Scala analysis: freefokkerblock
2.7.13 Fokker block (free-floating parallelogram definition) with UVs 343/338, 28672/28561
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 1183/1024 249.881230 3: 637/512 378.179475 4: 169/128 481.055324 5: 91/64 609.353568 6: 49/32 737.651813 7: 13/8 840.527662 tridecimal neutral sixth 8: 7/4 968.825906 harmonic seventh 9: 49/26 1097.124151 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 52/49 102.8758 1: 14/13 128.2982 2/3-tone 2: 2197/2048 121.5830 3: 14/13 128.2982 2/3-tone 4: 52/49 102.8758 5: 14/13 128.2982 2/3-tone 6: 14/13 128.2982 2/3-tone 7: 52/49 102.8758 8: 14/13 128.2982 2/3-tone 9: 14/13 128.2982 2/3-tone 10: 52/49 102.8758
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 52/49 102.876 cents 1: 1 2197/2048 121.583 cents 1: 6 14/13 128.298 cents 2/3-tone 2: 6 8/7 231.174 cents septimal whole tone 2: 2 1183/1024 249.881 cents 2: 2 196/169 256.596 cents two (2/3-tone) 3: 2 2197/1792 352.757 cents 3: 7 16/13 359.472 cents tridecimal neutral third 3: 1 637/512 378.179 cents 4: 2 64/49 462.348 cents 2 septatones or septatonic major third 4: 4 169/128 481.055 cents 4: 4 224/169 487.771 cents 5: 1 2197/1568 583.931 cents 5: 4 128/91 590.646 cents 5: 4 91/64 609.354 cents 5: 1 3136/2197 616.069 cents 6: 4 169/112 712.229 cents 6: 4 256/169 718.945 cents two (tridecimal neutral third) 6: 2 49/32 737.652 cents 7: 1 1024/637 821.821 cents 7: 7 13/8 840.528 cents tridecimal neutral sixth 7: 2 3584/2197 847.243 cents 8: 2 169/98 943.404 cents 8: 2 2048/1183 950.119 cents 8: 6 7/4 968.826 cents harmonic seventh 9: 6 13/7 1071.702 cents 16/3-tone 9: 1 4096/2197 1078.417 cents 9: 3 49/26 1097.124 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.11111 = 28/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 128.3 249.9 378.2 481.1 609.4 737.7 840.5 968.8 1097.1 1200.0 128.3 : 121.6 249.9 352.8 481.1 609.4 712.2 840.5 968.8 1071.7 1200.0 249.9 : 128.3 231.2 359.5 487.8 590.6 718.9 847.2 950.1 1078.4 1200.0 378.2 : 102.9 231.2 359.5 462.3 590.6 718.9 821.8 950.1 1071.7 1200.0 481.1 : 128.3 256.6 359.5 487.8 616.1 718.9 847.2 968.8 1097.1 1200.0 609.4 : 128.3 231.2 359.5 487.8 590.6 718.9 840.5 968.8 1071.7 1200.0 737.7 : 102.9 231.2 359.5 462.3 590.6 712.2 840.5 943.4 1071.7 1200.0 840.5 : 128.3 256.6 359.5 487.8 609.4 737.7 840.5 968.8 1097.1 1200.0 968.8 : 128.3 231.2 359.5 481.1 609.4 712.2 840.5 968.8 1071.7 1200.0 1097.1: 102.9 231.2 352.8 481.1 583.9 712.2 840.5 943.4 1071.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 102.8758 .. 128.2982 cents 343/338, 25.4224 cents 52/49, 102.8758 cents 2: 231.1741 .. 256.5965 cents 343/338, 25.4224 cents 52/49, 102.8758 cents 3: 352.7571 .. 378.1795 cents 343/338, 25.4224 cents 371293/351232, 96.1606 cents 4: 462.3482 .. 487.7706 cents 343/338, 25.4224 cents 32768/31213, 84.1687 cents 5: 583.9312 .. 616.0688 cents 4917248/4826809, 32.1377 cents 371293/351232, 96.1606 cents 6: 712.2294 .. 737.6518 cents 343/338, 25.4224 cents 371293/351232, 96.1606 cents 7: 821.8205 .. 847.2429 cents 343/338, 25.4224 cents 32768/31213, 84.1687 cents 8: 943.4035 .. 968.8259 cents 343/338, 25.4224 cents 371293/351232, 96.1606 cents 9: 1071.7018 .. 1097.1242 cents 343/338, 25.4224 cents 52/49, 102.8758 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 52/49, 102.8758 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 14/13, 128.2982 cents Average / Smallest step : 1.166455 Largest / Average step : 1.069152 Largest / Smallest step : 1.247117 Median interval of one step : 14/13, 128.2982 cents, amount: 6 Most common interval of one step : 14/13, 128.2982 cents, amount: 6 Least squares average step : 121.21537 cents, oct.: 1212.15370 cents Scale is strictly proper Step pattern alph. order: ABACAACAAC Step pattern size order : LMLSLLSLLS Scale is a Constant Structure, by a margin of 84.16871 cents Scale diversity : 1.171186 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.803736 Rothenberg efficiency : 0.447857 redundancy: 0.552143 Efficiency x scale size : 4.478571 Number of different interval sizes : 28 = 3.11111 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.11111 = 28/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 28672/28561, 6.7153 cents Most common intervals : 16/13, 359.4723 cents & inv., amount: 7 Most common triad is 0.0 359.472 840.528 cents, amount: 4 Number of recognisable fifths : 8, average 715.5870 cents Number of appreciable fifths : 4, average 712.2294 cents Best major thirds form a closed circle Best minor thirds form a closed circle Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 10.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited transpositions with margin 25.4224 cents: 2 4 7 Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 6-7 -- Rational properties -- Prime limit : 13 Odd number limit : 2197 (O: 2197 U: 2197) Highest odd numerator or denominator: 1183 Scale harmonicity : 0.010201 Average absolute harmonicity : 0.129335 Specific harmonicity : 0.053658 Fundamental : 1/13312, -13.7004 octaves, 0.0197 Hz. Guide tone : 16562, 14.0156 octaves, 4333042.613 Hz. Exponens Consonantiae : 2.204733E+08, 27.71603 octaves Euler's gradus suavitatis : 60 Sum of Mann's harmonic distance : 2013.0, average 201.30000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 16.51743, average 1.65174 Sum of Tenney's harmonic distance : 32.02282, average 3.20228 Vogel's harmonic complexity : 32.40000 Wille's k value : 7689 Wilson's harmonic complexity : 53 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 282.41433, average 5.13481 Lattice compactness (without 2's) : 95.62641, average 1.73866 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 1 -4.10000 45 1 7: 0 .. 2 1.00000 10 2 13: -1 .. 2 0.50000 9 7 Average exponent except 2's : 15 / 10 = 1.50000 Average absolute exponent except 2's: 19 / 10 = 1.90000 Scale is weakly epimorphic with val: <10 26 39| Scale is JI-epimorphic with val: <10 28 37| = patent Scale is weakly epimorphic with val: <10 29 37|
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.2632 c. M: 18.1795 c. 26: 3 2 3 2 3 3 2 3 3 2 SP D3 SD: 11.0669 c. M: 19.5169 c. 28: 3 3 3 2 3 3 3 3 3 2 SP D3 SD: 11.0815 c. M:-17.1616 c. 31: 3 3 4 2 4 3 3 3 3 3 SP D3 SD: 11.0280 c. M: 17.6232 c. 32: 3 4 3 3 3 4 2 4 3 3 SP D3 SD: 10.3551 c. M: 15.7982 c. 33: 4 3 3 3 4 3 3 4 3 3 SP M ME SD: 10.0368 c. M:-17.1563 c. 34: 4 3 4 3 3 4 3 3 4 3 SP D3 SD: 9.2168 c. M: 15.8847 c. 36: 4 3 4 3 4 4 3 4 4 3 SP D3 SD: 8.9977 c. M: 16.5479 c. 37: 4 4 4 3 4 4 3 4 4 3 SP M ME SD: 6.4505 c. M:-11.0097 c. Silver-10 47: 5 5 5 4 5 5 4 5 5 4 SP M ME SD: 3.0878 c. M:-5.4379 c. Silver-10 57: 6 6 6 5 6 6 5 6 6 5 SP M ME SD: 1.8006 c. M:-3.1552 c. Silver-10 120: 13 12 13 10 13 13 10 13 13 10 SP SD: 1.5231 c. M:-2.8758 c. 130: 14 13 14 11 14 14 11 14 14 11 SP SD: 0.7340 c. M:-1.3374 c. 140: 15 14 15 12 15 15 12 15 15 12 SP SD: 0.7206 c. M: 1.3098 c. 187: 20 19 20 16 20 20 16 20 20 16 SP SD: 0.2532 c. M:-0.4302 c. 327: 35 33 35 28 35 35 28 35 35 28 SP SD: 0.1879 c. M: 0.3399 c. 384: 41 39 41 33 41 41 33 41 41 33 SP SD: 0.1363 c. M: 0.2492 c. 514: 55 52 55 44 55 55 44 55 55 44 SP SD: 0.0838 c. M:-0.1521 c. 701: 75 71 75 60 75 75 60 75 75 60 SP SD: 0.0948 c. M:-0.1654 c. 711: 76 72 76 61 76 76 61 76 76 61 SP SD: 0.0703 c. M: 0.1204 c. 898: 96 91 96 77 96 96 77 96 96 77 SP SD: 0.0104 c. M: 0.0195 c. 2310: 247 234 247 198 247 247 198 247 247 198 SP SD: 0.0107 c. M:-0.0187 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: 17.8484 cents 3 x x x 4 x x 5 x x 6 S SD: 15.6695 cents 4 x x 5 x x 6 x 7 x 8 S SD: 9.1530 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 17.5846 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 12.9678 cents 7 x 8 x 9:10:11 x 12:13:14 S SD: 11.4826 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 10.3835 cents 9:10 x 11:12:13:14:15:16:17:18 S SD: 10.1407 cents 10:11 x 12:13:14:15:16:18:19:20 S SD: 11.7959 cents 11:12:13:14:15:16:17:18:19:21:22 SD: 9.8366 cents 12:13:14:15:16:17:18:20:21:23:24 SD: 6.9550 cents 13:14:15:16:17:18:20:21:23:25:26 SD: 6.7063 cents 16:17:18:20:21:23:25:26:28:30:32 SD: 6.7005 cents 17:18:20:21:22:24:26:28:30:32:34 S SD: 6.4219 cents 19:20:22:24:25:27:29:31:33:36:38 SD: 5.1365 cents 21:23:24:26:28:30:32:34:37:40:42 SD: 4.7078 cents 24:26:28:30:32:34:37:39:42:45:48 SD: 3.1711 cents 28:30:32:35:37:40:43:46:49:53:56 SD: 3.1675 cents 37:40:43:46:49:53:57:60:65:70:74 SD: 2.3564 cents 38:41:44:47:50:54:58:62:67:72:76 SD: 2.2368 cents 40:43:46:50:53:57:61:65:70:75:80 SD: 1.7864 cents 52:56:60:65:69:74:80:85:91:98:104 SD: 1.7836 cents 53:57:61:66:70:75:81:86:93:100:106 SD: 1.2737 cents 66:71:76:82:87:94:101:107:116:124:132 SD: 1.2622 cents 69:74:80:86:91:98:106:112:121:130:138 SD: 1.2476 cents 77:83:89:96:102:109:118:125:135:145:154 SD: 1.1186 cents 78:84:90:97:103:111:119:127:137:147:156 SD: 0.9972 cents 90:97:104:112:119:128:138:146:158:170:180 SD: 0.8275 cents 103:111:119:128:136:146:158:167:180:194:206 SD: 0.8099 cents 104:112:120:129:137:148:159:169:182:196:208 SD: 0.7555 cents 115:124:133:143:152:164:176:187:201:217:230 SD: 0.7080 cents 128:138:148:159:169:182:196:208:224:241:256 SD: 0.4002 cents 168:181:194:209:222:239:257:273:294:317:336 SD: 0.3370 cents 237:255:274:295:313:337:363:385:415:447:474 SD: 0.2890 cents 275:296:318:342:363:391:421:447:481:518:550 SD: 0.2478 cents 296:319:342:368:391:421:453:481:518:558:592 SD: 0.2294 cents 328:353:379:408:433:466:502:533:574:618:656 SD: 0.2103 cents 365:393:422:454:482:519:559:593:639:688:730 SD: 0.1713 cents 405:436:468:504:535:576:620:658:709:763:810 SD: 0.1654 cents 431:464:498:536:569:613:660:700:754:812:862 SD: 0.1648 cents 443:477:512:551:585:630:678:720:775:835:886 SD: 0.1499 cents 521:561:602:648:688:741:798:847:912:982:1042 SD: 0.1346 cents 574:618:663:714:758:816:879:933:1005:1082:1148 SD: 0.1314 cents 597:643:690:743:788:849:914:970:1045:1125:1194 SD: 0.1273 cents 599:645:692:745:791:852:917:973:1048:1129:1198 SD: 0.1273 cents