Scala analysis: xen12-wilson-15-diamond-eikosany-intersection
Intersection of Diamond & Eikosany (1 3 5 7 9 11), Figure 15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 14/11 417.507964 undecimal diminished fourth or major third 3: 4/3 498.044999 perfect fourth 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 16/11 648.682058 undecimal semi-diminished fifth 6: 3/2 701.955001 perfect fifth 7: 8/5 813.686286 minor sixth 8: 18/11 852.592059 undecimal neutral sixth 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: 7/6 266.8709 septimal minor third 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 22/21 80.5370 undecimal minor semitone 4: 21/20 84.4672 minor semitone 5: 80/77 66.1699 6: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 7: 16/15 111.7313 minor diatonic semitone 8: 45/44 38.9058 1/5-tone 9: 11/10 165.0042 Ptolemy's second, 4/5-tone 10: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 45/44 38.906 cents 1/5-tone 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 80/77 66.170 cents 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 15/14 119.443 cents major diatonic semitone 2: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 9/8 203.910 cents major whole tone 2: 1 8/7 231.174 cents septimal whole tone 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 2 9/8 203.910 cents major whole tone 3: 2 8/7 231.174 cents septimal whole tone 3: 2 6/5 315.641 cents minor third 3: 1 5/4 386.314 cents major third 3: 1 4/3 498.045 cents perfect fourth 3: 1 140/99 599.912 cents quasi-equal tritone 3: 1 77/54 614.279 cents 4: 1 90/77 270.080 cents 4: 1 33/28 284.447 cents undecimal minor third 4: 1 6/5 315.641 cents minor third 4: 1 99/80 368.914 cents 4: 1 96/77 381.811 cents 4: 1 4/3 498.045 cents perfect fourth 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 1 40/27 680.449 cents grave fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 5: 1 44/35 396.178 cents 5: 2 9/7 435.084 cents septimal major third, BP third 5: 1 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 16/11 648.682 cents undecimal semi-diminished fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 35/22 803.822 cents 5: 1 44/27 845.453 cents neutral sixth 6: 1 9/7 435.084 cents septimal major third, BP third 6: 1 27/20 519.551 cents acute fourth 6: 1 48/35 546.815 cents septimal semi-augmented fourth 6: 1 10/7 617.488 cents Euler's tritone 6: 1 3/2 701.955 cents perfect fifth 6: 1 77/48 818.189 cents 6: 1 160/99 831.086 cents 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 56/33 915.553 cents 6: 1 77/45 929.920 cents 7: 1 108/77 585.721 cents 7: 1 99/70 600.088 cents 2nd quasi-equal tritone 7: 1 3/2 701.955 cents perfect fifth 7: 1 8/5 813.686 cents minor sixth 7: 2 5/3 884.359 cents major sixth, BP sixth 7: 2 7/4 968.826 cents harmonic seventh 7: 2 16/9 996.090 cents Pythagorean minor seventh 8: 1 54/35 750.725 cents septimal semi-augmented fifth 8: 1 11/7 782.492 cents undecimal augmented fifth 8: 1 18/11 852.592 cents undecimal neutral sixth 8: 1 7/4 968.826 cents harmonic seventh 8: 1 16/9 996.090 cents Pythagorean minor seventh 8: 2 20/11 1034.996 cents large minor seventh 8: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 8: 1 28/15 1080.557 cents grave major seventh 9: 1 12/7 933.129 cents septimal major sixth 9: 1 9/5 1017.596 cents just minor seventh, BP seventh 9: 1 20/11 1034.996 cents large minor seventh 9: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 9: 1 15/8 1088.269 cents classic major seventh 9: 1 40/21 1115.533 cents acute major seventh 9: 1 21/11 1119.463 cents undecimal major seventh 9: 1 77/40 1133.830 cents 9: 1 64/33 1146.727 cents 33rd subharmonic 9: 1 88/45 1161.094 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 8.66667 = 26/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 266.9 417.5 498.0 582.5 648.7 702.0 813.7 852.6 1017.6 1200.0 266.9 : 150.6 231.2 315.6 381.8 435.1 546.8 585.7 750.7 933.1 1200.0 417.5 : 80.5 165.0 231.2 284.4 396.2 435.1 600.1 782.5 1049.4 1200.0 498.0 : 84.5 150.6 203.9 315.6 354.5 519.6 702.0 968.8 1119.5 1200.0 582.5 : 66.2 119.4 231.2 270.1 435.1 617.5 884.4 1035.0 1115.5 1200.0 648.7 : 53.3 165.0 203.9 368.9 551.3 818.2 968.8 1049.4 1133.8 1200.0 702.0 : 111.7 150.6 315.6 498.0 764.9 915.6 996.1 1080.6 1146.7 1200.0 813.7 : 38.9 203.9 386.3 653.2 803.8 884.4 968.8 1035.0 1088.3 1200.0 852.6 : 165.0 347.4 614.3 764.9 845.5 929.9 996.1 1049.4 1161.1 1200.0 1017.6: 182.4 449.3 599.9 680.4 764.9 831.1 884.4 996.1 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.9058 .. 266.8709 cents 154/135, 227.9651 cents 45/44, 38.9058 cents 2: 119.4428 .. 449.2746 cents 98/81, 329.8318 cents 45/49,-147.4281 cents 3: 203.9100 .. 614.2788 cents 308/243, 410.3688 cents 243/280,-245.3646 cents 4: 270.0799 .. 764.9159 cents 539/405, 494.8360 cents 4860/5929,-344.1990 cents 5: 354.5471 .. 845.4529 cents 968/729, 490.9059 cents 243/308,-410.3688 cents 6: 435.0841 .. 929.9201 cents 539/405, 494.8360 cents 243/308,-410.3688 cents 7: 585.7212 .. 996.0900 cents 308/243, 410.3688 cents 4860/5929,-344.1990 cents 8: 750.7254 .. 1080.5572 cents 98/81, 329.8318 cents 243/280,-245.3646 cents 9: 933.1291 .. 1161.0942 cents 154/135, 227.9651 cents 45/49,-147.4281 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 45/44, 38.9058 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 3.084375 Largest / Average step : 2.223924 Largest / Smallest step : 6.859417 Median interval of one step : 98.09924 cents, amount: 0 Least squares average step : 119.62628 cents, oct.: 1196.26280 cents Scale is not proper Step pattern alph. order: ABCDEFGHIJ Step pattern size order : JGDECBFAHI Scale is not a Constant Structure Scale diversity : 1.670706 Lumma stability : 0.064843 Lumma impropriety factor : 0.800929 Rothenberg efficiency : 0.249444 redundancy: 0.750556 Efficiency x scale size : 2.494444 Number of different interval sizes : 64 = 7.11111 / class Number of one step interval sizes : 10 Highest interval variety : 10 Mean interval variety : 8.66667 = 26/3 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 9801/9800, 0.1766 cents Number of recognisable fifths : 2, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 3 = 30.0000% Scale is n-1 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 : 99 (O: 99 U: 99) Highest odd numerator or denominator: 11 Scale harmonicity : 0.020891 Average absolute harmonicity : 0.193003 Specific harmonicity : 0.110318 Fundamental : 1/330, -8.3663 octaves, 0.7928 Hz. Guide tone : 1008, 9.9773 octaves, 263718.570 Hz. Exponens Consonantiae : 3.326400E+05, 18.34360 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 74.0, average 7.40000 Mersenne's string divisions : 7125300 Sum of van Prooijen's expressibility: 7.42183, average 0.74218 Sum of Tenney's harmonic distance : 15.31065, average 1.53107 Vogel's harmonic complexity : 19.20000 Wille's k value : 247 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 148.87220, average 2.70677 Lattice compactness (without 2's) : 93.69880, average 1.70361 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.00000 14 1 3: -1 .. 2 0.30000 7 2 5: -1 .. 0 -0.30000 3 2 7: 0 .. 1 0.30000 3 2 11: -1 .. 0 -0.30000 3 3 Average exponent except 2's : 0 / 10 = 0.00000 Average absolute exponent except 2's: 16 / 10 = 1.60000
FIT/MODE
10: 2 1 1 1 0 1 1 0 1 2 N SD: 33.9478 c. M: 57.5963 c. 11: 2 2 0 1 1 0 1 1 1 2 N SD: 37.9164 c. M: 61.6814 c. 12: 3 1 1 1 0 1 1 1 1 2 N SD: 26.1380 c. M: 48.6821 c. 13: 3 2 0 1 1 1 1 0 2 2 N SD: 25.1123 c. M:-44.0305 c. 14: 3 2 1 1 1 0 2 0 2 2 N SD: 21.0983 c. M:-43.4566 c. 15: 3 2 1 1 1 1 1 1 2 2 N SD: 19.2417 c. M:-27.4079 c. 17: 4 2 1 1 1 1 1 1 2 3 N SD: 17.5522 c. M: 37.2157 c. 19: 4 2 2 1 1 1 2 0 3 3 N SD: 18.3955 c. M: 38.5606 c. 20: 4 3 1 2 1 1 2 0 3 3 N SD: 16.3406 c. M: 26.8709 c. 21: 5 2 2 1 1 1 2 1 3 3 N SD: 14.2999 c. M: 20.1106 c. 22: 5 3 1 2 1 1 2 1 3 3 N SD: 12.6875 c. M:-20.1352 c. 26: 6 3 2 2 1 1 3 1 3 4 N SD: 12.2173 c. M:-24.3310 c. 27: 6 3 2 2 1 2 2 1 4 4 N SD: 12.1321 c. M: 26.4598 c. 28: 6 4 2 2 1 1 3 1 4 4 N SD: 11.0717 c. M:-17.4878 c. 31: 7 4 2 2 2 1 3 1 4 5 N SD: 5.9718 c. M: 11.1447 c. 41: 9 5 3 3 2 2 4 1 6 6 N SD: 4.4511 c. M: 7.7519 c. 58: 13 7 4 4 3 3 5 2 8 9 N SD: 4.0672 c. M: 7.3027 c. 66: 15 8 4 5 4 3 6 2 9 10 N SD: 4.4252 c. M:-7.1359 c. 68: 15 9 4 5 4 3 6 2 10 10 N SD: 3.9934 c. M:-6.0214 c. 72: 16 9 5 5 4 3 7 2 10 11 N SD: 1.6514 c. M:-2.9804 c. 118: 26 15 8 8 7 5 11 4 16 18 N SD: 1.4993 c. M: 2.8512 c. 130: 29 16 9 9 7 6 12 4 18 20 N SD: 1.7596 c. M: 3.3613 c. 152: 34 19 10 11 8 7 14 5 21 23 N SD: 0.9861 c. M:-1.6983 c. 224: 50 28 15 16 12 10 21 7 31 34 N SD: 0.6674 c. M:-1.4164 c. 255: 57 32 17 18 14 11 24 8 35 39 N SD: 0.9225 c. M:-1.3644 c. 270: 60 34 18 19 15 12 25 9 37 41 N SD: 0.3303 c. M:-0.7413 c. 342: 76 43 23 24 19 15 32 11 47 52 N SD: 0.2114 c. M:-0.4407 c. 494: 110 62 33 35 27 22 46 16 68 75 N SD: 0.2269 c. M:-0.4838 c. 612: 136 77 41 43 34 27 57 20 84 93 N SD: 0.1807 c. M:-0.3491 c. 742: 165 93 50 52 41 33 69 24 102 113 N SD: 0.2117 c. M: 0.3456 c. 764: 170 96 51 54 42 34 71 25 105 116 N SD: 0.1789 c. M:-0.2931 c. 836: 186 105 56 59 46 37 78 27 115 127 N SD: 0.1369 c. M:-0.2629 c. 1084: 241 136 73 76 60 48 101 35 149 165 N SD: 0.1455 c. M: 0.2531 c. 1106: 246 139 74 78 61 49 103 36 152 168 N SD: 0.1222 c. M:-0.2136 c. 1236: 275 155 83 87 68 55 115 40 170 188 N SD: 0.0925 c. M: 0.1649 c. 1506: 335 189 101 106 83 67 140 49 207 229 N SD: 0.0623 c. M: 0.1405 c. 1578: 351 198 106 111 87 70 147 51 217 240 N SD: 0.0587 c. M: 0.1206 c. 1848: 411 232 124 130 102 82 172 60 254 281 N SD: 0.0313 c. M: 0.0638 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 3 x x x 4 S SD: 0.0000 cents 3 x x 4 x x x x 5 x 6 S SD: 10.5889 cents 4 x 5 x x x 6 x x 7:8 S SD: 14.4733 cents 5:6 x x 7 x x 8 x 9:10 S SD: 9.7541 cents 6:7 x 8 x x 9 x 10:11:12 S SD: 7.4875 cents 7:8:9 x x 10 x 11 x 13:14 SD: 13.3923 cents 8:9:10 x 11 x 12 x 13:14:16 S SD: 13.1198 cents 9 x 11:12 x 13 x 14:15:16:18 SD: 13.4845 cents 10:12:13 x 14 x 15:16 x 18:20 S SD: 8.7200 cents 11:13:14:15 x 16:17 x 18:20:22 SD: 8.8269 cents 12:14:15:16:17 x 18:19:20:22:24 S SD: 6.7948 cents 13:15 x 17:18:19:20:21 x 23:26 SD: 8.8544 cents 14:16:18:19 x 20:21:22:23:25:28 SD: 7.6219 cents 15:18:19:20:21:22:23:24:25:27:30 SD: 7.1486 cents 16:19:20:21:22:23:24 x 26:29:32 SD: 7.3148 cents 17:20:22:23:24:25:26:27:28:31:34 SD: 6.4636 cents 18:21:23:24:25:26:27:29 x 32:36 SD: 3.4941 cents 21:25:27:28:29:31:32 x 34:38:42 SD: 6.9519 cents 22:26:28:29:31:32:33:35:36:40:44 SD: 3.7631 cents 25:29:32:33:35:36:38:40:41:45:50 SD: 3.6631 cents 30:35:38:40:42:44:45:48:49:54:60 SD: 1.6882 cents 48:56:61:64:67:70:72:77:79:86:96 SD: 1.5432 cents 55:64:70:73:77:80:83:88:90:99:110 SD: 1.3853 cents 60:70:76:80:84:87:90:96:98:108:120 SD: 1.0390 cents 66:77:84:88:92:96:99:106:108:119:132 SD: 1.0379 cents 88:103:112:117:123:128:132:141:144:158:176 SD: 0.9427 cents 90:105:115:120:126:131:135:144:147:162:180 SD: 0.7665 cents 102:119:130:136:143:148:153:163:167:184:204 SD: 0.7027 cents 110:128:140:147:154:160:165:176:180:198:220 SD: 0.5977 cents 132:154:168:176:185:192:198:211:216:238:264 SD: 0.3831 cents 150:175:191:200:210:218:225:240:245:270:300 SD: 0.3614 cents 180:210:229:240:252:262:270:288:295:324:360 SD: 0.3007 cents 198:231:252:264:277:288:297:317:324:356:396 SD: 0.2556 cents 270:315:344:360:378:393:405:432:442:486:540 SD: 0.2303 cents 300:350:382:400:420:436:450:480:491:540:600 SD: 0.1693 cents 330:385:420:440:462:480:495:528:540:594:660 SD: 0.0000 cents