Scala analysis: cw12_11
CalkinWilf(<12 19 28 34 42|)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 8/7 231.174094 septimal whole tone 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 7/4 968.825906 harmonic seventh 11: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 22/21 80.5370 undecimal minor semitone 3: 21/20 84.4672 minor semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 16/15 111.7313 minor diatonic semitone 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 21/20 84.4672 minor semitone 11: 22/21 80.5370 undecimal minor semitone 12: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 22/21 80.537 cents undecimal minor semitone 1: 3 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 2 35/32 155.140 cents septimal neutral second 2: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 2 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 2: 1 9/8 203.910 cents major whole tone 2: 3 8/7 231.174 cents septimal whole tone 2: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 3: 2 55/48 235.677 cents undecimal semi-augmented whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 4 6/5 315.641 cents minor third 3: 2 96/77 381.811 cents 4: 2 11/9 347.408 cents undecimal neutral third 4: 1 49/40 351.338 cents larger approximation to neutral third 4: 5 5/4 386.314 cents major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 1 64/49 462.348 cents 2 septatones or septatonic major third 4: 2 72/55 466.278 cents undecimal semi-diminished fourth 5: 1 77/60 431.875 cents 5: 1 55/42 466.851 cents 5: 2 21/16 470.781 cents narrow fourth 5: 4 4/3 498.045 cents perfect fourth 5: 2 15/11 536.951 cents undecimal augmented fourth 5: 2 48/35 546.815 cents septimal semi-augmented fourth 6: 2 11/8 551.318 cents undecimal semi-augmented fourth 6: 1 25/18 568.717 cents classic augmented fourth 6: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 3 10/7 617.488 cents Euler's tritone 6: 1 36/25 631.283 cents classic diminished fifth 6: 2 16/11 648.682 cents undecimal semi-diminished fifth 7: 2 35/24 653.185 cents septimal semi-diminished fifth 7: 2 22/15 663.049 cents undecimal diminished fifth 7: 4 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 7: 1 84/55 733.149 cents 7: 1 120/77 768.125 cents 8: 2 55/36 733.722 cents undecimal semi-augmented fifth 8: 1 49/32 737.652 cents 8: 1 25/16 772.627 cents classic augmented fifth 8: 5 8/5 813.686 cents minor sixth 8: 1 80/49 848.662 cents smaller approximation to neutral sixth 8: 2 18/11 852.592 cents undecimal neutral sixth 9: 2 77/48 818.189 cents 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 3 12/7 933.129 cents septimal major sixth 9: 2 96/55 964.323 cents 10: 1 121/72 898.726 cents 10: 3 7/4 968.826 cents harmonic seventh 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 1 25/14 1003.802 cents middle minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 20/11 1034.996 cents large minor seventh 10: 2 64/35 1044.860 cents septimal neutral seventh 11: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 11: 1 28/15 1080.557 cents grave major seventh 11: 2 15/8 1088.269 cents classic major seventh 11: 3 40/21 1115.533 cents acute major seventh 11: 2 21/11 1119.463 cents undecimal major seventh 11: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 150.6 231.2 315.6 386.3 498.0 582.5 702.0 813.7 884.4 968.8 1049.4 1200.0 150.6 : 80.5 165.0 235.7 347.4 431.9 551.3 663.0 733.7 818.2 898.7 1049.4 1200.0 231.2 : 84.5 155.1 266.9 351.3 470.8 582.5 653.2 737.7 818.2 968.8 1119.5 1200.0 315.6 : 70.7 182.4 266.9 386.3 498.0 568.7 653.2 733.7 884.4 1035.0 1115.5 1200.0 386.3 : 111.7 196.2 315.6 427.4 498.0 582.5 663.0 813.7 964.3 1044.9 1129.3 1200.0 498.0 : 84.5 203.9 315.6 386.3 470.8 551.3 702.0 852.6 933.1 1017.6 1088.3 1200.0 582.5 : 119.4 231.2 301.8 386.3 466.9 617.5 768.1 848.7 933.1 1003.8 1115.5 1200.0 702.0 : 111.7 182.4 266.9 347.4 498.0 648.7 729.2 813.7 884.4 996.1 1080.6 1200.0 813.7 : 70.7 155.1 235.7 386.3 537.0 617.5 702.0 772.6 884.4 968.8 1088.3 1200.0 884.4 : 84.5 165.0 315.6 466.3 546.8 631.3 702.0 813.7 898.2 1017.6 1129.3 1200.0 968.8 : 80.5 231.2 381.8 462.3 546.8 617.5 729.2 813.7 933.1 1044.9 1115.5 1200.0 1049.4: 150.6 301.3 381.8 466.3 537.0 648.7 733.1 852.6 964.3 1035.0 1119.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 150.6371 cents 288/275, 79.9646 cents 25/24, 70.6724 cents 2: 155.1396 .. 301.2741 cents 4608/4235, 146.1345 cents 385/384, 4.5026 cents 3: 235.6767 .. 381.8112 cents 4608/4235, 146.1345 cents 6655/6912,-65.5975 cents 4: 347.4079 .. 466.2783 cents 648/605, 118.8704 cents 847/864,-34.4032 cents 5: 431.8751 .. 546.8154 cents 576/539, 114.9402 cents 847/864,-34.4032 cents 6: 551.3179 .. 648.6821 cents 128/121, 97.3641 cents 385/384, 4.5026 cents 7: 653.1846 .. 768.1249 cents 576/539, 114.9402 cents 385/384, 4.5026 cents 8: 733.7217 .. 852.5921 cents 648/605, 118.8704 cents 847/864,-34.4032 cents 9: 818.1888 .. 964.3233 cents 4608/4235, 146.1345 cents 847/864,-34.4032 cents 10: 898.7259 .. 1044.8604 cents 4608/4235, 146.1345 cents 6655/6912,-65.5975 cents 11: 1049.3629 .. 1129.3276 cents 288/275, 79.9646 cents 385/384, 4.5026 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 12/11, 150.6371 cents Average / Smallest step : 1.414979 Largest / Average step : 1.506371 Largest / Smallest step : 2.131483 Median interval of one step : 21/20, 84.4672 cents, amount: 3 Most common interval of one step : 21/20, 84.4672 cents, amount: 3 Least squares average step : 98.62172 cents, oct.: 1183.46063 cents Scale is not proper Step pattern alph. order: ABCDECFEDCBA Step pattern size order : FBCADCEDACBF Scale is a Constant Structure, by a margin of 0.57240 cents Scale diversity : 1.467382 Lumma stability : 0.132796 Lumma impropriety factor : 0.224006 Rothenberg efficiency : 0.253072 redundancy: 0.746928 Efficiency x scale size : 3.036869 Number of different interval sizes : 66 = 6.00000 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 6.00000 = 6 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 3025/3024, 0.5724 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 5 Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 1 3 5 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 11 = 91.6667% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 11 Odd number limit : 121 (O: 121 U: 121) Highest odd numerator or denominator: 11 Scale harmonicity : 0.012489 Average absolute harmonicity : 0.185684 Specific harmonicity : 0.117616 Fundamental : 1/4620, -12.1737 octaves, 0.0566 Hz. Guide tone : 9240, 13.1737 octaves, 2417420.223 Hz. Exponens Consonantiae : 4.268880E+07, 25.34735 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 67.0, average 5.58333 Mersenne's string divisions : 140900760 Sum of van Prooijen's expressibility: 8.36820, average 0.69735 Sum of Tenney's harmonic distance : 16.39420, average 1.36618 Vogel's harmonic complexity : 28.66667 Wille's k value : 4042 Wilson's harmonic complexity : 52 Rectangular lattice diameter : 8 Triangular lattice diameter : 2 Lattice compactness : 211.91331, average 2.71684 Lattice compactness (without 2's) : 120.49792, average 1.54485 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.50000 18 1 3: -1 .. 1 0.00000 6 2 5: -1 .. 1 -0.08333 5 4 7: -1 .. 1 0.08333 3 3 11: -1 .. 1 0.00000 2 2 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 16 / 12 = 1.33333 Scale is weakly epimorphic with val: <12 17 26 32 40| Scale is weakly epimorphic with val: <12 17 26 32 42| Scale is weakly epimorphic with val: <12 17 28 34 44| Scale is JI-epimorphic with val: <12 19 28 34 42| = patent Scale is weakly epimorphic with val: <12 19 28 34 44| Scale is weakly epimorphic with val: <12 20 29 35 42| Scale is weakly epimorphic with val: <12 21 25 31 43| Scale is weakly epimorphic with val: <12 21 26 32 44| Scale is weakly epimorphic with val: <12 21 28 34 44| Scale is weakly epimorphic with val: <12 21 29 35 43| Scale is weakly epimorphic with val: <12 21 31 37 41|
FIT/MODE
12: 2 0 1 1 1 1 1 1 1 1 1 1 N T3 SD: 26.0158 c. M:-50.6371 c. 15: 2 1 1 1 1 1 2 1 1 1 1 2 N D3 SD: 12.5890 c. M: 22.5122 c. 22: 3 1 2 1 2 2 2 2 1 2 1 3 N I SD: 10.7789 c. M:-17.4878 c. 27: 3 2 2 2 2 2 3 2 2 2 2 3 P D3 SD: 10.6648 c. M:-17.3037 c. 29: 4 2 2 1 3 2 3 3 1 2 2 4 N SD: 12.5924 c. M:-17.1018 c. 31: 4 2 2 2 3 2 3 3 2 2 2 4 N SD: 3.7326 c. M: 5.9639 c. 56: 7 4 4 3 5 4 6 5 3 4 4 7 N SD: 3.8633 c. M: 5.7873 c. 72: 9 5 5 4 7 5 7 7 4 5 5 9 N SD: 1.7871 c. M: 2.9804 c. 103: 13 7 7 6 10 7 10 10 6 7 7 13 N SD: 1.6920 c. M:-2.9259 c. 118: 15 8 8 7 11 8 12 11 7 8 8 15 N SD: 1.5995 c. M: 2.8512 c. 130: 16 9 9 8 12 9 13 12 8 9 9 16 N SD: 1.5602 c. M:-2.9448 c. 149: 19 10 10 9 14 10 15 14 9 10 10 19 N SD: 1.7782 c. M: 2.6464 c. 152: 19 10 11 9 14 11 15 14 9 11 10 19 N SD: 1.1229 c. M: 2.2267 c. 183: 23 12 13 11 17 13 18 17 11 13 12 23 N SD: 0.8776 c. M:-1.6659 c. 198: 25 13 14 12 18 14 20 18 12 14 13 25 N SD: 0.9675 c. M:-1.5651 c. 217: 27 15 15 13 20 15 22 20 13 15 15 27 N SD: 0.9666 c. M: 1.8670 c. 224: 28 15 16 13 21 16 22 21 13 16 15 28 N SD: 0.6645 c. M:-1.4164 c. 239: 30 16 17 14 22 17 24 22 14 17 16 30 N SD: 0.5072 c. M: 0.9739 c. 270: 34 18 19 16 25 19 27 25 16 19 18 34 N SD: 0.2811 c. M:-0.4741 c. 342: 43 23 24 20 32 24 34 32 20 24 23 43 N SD: 0.2605 c. M:-0.4049 c. 494: 62 33 35 29 46 35 49 46 29 35 33 62 N SD: 0.2291 c. M:-0.4838 c. 525: 66 35 37 31 49 37 52 49 31 37 35 66 N SD: 0.2282 c. M:-0.3450 c. 581: 73 39 41 34 54 41 58 54 34 41 39 73 N SD: 0.2099 c. M:-0.3656 c. 612: 77 41 43 36 57 43 61 57 36 43 41 77 N SD: 0.1701 c. M:-0.3433 c. 742: 93 50 52 44 69 52 74 69 44 52 50 93 N SD: 0.1974 c. M: 0.3020 c. 764: 96 51 54 45 71 54 76 71 45 54 51 96 N SD: 0.1602 c. M:-0.2840 c. 814: 102 55 57 48 76 57 81 76 48 57 55 102 N SD: 0.2063 c. M:-0.2755 c. 836: 105 56 59 49 78 59 83 78 49 59 56 105 N SD: 0.1329 c. M:-0.2629 c. 867: 109 58 61 51 81 61 86 81 51 61 58 109 N SD: 0.1580 c. M:-0.2280 c. 966: 121 65 68 57 90 68 96 90 57 68 65 121 N SD: 0.1565 c. M:-0.3265 c. 1053: 132 71 74 62 98 74 105 98 62 74 71 132 N SD: 0.1219 c. M:-0.2097 c. 1106: 139 74 78 65 103 78 110 103 65 78 74 139 N SD: 0.0976 c. M:-0.1767 c. 1236: 155 83 87 73 115 87 123 115 73 87 83 155 N SD: 0.0956 c. M:-0.1516 c. 1323: 166 89 93 78 123 93 132 123 78 93 89 166 N SD: 0.0937 c. M: 0.1993 c. 1475: 185 99 104 87 137 104 147 137 87 104 99 185 N SD: 0.1078 c. M:-0.1467 c. 1506: 189 101 106 89 140 106 150 140 89 106 101 189 N SD: 0.0856 c. M: 0.1405 c. 1547: 194 104 109 91 144 109 154 144 91 109 104 194 N SD: 0.0721 c. M:-0.1522 c. 1578: 198 106 111 93 147 111 157 147 93 111 106 198 N SD: 0.0410 c. M:-0.0667 c. 1848: 232 124 130 109 172 130 184 172 109 130 124 232 N SD: 0.0340 c. M: 0.0569 c.
FIT/HARMONIC
1 x x 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 x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.0000 cents 5 x x 6 x x 7 x 8 x x 9:10 S SD: 6.3533 cents 6 x 7 x x 8 x 9 x 10 x 11:12 S SD: 5.9495 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 11.3822 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.8567 cents 9:10 x 11 x 12:13 x 14:15:16:17:18 S SD: 11.5141 cents 10:11 x 12 x 13:14:15:16:17 x 18:20 S SD: 7.2962 cents 11:12 x 13:14:15 x 17 x 18:19:20:22 SD: 9.6763 cents 12:13:14 x 15:16:17:18:19:20:21:22:24 S SD: 4.2331 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 7.2658 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 5.8599 cents 17 x 19:20:21:23:24:26:27:28:30:31:34 SD: 7.0089 cents 18:20:21:22:23:24:25:27:29:30:32:33:36 SD: 6.3561 cents 19:21:22:23:24:25:27:29:30:32:33:35:38 SD: 5.7585 cents 20:22:23:24:25:27:28:30:32:33:35:37:40 SD: 3.0431 cents 30:33:34:36:38:40:42:45:48:50:53:55:60 SD: 2.9004 cents 35:38:40:42:44:47:49:53:56:58:61:64:70 SD: 2.2906 cents 36:39:41:43:45:48:50:54:58:60:63:66:72 SD: 2.0073 cents 40:44:46:48:50:53:56:60:64:67:70:73:80 SD: 2.0023 cents 44:48:50:53:55:59:62:66:70:73:77:81:88 SD: 1.9938 cents 48:52:55:58:60:64:67:72:77:80:84:88:96 SD: 1.5729 cents 55:60:63:66:69:73:77:83:88:92:96:101:110 SD: 1.4301 cents 60:65:69:72:75:80:84:90:96:100:105:110:120 SD: 1.3486 cents 64:70:73:77:80:85:90:96:102:107:112:117:128 SD: 1.3352 cents 65:71:74:78:81:87:91:98:104:108:114:119:130 SD: 1.3157 cents 68:74:78:82:85:91:95:102:109:113:119:125:136 SD: 1.2942 cents 72:79:82:86:90:96:101:108:115:120:126:132:144 SD: 1.2400 cents 75:82:86:90:94:100:105:113:120:125:131:138:150 SD: 1.1135 cents 76:83:87:91:95:101:106:114:122:127:133:139:152 SD: 1.0911 cents 80:87:91:96:100:107:112:120:128:133:140:147:160 SD: 1.0506 cents 84:92:96:101:105:112:118:126:134:140:147:154:168 SD: 0.9128 cents 90:98:103:108:113:120:126:135:144:150:158:165:180 SD: 0.8544 cents 96:105:110:115:120:128:134:144:154:160:168:176:192 SD: 0.8186 cents 100:109:114:120:125:133:140:150:160:167:175:183:200 SD: 0.6537 cents 120:131:137:144:150:160:168:180:192:200:210:220:240 SD: 0.1807 cents 300:327:343:360:375:400:420:450:480:500:525:550:600 SD: 0.1345 cents 420:458:480:504:525:560:588:630:672:700:735:770:840 SD: 0.0573 cents 540:589:617:648:675:720:756:810:864:900:945:990:1080 SD: 0.0401 cents