Scala analysis: quasi_11-EDO
Emulation of 11-EDO
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: 44/39 208.835280 3: 63/52 332.208246 4: 14/11 417.507964 undecimal diminished fourth or major third 5: 231/169 541.043526 6: 16/11 648.682058 undecimal semi-diminished fifth 7: 264/169 772.217620 8: 18/11 852.592059 undecimal neutral sixth 9: 252/143 980.890304 10: 24/13 1061.427339 tridecimal neutral seventh 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 14/13 128.2982 2/3-tone 2: 22/21 80.5370 undecimal minor semitone 3: 189/176 123.3730 4: 104/99 85.2997 5: 363/338 123.5356 6: 2704/2541 107.6385 7: 363/338 123.5356 8: 507/484 80.3744 9: 14/13 128.2982 2/3-tone 10: 22/21 80.5370 undecimal minor semitone 11: 13/12 138.5727 tridecimal 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 507/484 80.374 cents 1: 2 22/21 80.537 cents undecimal minor semitone 1: 1 104/99 85.300 cents 1: 1 2704/2541 107.639 cents 1: 1 189/176 123.373 cents 1: 2 363/338 123.536 cents 1: 2 14/13 128.298 cents 2/3-tone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 2: 2 9/8 203.910 cents major whole tone 2: 2 273/242 208.673 cents 2: 3 44/39 208.835 cents 2: 1 143/126 219.110 cents 2: 2 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 3: 2 13/11 289.210 cents tridecimal minor third 3: 1 1014/847 311.549 cents 3: 1 832/693 316.474 cents 3: 3 63/52 332.208 cents 3: 3 11/9 347.408 cents undecimal neutral third 3: 1 1452/1183 354.710 cents 4: 2 33/26 412.745 cents tridecimal major third 4: 1 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 169/132 427.782 cents 4: 1 242/189 427.945 cents 4: 1 9/7 435.084 cents septimal major third, BP third 4: 2 156/121 439.847 cents 4: 1 352/273 440.009 cents 4: 1 21/16 470.781 cents narrow fourth 4: 1 154/117 475.706 cents 5: 3 104/77 520.384 cents 5: 1 231/169 541.044 cents 5: 2 11/8 551.318 cents undecimal semi-augmented fourth 5: 2 91/66 556.081 cents 5: 1 484/351 556.243 cents 5: 2 18/13 563.382 cents tridecimal augmented fourth 6: 2 13/9 636.618 cents tridecimal diminished fifth 6: 1 351/242 643.757 cents 6: 2 132/91 643.919 cents 6: 2 16/11 648.682 cents undecimal semi-diminished fifth 6: 1 338/231 658.956 cents 6: 3 77/52 679.616 cents 7: 1 117/77 724.294 cents 7: 1 32/21 729.219 cents wide fifth 7: 1 273/176 759.991 cents 7: 2 121/78 760.153 cents 7: 1 14/9 764.916 cents septimal minor sixth 7: 1 189/121 772.055 cents 7: 1 264/169 772.218 cents 7: 1 11/7 782.492 cents undecimal augmented fifth 7: 2 52/33 787.255 cents tridecimal minor sixth 8: 1 1183/726 845.290 cents 8: 3 18/11 852.592 cents undecimal neutral sixth 8: 3 104/63 867.792 cents 8: 1 693/416 883.526 cents 8: 1 847/507 888.451 cents 8: 2 22/13 910.790 cents tridecimal major sixth 9: 1 12/7 933.129 cents septimal major sixth 9: 2 7/4 968.826 cents harmonic seventh 9: 1 252/143 980.890 cents 9: 3 39/22 991.165 cents 9: 2 484/273 991.327 cents 9: 2 16/9 996.090 cents Pythagorean minor seventh 10: 1 24/13 1061.427 cents tridecimal neutral seventh 10: 2 13/7 1071.702 cents 16/3-tone 10: 2 676/363 1076.464 cents 10: 1 352/189 1076.627 cents 10: 1 2541/1352 1092.361 cents 10: 1 99/52 1114.700 cents 10: 2 21/11 1119.463 cents undecimal major seventh 10: 1 968/507 1119.626 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 128.3 208.8 332.2 417.5 541.0 648.7 772.2 852.6 980.9 1061.4 1200.0 128.3 : 80.5 203.9 289.2 412.7 520.4 643.9 724.3 852.6 933.1 1071.7 1200.0 208.8 : 123.4 208.7 332.2 439.8 563.4 643.8 772.1 852.6 991.2 1119.5 1200.0 332.2 : 85.3 208.8 316.5 440.0 520.4 648.7 729.2 867.8 996.1 1076.6 1200.0 417.5 : 123.5 231.2 354.7 435.1 563.4 643.9 782.5 910.8 991.3 1114.7 1200.0 541.0 : 107.6 231.2 311.5 439.8 520.4 659.0 787.3 867.8 991.2 1076.5 1200.0 648.7 : 123.5 203.9 332.2 412.7 551.3 679.6 760.2 883.5 968.8 1092.4 1200.0 772.2 : 80.4 208.7 289.2 427.8 556.1 636.6 760.0 845.3 968.8 1076.5 1200.0 852.6 : 128.3 208.8 347.4 475.7 556.2 679.6 764.9 888.5 996.1 1119.6 1200.0 980.9 : 80.5 219.1 347.4 427.9 551.3 636.6 760.2 867.8 991.3 1071.7 1200.0 1061.4: 138.6 266.9 347.4 470.8 556.1 679.6 787.3 910.8 991.2 1119.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.3744 .. 138.5727 cents 121/117, 58.1982 cents 507/484, 80.3744 cents 2: 203.9100 .. 266.8709 cents 28/27, 62.9609 cents 27/26, 65.3373 cents 3: 289.2097 .. 354.7097 cents 15972/15379, 65.4999 cents 78/77, 22.3388 cents 4: 412.7453 .. 475.7062 cents 28/27, 62.9609 cents 91/88, 58.0356 cents 5: 520.3838 .. 563.3823 cents 693/676, 42.9985 cents 6084/5929, 44.6776 cents 6: 636.6177 .. 679.6162 cents 693/676, 42.9985 cents 169/162, 73.2353 cents 7: 724.2938 .. 787.2547 cents 28/27, 62.9609 cents 6084/5929, 44.6776 cents 8: 845.2903 .. 910.7903 cents 15972/15379, 65.4999 cents 91/88, 58.0356 cents 9: 933.1291 .. 996.0900 cents 28/27, 62.9609 cents 78/77, 22.3388 cents 10: 1061.4273 .. 1119.6256 cents 121/117, 58.1982 cents 27/26, 65.3373 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 507/484, 80.3744 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 13/12, 138.5727 cents Average / Smallest step : 1.357284 Largest / Average step : 1.270249 Largest / Smallest step : 1.724089 Median interval of one step : 189/176, 123.3730 cents, amount: 1 Least squares average step : 108.06024 cents, oct.: 1188.66264 cents Scale is strictly proper Step pattern alph. order: ABCDEFEGABH Step pattern size order : GBECFDFAGBH Scale is a Constant Structure, by a margin of 22.33881 cents Scale diversity : 1.408893 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.512303 Rothenberg efficiency : 0.245730 redundancy: 0.754270 Efficiency x scale size : 2.703030 Number of different interval sizes : 70 = 7.00000 / class Number of one step interval sizes : 8 Highest interval variety : 9 Mean interval variety : 7.00000 = 7 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 10648/10647, 0.1626 cents Number of recognisable fifths : 0 Best minor thirds form a closed circle Length of longest harmonic part : 2 at degree 10 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 9.0909% -- Rational properties -- Prime limit : 13 Odd number limit : 2541 (O: 2541 U: 2541) Highest odd numerator or denominator: 231 Scale harmonicity : 0.009528 Average absolute harmonicity : 0.116200 Specific harmonicity : 0.048476 Fundamental : 1/22308, -14.4453 octaves, 0.0117 Hz. Guide tone : 11088, 13.4367 octaves, 2900904.268 Hz. Exponens Consonantiae : 2.473511E+08, 27.88199 octaves Euler's gradus suavitatis : 63 Sum of Mann's harmonic distance : 787.0, average 71.54545 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 15.48930, average 1.40812 Sum of Tenney's harmonic distance : 32.33254, average 2.93932 Vogel's harmonic complexity : 37.18182 Wille's k value : 13513 Wilson's harmonic complexity : 64 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 198.27016, average 3.00409 Lattice compactness (without 2's) : 137.75957, average 2.08727 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.45455 20 1 3: -1 .. 2 0.72727 10 7: 0 .. 1 0.45455 5 11: -1 .. 1 -0.09091 7 3 13: -2 .. 0 -0.81818 9 7 Average exponent except 2's : 3 / 11 = 0.27273 Average absolute exponent except 2's: 31 / 11 = 2.81818 Scale is weakly epimorphic with val: <11 15 32 38 44| Scale is weakly epimorphic with val: <11 17 32 37 41| Scale is weakly epimorphic with val: <11 18 34 39 44|
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 14.2673 c. M:-29.4818 c. 17: 2 1 2 1 2 1 2 1 2 1 2 P M ME I SD: 11.6351 c. M:-23.6624 c. 24: 3 1 3 1 3 2 2 2 3 1 3 N T3 SD: 14.3025 c. M: 22.2176 c. 25: 3 1 3 2 2 3 2 2 2 2 3 P D3 SD: 13.7577 c. M:-23.3179 c. 26: 3 2 2 2 3 2 3 1 3 2 3 P T3 SD: 12.0924 c. M:-21.9340 c. 28: 3 2 3 2 3 2 3 2 3 2 3 SP M ME I SD: 7.9962 c. M:-16.0993 c. 34: 4 2 3 3 3 3 4 2 4 2 4 P SD: 8.7733 c. M: 14.5612 c. 35: 4 2 4 2 4 3 4 2 4 2 4 P I SD: 8.3784 c. M:-16.3538 c. 37: 4 2 4 3 4 3 4 2 4 3 4 SP T3 SD: 7.7249 c. M: 14.2407 c. 40: 4 3 4 3 4 4 4 2 5 2 5 P SD: 7.6467 c. M: 12.5921 c. 44: 5 3 4 3 5 4 4 3 5 3 5 P SD: 6.2652 c. M:-9.3465 c. 46: 5 3 5 3 5 4 5 3 5 3 5 SP I SD: 6.4799 c. M:-10.4140 c. 48: 5 3 5 4 5 4 5 3 5 3 6 P SD: 6.4577 c. M: 11.4273 c. 51: 5 4 5 4 5 5 5 3 6 3 6 SP SD: 5.8652 c. M: 10.6512 c. 54: 6 3 6 4 5 5 6 3 6 4 6 SP SD: 5.5493 c. M: 8.8353 c. 55: 6 4 5 4 6 5 5 4 6 4 6 SP SD: 5.3700 c. M:-9.3465 c. 58: 6 4 6 4 6 5 6 4 6 4 7 SP SD: 4.9887 c. M: 8.4765 c. 68: 7 5 7 5 7 6 7 4 8 4 8 SP SD: 4.6794 c. M:-7.3450 c. 69: 7 5 7 5 7 6 7 5 7 5 8 SP SD: 3.9899 c. M: 7.0002 c. 76: 8 5 8 5 8 7 8 5 8 5 9 SP SD: 3.0691 c. M: 6.9816 c. 78: 8 6 8 5 8 7 8 5 9 5 9 SP SD: 4.1679 c. M:-6.5493 c. 82: 9 5 9 6 8 7 9 5 9 6 9 SP SD: 4.1578 c. M:-6.8823 c. 83: 9 5 9 6 8 8 8 6 9 5 10 SP SD: 3.8787 c. M: 6.4256 c. 84: 9 6 8 6 9 7 9 6 9 5 10 SP SD: 3.7364 c. M: 5.8249 c. 86: 9 6 9 6 9 7 9 6 9 6 10 SP SD: 3.2381 c. M: 6.8216 c. 87: 9 6 9 6 9 8 9 6 9 6 10 SP SD: 2.2503 c. M: 4.1603 c. 104: 11 7 11 7 11 9 11 7 11 7 12 SP SD: 1.4718 c. M: 2.5282 c. 155: 17 10 16 11 16 14 16 10 17 10 18 SP SD: 1.5443 c. M:-3.3147 c. 166: 18 11 17 12 17 15 17 11 18 11 19 SP SD: 1.3646 c. M:-2.2422 c. 196: 21 13 20 14 20 18 20 13 21 13 23 SP SD: 1.3319 c. M: 2.2680 c. 207: 22 14 21 15 21 19 21 14 22 14 24 SP SD: 1.0044 c. M: 1.9131 c. 224: 24 15 23 16 23 20 23 15 24 15 26 SP SD: 0.4762 c. M: 0.8063 c. 459: 49 31 47 33 47 41 47 31 49 31 53 SP SD: 0.4481 c. M: 0.9758 c. 466: 50 31 48 33 48 42 48 31 50 31 54 SP SD: 0.2953 c. M: 0.4831 c. 477: 51 32 49 34 49 43 49 32 51 32 55 SP SD: 0.1825 c. M:-0.3745 c. 701: 75 47 72 50 72 63 72 47 75 47 81 SP SD: 0.1058 c. M:-0.1811 c. 1178: 126 79 121 84 121 106 121 79 126 79 136 SP SD: 0.1031 c. M:-0.2144 c. 1282: 137 86 132 91 132 115 132 86 137 86 148 SP SD: 0.0667 c. M:-0.1380 c. 1506: 161 101 155 107 155 135 155 101 161 101 174 SP SD: 0.0540 c. M: 0.1061 c. 1983: 212 133 204 141 204 178 204 133 212 133 229 SP SD: 0.0394 c. M: 0.0607 c.
FIT/HARMONIC
1 x 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 x 4 S SD: 26.6365 cents 3 x x x x 4 x x 5 x x 6 S SD: 17.8201 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 15.7255 cents 5 x x 6 x 7 x x 8:9 x 10 S SD: 13.9357 cents 6 x 7 x x 8:9 x 10 x 11:12 S SD: 15.9945 cents 7 x 8 x 9 x 10:11 x 12:13:14 S SD: 9.3386 cents 8 x 9 x 10:11:12 x 13:14:15:16 S SD: 8.7967 cents 9 x 10:11 x 12:13:14:15:16:17:18 S SD: 8.4526 cents 10:11 x 12:13:14:15 x 16:18 x 20 S SD: 12.7400 cents 11:12 x 13:14:15:16:17:18:19:20:22 S SD: 6.7914 cents 12:13:14 x 15:16:17:19:20:21:22:24 SD: 10.1131 cents 13:14:15:16:17:18:19:20:21:23:24:26 SD: 7.1991 cents 14:15:16:17:18:19:20:22:23:25:26:28 SD: 4.8195 cents 22:24:25:27:28:30:32:34:36:39:41:44 SD: 3.9495 cents 25:27:28:30:32:34:36:39:41:44:46:50 SD: 2.8650 cents 33:36:37:40:42:45:48:52:54:58:61:66 SD: 2.7033 cents 37:40:42:45:47:51:54:58:61:65:68:74 SD: 2.4924 cents 38:41:43:46:48:52:55:59:62:67:70:76 SD: 1.9064 cents 52:56:59:63:66:71:76:81:85:92:96:104 SD: 1.4828 cents 55:59:62:67:70:75:80:86:90:97:102:110 SD: 1.3497 cents 63:68:71:76:80:86:92:98:103:111:116:126 SD: 1.3437 cents 66:71:74:80:84:90:96:103:108:116:122:132 SD: 1.1695 cents 77:83:87:93:98:105:112:120:126:136:142:154 SD: 0.8636 cents 103:111:116:125:131:141:150:161:169:182:190:206 SD: 0.8065 cents 117:126:132:142:149:160:170:183:191:206:216:234 SD: 0.5647 cents 132:142:149:160:168:180:192:206:216:233:244:264 SD: 0.5572 cents 155:167:175:188:197:212:225:242:254:273:286:310 SD: 0.5299 cents 156:168:176:189:199:213:227:244:255:275:288:312 SD: 0.4827 cents 169:182:191:205:215:231:246:264:277:298:312:338 SD: 0.4544 cents 180:194:203:218:229:246:262:281:295:317:332:360 SD: 0.3734 cents 194:209:219:235:247:265:282:303:317:342:358:388 SD: 0.3100 cents 235:253:265:285:299:321:342:367:385:414:434:470 SD: 0.3090 cents 264:284:298:320:336:361:384:412:432:465:487:528 SD: 0.3011 cents 275:296:310:333:350:376:400:430:450:485:508:550 SD: 0.2832 cents 297:320:335:360:378:406:432:464:486:523:548:594 SD: 0.1857 cents 374:403:422:453:476:511:544:584:612:659:690:748 SD: 0.1722 cents 429:462:484:520:546:586:624:670:702:756:792:858 SD: 0.1330 cents 572:616:645:693:728:782:832:894:936:1008:1056:1144 SD: 0.1191 cents