2: 8 249.02250 cents 3: 3 328.42125 cents 3: 7 373.53375 cents 4: 4 452.93250 cents 4: 6 4/3 498.045 cents perfect fourth 5: 5 577.44375 cents 5: 5 622.55625 cents 6: 6 3/2 701.955 cents perfect fifth 6: 4 747.06750 cents 7: 7 826.46625 cents 7: 3 871.57875 cents 8: 8 950.97750 cents 8: 2 16/9 996.090 cents Pythagorean minor seventh 9: 9 1075.48875 cents 9: 1 1120.60125 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 0.0 : 124.5 249.0 373.5 498.0 622.6 702.0 826.5 951.0 1075.5 1200.0 124.5 : 124.5 249.0 373.5 498.0 577.4 702.0 826.5 951.0 1075.5 1200.0 249.0 : 124.5 249.0 373.5 452.9 577.4 702.0 826.5 951.0 1075.5 1200.0 373.5 : 124.5 249.0 328.4 452.9 577.4 702.0 826.5 951.0 1075.5 1200.0 498.0 : 124.5 203.9 328.4 452.9 577.4 702.0 826.5 951.0 1075.5 1200.0 622.6 : 79.4 203.9 328.4 452.9 577.4 702.0 826.5 951.0 1075.5 1200.0 702.0 : 124.5 249.0 373.5 498.0 622.6 747.1 871.6 996.1 1120.6 1200.0 826.5 : 124.5 249.0 373.5 498.0 622.6 747.1 871.6 996.1 1075.5 1200.0 951.0 : 124.5 249.0 373.5 498.0 622.6 747.1 871.6 951.0 1075.5 1200.0 1075.5: 124.5 249.0 373.5 498.0 622.6 747.1 826.5 951.0 1075.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 79.3988 .. 124.5112 cents 45.11250 cents 79.39875 cents 2: 203.9100 .. 249.0225 cents 45.11250 cents 79.39875 cents 3: 328.4213 .. 373.5337 cents 45.11250 cents 79.39875 cents 4: 452.9325 .. 498.0450 cents 45.11250 cents 79.39875 cents 5: 577.4438 .. 622.5562 cents 45.11250 cents 79.39875 cents 6: 701.9550 .. 747.0675 cents 45.11250 cents 79.39875 cents 7: 826.4662 .. 871.5787 cents 45.11250 cents 79.39875 cents 8: 950.9775 .. 996.0900 cents 45.11250 cents 79.39875 cents 9: 1075.4888 .. 1120.6012 cents 45.11250 cents 79.39875 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 79.39875 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 124.51125 cents Average / Smallest step : 1.511359 Largest / Average step : 1.037594 Largest / Smallest step : 1.568176 Median interval of one step : 124.51125 cents, amount: 9 Most common interval of one step : 124.51125 cents, amount: 9 Least squares average step : 119.82424 cents, oct.: 1198.24237 cents Scale is strictly proper Scale has Myhill's property chromas: 45.11250 cents and 34.28625 cents, ratio: 1.315761 generators: 1 of 124.51125 cents and 9 of 1075.48875 cents ET pair of linear temperament : 10&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 665-tone equal temperament with octave 2/1 degrees: 69 138 207 276 345 389 458 527 596 665 generators: 69 and 596 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAAABAAAA Step pattern size order : LLLLLSLLLL Scale is a Constant Structure, by a margin of 79.39875 cents Scale diversity : 1.247963 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.661656 Rothenberg efficiency : 0.733333 redundancy: 0.266667 Efficiency x scale size : 7.333333 Number of different interval sizes : 18 = 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 : 45.11250 cents Most common intervals : 124.51125 cents & inv., amount: 9 Scale is a chain of 5 triads 0.0 498.045 1075.489 cents Most common triad is 0.0 124.511 1075.489 cents, amount: 8 Number of recognisable fifths : 6, average 701.9550 cents Scale contains two identical disjunct pentachords Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 Formal octave complements present : 9 = 90.0000% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 5-6 -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 13.1524 c. M: 22.5562 c. 19: 2 2 2 2 2 1 2 2 2 2 SP M ME SD: 5.2611 c. M:-9.0227 c. 29: 3 3 3 3 3 2 3 3 3 3 SP M ME SD: 1.0884 c. M: 1.8666 c. 77: 8 8 8 8 8 5 8 8 8 8 SP M DE SD: 0.4784 c. M:-0.8204 c. 106: 11 11 11 11 11 7 11 11 11 11 SP M DE SD: 0.0497 c. M:-0.0853 c. 347: 36 36 36 36 36 23 36 36 36 36 SP M DE SD: 0.0454 c. M: 0.0779 c. 453: 47 47 47 47 47 30 47 47 47 47 SP M DE SD: 0.0231 c. M: 0.0397 c. 559: 58 58 58 58 58 37 58 58 58 58 SP M DE SD: 0.0093 c. M: 0.0160 c. 665: 69 69 69 69 69 44 69 69 69 69 SP M DE SD: 0.0001 c. M:-0.0001 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x x 4 x x 5 x x 6 S SD: 19.2975 cents 4 x x 5 x x 6 x 7 x 8 S SD: 5.4880 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 18.4064 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 10.9958 cents 7 x 8:9 x 10 x 11:12:13:14 S SD: 11.4280 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 9.4506 cents 9:10 x 11:12:13 x 15:16:17:18 SD: 12.6686 cents 10:11 x 12:13:14:15:16:17:19:20 SD: 11.6535 cents 11:12:13:14:15:16:17:18:19:20:22 S SD: 10.6975 cents 12:13:14:15:16:17:18:19:21:22:24 SD: 5.4941 cents 18:19:21:22:24:26:27:29:31:34:36 SD: 5.3898 cents 21:23:24:26:28:30:32:34:36:39:42 SD: 5.0814 cents 24:26:28:30:32:34:36:39:42:45:48 S SD: 4.1733 cents 25:27:29:31:33:36:38:40:43:47:50 SD: 4.0704 cents 26:28:30:32:35:37:39:42:45:48:52 SD: 2.8978 cents 30:32:35:37:40:43:45:48:52:56:60 SD: 2.7972 cents 37:40:43:46:49:53:56:60:64:69:74 SD: 2.7397 cents 38:41:44:47:51:54:57:61:66:71:76 SD: 2.3490 cents 42:45:49:52:56:60:63:68:73:78:84 SD: 2.2235 cents 44:47:51:55:59:63:66:71:76:82:88 SD: 2.1028 cents 50:54:58:62:67:72:75:81:87:93:100 SD: 2.0766 cents 51:55:59:63:68:73:77:82:88:95:102 SD: 1.7387 cents 57:61:66:71:76:82:86:92:99:106:114 SD: 1.7318 cents 58:62:67:72:77:83:87:93:100:108:116 SD: 1.6994 cents 64:69:74:79:85:92:96:103:111:119:128 SD: 1.4596 cents 66:71:76:82:88:95:99:106:114:123:132 SD: 1.2744 cents 70:75:81:87:93:100:105:113:121:130:140 SD: 1.2023 cents 72:77:83:89:96:103:108:116:125:134:144 SD: 1.2004 cents 78:84:90:97:104:112:117:126:135:145:156 SD: 0.8105 cents 104:112:120:129:139:149:156:168:180:194:208 SD: 0.8040 cents 108:116:125:134:144:155:162:174:187:201:216 SD: 0.5160 cents 150:161:173:186:200:215:225:242:260:279:300 SD: 0.3919 cents 224:241:259:278:299:321:336:361:388:417:448 SD: 0.3758 cents 240:258:277:298:320:344:360:387:416:447:480 SD: 0.2569 cents 310:333:358:385:413:444:465:500:537:577:620 SD: 0.2554 cents 312:335:360:387:416:447:468:503:540:581:624 SD: 0.2541 cents 324:348:374:402:432:464:486:522:561:603:648 SD: 0.1606 cents 402:432:464:499:536:576:603:648:696:748:804 SD: 0.1310 cents 510:548:589:633:680:731:765:822:883:949:1020 SD: 0.1214 cents 564:606:651:700:752:808:846:909:977:1050:1128 SD: 0.0997 cents