Scala analysis: xen12-wilson-40-5C3-dekany-04
1-5-7-9-11 5C3 Dekany, Figure 40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 9/8 203.910002 major whole tone 3: 99/80 368.914230 4: 9/7 435.084095 septimal major third, BP third 5: 11/8 551.317942 undecimal semi-augmented fourth 6: 99/70 600.088324 2nd quasi-equal tritone 7: 11/7 782.492036 undecimal augmented fifth 8: 99/56 986.402038 9: 9/5 1017.596288 just minor seventh, BP seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 45/44 38.9058 1/5-tone 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 80/77 66.1699 5: 77/72 116.2338 undecimal secor 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 10/9 182.4037 minor whole tone 8: 9/8 203.9100 major whole tone 9: 56/55 31.1943 undecimal diesis, konbini comma 10: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 45/44 38.906 cents 1/5-tone 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 80/77 66.170 cents 1: 1 77/72 116.234 cents undecimal secor 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 1 112/99 213.598 cents 2: 2 8/7 231.174 cents septimal whole tone 2: 1 63/55 235.104 cents 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 5/4 386.314 cents major third 3: 1 8/7 231.174 cents septimal whole tone 3: 1 90/77 270.080 cents 3: 2 11/9 347.408 cents undecimal neutral third 3: 1 99/80 368.914 cents 3: 1 56/45 378.602 cents septimal narrow major third 3: 1 5/4 386.314 cents major third 3: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 9/7 435.084 cents septimal major third, BP third 4: 1 5/4 386.314 cents major third 4: 1 44/35 396.178 cents 4: 1 80/63 413.578 cents wide major third 4: 1 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 72/55 466.278 cents undecimal semi-diminished fourth 4: 2 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 140/99 599.912 cents quasi-equal tritone 5: 1 9/7 435.084 cents septimal major third, BP third 5: 1 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 88/63 578.582 cents 5: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 2 10/7 617.488 cents Euler's tritone 5: 1 63/44 621.418 cents 5: 1 16/11 648.682 cents undecimal semi-diminished fifth 5: 1 14/9 764.916 cents septimal minor sixth 6: 1 99/70 600.088 cents 2nd quasi-equal tritone 6: 1 10/7 617.488 cents Euler's tritone 6: 2 16/11 648.682 cents undecimal semi-diminished fifth 6: 1 55/36 733.722 cents undecimal semi-augmented fifth 6: 1 14/9 764.916 cents septimal minor sixth 6: 1 11/7 782.492 cents undecimal augmented fifth 6: 1 63/40 786.422 cents narrow minor sixth 6: 1 35/22 803.822 cents 6: 1 8/5 813.686 cents minor sixth 7: 1 14/9 764.916 cents septimal minor sixth 7: 2 11/7 782.492 cents undecimal augmented fifth 7: 1 8/5 813.686 cents minor sixth 7: 1 45/28 821.398 cents septimale wide minor sixth 7: 1 160/99 831.086 cents 7: 2 18/11 852.592 cents undecimal neutral sixth 7: 1 77/45 929.920 cents 7: 1 7/4 968.826 cents harmonic seventh 8: 1 8/5 813.686 cents minor sixth 8: 1 18/11 852.592 cents undecimal neutral sixth 8: 1 110/63 964.896 cents 8: 2 7/4 968.826 cents harmonic seventh 8: 1 99/56 986.402 cents 8: 2 16/9 996.090 cents Pythagorean minor seventh 8: 1 9/5 1017.596 cents just minor seventh, BP seventh 8: 1 20/11 1034.996 cents large minor seventh 9: 1 16/9 996.090 cents Pythagorean minor seventh 9: 2 9/5 1017.596 cents just minor seventh, BP seventh 9: 2 20/11 1034.996 cents large minor seventh 9: 1 144/77 1083.766 cents 9: 1 77/40 1133.830 cents 9: 1 35/18 1151.230 cents septimal semi-diminished octave 9: 1 88/45 1161.094 cents 9: 1 55/28 1168.806 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 8.22222 = 74/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 165.0 203.9 368.9 435.1 551.3 600.1 782.5 986.4 1017.6 1200.0 165.0 : 38.9 203.9 270.1 386.3 435.1 617.5 821.4 852.6 1035.0 1200.0 203.9 : 165.0 231.2 347.4 396.2 578.6 782.5 813.7 996.1 1161.1 1200.0 368.9 : 66.2 182.4 231.2 413.6 617.5 648.7 831.1 996.1 1035.0 1200.0 435.1 : 116.2 165.0 347.4 551.3 582.5 764.9 929.9 968.8 1133.8 1200.0 551.3 : 48.8 231.2 435.1 466.3 648.7 813.7 852.6 1017.6 1083.8 1200.0 600.1 : 182.4 386.3 417.5 599.9 764.9 803.8 968.8 1035.0 1151.2 1200.0 782.5 : 203.9 235.1 417.5 582.5 621.4 786.4 852.6 968.8 1017.6 1200.0 986.4 : 31.2 213.6 378.6 417.5 582.5 648.7 764.9 813.7 996.1 1200.0 1017.6: 182.4 347.4 386.3 551.3 617.5 733.7 782.5 964.9 1168.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 203.9100 cents 495/448, 172.7158 cents 56/55, 31.1943 cents 2: 165.0042 .. 386.3137 cents 25/22, 221.3095 cents 44/45,-38.9058 cents 3: 231.1741 .. 435.0841 cents 9/8, 203.9100 cents 32/35,-155.1396 cents 4: 386.3137 .. 599.9117 cents 112/99, 213.5980 cents 35/36,-48.7704 cents 5: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 891/980,-164.8276 cents 6: 600.0883 .. 813.6863 cents 112/99, 213.5980 cents 891/980,-164.8276 cents 7: 764.9159 .. 968.8259 cents 9/8, 203.9100 cents 35/36,-48.7704 cents 8: 813.6863 .. 1034.9958 cents 25/22, 221.3095 cents 32/35,-155.1396 cents 9: 996.0900 .. 1168.8057 cents 495/448, 172.7158 cents 44/45,-38.9058 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 56/55, 31.1943 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 3.846863 Largest / Average step : 1.699250 Largest / Smallest step : 6.536782 Median interval of one step : 140.61904 cents, amount: 0 Least squares average step : 115.07545 cents, oct.: 1150.75455 cents Scale is not proper Step pattern alph. order: ABACDEFGHF Step pattern size order : FBFDECGHAG Scale is not a Constant Structure Scale diversity : 1.454030 Lumma stability : 0.051990 Lumma impropriety factor : 0.679406 Rothenberg efficiency : 0.283333 redundancy: 0.716667 Efficiency x scale size : 2.833333 Number of different interval sizes : 50 = 5.55556 / class Number of one step interval sizes : 8 Highest interval variety : 9 Mean interval variety : 8.22222 = 74/9 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 9801/9800, 0.1766 cents Number of recognisable fifths : 0 Length of longest harmonic part : 2 at degree 9 Length of longest subharmonic part : 2 at degree 6 Formal octave complements present : 1 = 10.0000% Scale is differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.022123 Average absolute harmonicity : 0.147161 Specific harmonicity : 0.094630 Fundamental : 1/560, -9.1293 octaves, 0.4672 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 1.108800E+05, 16.75864 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 305.5, average 30.55000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.97381, average 1.19738 Sum of Tenney's harmonic distance : 22.96656, average 2.29666 Vogel's harmonic complexity : 20.00000 Wille's k value : 346 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 159.16691, average 2.89394 Lattice compactness (without 2's) : 100.87664, average 1.83412 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.40000 16 1 3: 0 .. 2 1.20000 12 1 5: -1 .. 0 -0.40000 4 1 7: -1 .. 0 -0.40000 4 1 11: 0 .. 1 0.60000 6 6 Average exponent except 2's : 10 / 10 = 1.00000 Average absolute exponent except 2's: 26 / 10 = 2.60000
FIT/MODE
10: 1 0 2 0 1 1 1 2 0 2 N T3 SD: 52.7155 c. M: 83.9100 c. 11: 2 0 1 1 1 1 1 2 0 2 N SD: 30.6982 c. M:-54.4571 c. 12: 2 0 2 0 2 0 2 2 0 2 N D3 SD: 25.7065 c. M:-48.6821 c. 13: 2 0 2 1 1 1 2 2 0 2 N SD: 26.0016 c. M:-48.2772 c. 14: 2 0 2 1 1 1 2 2 1 2 N SD: 23.0827 c. M: 43.5449 c. 16: 2 1 2 1 1 1 2 3 1 2 N SD: 19.6413 c. M: 32.4920 c. 17: 2 1 2 1 2 0 3 3 0 3 N SD: 18.3056 c. M: 35.3824 c. 20: 3 0 3 1 2 1 3 3 1 3 N SD: 13.9310 c. M: 26.4020 c. 22: 3 1 3 1 2 1 3 4 1 3 N SD: 10.6623 c. M: 18.8557 c. 28: 4 1 4 1 3 1 4 5 1 4 N SD: 8.6652 c. M:-16.8001 c. 32: 4 1 5 2 3 1 5 5 1 5 N SD: 10.2958 c. M: 16.4100 c. 34: 5 1 4 2 4 1 5 6 1 5 N SD: 9.1427 c. M: 15.9731 c. 35: 5 1 5 2 3 2 5 6 1 5 N SD: 8.6209 c. M:-17.0545 c. 38: 5 1 6 2 3 2 6 6 1 6 N SD: 8.7907 c. M: 14.4758 c. 40: 6 1 5 3 3 2 6 7 1 6 N SD: 8.4673 c. M:-14.9958 c. 42: 6 1 6 2 4 2 6 8 1 6 N SD: 7.7759 c. M:-13.5980 c. 45: 6 2 6 2 5 2 6 8 1 7 N SD: 7.4643 c. M:-13.2450 c. 46: 6 2 6 3 4 2 7 8 1 7 N SD: 4.6398 c. M: 8.4825 c. 52: 7 2 7 3 5 2 8 9 1 8 N SD: 2.9749 c. M:-5.9057 c. 66: 9 2 9 4 6 3 10 11 2 10 N SD: 3.2070 c. M: 5.8634 c. 72: 10 2 10 4 7 3 11 12 2 11 N SD: 1.9724 c. M: 3.9100 c. 94: 13 3 13 5 9 4 14 16 3 14 N SD: 2.2124 c. M: 3.7686 c. 100: 14 3 14 5 10 4 15 17 3 15 N SD: 2.1505 c. M:-3.0858 c. 118: 16 4 16 7 11 5 18 20 3 18 N SD: 1.5402 c. M: 2.8125 c. 124: 17 4 17 7 12 5 19 21 3 19 N SD: 0.8290 c. M: 1.4673 c. 218: 30 7 30 12 21 9 33 37 6 33 N SD: 0.5765 c. M: 1.0809 c. 270: 37 9 37 15 26 11 41 46 7 41 N SD: 0.3238 c. M: 0.5598 c. 342: 47 11 47 19 33 14 52 58 9 52 N SD: 0.2846 c. M: 0.4932 c. 494: 68 16 68 27 48 20 75 84 13 75 N SD: 0.2021 c. M:-0.3165 c. 612: 84 20 84 34 59 25 93 104 16 93 N SD: 0.1938 c. M: 0.3376 c. 618: 85 20 85 34 60 25 94 105 16 94 N SD: 0.0795 c. M:-0.1384 c. 1230: 169 40 169 68 119 50 187 209 32 187 N SD: 0.0778 c. M: 0.1337 c. 1506: 207 49 207 83 146 61 229 256 39 229 N SD: 0.0562 c. M: 0.0883 c. 1724: 237 56 237 95 167 70 262 293 45 262 N SD: 0.0633 c. M: 0.1254 c. 1848: 254 60 254 102 179 75 281 314 48 281 N SD: 0.0515 c. M: 0.0883 c. 2342: 322 76 322 129 227 95 356 398 61 356 N SD: 0.0499 c. M: 0.0883 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: 40.2685 cents 3 x x x x 4 x 5 x x 6 S SD: 38.3186 cents 4 x x 5 x x x 6:7 x 8 S SD: 21.0622 cents 5 x x 6 x x 7:8 x 9:10 S SD: 12.8375 cents 6 x 7 x x 8 x 9 x 11:12 SD: 23.9144 cents 7 x 8 x 9 x 10:11:12:13:14 S SD: 11.7902 cents 8 x 9:10 x 11 x 13:14 x 16 SD: 10.5143 cents 9:10 x 11 x 12:13:14:16 x 18 S SD: 10.4398 cents 10:11 x 12:13 x 14:16 x 18:20 S SD: 9.5682 cents 11:12 x x 14:15:16:17:19:20:22 SD: 9.5484 cents 12:13:14:15 x x 17:19:21:22:24 SD: 10.0489 cents 13:14:15:16:17:18 x 20:23 x 26 SD: 9.4484 cents 14:15:16:17:18:19:20:22 x 25:28 SD: 7.7771 cents 15 x 17 x 19 x 21:24 x 27:30 SD: 7.6611 cents 16 x 18:20:21:22:23:25:28:29:32 SD: 6.0054 cents 17 x 19:21:22:23:24:27:30:31:34 SD: 4.8602 cents 18:20 x 22:23:25 x 28:32 x 36 SD: 5.6887 cents 19:21 x x 24:26:27:30 x 34:38 SD: 5.1821 cents 20:22:23:25:26 x 28:31:35:36:40 SD: 6.3823 cents 21:23:24:26:27:29:30:33:37:38:42 SD: 3.5730 cents 23:25:26:28:30:32:33:36:41 x 46 SD: 6.2972 cents 24:26:27:30:31:33:34:38:42:43:48 SD: 4.0224 cents 25 x 28:31:32:34:35:39:44:45:50 SD: 3.5483 cents 26 x 29:32:33:36:37:41:46:47:52 SD: 3.7883 cents 27:30 x 33:35:37:38:42:48:49:54 SD: 4.5489 cents 28:31:32:35:36:39:40:44 x 50:56 SD: 5.1684 cents 29:32:33:36:37:40:41:46:51:52:58 SD: 3.2346 cents 30:33:34:37:39:41:42:47:53:54:60 SD: 3.1811 cents 31:34:35:38:40:43:44:49:55:56:62 SD: 2.8641 cents 35 x 39:43:45:48:50:55:62:63:70 SD: 3.0769 cents 38:42:43:47:49:52:54:60:67:68:76 SD: 2.2944 cents 39:43:44:48:50:54:55:61:69:70:78 SD: 2.0388 cents 49:54:55:61:63:67:69:77:87:88:98 SD: 1.8798 cents 51:56:57:63:66:70:72:80:90:92:102 SD: 1.8097 cents 56:62:63:69:72:77:79:88:99:101:112 SD: 1.4591 cents 63:69:71:78:81:87:89:99:111:113:126 SD: 1.4058 cents 70:77:79:87:90:96:99:110:124:126:140 SD: 1.0887 cents 80:88:90:99:103:110:113:126:141:144:160 SD: 0.7322 cents 119:131:134:147:153:164:168:187:210:214:238 SD: 0.7162 cents 126:139:142:156:162:173:178:198:223:227:252 SD: 0.7143 cents 130:143:146:161:167:179:184:204:230:234:260 SD: 0.5302 cents 160:176:180:198:206:220:226:251:283:288:320 SD: 0.4477 cents 168:185:189:208:216:231:238:264:297:302:336 SD: 0.4235 cents 189:208:213:234:243:260:267:297:334:340:378 SD: 0.4077 cents 210:231:236:260:270:289:297:330:371:378:420 SD: 0.2767 cents 270:297:304:334:347:371:382:424:477:486:540 SD: 0.2730 cents 280:308:315:347:360:385:396:440:495:504:560 SD: 0.2496 cents 311:342:350:385:400:428:440:489:550:560:622 SD: 0.2424 cents 329:362:370:407:423:452:465:517:582:592:658 SD: 0.2410 cents 336:370:378:416:432:462:475:528:594:605:672 SD: 0.2249 cents 350:385:394:433:450:481:495:550:619:630:700 SD: 0.1660 cents 430:473:484:532:553:591:608:676:760:774:860 SD: 0.1603 cents 480:528:540:594:617:660:679:754:849:864:960 SD: 0.1220 cents 560:616:630:693:720:770:792:880:990:1008:1120 SD: 0.0000 cents