Scala analysis: quasi_9-EDO
Emulation of 9-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: 7/6 266.870906 septimal minor third 3: 441/352 390.243872 4: 11/8 551.317942 undecimal semi-augmented fourth 5: 3/2 701.955001 perfect fifth 6: 21/13 830.253246 7: 7/4 968.825906 harmonic seventh 8: 1323/704 1092.198873 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 1408/1323 107.8011 1: 14/13 128.2982 2/3-tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 189/176 123.3730 4: 484/441 161.0741 two (undecimal minor semitone) 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 14/13 128.2982 2/3-tone 7: 13/12 138.5727 tridecimal 2/3-tone 8: 189/176 123.3730 9: 1408/1323 107.8011
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1408/1323 107.801 cents 1: 2 189/176 123.373 cents 1: 2 14/13 128.298 cents 2/3-tone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 484/441 161.074 cents two (undecimal minor semitone) 2: 1 8/7 231.174 cents septimal whole tone 2: 1 2816/2457 236.099 cents 2: 2 819/704 261.946 cents 2: 2 7/6 266.871 cents septimal minor third 2: 1 168/143 278.935 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 1 176/147 311.711 cents 3: 1 16/13 359.472 cents tridecimal neutral third 3: 1 26/21 369.747 cents 3: 1 704/567 374.672 cents 3: 2 441/352 390.244 cents 3: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 143/112 423.020 cents 3: 1 9/7 435.084 cents septimal major third, BP third 3: 1 352/273 440.009 cents 4: 4 4/3 498.045 cents perfect fourth 4: 1 1323/968 540.881 cents 4: 1 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 18/13 563.382 cents tridecimal augmented fourth 4: 1 39/28 573.657 cents 4: 1 88/63 578.582 cents 5: 1 63/44 621.418 cents 5: 1 56/39 626.343 cents 5: 1 13/9 636.618 cents tridecimal diminished fifth 5: 1 16/11 648.682 cents undecimal semi-diminished fifth 5: 1 1936/1323 659.119 cents 5: 4 3/2 701.955 cents perfect fifth 6: 1 273/176 759.991 cents 6: 1 14/9 764.916 cents septimal minor sixth 6: 1 224/143 776.980 cents 6: 1 11/7 782.492 cents undecimal augmented fifth 6: 2 704/441 809.756 cents 6: 1 567/352 825.328 cents 6: 1 21/13 830.253 cents 6: 1 13/8 840.528 cents tridecimal neutral sixth 7: 1 147/88 888.289 cents 7: 1 56/33 915.553 cents 7: 1 143/84 921.065 cents 7: 2 12/7 933.129 cents septimal major sixth 7: 2 1408/819 938.054 cents 7: 1 2457/1408 963.901 cents 7: 1 7/4 968.826 cents harmonic seventh 8: 1 441/242 1038.926 cents 8: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 8: 2 24/13 1061.427 cents tridecimal neutral seventh 8: 2 13/7 1071.702 cents 16/3-tone 8: 2 352/189 1076.627 cents 8: 1 1323/704 1092.199 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.75000 = 27/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 128.3 266.9 390.2 551.3 702.0 830.3 968.8 1092.2 1200.0 128.3 : 138.6 261.9 423.0 573.7 702.0 840.5 963.9 1071.7 1200.0 266.9 : 123.4 284.4 435.1 563.4 702.0 825.3 933.1 1061.4 1200.0 390.2 : 161.1 311.7 440.0 578.6 702.0 809.8 938.1 1076.6 1200.0 551.3 : 150.6 278.9 417.5 540.9 648.7 777.0 915.6 1038.9 1200.0 702.0 : 128.3 266.9 390.2 498.0 626.3 764.9 888.3 1049.4 1200.0 830.3 : 138.6 261.9 369.7 498.0 636.6 760.0 921.1 1071.7 1200.0 968.8 : 123.4 231.2 359.5 498.0 621.4 782.5 933.1 1061.4 1200.0 1092.2: 107.8 236.1 374.7 498.0 659.1 809.8 938.1 1076.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 107.8011 .. 161.0741 cents 33/32, 53.2729 cents 1408/1323, 107.8011 cents 2: 231.1741 .. 311.7111 cents 22/21, 80.5370 cents 126/121, 70.1000 cents 3: 359.4723 .. 440.0094 cents 22/21, 80.5370 cents 147/143, 47.7612 cents 4: 498.0450 .. 578.5820 cents 22/21, 80.5370 cents 91/88, 58.0356 cents 5: 621.4180 .. 701.9550 cents 22/21, 80.5370 cents 3969/3872, 42.8359 cents 6: 759.9906 .. 840.5277 cents 22/21, 80.5370 cents 91/88, 58.0356 cents 7: 888.2889 .. 968.8259 cents 22/21, 80.5370 cents 147/143, 47.7612 cents 8: 1038.9259 .. 1092.1989 cents 33/32, 53.2729 cents 126/121, 70.1000 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 1408/1323, 107.8011 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 484/441, 161.0741 cents Average / Smallest step : 1.236845 Largest / Average step : 1.208056 Largest / Smallest step : 1.494178 Median interval of one step : 14/13, 128.2982 cents, amount: 2 Least squares average step : 136.31126 cents, oct.: 1226.80138 cents Scale is strictly proper Step pattern alph. order: ABCDEABCF Step pattern size order : CDBFECDBA Scale is a Constant Structure, by a margin of 42.83593 cents Scale diversity : 1.463405 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.508527 Rothenberg efficiency : 0.283951 redundancy: 0.716049 Efficiency x scale size : 2.555556 Number of different interval sizes : 54 = 6.75000 / class Number of one step interval sizes : 6 Highest interval variety : 8 Mean interval variety : 6.75000 = 27/4 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 352/351, 4.9253 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 11.1111% Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 80.5370 cents: 8 -- Rational properties -- Prime limit : 13 Odd number limit : 2457 (O: 2457 U: 2457) Highest odd numerator or denominator: 1323 Scale harmonicity : 0.010335 Average absolute harmonicity : 0.174524 Specific harmonicity : 0.066617 Fundamental : 1/27456, -14.7448 octaves, 0.0095 Hz. Guide tone : 29106, 14.8290 octaves, 7614873.704 Hz. Exponens Consonantiae : 7.991343E+08, 29.57386 octaves Euler's gradus suavitatis : 60 Sum of Mann's harmonic distance : 1466.0, average 162.88889 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.41087, average 1.26787 Sum of Tenney's harmonic distance : 21.95042, average 2.43894 Vogel's harmonic complexity : 35.33333 Wille's k value : 25798 Wilson's harmonic complexity : 61 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 160.58580, average 3.56857 Lattice compactness (without 2's) : 89.87552, average 1.99723 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -6 .. 1 -1.77778 20 1 3: -1 .. 3 0.66667 8 1 7: 0 .. 2 0.88889 8 2 11: -1 .. 1 -0.11111 3 3 13: -1 .. 0 -0.22222 2 2 Average exponent except 2's : 11 / 9 = 1.22222 Average absolute exponent except 2's: 21 / 9 = 2.33333
FIT/MODE
9: 1 1 1 1 1 1 1 1 1 SP B ME I SD: 22.4008 c. M: 35.4926 c. Pelog Nawanada: Sunda 15: 2 1 2 2 2 1 2 2 1 P D3 SD: 21.0536 c. M:-31.7018 c. 17: 2 2 2 2 2 2 2 2 1 SP M ME S SD: 20.4181 c. M:-37.2129 c. Jerome-9, Progression-9 19: 2 2 2 3 2 2 2 2 2 SP M ME S SD: 13.1942 c. M: 21.4575 c. 22: 2 3 2 3 3 2 3 2 2 P D3 S SD: 9.8640 c. M: 19.2073 c. 29: 3 3 3 4 4 3 3 3 3 SP D3 S SD: 12.6003 c. M: 18.5950 c. 30: 3 4 3 4 4 3 3 3 3 P SD: 10.8481 c. M:-18.0450 c. 31: 3 4 3 4 4 3 4 3 3 SP D3 S SD: 8.5713 c. M: 17.3500 c. 32: 3 4 3 5 4 3 4 3 3 P SD: 9.5748 c. M: 15.7982 c. 35: 4 4 3 5 4 4 4 4 3 SP SD: 9.0258 c. M: 16.2407 c. 36: 4 4 4 5 4 4 4 4 3 SP T3 SD: 6.9521 c. M:-15.3487 c. 37: 4 4 4 5 5 4 4 4 3 SP S SD: 7.3633 c. M:-12.9900 c. 41: 4 5 4 6 5 4 5 4 4 SP SD: 7.1986 c. M: 11.2251 c. 43: 5 5 4 6 5 5 5 4 4 SP SD: 7.1947 c. M:-12.1989 c. 45: 5 5 5 6 5 5 5 5 4 SP T3 SD: 6.3450 c. M:-9.7561 c. 46: 5 5 5 6 6 5 5 5 4 SP S SD: 3.4170 c. M: 6.0013 c. 58: 6 7 6 8 7 6 7 6 5 SP SD: 3.7173 c. M:-7.3027 c. 67: 7 8 7 9 8 7 8 7 6 SP SD: 3.2780 c. M: 6.3726 c. 68: 7 8 7 9 9 7 8 7 6 SP S SD: 2.8387 c. M: 4.7688 c. 77: 8 9 8 10 10 8 9 8 7 SP S SD: 2.9586 c. M: 5.8634 c. 94: 10 11 10 12 12 10 11 10 8 SP S SD: 2.8318 c. M:-5.6735 c. 104: 11 12 11 14 13 11 12 11 9 SP SD: 1.9550 c. M:-3.9550 c. 111: 12 13 11 15 14 12 13 11 10 SP SD: 2.0363 c. M:-4.1471 c. 113: 12 13 12 15 14 12 13 12 10 SP SD: 1.6370 c. M:-2.6765 c. 130: 14 15 13 18 16 14 15 13 12 SP SD: 1.6282 c. M: 2.9681 c. 156: 17 18 16 21 19 17 18 16 14 SP SD: 1.7188 c. M:-2.5282 c. 157: 17 18 16 21 20 17 18 16 14 SP SD: 1.4209 c. M:-2.8678 c. 166: 18 19 17 22 21 18 19 17 15 SP SD: 1.0283 c. M: 1.9204 c. 176: 19 20 18 24 22 19 20 18 16 SP SD: 1.0855 c. M: 1.6075 c. 198: 21 23 20 27 25 21 23 20 18 SP SD: 1.0701 c. M: 2.3651 c. 207: 22 24 21 28 26 22 24 21 19 SP SD: 1.1649 c. M: 2.3438 c. 224: 24 26 23 30 28 24 26 23 20 SP SD: 0.5861 c. M:-0.9862 c. 311: 33 36 32 42 39 33 36 32 28 SP SD: 0.5303 c. M: 0.9671 c. 390: 42 45 40 52 49 42 45 40 35 SP SD: 0.5515 c. M:-0.9325 c. 400: 43 46 41 54 50 43 46 41 36 SP SD: 0.4299 c. M:-0.7468 c. 431: 46 50 44 58 54 46 50 44 39 SP SD: 0.4037 c. M: 0.7836 c. 468: 50 54 48 63 59 50 54 48 42 SP SD: 0.3520 c. M:-0.6091 c. 477: 51 55 49 64 60 51 55 49 43 SP SD: 0.2356 c. M: 0.3750 c. 701: 75 81 72 94 88 75 81 72 63 SP SD: 0.0890 c. M:-0.1762 c. 1178: 126 136 121 158 148 126 136 121 106 SP SD: 0.1068 c. M: 0.2144 c. 1236: 132 143 127 166 155 132 143 127 111 SP SD: 0.1017 c. M: 0.1562 c. 1282: 137 148 132 172 161 137 148 132 115 SP SD: 0.0758 c. M:-0.1568 c. 1713: 183 198 176 230 215 183 198 176 154 SP SD: 0.0651 c. M: 0.1307 c. 1759: 188 203 181 236 221 188 203 181 158 SP SD: 0.0652 c. M: 0.1284 c. 1983: 212 229 204 266 249 212 229 204 178 SP SD: 0.0396 c. M:-0.0855 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x x 4 x 5 x x 6 S SD: 25.3101 cents 4 x x 5 x 6 x 7 x 8 S SD: 0.9825 cents 5 x 6 x 7 x 8:9 x 10 S SD: 15.4979 cents 6 x 7 x 8:9:10 x 11:12 S SD: 14.5300 cents 7 x 8:9:10 x 11:12:13:14 S SD: 15.4120 cents 8 x 9:10:11:12:13:14:15:16 S SD: 8.0044 cents 9:10 x 11:12:14:15:16:17:18 S SD: 15.4684 cents 10:11:12:13:14:15:16:18:19:20 S SD: 12.0724 cents 11:12:13:14:15:17:18:19:21:22 SD: 8.8704 cents 12:13:14:15:17:18:19:21:23:24 SD: 7.9815 cents 13:14:15:16:18:20:21:23:24:26 SD: 7.6048 cents 16:17:19:20:22:24:26:28:30:32 SD: 4.4725 cents 24:26:28:30:33:36:39:42:45:48 S SD: 1.7286 cents 64:69:75:80:88:96:103:112:120:128 SD: 1.2945 cents 78:84:91:98:107:117:126:137:147:156 SD: 1.1381 cents 80:86:93:100:110:120:129:140:150:160 SD: 1.0447 cents 88:95:103:110:121:132:142:154:165:176 SD: 1.0161 cents 90:97:105:113:124:135:145:158:169:180 SD: 1.0009 cents 91:98:106:114:125:137:147:159:171:182 SD: 0.8454 cents 104:112:121:130:143:156:168:182:195:208 SD: 0.8133 cents 114:123:133:143:157:171:184:200:214:228 SD: 0.7637 cents 115:124:134:144:158:173:186:201:216:230 SD: 0.7632 cents 120:129:140:150:165:180:194:210:226:240 SD: 0.7110 cents 142:153:166:178:195:213:229:249:267:284 SD: 0.7036 cents 143:154:167:179:197:215:231:250:269:286 SD: 0.6878 cents 144:155:168:180:198:216:233:252:271:288 SD: 0.6133 cents 158:170:184:198:217:237:255:277:297:316 SD: 0.5971 cents 166:179:194:208:228:249:268:291:312:332 SD: 0.5818 cents 168:181:196:210:231:252:271:294:316:336 SD: 0.5493 cents 174:187:203:218:239:261:281:305:327:348 SD: 0.5469 cents 181:195:211:227:249:272:292:317:340:362 SD: 0.5453 cents 182:196:212:228:250:273:294:319:342:364 SD: 0.4688 cents 192:207:224:241:264:288:310:336:361:384 SD: 0.4432 cents 198:213:231:248:272:297:320:347:372:396 SD: 0.4060 cents 208:224:243:261:286:312:336:364:391:416 SD: 0.4048 cents 221:238:258:277:304:332:357:387:415:442 SD: 0.3872 cents 222:239:259:278:305:333:359:389:417:444 SD: 0.3857 cents 232:250:271:291:319:348:375:406:436:464 SD: 0.3674 cents 234:252:273:293:322:351:378:410:440:468 SD: 0.3183 cents 272:293:317:341:374:408:439:476:511:544 SD: 0.3030 cents 288:310:336:361:396:432:465:504:541:576 SD: 0.1848 cents 312:336:364:391:429:468:504:546:586:624 SD: 0.1217 cents 546:588:637:684:751:819:882:956:1026:1092 SD: 0.1210 cents