Scala analysis: LIMITofSEVEN
Limit of Seven
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: 8/7 231.174094 septimal whole tone 3: 5/4 386.313714 major third 4: 10/7 617.487807 Euler's tritone 5: 12/7 933.129094 septimal major sixth 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 15/14 119.4428 major diatonic semitone 2: 16/15 111.7313 minor diatonic semitone 3: 35/32 155.1396 septimal neutral second 4: 8/7 231.1741 septimal whole tone 5: 6/5 315.6413 minor third 6: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 35/32 155.140 cents septimal neutral second 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 6/5 315.641 cents minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 2 5/4 386.314 cents major third 2: 1 48/35 546.815 cents septimal semi-augmented fourth 2: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 5/4 386.314 cents major third 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 3: 1 8/5 813.686 cents minor sixth 4: 1 10/7 617.488 cents Euler's tritone 4: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 2 8/5 813.686 cents minor sixth 4: 1 12/7 933.129 cents septimal major sixth 4: 1 7/4 968.826 cents harmonic seventh 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 1 7/4 968.826 cents harmonic seventh 5: 1 64/35 1044.860 cents septimal neutral seventh 5: 1 28/15 1080.557 cents grave major seventh 5: 1 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.20000 = 26/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 119.4 231.2 386.3 617.5 933.1 1200.0 119.4 : 111.7 266.9 498.0 813.7 1080.6 1200.0 231.2 : 155.1 386.3 702.0 968.8 1088.3 1200.0 386.3 : 231.2 546.8 813.7 933.1 1044.9 1200.0 617.5 : 315.6 582.5 702.0 813.7 968.8 1200.0 933.1 : 266.9 386.3 498.0 653.2 884.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 315.6413 cents 9/8, 203.9100 cents 16/15, 111.7313 cents 2: 231.1741 .. 582.5122 cents 49/40, 351.3381 cents 20/21,-84.4672 cents 3: 386.3137 .. 813.6863 cents 32/25, 427.3726 cents 25/28,-196.1985 cents 4: 617.4878 .. 968.8259 cents 49/40, 351.3381 cents 25/28,-196.1985 cents 5: 884.3587 .. 1088.2687 cents 9/8, 203.9100 cents 20/21,-84.4672 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 1.790009 Largest / Average step : 1.578206 Largest / Smallest step : 2.825004 Median interval of one step : 193.15686 cents, amount: 0 Least squares average step : 176.66295 cents, oct.: 1059.97773 cents Scale is not proper Step pattern alph. order: ABCDEF Step pattern size order : BACDFE Scale is not a Constant Structure Scale diversity : 1.547478 Lumma stability : 0.186219 Lumma impropriety factor : 0.467776 Rothenberg efficiency : 0.450000 redundancy: 0.550000 Efficiency x scale size : 2.700000 Number of different interval sizes : 20 = 4.00000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.20000 = 26/5 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 3 Most common triad is 0.0 386.314 1088.269 cents, amount: 1 Number of recognisable fifths : 2, average 701.9550 cents Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 16.6667% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 7 Odd number limit : 35 (O: 35 U: 35) Highest odd numerator or denominator: 15 Scale harmonicity : 0.041064 Average absolute harmonicity : 0.227812 Specific harmonicity : 0.180881 Fundamental : 1/28, -4.8074 octaves, 9.3438 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 3.360000E+03, 11.71425 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 46.0, average 7.66667 Mersenne's string divisions : 421515 Sum of van Prooijen's expressibility: 4.41036, average 0.73506 Sum of Tenney's harmonic distance : 9.44184, average 1.57364 Vogel's harmonic complexity : 8.50000 Wille's k value : 17 Wilson's harmonic complexity : 15 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 53.24295, average 2.53538 Lattice compactness (without 2's) : 25.50986, average 1.21476 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.66667 10 1 3: 0 .. 1 0.33333 2 5: 0 .. 1 0.50000 3 1 7: -1 .. 0 -0.66667 4 4 Average exponent except 2's : 1 / 6 = 0.16667 Average absolute exponent except 2's: 9 / 6 = 1.50000 Scale is weakly epimorphic with val: <6 10 15 17| Scale is weakly epimorphic with val: <6 11 15 16| Scale is weakly epimorphic with val: <6 11 15 19|
FIT/MODE
6: 1 0 1 1 2 1 N D3 SD: 45.5085 c. M:-80.5572 c. 7: 1 0 1 2 1 2 N SD: 55.6616 c. M: 75.9862 c. 9: 1 1 1 2 2 2 N SD: 26.0083 c. M:-49.1789 c. 10: 1 1 1 2 3 2 N SD: 17.3132 c. M:-26.8709 c. 18: 2 1 3 3 5 4 N SD: 16.6230 c. M: 31.1741 c. 19: 2 2 2 4 5 4 N SD: 12.6705 c. M:-21.4575 c. 21: 2 2 3 4 5 5 N SD: 10.7905 c. M: 18.8434 c. 22: 2 2 3 4 6 5 N SD: 10.2980 c. M: 17.4878 c. 27: 3 2 4 5 7 6 N SD: 8.9708 c. M:-13.8905 c. 31: 3 3 4 6 8 7 N SD: 2.3466 c. M: 4.0968 c. 68: 7 6 9 13 18 15 N SD: 2.1684 c. M:-4.0866 c. 72: 7 7 9 14 19 16 N SD: 1.9135 c. M: 2.9804 c. 99: 10 9 13 19 26 22 N SD: 1.0694 c. M:-1.7693 c. 130: 13 12 17 25 34 29 N SD: 0.8163 c. M:-1.3786 c. 140: 14 13 18 27 37 31 N SD: 0.6043 c. M:-1.1566 c. 171: 17 16 22 33 45 38 N SD: 0.2420 c. M:-0.4049 c. 441: 44 41 57 85 116 98 N SD: 0.1748 c. M:-0.2851 c. 472: 47 44 61 91 124 105 N SD: 0.1597 c. M:-0.3088 c. 612: 61 57 79 118 161 136 N SD: 0.1501 c. M:-0.2042 c. 643: 64 60 83 124 169 143 N SD: 0.1394 c. M:-0.2416 c. 904: 90 84 117 174 238 201 N SD: 0.1282 c. M: 0.2312 c. 913: 91 85 118 176 240 203 N SD: 0.1468 c. M:-0.2559 c. 935: 93 87 121 180 246 208 N SD: 0.1039 c. M: 0.1616 c. 1075: 107 100 139 207 283 239 N SD: 0.0986 c. M: 0.1855 c. 1106: 110 103 143 213 291 246 N SD: 0.0762 c. M: 0.1280 c. 1205: 120 112 156 232 317 268 N SD: 0.0730 c. M: 0.1367 c. 1236: 123 115 160 238 325 275 N SD: 0.0765 c. M: 0.1194 c. 1277: 127 119 165 246 336 284 N SD: 0.0708 c. M: 0.1033 c. 1376: 137 128 178 265 362 306 N SD: 0.0382 c. M: 0.0694 c. 1547: 154 144 200 298 407 344 N SD: 0.0224 c. M: 0.0347 c. 2019: 201 188 261 389 531 449 N SD: 0.0250 c. M:-0.0456 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 42.2336 cents 3 x x 4 x 5:6 S SD: 40.6372 cents 4 x x 5:6:7:8 S SD: 22.9251 cents 5 x x 6:7:9:10 SD: 28.8884 cents 6 x 7:8:9:10:12 S SD: 30.5099 cents 7 x 8:9:10:12:14 S SD: 9.7541 cents 8 x 9:10:11:14:16 SD: 15.9951 cents 9 x 10:11:13:15:18 SD: 16.2932 cents 10:11 x 13:14:17:20 SD: 18.0216 cents 11:12:13:14:16:19:22 SD: 13.3937 cents 12:13:14:15:17:21:24 SD: 9.3160 cents 14:15:16:18:20:24:28 S SD: 8.1284 cents 16:17:18:20:23:27:32 SD: 7.0964 cents 21:23:24:26:30:36:42 SD: 6.9168 cents 23:25:26:29:33:39:46 SD: 6.7032 cents 24:26:27:30:34:41:48 SD: 6.1360 cents 25:27:29:31:36:43:50 SD: 5.9431 cents 27:29:31:34:39:46:54 SD: 4.4916 cents 28:30:32:35:40:48:56 SD: 0.0000 cents