Scala analysis: fokkerblock
2.7.13 Fokker block (Carl Lumma's 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: 196/169 256.596489 two (2/3-tone) 3: 2744/2197 384.894734 4: 224/169 487.770583 5: 3136/2197 616.068828 6: 43904/28561 744.367072 7: 3584/2197 847.242921 8: 50176/28561 975.541166 9: 702464/371293 1103.839411 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 371293/351232 96.1606 1: 14/13 128.2982 2/3-tone 2: 14/13 128.2982 2/3-tone 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: 371293/351232 96.1606
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 371293/351232 96.161 cents 1: 2 52/49 102.876 cents 1: 7 14/13 128.298 cents 2/3-tone 2: 2 28561/25088 224.459 cents 2: 4 8/7 231.174 cents septimal whole tone 2: 4 196/169 256.596 cents two (2/3-tone) 3: 3 2197/1792 352.757 cents 3: 6 16/13 359.472 cents tridecimal neutral third 3: 1 2744/2197 384.895 cents 4: 1 28561/21952 455.633 cents 4: 1 64/49 462.348 cents 2 septatones or septatonic major third 4: 3 169/128 481.055 cents 4: 5 224/169 487.771 cents 5: 3 2197/1568 583.931 cents 5: 2 128/91 590.646 cents 5: 2 91/64 609.354 cents 5: 3 3136/2197 616.069 cents 6: 5 169/112 712.229 cents 6: 3 256/169 718.945 cents two (tridecimal neutral third) 6: 1 49/32 737.652 cents 6: 1 43904/28561 744.367 cents 7: 1 2197/1372 815.105 cents 7: 6 13/8 840.528 cents tridecimal neutral sixth 7: 3 3584/2197 847.243 cents 8: 4 169/98 943.404 cents 8: 4 7/4 968.826 cents harmonic seventh 8: 2 50176/28561 975.541 cents 9: 7 13/7 1071.702 cents 16/3-tone 9: 2 49/26 1097.124 cents 9: 1 702464/371293 1103.839 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 128.3 256.6 384.9 487.8 616.1 744.4 847.2 975.5 1103.8 1200.0 128.3 : 128.3 256.6 359.5 487.8 616.1 718.9 847.2 975.5 1071.7 1200.0 256.6 : 128.3 231.2 359.5 487.8 590.6 718.9 847.2 943.4 1071.7 1200.0 384.9 : 102.9 231.2 359.5 462.3 590.6 718.9 815.1 943.4 1071.7 1200.0 487.8 : 128.3 256.6 359.5 487.8 616.1 712.2 840.5 968.8 1097.1 1200.0 616.1 : 128.3 231.2 359.5 487.8 583.9 712.2 840.5 968.8 1071.7 1200.0 744.4 : 102.9 231.2 359.5 455.6 583.9 712.2 840.5 943.4 1071.7 1200.0 847.2 : 128.3 256.6 352.8 481.1 609.4 737.7 840.5 968.8 1097.1 1200.0 975.5 : 128.3 224.5 352.8 481.1 609.4 712.2 840.5 968.8 1071.7 1200.0 1103.8: 96.2 224.5 352.8 481.1 583.9 712.2 840.5 943.4 1071.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 96.1606 .. 128.2982 cents 4917248/4826809, 32.1377 cents 371293/351232, 96.1606 cents 2: 224.4588 .. 256.5965 cents 4917248/4826809, 32.1377 cents 371293/351232, 96.1606 cents 3: 352.7571 .. 384.8947 cents 4917248/4826809, 32.1377 cents 371293/351232, 96.1606 cents 4: 455.6329 .. 487.7706 cents 4917248/4826809, 32.1377 cents 62748517/60236288, 70.7382 cents 5: 583.9312 .. 616.0688 cents 4917248/4826809, 32.1377 cents 371293/351232, 96.1606 cents 6: 712.2294 .. 744.3671 cents 4917248/4826809, 32.1377 cents 371293/351232, 96.1606 cents 7: 815.1053 .. 847.2429 cents 4917248/4826809, 32.1377 cents 62748517/60236288, 70.7382 cents 8: 943.4035 .. 975.5412 cents 4917248/4826809, 32.1377 cents 371293/351232, 96.1606 cents 9: 1071.7018 .. 1103.8394 cents 4917248/4826809, 32.1377 cents 371293/351232, 96.1606 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 371293/351232, 96.1606 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 14/13, 128.2982 cents Average / Smallest step : 1.247912 Largest / Average step : 1.069152 Largest / Smallest step : 1.334208 Median interval of one step : 14/13, 128.2982 cents, amount: 7 Most common interval of one step : 14/13, 128.2982 cents, amount: 7 Least squares average step : 121.98283 cents, oct.: 1219.82828 cents Scale is strictly proper Step pattern alph. order: AAABAABAAC Step pattern size order : LLLMLLMLLS Scale is a Constant Structure, by a margin of 70.73819 cents Scale diversity : 1.206775 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.758968 Rothenberg efficiency : 0.434762 redundancy: 0.565238 Efficiency x scale size : 4.347619 Number of different interval sizes : 30 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 28672/28561, 6.7153 cents Most common intervals : 14/13, 128.2982 cents & inv., amount: 7 Most common triad is 0.0 128.298 1071.702 cents, amount: 4 Number of recognisable fifths : 8, average 714.7476 cents Number of appreciable fifths : 5, average 712.2294 cents Best major 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 inverse transpositions with margin 32.1377 cents: 3 -- Rational properties -- Prime limit : 13 Odd number limit : 371293 (O: 371293 U: 371293) Highest odd numerator or denominator: 371293 Scale harmonicity : 0.006552 Average absolute harmonicity : 0.111686 Specific harmonicity : 0.036174 Fundamental : 1/371293, -18.5022 octaves, 0.0007 Hz. Guide tone : 702464, 19.4221 octaves, 183782541.104 Hz. Exponens Consonantiae : 2.608200E+11, 37.92426 octaves Euler's gradus suavitatis : 90 Sum of Mann's harmonic distance : 620901.0, average 62090.10000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 30.07647, average 3.00765 Sum of Tenney's harmonic distance : 61.84488, average 6.18449 Vogel's harmonic complexity : 48.00000 Wille's k value : 185646 Wilson's harmonic complexity : 86 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 298.76604, average 5.43211 Lattice compactness (without 2's) : 134.80772, average 2.45105 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 11 5.50000 55 1 7: 0 .. 3 1.80000 18 13: -5 .. 0 -2.70000 27 9 Average exponent except 2's :-9 / 10 =-0.90000 Average absolute exponent except 2's: 45 / 10 = 4.50000 Scale is weakly epimorphic with val: <10 26 39| Scale is JI-epimorphic with val: <10 28 37| = patent
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 16.5490 c. M: 24.8947 c. 22: 2 3 2 2 2 3 2 2 2 2 SP D3 SD: 14.6082 c. M:-25.4844 c. 24: 3 2 3 2 2 3 2 3 2 2 SP B ME S SD: 13.4265 c. M:-24.4588 c. 25: 3 2 3 2 3 3 2 2 3 2 SP D3 SD: 13.1413 c. M:-23.6329 c. 26: 3 3 2 3 2 3 2 3 3 2 SP D3 SD: 13.3335 c. M:-20.3266 c. 27: 3 3 3 2 3 3 2 3 3 2 SP M ME SD: 7.6481 c. M:-15.1053 c. 37: 4 4 4 3 4 4 3 4 4 3 SP M ME SD: 2.3819 c. M:-4.2945 c. Silver-10 84: 9 9 9 7 9 9 7 9 9 7 SP M DE SD: 2.4824 c. M: 4.3858 c. Silver-10 103: 11 11 11 9 11 11 9 11 11 8 SP SD: 1.8743 c. M:-3.2425 c. 113: 12 12 12 10 12 12 10 12 12 9 SP SD: 1.4079 c. M: 2.5938 c. 140: 15 15 15 12 15 15 12 15 15 11 SP SD: 1.1180 c. M:-1.8749 c. 150: 16 16 16 13 16 16 13 16 16 12 SP SD: 0.4740 c. M: 0.8947 c. 187: 20 20 20 16 20 20 16 20 20 15 SP SD: 0.0979 c. M: 0.1841 c. 524: 56 56 56 45 56 56 45 56 56 42 SP SD: 0.0773 c. M: 0.1619 c. 711: 76 76 76 61 76 76 61 76 76 57 SP SD: 0.0431 c. M: 0.0846 c. 898: 96 96 96 77 96 96 77 96 96 72 SP SD: 0.0335 c. M: 0.0532 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: 21.2060 cents 3 x x x 4 x x 5 x x 6 S SD: 12.8372 cents 4 x x 5 x x 6 x 7 x 8 S SD: 10.7410 cents 5 x 6 x x 7 x 8:9 x 10 S SD: 17.3286 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 13.2866 cents 7 x 8:9 x 10:11 x 12:13:14 S SD: 12.3325 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 11.8239 cents 9:10 x 11:12:13:14:15:16:17:18 S SD: 9.3560 cents 10:11:12 x 13:14:15:16:18:19:20 S SD: 12.0868 cents 11:12:13:14:15:16:17:18:19:21:22 SD: 8.5606 cents 12:13:14:15:16:17:18:20:21:23:24 SD: 6.4933 cents 13:14:15:16:17:19:20:21:23:25:26 SD: 6.4669 cents 16:17:19:20:21:23:25:26:28:30:32 SD: 6.1563 cents 19:20:22:24:25:27:29:31:33:36:38 SD: 5.2144 cents 21:23:24:26:28:30:32:34:37:40:42 SD: 4.8968 cents 24:26:28:30:32:34:37:39:42:45:48 SD: 2.9109 cents 36:39:42:45:48:51:55:59:63:68:72 SD: 2.6833 cents 37:40:43:46:49:53:57:60:65:70:74 SD: 1.6750 cents 49:53:57:61:65:70:75:80:86:93:98 SD: 1.4518 cents 56:60:65:70:74:80:86:91:98:106:112 SD: 1.4344 cents 65:70:75:81:86:93:100:106:114:123:130 SD: 1.1443 cents 80:86:93:100:106:114:123:131:141:151:160 SD: 1.1317 cents 82:88:95:102:109:117:126:134:144:155:164 SD: 1.1282 cents 87:94:101:109:115:124:134:142:153:165:174 SD: 1.1249 cents 89:96:103:111:118:127:137:145:156:168:178 SD: 0.8344 cents 101:109:117:126:134:144:155:165:177:191:202 SD: 0.7856 cents 108:116:125:135:143:154:166:176:190:204:216 SD: 0.7665 cents 117:126:136:146:155:167:180:191:206:221:234 SD: 0.6667 cents 119:128:138:149:158:170:183:194:209:225:238 SD: 0.6095 cents 132:142:153:165:175:188:203:215:232:250:264 SD: 0.5756 cents 145:156:168:181:192:207:223:237:255:274:290 SD: 0.5410 cents 156:168:181:195:207:223:240:254:274:295:312 SD: 0.5143 cents 157:169:182:196:208:224:241:256:276:297:314 SD: 0.3324 cents 206:222:239:257:273:294:317:336:362:390:412 SD: 0.3285 cents 258:278:299:322:342:368:397:421:453:488:516 SD: 0.3197 cents 274:295:318:342:363:391:421:447:481:518:548 SD: 0.2809 cents 276:297:320:345:366:394:424:450:485:522:552 SD: 0.2723 cents 288:310:334:360:382:411:443:470:506:545:576 SD: 0.2508 cents 313:337:363:391:415:447:481:511:550:592:626 SD: 0.1957 cents 325:350:377:406:431:464:500:530:571:615:650 SD: 0.1927 cents 350:377:406:437:464:500:538:571:615:662:700 SD: 0.1747 cents 445:479:516:556:590:635:684:726:782:842:890 SD: 0.1441 cents 482:519:559:602:639:688:741:786:847:912:964 SD: 0.0938 cents