Scala analysis: tetratetra
tetratetradic scale on 6:7:9:11! 22:27:33 on degree 11! spooky pentatonic!
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 77/72 116.233847 undecimal secor 2: 12/11 150.637059 undecimal neutral second, 3/4-tone 3: 9/8 203.910002 major whole tone 4: 7/6 266.870906 septimal minor third 5: 14/11 417.507964 undecimal diminished fourth or major third 6: 11/8 551.317942 undecimal semi-augmented fourth 7: 3/2 701.955001 perfect fifth 8: 18/11 852.592059 undecimal neutral sixth 9: 121/72 898.725883 10: 7/4 968.825906 harmonic seventh 11: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 77/72 116.2338 undecimal secor 2: 864/847 34.4032 3: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 121/112 133.8100 7: 12/11 150.6371 undecimal neutral second, 3/4-tone 8: 12/11 150.6371 undecimal neutral second, 3/4-tone 9: 1331/1296 46.1338 10: 126/121 70.1000 11: 22/21 80.5370 undecimal minor semitone 12: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 864/847 34.403 cents 1: 1 1331/1296 46.134 cents 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 126/121 70.100 cents 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 77/72 116.234 cents undecimal secor 1: 1 121/112 133.810 cents 1: 4 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 81/77 87.676 cents 2: 2 77/72 116.234 cents undecimal secor 2: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 121/108 196.771 cents 2: 1 112/99 213.598 cents 2: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 2 33/28 284.447 cents undecimal minor third 2: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 3: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 3: 1 121/108 196.771 cents 3: 1 9/8 203.910 cents major whole tone 3: 2 7/6 266.871 cents septimal minor third 3: 2 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 3: 3 11/9 347.408 cents undecimal neutral third 3: 2 9/7 435.084 cents septimal major third, BP third 4: 1 7/6 266.871 cents septimal minor third 4: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 4: 2 11/9 347.408 cents undecimal neutral third 4: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 4: 1 96/77 381.811 cents 4: 1 121/96 400.681 cents 4: 2 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 1331/1008 481.218 cents 4: 1 4/3 498.045 cents perfect fourth 4: 1 108/77 585.721 cents 5: 2 14/11 417.508 cents undecimal diminished fourth or major third 5: 2 9/7 435.084 cents septimal major third, BP third 5: 1 1728/1331 451.911 cents 5: 1 847/648 463.642 cents 5: 2 4/3 498.045 cents perfect fourth 5: 2 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 121/84 631.855 cents 5: 1 16/11 648.682 cents undecimal semi-diminished fifth 6: 2 4/3 498.045 cents perfect fourth 6: 1 162/121 505.184 cents 6: 1 11/8 551.318 cents undecimal semi-augmented fourth 6: 1 168/121 568.145 cents 6: 1 108/77 585.721 cents 6: 1 77/54 614.279 cents 6: 1 121/84 631.855 cents 6: 1 16/11 648.682 cents undecimal semi-diminished fifth 6: 1 121/81 694.816 cents two (undecimal neutral third) 6: 2 3/2 701.955 cents perfect fifth 7: 1 11/8 551.318 cents undecimal semi-augmented fourth 7: 1 168/121 568.145 cents 7: 2 16/11 648.682 cents undecimal semi-diminished fifth 7: 2 3/2 701.955 cents perfect fifth 7: 1 1296/847 736.358 cents 7: 1 1331/864 748.089 cents 7: 2 14/9 764.916 cents septimal minor sixth 7: 2 11/7 782.492 cents undecimal augmented fifth 8: 1 77/54 614.279 cents 8: 1 3/2 701.955 cents perfect fifth 8: 1 2016/1331 718.782 cents 8: 2 11/7 782.492 cents undecimal augmented fifth 8: 1 192/121 799.319 cents 8: 1 77/48 818.189 cents 8: 1 44/27 845.453 cents neutral sixth 8: 2 18/11 852.592 cents undecimal neutral sixth 8: 1 121/72 898.726 cents 8: 1 12/7 933.129 cents septimal major sixth 9: 2 14/9 764.916 cents septimal minor sixth 9: 3 18/11 852.592 cents undecimal neutral sixth 9: 2 121/72 898.726 cents 9: 2 12/7 933.129 cents septimal major sixth 9: 1 16/9 996.090 cents Pythagorean minor seventh 9: 1 216/121 1003.229 cents 9: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 10: 1 121/72 898.726 cents 10: 2 56/33 915.553 cents 10: 1 12/7 933.129 cents septimal major sixth 10: 1 7/4 968.826 cents harmonic seventh 10: 1 99/56 986.402 cents 10: 1 216/121 1003.229 cents 10: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 10: 2 144/77 1083.766 cents 10: 1 154/81 1112.324 cents 11: 4 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 11: 1 224/121 1066.190 cents 11: 1 144/77 1083.766 cents 11: 1 21/11 1119.463 cents undecimal major seventh 11: 1 121/63 1129.900 cents 11: 1 27/14 1137.039 cents septimal major seventh 11: 1 64/33 1146.727 cents 33rd subharmonic 11: 1 2592/1331 1153.866 cents 11: 1 847/432 1165.597 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 8.72727 = 96/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 116.2 150.6 203.9 266.9 417.5 551.3 702.0 852.6 898.7 968.8 1049.4 1200.0 116.2 : 34.4 87.7 150.6 301.3 435.1 585.7 736.4 782.5 852.6 933.1 1083.8 1200.0 150.6 : 53.3 116.2 266.9 400.7 551.3 702.0 748.1 818.2 898.7 1049.4 1165.6 1200.0 203.9 : 63.0 213.6 347.4 498.0 648.7 694.8 764.9 845.5 996.1 1112.3 1146.7 1200.0 266.9 : 150.6 284.4 435.1 585.7 631.9 702.0 782.5 933.1 1049.4 1083.8 1137.0 1200.0 417.5 : 133.8 284.4 435.1 481.2 551.3 631.9 782.5 898.7 933.1 986.4 1049.4 1200.0 551.3 : 150.6 301.3 347.4 417.5 498.0 648.7 764.9 799.3 852.6 915.6 1066.2 1200.0 702.0 : 150.6 196.8 266.9 347.4 498.0 614.3 648.7 702.0 764.9 915.6 1049.4 1200.0 852.6 : 46.1 116.2 196.8 347.4 463.6 498.0 551.3 614.3 764.9 898.7 1049.4 1200.0 898.7 : 70.1 150.6 301.3 417.5 451.9 505.2 568.1 718.8 852.6 1003.2 1153.9 1200.0 968.8 : 80.5 231.2 347.4 381.8 435.1 498.0 648.7 782.5 933.1 1083.8 1129.9 1200.0 1049.4: 150.6 266.9 301.3 354.5 417.5 568.1 702.0 852.6 1003.2 1049.4 1119.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.4032 .. 150.6371 cents 77/72, 116.2338 cents 864/847, 34.4032 cents 2: 87.6762 .. 301.2741 cents 112/99, 213.5980 cents 27/28,-62.9609 cents 3: 150.6371 .. 435.0841 cents 33/28, 284.4470 cents 11/12,-150.6371 cents 4: 266.8709 .. 585.7212 cents 648/539, 318.8502 cents 49/54,-168.2132 cents 5: 417.5080 .. 648.6821 cents 8/7, 231.1741 cents 49/54,-168.2132 cents 6: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 11/12,-150.6371 cents 7: 551.3179 .. 782.4920 cents 8/7, 231.1741 cents 11/12,-150.6371 cents 8: 614.2788 .. 933.1291 cents 648/539, 318.8502 cents 49/54,-168.2132 cents 9: 764.9159 .. 1049.3629 cents 33/28, 284.4470 cents 49/54,-168.2132 cents 10: 898.7259 .. 1112.3238 cents 112/99, 213.5980 cents 11/12,-150.6371 cents 11: 1049.3629 .. 1165.5968 cents 77/72, 116.2338 cents 27/28,-62.9609 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 864/847, 34.4032 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 12/11, 150.6371 cents Average / Smallest step : 2.906705 Largest / Average step : 1.506371 Largest / Smallest step : 4.378575 Median interval of one step : 98.38544 cents, amount: 0 Most common interval of one step : 12/11, 150.6371 cents, amount: 4 Least squares average step : 96.84058 cents, oct.: 1162.08692 cents Scale is not proper Step pattern alph. order: ABCDEFEEGHIE Step pattern size order : GACDIHIIBEFI Scale is not a Constant Structure Scale diversity : 1.542215 Lumma stability : 0.057339 Lumma impropriety factor : 0.853873 Rothenberg efficiency : 0.276199 redundancy: 0.723801 Efficiency x scale size : 3.314394 Number of different interval sizes : 62 = 5.63636 / class Number of one step interval sizes : 9 Highest interval variety : 10 Mean interval variety : 8.72727 = 96/11 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 12/11, 150.6371 cents & inv., amount: 7 Number of recognisable fifths : 7, average 703.3390 cents Number of appreciable fifths : 6, average 700.7651 cents Scale contains a complete diamond : 3 11 Formal octave complements present : 3 = 25.0000% -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.012423 Average absolute harmonicity : 0.150567 Specific harmonicity : 0.074719 Fundamental : 1/792, -9.6294 octaves, 0.3303 Hz. Guide tone : 30492, 14.8961 octaves, 7977486.737 Hz. Exponens Consonantiae : 2.414966E+07, 24.52550 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 252.0, average 21.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.29780, average 1.02482 Sum of Tenney's harmonic distance : 24.05965, average 2.00497 Vogel's harmonic complexity : 23.16667 Wille's k value : 665 Wilson's harmonic complexity : 52 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 247.86521, average 3.17776 Lattice compactness (without 2's) : 163.52607, average 2.09649 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -1.00000 22 1 3: -2 .. 2 0.00000 12 2 7: 0 .. 1 0.33333 4 2 11: -1 .. 2 0.16667 8 7 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 24 / 12 = 2.00000
FIT/MODE
12: 1 0 1 0 2 1 2 1 1 0 1 2 N SD: 41.0282 c. M: 68.8259 c. 13: 1 0 1 0 2 2 1 2 0 1 1 2 N SD: 45.5574 c. M: 82.2555 c. 14: 1 1 0 1 2 1 2 2 0 1 1 2 N SD: 24.3712 c. M: 41.5830 c. 15: 1 1 1 0 2 2 2 2 0 1 1 2 N SD: 21.2133 c. M: 36.2338 c. 16: 2 0 1 1 2 1 2 2 1 1 1 2 N SD: 22.2847 c. M:-33.7662 c. 17: 2 0 1 1 2 2 2 2 1 1 1 2 N SD: 13.2250 c. M:-24.9426 c. 21: 2 1 1 1 2 3 2 3 1 1 1 3 N SD: 16.0103 c. M:-24.6614 c. 22: 2 1 1 1 3 2 3 3 1 1 1 3 N SD: 14.3089 c. M:-28.5468 c. 24: 2 1 1 1 3 3 3 3 1 1 2 3 N SD: 10.1617 c. M: 18.8259 c. 27: 3 0 2 1 3 3 4 3 1 2 2 3 N SD: 13.4898 c. M:-18.3122 c. 29: 3 1 1 1 4 3 4 4 1 1 2 4 N SD: 12.0789 c. M: 18.5950 c. 30: 3 1 1 2 3 4 4 3 1 2 2 4 N SD: 11.8033 c. M: 18.7259 c. 31: 3 1 1 2 4 3 4 4 1 2 2 4 N SD: 5.8875 c. M: 10.3616 c. 41: 4 1 2 2 5 5 5 5 2 2 3 5 N SD: 4.3859 c. M:-8.5912 c. 48: 5 1 2 3 6 5 6 6 2 3 3 6 N SD: 4.7186 c. M:-8.7662 c. 55: 5 2 2 3 7 6 7 7 2 3 4 7 N SD: 4.9819 c. M: 8.8259 c. 61: 6 2 2 4 7 7 8 7 3 3 4 8 N SD: 5.6585 c. M:-8.5389 c. 63: 6 2 3 3 8 7 8 8 2 4 4 8 N SD: 2.7758 c. M:-5.6138 c. 72: 7 2 3 4 9 8 9 9 3 4 5 9 N SD: 1.7224 c. M: 3.9100 c. 104: 10 3 5 5 13 12 13 13 4 6 7 13 N SD: 1.7293 c. M:-3.7823 c. 130: 13 3 6 7 16 15 16 16 5 8 9 16 N SD: 2.3558 c. M:-3.7662 c. 135: 13 4 6 7 17 15 17 17 5 8 9 17 N SD: 0.4896 c. M: 0.9481 c. 207: 20 6 9 11 26 23 26 26 8 12 14 26 N SD: 0.4561 c. M: 1.0115 c. 311: 30 9 14 16 39 35 39 39 12 18 21 39 N SD: 0.4250 c. M: 0.7877 c. 342: 33 10 15 18 43 38 43 43 13 20 23 43 N SD: 0.3092 c. M: 0.4803 c. 494: 48 14 22 26 62 55 62 62 19 29 33 62 N SD: 0.2130 c. M:-0.4049 c. 566: 55 16 25 30 71 63 71 71 22 33 38 71 N SD: 0.2203 c. M: 0.3764 c. 629: 61 18 28 33 79 70 79 79 24 37 42 79 N SD: 0.1834 c. M:-0.3315 c. 701: 68 20 31 37 88 78 88 88 27 41 47 88 N SD: 0.1189 c. M: 0.2010 c. 836: 81 24 37 44 105 93 105 105 32 49 56 105 N SD: 0.1007 c. M:-0.1954 c. 1012: 98 29 45 53 127 113 127 127 39 59 68 127 N SD: 0.0585 c. M: 0.1167 c. 1147: 111 33 51 60 144 128 144 144 44 67 77 144 N SD: 0.0613 c. M: 0.1048 c. 1506: 146 43 67 79 189 168 189 189 58 88 101 189 N SD: 0.0620 c. M:-0.1008 c. 1641: 159 47 73 86 206 183 206 206 63 96 110 206 N SD: 0.0546 c. M:-0.1119 c. 1713: 166 49 76 90 215 191 215 215 66 100 115 215 N SD: 0.0343 c. M: 0.0571 c. 1848: 179 53 82 97 232 206 232 232 71 108 124 232 N SD: 0.0139 c. M: 0.0246 c.
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: 0.0000 cents 3 x x x x x 4 x x 5 x x 6 S SD: 18.3921 cents 4 x x x x 5 x 6 x x 7 x 8 S SD: 7.7986 cents 5 x x x 6 x 7 x 8 x x 9:10 S SD: 15.3289 cents 6 x x x 7 x 8:9 x 10 x 11:12 S SD: 9.1960 cents 7 x x 8 x 9:10 x 11:12 x 13:14 S SD: 15.6670 cents 8 x x 9 x 10:11:12:13 x 14:15:16 S SD: 6.4132 cents 9 x x 10 x 11:12:14 x 15:16:17:18 S SD: 15.7120 cents 10 x 11 x 12:13:14:15:16:17 x 18:20 S SD: 9.8287 cents 11 x 12 x 13:14:15:17:18 x 19:20:22 SD: 7.1103 cents 12 x 13 x 14:15:17:18 x 20:21:22:24 SD: 7.0239 cents 13:14 x x 15:17:18:20:21:22:23:24:26 SD: 7.6992 cents 14:15 x 16 x 18:19:21:23:24:25:26:28 SD: 6.7288 cents 15:16 x 17:18:19:21:23 x 25:26:28:30 SD: 8.0655 cents 16:17 x 18:19:20:22:24:26:27:28:29:32 SD: 4.6597 cents 17:18 x 19:20:22:23:26:28:29:30:31:34 SD: 6.0833 cents 18:19 x 20:21:23:25:27:29:30:32:33:36 SD: 4.9786 cents 19:20:21 x 22:24:26:29:31:32:33:35:38 SD: 4.8622 cents 20:21:22 x 23:25:28:30:33:34:35:37:40 SD: 6.1863 cents 22 x 24:25:26:28:30:33:36:37:39:40:44 SD: 3.7651 cents 23 x 25:26:27:29:32:35:38:39:40:42:46 SD: 4.2677 cents 24 x 26:27:28:31:33:36:39:40:42:44:48 SD: 3.0849 cents 25:27 x 28:29:32:34:38:41:42:44:46:50 SD: 3.6166 cents 26:28 x 29:30:33:36:39:43:44:46:48:52 SD: 3.9503 cents 27:29 x 30:32:34:37:41:44:45:47:50:54 SD: 4.7506 cents 28:30:31:32:33:36:39:42:46:47:49:51:56 SD: 4.3324 cents 29:31:32:33:34:37:40:44:47:49:51:53:58 SD: 3.4979 cents 30:32:33:34:35:38:41:45:49:50:53:55:60 SD: 2.7067 cents 32:34:35:36:37:41:44:48:52:54:56:59:64 SD: 2.3787 cents 36 x 39:41:42:46:50:54:59:61:63:66:72 SD: 3.0918 cents 37 x 40:42:43:47:51:56:61:62:65:68:74 SD: 2.9560 cents 38:41 x 43:44:48:52:57:62:64:67:70:76 SD: 2.9079 cents 40:43:44:45:47:51:55:60:65:67:70:73:80 SD: 2.1872 cents 41:44:45:46:48:52:56:62:67:69:72:75:82 SD: 2.0989 cents 47:50:51:53:55:60:65:71:77:79:82:86:94 SD: 1.9249 cents 48:51:52:54:56:61:66:72:79:81:84:88:96 SD: 1.7284 cents 54:58:59:61:63:69:74:81:88:91:95:99:108 SD: 1.5631 cents 55:59:60:62:64:70:76:83:90:92:96:101:110 SD: 1.5302 cents 56:60:61:63:65:71:77:84:92:94:98:103:112 SD: 1.2419 cents 66:71:72:74:77:84:91:99:108:111:116:121:132 SD: 1.2310 cents 72:77:79:81:84:92:99:108:118:121:126:132:144 SD: 1.0339 cents 88:94:96:99:103:112:121:132:144:148:154:161:176 SD: 0.5904 cents 120:128:131:135:140:153:165:180:196:202:210:220:240 SD: 0.5877 cents 143:153:156:161:167:182:197:215:234:240:250:262:286 SD: 0.5404 cents 144:154:157:162:168:183:198:216:236:242:252:264:288 SD: 0.3204 cents 216:231:236:243:252:275:297:324:353:363:378:396:432 SD: 0.2937 cents 256:274:279:288:299:326:352:384:419:430:448:469:512 SD: 0.2881 cents 264:282:288:297:308:336:363:396:432:444:462:484:528 SD: 0.2020 cents 344:368:375:387:401:438:473:516:563:578:602:631:688 SD: 0.1949 cents 360:385:393:405:420:458:495:540:589:605:630:660:720 SD: 0.1175 cents 432:462:471:486:504:550:594:648:707:726:756:792:864 SD: 0.0979 cents