Scala analysis: xen09-grady-dekany-b
Dekany B
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 9/8 203.910002 major whole tone 3: 55/48 235.676655 undecimal semi-augmented whole tone 4: 9/7 435.084095 septimal major third, BP third 5: 55/42 466.850749 6: 11/8 551.317942 undecimal semi-augmented fourth 7: 165/112 670.760751 8: 45/28 821.397809 septimale wide minor sixth 9: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 15/14 119.4428 major diatonic semitone 2: 21/20 84.4672 minor semitone 3: 55/54 31.7667 telepathma 4: 432/385 199.4074 5: 55/54 31.7667 telepathma 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 12/11 150.6371 undecimal neutral second, 3/4-tone 9: 154/135 227.9651 10: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 55/54 31.767 cents telepathma 1: 2 21/20 84.467 cents minor semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 432/385 199.407 cents 1: 1 154/135 227.965 cents 2: 2 77/72 116.234 cents undecimal secor 2: 2 9/8 203.910 cents major whole tone 2: 2 8/7 231.174 cents septimal whole tone 2: 2 90/77 270.080 cents 2: 2 56/45 378.602 cents septimal narrow major third 3: 2 55/48 235.677 cents undecimal semi-augmented whole tone 3: 1 220/189 262.941 cents 3: 2 6/5 315.641 cents minor third 3: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 2 4/3 498.045 cents perfect fourth 3: 1 224/165 529.239 cents 4: 2 11/9 347.408 cents undecimal neutral third 4: 2 5/4 386.314 cents major third 4: 2 9/7 435.084 cents septimal major third, BP third 4: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 16/11 648.682 cents undecimal semi-diminished fifth 5: 1 77/60 431.875 cents 5: 2 55/42 466.851 cents 5: 2 108/77 585.721 cents 5: 2 77/54 614.279 cents 5: 2 84/55 733.149 cents 5: 1 120/77 768.125 cents 6: 2 11/8 551.318 cents undecimal semi-augmented fourth 6: 2 10/7 617.488 cents Euler's tritone 6: 2 14/9 764.916 cents septimal minor sixth 6: 2 8/5 813.686 cents minor sixth 6: 2 18/11 852.592 cents undecimal neutral sixth 7: 1 165/112 670.761 cents 7: 2 3/2 701.955 cents perfect fifth 7: 2 44/27 845.453 cents neutral sixth 7: 2 5/3 884.359 cents major sixth, BP sixth 7: 1 189/110 937.059 cents 7: 2 96/55 964.323 cents 8: 2 45/28 821.398 cents septimale wide minor sixth 8: 2 77/45 929.920 cents 8: 2 7/4 968.826 cents harmonic seventh 8: 2 16/9 996.090 cents Pythagorean minor seventh 8: 2 144/77 1083.766 cents 9: 1 135/77 972.035 cents 9: 1 385/216 1000.593 cents 9: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 9: 2 28/15 1080.557 cents grave major seventh 9: 2 40/21 1115.533 cents acute major seventh 9: 2 108/55 1168.233 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.55556 = 50/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 119.4 203.9 235.7 435.1 466.9 551.3 670.8 821.4 1049.4 1200.0 119.4 : 84.5 116.2 315.6 347.4 431.9 551.3 702.0 929.9 1080.6 1200.0 203.9 : 31.8 231.2 262.9 347.4 466.9 617.5 845.5 996.1 1115.5 1200.0 235.7 : 199.4 231.2 315.6 435.1 585.7 813.7 964.3 1083.8 1168.2 1200.0 435.1 : 31.8 116.2 235.7 386.3 614.3 764.9 884.4 968.8 1000.6 1200.0 466.9 : 84.5 203.9 354.5 582.5 733.1 852.6 937.1 968.8 1168.2 1200.0 551.3 : 119.4 270.1 498.0 648.7 768.1 852.6 884.4 1083.8 1115.5 1200.0 670.8 : 150.6 378.6 529.2 648.7 733.1 764.9 964.3 996.1 1080.6 1200.0 821.4 : 228.0 378.6 498.0 582.5 614.3 813.7 845.5 929.9 1049.4 1200.0 1049.4: 150.6 270.1 354.5 386.3 585.7 617.5 702.0 821.4 972.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 227.9651 cents 28/25, 196.1985 cents 55/54, 31.7667 cents 2: 116.2338 .. 378.6022 cents 64/55, 262.3683 cents 15/16,-111.7313 cents 3: 235.6767 .. 529.2392 cents 3584/3025, 293.5626 cents 825/896,-142.9255 cents 4: 347.4079 .. 648.6821 cents 144/121, 301.2741 cents 605/672,-181.8313 cents 5: 431.8751 .. 768.1249 cents 7200/5929, 336.2497 cents 847/960,-216.8069 cents 6: 551.3179 .. 852.5921 cents 144/121, 301.2741 cents 847/960,-216.8069 cents 7: 670.7608 .. 964.3233 cents 3584/3025, 293.5626 cents 605/672,-181.8313 cents 8: 821.3978 .. 1083.7662 cents 64/55, 262.3683 cents 825/896,-142.9255 cents 9: 972.0349 .. 1168.2333 cents 28/25, 196.1985 cents 15/16,-111.7313 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 55/54, 31.7667 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 154/135, 227.9651 cents Average / Smallest step : 3.777546 Largest / Average step : 1.899709 Largest / Smallest step : 7.176240 Median interval of one step : 15/14, 119.4428 cents, amount: 2 Least squares average step : 107.34432 cents, oct.: 1073.44324 cents Scale is not proper Step pattern alph. order: ABCDCBAEFE Step pattern size order : CBAEABCDFD Scale is a Constant Structure, by a margin of 3.20896 cents Scale diversity : 1.550363 Lumma stability : 0.052944 Lumma impropriety factor : 0.793424 Rothenberg efficiency : 0.288889 redundancy: 0.711111 Efficiency x scale size : 2.888889 Number of different interval sizes : 50 = 5.55556 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.55556 = 50/9 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 540/539, 3.2090 cents Number of recognisable fifths : 2, average 701.9550 cents 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 : 7 Inversional symmetry on intervals : 3-4 8-9 -- Rational properties -- Prime limit : 11 Odd number limit : 385 (O: 385 U: 385) Highest odd numerator or denominator: 165 Scale harmonicity : 0.020891 Average absolute harmonicity : 0.144980 Specific harmonicity : 0.088708 Fundamental : 1/336, -8.3923 octaves, 0.7786 Hz. Guide tone : 990, 9.9513 octaves, 259009.310 Hz. Exponens Consonantiae : 3.326400E+05, 18.34360 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 325.5, average 32.55000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.51878, average 1.25188 Sum of Tenney's harmonic distance : 24.19624, average 2.41962 Vogel's harmonic complexity : 18.20000 Wille's k value : 247 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 167.42110, average 3.04402 Lattice compactness (without 2's) : 109.45855, average 1.99016 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.80000 20 1 3: -1 .. 2 0.50000 11 1 5: 0 .. 1 0.50000 5 7: -1 .. 0 -0.50000 5 3 11: 0 .. 1 0.50000 5 5 Average exponent except 2's : 10 / 10 = 1.00000 Average absolute exponent except 2's: 26 / 10 = 2.60000 Scale is weakly epimorphic with val: <10 16 21 26 34| Scale is weakly epimorphic with val: <10 16 23 26 34| Scale is weakly epimorphic with val: <10 16 25 26 34| Scale is weakly epimorphic with val: <10 17 21 26 33| Scale is weakly epimorphic with val: <10 17 21 27 32| Scale is weakly epimorphic with val: <10 17 21 29 38| Scale is weakly epimorphic with val: <10 17 22 27 33| Scale is weakly epimorphic with val: <10 17 22 28 32| Scale is weakly epimorphic with val: <10 17 23 28 35| Scale is weakly epimorphic with val: <10 17 23 29 36| Scale is weakly epimorphic with val: <10 17 23 31 32| Scale is weakly epimorphic with val: <10 17 24 25 35| Scale is weakly epimorphic with val: <10 17 24 26 36| Scale is weakly epimorphic with val: <10 17 25 27 38| Scale is weakly epimorphic with val: <10 18 21 25 35| Scale is weakly epimorphic with val: <10 18 21 28 32| Scale is weakly epimorphic with val: <10 18 23 27 33| Scale is weakly epimorphic with val: <10 18 23 28 32| Scale is weakly epimorphic with val: <10 18 24 25 32| Scale is weakly epimorphic with val: <10 18 24 27 32| Scale is weakly epimorphic with val: <10 18 24 28 33| Scale is weakly epimorphic with val: <10 18 24 28 35| Scale is weakly epimorphic with val: <10 18 24 28 37| Scale is weakly epimorphic with val: <10 18 24 29 32| Scale is weakly epimorphic with val: <10 18 24 31 32| Scale is weakly epimorphic with val: <10 18 25 28 32|
FIT/MODE
10: 1 1 0 2 0 1 1 1 2 1 N T3 SD: 30.9693 c. M:-49.2392 c. 11: 1 1 0 2 0 1 1 2 2 1 N SD: 24.9121 c. M:-51.3295 c. 15: 1 1 1 2 1 1 1 2 3 2 N SD: 25.4430 c. M: 43.9100 c. 16: 2 1 0 3 0 1 2 2 3 2 N SD: 16.5013 c. M:-30.5572 c. 19: 2 1 1 3 0 2 2 2 4 2 N SD: 16.3210 c. M: 24.7455 c. 20: 2 1 1 3 1 1 2 3 3 3 N SD: 15.6309 c. M: 29.3629 c. 22: 2 2 0 4 0 2 2 3 4 3 N SD: 14.2290 c. M: 30.4871 c. 23: 2 2 1 3 1 2 2 3 4 3 N SD: 14.0940 c. M:-25.1929 c. 25: 2 2 1 4 1 1 3 3 5 3 N SD: 12.2921 c. M: 23.4428 c. 26: 3 1 1 4 1 2 3 3 5 3 N SD: 13.7153 c. M:-21.5469 c. 28: 3 2 1 4 1 2 3 3 6 3 N SD: 12.2889 c. M:-22.0656 c. 29: 3 2 1 4 1 2 3 4 5 4 N SD: 11.3748 c. M: 21.2910 c. 30: 3 2 1 5 1 2 3 4 5 4 N SD: 9.0874 c. M:-18.6022 c. 31: 3 2 1 5 1 2 3 4 6 4 N SD: 7.4873 c. M: 12.6962 c. 39: 4 3 1 6 1 3 4 5 7 5 N SD: 6.6631 c. M:-11.4746 c. 41: 4 3 1 7 1 3 4 5 8 5 N SD: 2.7778 c. M:-4.7796 c. 72: 7 5 2 12 2 5 7 9 14 9 N SD: 2.6995 c. M: 4.7311 c. 93: 9 7 2 16 2 7 9 12 17 12 N SD: 3.1185 c. M:-4.4086 c. 98: 10 7 2 17 2 7 10 12 19 12 N SD: 3.0593 c. M:-5.7322 c. 100: 10 7 3 16 3 7 10 12 19 13 N SD: 2.9957 c. M: 5.3978 c. 102: 10 7 3 17 3 7 10 13 19 13 N SD: 2.1258 c. M: 3.9100 c. 111: 11 8 3 18 3 8 11 14 21 14 N SD: 1.3769 c. M: 2.6517 c. 118: 12 8 3 20 3 8 12 15 22 15 N SD: 1.7272 c. M:-2.5911 c. 143: 14 10 4 24 4 10 14 18 27 18 N SD: 1.7210 c. M:-3.0793 c. 152: 15 11 4 25 4 11 15 19 29 19 N SD: 0.9197 c. M:-1.3532 c. 224: 22 16 6 37 6 16 22 28 43 28 N SD: 0.9761 c. M: 1.7550 c. 229: 23 16 6 38 6 16 23 29 43 29 N SD: 0.7957 c. M: 1.3280 c. 270: 27 19 7 45 7 19 27 34 51 34 N SD: 0.4401 c. M:-0.8244 c. 311: 31 22 8 52 8 22 31 39 59 39 N SD: 0.4657 c. M:-0.9288 c. 342: 34 24 9 57 9 24 34 43 65 43 N SD: 0.3573 c. M: 0.5889 c. 383: 38 27 10 64 10 27 38 48 73 48 N SD: 0.3567 c. M: 0.6897 c. 494: 49 35 13 82 13 35 49 62 94 62 N SD: 0.2645 c. M: 0.4540 c. 612: 61 43 16 102 16 43 61 77 116 77 N SD: 0.2329 c. M: 0.3825 c. 653: 65 46 17 109 17 46 65 82 124 82 N SD: 0.2051 c. M: 0.4546 c. 764: 76 54 20 127 20 54 76 96 145 96 N SD: 0.1581 c. M: 0.3586 c. 805: 80 57 21 134 21 57 80 101 153 101 N SD: 0.1816 c. M:-0.3136 c. 1043: 104 73 28 173 28 73 104 131 198 131 N SD: 0.1766 c. M: 0.2667 c. 1084: 108 76 29 180 29 76 108 136 206 136 N SD: 0.1364 c. M:-0.3079 c. 1236: 123 87 33 205 33 87 123 155 235 155 N SD: 0.1246 c. M:-0.2457 c. 1354: 135 95 36 225 36 95 135 170 257 170 N SD: 0.1234 c. M:-0.2098 c. 1395: 139 98 37 232 37 98 139 175 265 175 N SD: 0.1355 c. M:-0.2460 c. 1426: 142 100 38 237 38 100 142 179 271 179 N SD: 0.1179 c. M: 0.2634 c. 1506: 150 106 40 250 40 106 150 189 286 189 N SD: 0.0982 c. M:-0.1799 c. 1578: 157 111 42 262 42 111 157 198 300 198 N SD: 0.0714 c. M: 0.1077 c. 1848: 184 130 49 307 49 130 184 232 351 232 N SD: 0.0250 c. M:-0.0377 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 x 3 x x 4 S SD: 15.5971 cents 3 x x x x 4 x x 5 x 6 S SD: 23.4216 cents 4 x x x 5 x x 6 x 7:8 S SD: 24.7965 cents 5 x x 6 x x 7 x 8:9:10 S SD: 18.3696 cents 6 x x 7 x 8 x 9:10:11:12 S SD: 13.8276 cents 7 x x 8:9 x x 10:11:13:14 SD: 11.6320 cents 8 x 9 x 10 x 11:12:13:15:16 SD: 10.3325 cents 9 x 10 x x 12 x 13:14:17:18 SD: 15.3321 cents 10 x 11 x x 13:14:15:16:18:20 SD: 9.7814 cents 11:12 x 13:14 x 15:16:18:20:22 S SD: 9.6995 cents 12:13 x 14:15:16:17:18:19:22:24 SD: 10.5424 cents 13:14 x 15 x 17:18:19:21:24:26 SD: 3.5114 cents 14:15 x 16:18 x 19:21:23:26:28 SD: 7.3446 cents 15:16:17 x 19:20:21:22:24:28:30 SD: 6.9643 cents 16:17:18 x x 21:22:24:26:29:32 SD: 5.5281 cents 17:18:19 x 22 x 23:25:27:31:34 SD: 5.5555 cents 20:21 x 23 x 26:28:29:32:37:40 SD: 7.3491 cents 21:23 x 24:27:28:29:31:34:39:42 SD: 6.2574 cents 22:24 x 25:28:29:30:32:35:40:44 SD: 5.9086 cents 23:25:26 x x 30:32:34:37:42:46 SD: 4.3990 cents 24:26:27:28:31 x 33:35:39:44:48 SD: 5.0648 cents 25:27:28:29:32:33:34:37:40:46:50 SD: 3.8405 cents 27:29:30:31:35 x 37:40:43:50:54 SD: 4.1170 cents 28:30 x 32:36:37:39:41:45:51:56 SD: 3.5184 cents 29:31 x 33:37:38:40:43:47:53:58 SD: 3.0082 cents 30:32:34 x x 39:41:44:48:55:60 SD: 3.0926 cents 32:34:36:37:41:42:44:47:51:59:64 SD: 2.8996 cents 36:39 x 41:46:47:50:53:58:66:72 SD: 3.4094 cents 37:40:42 x 48 x 51:55:59:68:74 SD: 4.3022 cents 38:41:43:44:49:50:52:56:61:70:76 SD: 2.8506 cents 40:43:45:46:51:52:55:59:64:73:80 SD: 2.3840 cents 41:44:46:47:53:54:56:60:66:75:82 SD: 2.2514 cents 42:45:47:48:54:55:58:62:68:77:84 SD: 1.8330 cents 44:47 x 50:57:58:61:65:71:81:88 SD: 3.2590 cents 45:48:51:52:58:59:62:66:72:83:90 SD: 2.6455 cents 46:49:52:53:59:60:63:68:74:84:92 SD: 2.1415 cents 48:51:54:55:62:63:66:71:77:88:96 SD: 1.8663 cents 55:59:62:63:71:72:76:81:88:101:110 SD: 1.4398 cents 70:75:79:80:90:92:96:103:113:128:140 SD: 1.3920 cents 71:76:80:81:91:93:98:105:114:130:142 SD: 1.3869 cents 74:79:83:85:95:97:102:109:119:136:148 SD: 1.1452 cents 87:93:98:100:112:114:120:128:140:160:174 SD: 1.1182 cents 88:94:99:101:113:115:121:130:141:161:176 SD: 1.0793 cents 95:102:107:109:122:124:131:140:153:174:190 SD: 0.9980 cents 96:103:108:110:123:126:132:141:154:176:192 SD: 0.9766 cents 97:104:109:111:125:127:133:143:156:178:194 SD: 0.7452 cents 112:120:126:128:144:147:154:165:180:205:224 SD: 0.6605 cents 137:147:154:157:176:179:188:202:220:251:274 SD: 0.6556 cents 143:153:161:164:184:187:197:211:230:262:286 SD: 0.6244 cents 150:161:169:172:193:196:206:221:241:275:300 SD: 0.6184 cents 152:163:171:174:195:199:209:224:244:279:304 SD: 0.5326 cents 158:169:178:181:203:207:217:233:254:290:316 SD: 0.5282 cents 171:183:192:196:220:224:235:252:275:314:342 SD: 0.5236 cents 178:191:200:204:229:233:245:262:286:326:356 SD: 0.4688 cents 184:197:207:211:237:241:253:271:296:337:368 SD: 0.4395 cents 224:240:252:257:288:293:308:330:360:411:448 SD: 0.3301 cents 239:256:269:274:307:313:329:352:384:438:478 SD: 0.3023 cents 280:300:315:321:360:367:385:413:450:513:560 SD: 0.2991 cents 281:301:316:322:361:368:386:414:452:515:562 SD: 0.2821 cents 294:315:331:337:378:385:404:433:473:539:588 SD: 0.2622 cents 323:346:363:370:415:423:444:476:519:592:646 SD: 0.2428 cents 336:360:378:385:432:440:462:495:540:616:672 SD: 0.0000 cents