Scala analysis: xen09-grady-dekany-a
Dekany A
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 11/10 165.004228 Ptolemy's second, 4/5-tone 3: 7/6 266.870906 septimal minor third 4: 99/80 368.914230 5: 21/16 470.780907 narrow fourth 6: 11/8 551.317942 undecimal semi-augmented fourth 7: 231/160 635.785136 8: 33/20 866.959229 9: 7/4 968.825906 harmonic seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 21/20 84.4672 minor semitone 2: 22/21 80.5370 undecimal minor semitone 3: 35/33 101.8667 4: 297/280 102.0433 5: 35/33 101.8667 6: 22/21 80.5370 undecimal minor semitone 7: 21/20 84.4672 minor semitone 8: 8/7 231.1741 septimal whole tone 9: 35/33 101.8667 10: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 2 21/20 84.467 cents minor semitone 1: 3 35/33 101.867 cents 1: 1 297/280 102.043 cents 1: 2 8/7 231.174 cents septimal whole tone 2: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 2 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 2 6/5 315.641 cents minor third 2: 2 40/33 333.041 cents 3: 2 7/6 266.871 cents septimal minor third 3: 2 33/28 284.447 cents undecimal minor third 3: 1 105/88 305.777 cents 3: 2 44/35 396.178 cents 3: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 320/231 564.215 cents 4: 2 99/80 368.914 cents 4: 2 5/4 386.314 cents major third 4: 4 4/3 498.045 cents perfect fourth 4: 2 16/11 648.682 cents undecimal semi-diminished fifth 5: 1 55/42 466.851 cents 5: 2 21/16 470.781 cents narrow fourth 5: 2 140/99 599.912 cents quasi-equal tritone 5: 2 99/70 600.088 cents 2nd quasi-equal tritone 5: 2 32/21 729.219 cents wide fifth 5: 1 84/55 733.149 cents 6: 2 11/8 551.318 cents undecimal semi-augmented fourth 6: 4 3/2 701.955 cents perfect fifth 6: 2 8/5 813.686 cents minor sixth 6: 2 160/99 831.086 cents 7: 1 231/160 635.785 cents 7: 2 11/7 782.492 cents undecimal augmented fifth 7: 2 35/22 803.822 cents 7: 1 176/105 894.223 cents 7: 2 56/33 915.553 cents 7: 2 12/7 933.129 cents septimal major sixth 8: 2 33/20 866.959 cents 8: 2 5/3 884.359 cents major sixth, BP sixth 8: 2 16/9 996.090 cents Pythagorean minor seventh 8: 2 9/5 1017.596 cents just minor seventh, BP seventh 8: 2 20/11 1034.996 cents large minor seventh 9: 2 7/4 968.826 cents harmonic seventh 9: 1 560/297 1097.957 cents 9: 3 66/35 1098.133 cents 9: 2 40/21 1115.533 cents acute major seventh 9: 2 21/11 1119.463 cents undecimal major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.11111 = 46/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 84.5 165.0 266.9 368.9 470.8 551.3 635.8 867.0 968.8 1200.0 84.5 : 80.5 182.4 284.4 386.3 466.9 551.3 782.5 884.4 1115.5 1200.0 165.0 : 101.9 203.9 305.8 386.3 470.8 702.0 803.8 1035.0 1119.5 1200.0 266.9 : 102.0 203.9 284.4 368.9 600.1 702.0 933.1 1017.6 1098.1 1200.0 368.9 : 101.9 182.4 266.9 498.0 599.9 831.1 915.6 996.1 1098.0 1200.0 470.8 : 80.5 165.0 396.2 498.0 729.2 813.7 894.2 996.1 1098.1 1200.0 551.3 : 84.5 315.6 417.5 648.7 733.1 813.7 915.6 1017.6 1119.5 1200.0 635.8 : 231.2 333.0 564.2 648.7 729.2 831.1 933.1 1035.0 1115.5 1200.0 867.0 : 101.9 333.0 417.5 498.0 599.9 702.0 803.8 884.4 968.8 1200.0 968.8 : 231.2 315.6 396.2 498.0 600.1 702.0 782.5 867.0 1098.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 231.1741 cents 12/11, 150.6371 cents 22/21, 80.5370 cents 2: 165.0042 .. 333.0408 cents 400/363, 168.0365 cents 77/80,-66.1699 cents 3: 266.8709 .. 564.2149 cents 640/539, 297.3440 cents 77/80,-66.1699 cents 4: 368.9142 .. 648.6821 cents 1280/1089, 279.7678 cents 22869/25600,-195.3006 cents 5: 466.8507 .. 733.1493 cents 3528/3025, 266.2985 cents 605/672,-181.8313 cents 6: 551.3179 .. 831.0858 cents 1280/1089, 279.7678 cents 605/672,-181.8313 cents 7: 635.7851 .. 933.1291 cents 640/539, 297.3440 cents 22869/25600,-195.3006 cents 8: 866.9592 .. 1034.9958 cents 400/363, 168.0365 cents 77/80,-66.1699 cents 9: 968.8259 .. 1119.4630 cents 12/11, 150.6371 cents 77/80,-66.1699 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.489998 Largest / Average step : 1.926451 Largest / Smallest step : 2.870407 Median interval of one step : 35/33, 101.8667 cents, amount: 3 Most common interval of one step : 35/33, 101.8667 cents, amount: 3 Least squares average step : 105.08613 cents, oct.: 1050.86131 cents Scale is not proper Step pattern alph. order: ABCDCBAECE Step pattern size order : BACDCABECE Scale is a Constant Structure, by a margin of 9.86461 cents Scale diversity : 1.471203 Lumma stability : 0.134228 Lumma impropriety factor : 0.605709 Rothenberg efficiency : 0.300397 redundancy: 0.699603 Efficiency x scale size : 3.003968 Number of different interval sizes : 46 = 5.11111 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.11111 = 46/9 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 9801/9800, 0.1766 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 5 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 : 297 (O: 297 U: 297) Highest odd numerator or denominator: 231 Scale harmonicity : 0.020463 Average absolute harmonicity : 0.143237 Specific harmonicity : 0.093266 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 1386, 10.4367 octaves, 362613.034 Hz. Exponens Consonantiae : 6.652800E+05, 19.34360 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 384.0, average 38.40000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.29518, average 1.22952 Sum of Tenney's harmonic distance : 23.79290, average 2.37929 Vogel's harmonic complexity : 18.70000 Wille's k value : 346 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 157.18659, average 2.85794 Lattice compactness (without 2's) : 89.74560, average 1.63174 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.30000 25 1 3: -1 .. 2 0.50000 7 5: -1 .. 0 -0.50000 5 7: 0 .. 1 0.50000 5 4 11: 0 .. 1 0.50000 5 5 Average exponent except 2's : 10 / 10 = 1.00000 Average absolute exponent except 2's: 22 / 10 = 2.20000 Scale is weakly epimorphic with val: <10 16 21 28 36| Scale is weakly epimorphic with val: <10 16 21 29 37| Scale is weakly epimorphic with val: <10 16 21 31 33| Scale is weakly epimorphic with val: <10 16 23 28 36| Scale is weakly epimorphic with val: <10 16 24 25 36| Scale is weakly epimorphic with val: <10 16 24 27 36| Scale is JI-epimorphic with val: <10 16 24 29 36| Scale is weakly epimorphic with val: <10 16 24 31 36| Scale is weakly epimorphic with val: <10 16 25 25 37| Scale is weakly epimorphic with val: <10 16 25 28 36| Scale is weakly epimorphic with val: <10 17 21 26 35| Scale is weakly epimorphic with val: <10 17 21 28 33| Scale is weakly epimorphic with val: <10 17 21 29 38| Scale is weakly epimorphic with val: <10 17 21 31 36| Scale is weakly epimorphic with val: <10 17 22 28 34| Scale is weakly epimorphic with val: <10 17 22 29 33| Scale is weakly epimorphic with val: <10 17 22 31 37| Scale is weakly epimorphic with val: <10 17 23 29 34| Scale is weakly epimorphic with val: <10 17 23 31 32| Scale is weakly epimorphic with val: <10 17 25 25 34| Scale is weakly epimorphic with val: <10 18 21 26 32| Scale is weakly epimorphic with val: <10 18 21 31 37| Scale is weakly epimorphic with val: <10 18 22 25 38| Scale is weakly epimorphic with val: <10 18 22 26 33| Scale is weakly epimorphic with val: <10 18 22 26 35| Scale is weakly epimorphic with val: <10 18 22 26 37| Scale is weakly epimorphic with val: <10 18 22 27 38| Scale is weakly epimorphic with val: <10 18 22 29 38| Scale is weakly epimorphic with val: <10 18 22 31 38| Scale is weakly epimorphic with val: <10 18 23 26 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 29 32| Scale is weakly epimorphic with val: <10 18 24 31 32| Scale is weakly epimorphic with val: <10 18 25 26 32| Scale is weakly epimorphic with val: <10 18 25 29 33|
FIT/MODE
10: 0 1 1 1 1 0 1 2 1 2 N SD: 41.4947 c. M: 84.4672 c. 11: 1 0 1 1 1 1 1 2 1 2 N SD: 31.0003 c. M: 55.9133 c. 13: 1 1 1 1 1 1 1 2 1 3 N SD: 20.3697 c. M: 45.7490 c. 14: 1 1 1 1 1 1 1 3 1 3 N D3 SD: 24.5373 c. M: 42.2095 c. 15: 1 1 1 2 1 1 1 3 1 3 N SD: 14.6951 c. M:-31.0858 c. 17: 1 1 2 1 2 1 1 3 2 3 N SD: 16.5893 c. M: 23.8278 c. 22: 2 1 2 2 2 1 2 4 2 4 N SD: 13.4259 c. M:-24.6237 c. 25: 2 1 3 2 2 1 2 5 2 5 N SD: 14.4999 c. M: 23.3179 c. 26: 2 2 2 2 2 2 2 5 2 5 N D3 SD: 9.1977 c. M:-19.6112 c. 28: 2 2 2 3 2 2 2 5 3 5 N SD: 9.4109 c. M:-16.8884 c. 30: 2 2 3 2 3 2 2 6 2 6 N SD: 8.5025 c. M:-13.1291 c. 36: 3 2 3 3 3 3 2 7 3 7 N SD: 7.1582 c. M:-15.5328 c. 41: 3 3 3 4 3 3 3 8 3 8 N SD: 7.0445 c. M:-11.5736 c. 43: 3 3 4 3 4 3 3 8 4 8 N SD: 5.9631 c. M:-12.1989 c. 46: 3 3 4 4 4 3 3 9 4 9 N SD: 5.6390 c. M: 9.6982 c. 53: 4 3 5 4 5 3 4 10 5 10 N SD: 5.4882 c. M: 7.9217 c. 57: 4 4 5 5 4 4 4 11 5 11 N SD: 5.1463 c. M:-10.0331 c. 58: 4 4 5 5 5 4 4 11 5 11 N SD: 3.8361 c. M:-7.3027 c. 66: 5 4 6 5 6 4 5 13 5 13 N SD: 4.5191 c. M:-6.4419 c. 68: 5 4 6 6 6 4 5 13 6 13 N SD: 3.4471 c. M: 6.1807 c. 72: 5 5 6 6 6 5 5 14 6 14 N SD: 1.9638 c. M: 4.1142 c. 100: 7 7 8 9 8 7 7 19 9 19 N SD: 2.3245 c. M:-3.1741 c. 104: 7 7 9 9 9 7 7 20 9 20 N SD: 2.0898 c. M: 3.6980 c. 130: 9 9 11 11 11 9 9 25 11 25 N SD: 1.1143 c. M:-2.5282 c. 166: 12 11 14 14 14 11 12 32 14 32 N SD: 1.1007 c. M:-2.2798 c. 176: 12 12 15 15 15 12 12 34 15 34 N SD: 1.2552 c. M: 2.6490 c. 183: 13 12 16 15 16 12 13 35 16 35 N SD: 1.2416 c. M:-1.9816 c. 198: 14 13 17 17 17 13 14 38 17 38 N SD: 0.8762 c. M:-1.9464 c. 202: 14 14 17 17 17 14 14 39 17 39 N SD: 0.8918 c. M: 1.4740 c. 224: 16 15 19 19 19 15 16 43 19 43 N SD: 0.9618 c. M:-1.7149 c. 253: 18 17 21 22 21 17 18 49 21 49 N SD: 0.9934 c. M: 1.2583 c. 255: 18 17 22 21 22 17 18 49 22 49 N SD: 0.8811 c. M: 1.8554 c. 270: 19 18 23 23 23 18 19 52 23 52 N SD: 0.2550 c. M: 0.5598 c. 566: 40 38 48 48 48 38 40 109 48 109 N SD: 0.2105 c. M:-0.3668 c. 670: 47 45 57 57 57 45 47 129 57 129 N SD: 0.1838 c. M:-0.3238 c. 742: 52 50 63 63 63 50 52 143 63 143 N SD: 0.1700 c. M: 0.3702 c. 836: 59 56 71 71 71 56 59 161 71 161 N SD: 0.0996 c. M:-0.2218 c. 1106: 78 74 94 94 94 74 78 213 94 213 N SD: 0.0864 c. M:-0.1621 c. 1236: 87 83 105 105 105 83 87 238 105 238 N SD: 0.0868 c. M:-0.1384 c. 1308: 92 88 111 111 111 88 92 252 111 252 N SD: 0.0817 c. M: 0.1387 c. 1506: 106 101 128 128 128 101 106 290 128 290 N SD: 0.0691 c. M:-0.1354 c. 1578: 111 106 134 134 134 106 111 304 134 304 N SD: 0.0464 c. M: 0.0929 c. 1848: 130 124 157 157 157 124 130 356 157 356 N SD: 0.0507 c. M: 0.0831 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: 33.0849 cents 3 x x x x 4 x x 5 x 6 S SD: 10.7810 cents 4 x x x 5 x x 6 x 7:8 S SD: 17.1048 cents 5 x x 6 x x 7 x 8:9:10 S SD: 18.5129 cents 6 x x 7 x 8 x 9:10:11:12 S SD: 18.1894 cents 7 x x 8 x 9 x 10 x 12:14 S SD: 12.8959 cents 8 x 9 x 10 x 11:12:13:14:16 S SD: 11.8610 cents 9 x 10 x 11:12 x 13:15:16:18 SD: 7.2215 cents 10 x 11:12 x 13:14 x x 18:20 SD: 12.9149 cents 11 x 12:13:14 x 15:16:18:19:22 SD: 8.0604 cents 12 x 13:14:15:16 x 17:20:21:24 SD: 6.9847 cents 13 x 14:15:16:17:18:19:21:23:26 SD: 7.1519 cents 14:15 x 16:17:18:19:20:23:25:28 SD: 9.2785 cents 15:16 x 18:19:20:21:22:25:26:30 SD: 9.8038 cents 16:17:18:19:20:21:22:23:26:28:32 SD: 6.2691 cents 17:18:19:20:21:22:23:25:28:30:34 SD: 6.1684 cents 18:19:20:21:22:24:25:26:30:32:36 SD: 5.4236 cents 19:20:21:22:24:25:26:27:31:33:38 SD: 5.3933 cents 20:21:22:23:25:26:28:29:33:35:40 SD: 4.7188 cents 22:23:24:26:27:29:30:32:36:39:44 SD: 4.5852 cents 25:26:28:29:31:33:34:36:41:44:50 SD: 4.5216 cents 29:30:32:34:36:38:40:42:48:51:58 SD: 3.1049 cents 37:39:41:43:46:49:51:53:61:65:74 SD: 2.8400 cents 38:40:42:44:47:50:52:55:63:67:76 SD: 2.4527 cents 41:43:45:48:51:54:56:59:68:72:82 SD: 2.1282 cents 42:44:46:49:52:55:58:61:69:74:84 SD: 2.1085 cents 54:57:59:63:67:71:74:78:89:95:108 SD: 1.9291 cents 58:61:64:68:72:76:80:84:96:102:116 SD: 1.7542 cents 59:62:65:69:73:77:81:85:97:103:118 SD: 1.4146 cents 72:76:79:84:89:95:99:104:119:126:144 SD: 1.4108 cents 77:81:85:90:95:101:106:111:127:135:154 SD: 1.0413 cents 80:84:88:93:99:105:110:116:132:140:160 SD: 0.9710 cents 83:87:91:97:103:109:114:120:137:145:166 SD: 0.9667 cents 97:102:107:113:120:127:133:140:160:170:194 SD: 0.9266 cents 101:106:111:118:125:133:139:146:167:177:202 SD: 0.8239 cents 119:125:131:139:147:156:164:172:196:208:238 SD: 0.7334 cents 131:138:144:153:162:172:180:189:216:229:262 SD: 0.6835 cents 138:145:152:161:171:181:190:199:228:242:276 SD: 0.6381 cents 144:151:158:168:178:189:198:208:238:252:288 SD: 0.6113 cents 157:165:173:183:194:206:216:227:259:275:314 SD: 0.5552 cents 160:168:176:187:198:210:220:231:264:280:320 SD: 0.3089 cents 240:252:264:280:297:315:330:347:396:420:480 SD: 0.2496 cents 320:336:352:373:396:420:440:462:528:560:640 SD: 0.1546 cents 480:504:528:560:594:630:660:693:792:840:960 SD: 0.0000 cents