Scala analysis: 351_C29
Chromatic tetrachord 18/17 * 85/78 * 52/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 18/17 98.954592 Arabic lute index finger 2: 15/13 247.741053 tridecimal 5/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/45 250.3039 1: 18/17 98.9546 Arabic lute index finger 2: 85/78 148.7865 3: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 85/78 148.786 cents 1: 1 52/45 250.304 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 104/85 349.259 cents 2: 1 34/27 399.090 cents septendecimal major third Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 99.0 247.7 498.0 99.0 : 148.8 399.1 498.0 247.7: 250.3 349.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.9546 .. 250.3039 cents 442/405, 151.3494 cents 18/17, 98.9546 cents 2: 247.7411 .. 399.0904 cents 442/405, 151.3494 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 18/17, 98.9546 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 1.677689 Largest / Average step : 1.507719 Largest / Smallest step : 2.529483 Median interval of one step : 85/78, 148.7865 cents, amount: 1 Least squares average step : 149.18369 cents, oct.: 447.55108 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1359-tone equal temperament with octave 4/3 degrees: 270 676 1359 Least number of segments generator : 680 of 249.206 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1223 of 448.204 cents and inv. generated superset size: 36 = 33 more = 1200.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.134053 Lumma stability : 0.397372 Lumma impropriety factor : 0.005146 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 676/675, 2.5629 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 17 Odd number limit : 85 (O: 85 U: 85) Highest odd numerator or denominator: 17 Scale harmonicity : 0.014562 Average absolute harmonicity : 0.091250 Specific harmonicity : 0.076306 Fundamental : 1/663, -9.3729 octaves, 0.3946 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 1.193400E+05, 16.86472 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 35.0, average 11.66667 Mersenne's string divisions : 140 Sum of van Prooijen's expressibility: 2.88366, average 0.96122 Sum of Tenney's harmonic distance : 5.85494, average 1.95165 Vogel's harmonic complexity : 27.66667 Wille's k value : 382 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.13258, average 2.52210 Lattice compactness (without 2's) : 12.57989, average 2.09665 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 3 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.33333 1 13: -1 .. 0 -0.33333 1 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 18 25 28| Scale is weakly epimorphic with val: <6 10 18 25 31| Scale is weakly epimorphic with val: <6 10 19 26 28| Scale is weakly epimorphic with val: <6 10 19 26 31| Scale is weakly epimorphic with val: <6 11 17 25 29| Scale is weakly epimorphic with val: <6 11 17 25 32| Scale is weakly epimorphic with val: <6 11 18 26 29| Scale is weakly epimorphic with val: <6 11 18 26 32| Scale is weakly epimorphic with val: <6 11 19 27 29| Scale is weakly epimorphic with val: <6 11 19 27 32| Scale is weakly epimorphic with val: <7 10 18 25 28| Scale is weakly epimorphic with val: <7 10 18 25 31| Scale is weakly epimorphic with val: <7 10 19 26 28| Scale is weakly epimorphic with val: <7 10 19 26 31| Scale is weakly epimorphic with val: <7 11 15 25 27| Scale is weakly epimorphic with val: <7 11 15 25 30| Scale is weakly epimorphic with val: <7 11 15 25 33| Scale is weakly epimorphic with val: <7 11 15 27 28| Scale is weakly epimorphic with val: <7 11 15 27 31| Scale is weakly epimorphic with val: <7 11 15 28 30| Scale is weakly epimorphic with val: <7 11 15 28 33| Scale is weakly epimorphic with val: <7 11 15 30 31| Scale is JI-epimorphic with val: <7 11 16 25 28| Scale is weakly epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 26 27| Scale is weakly epimorphic with val: <7 11 16 26 30| Scale is weakly epimorphic with val: <7 11 16 26 33| Scale is weakly epimorphic with val: <7 11 16 28 28| Scale is weakly epimorphic with val: <7 11 16 28 31| Scale is weakly epimorphic with val: <7 11 16 29 30| Scale is weakly epimorphic with val: <7 11 16 29 33| Scale is JI-epimorphic with val: <7 11 17 26 28| Scale is weakly epimorphic with val: <7 11 17 26 31| Scale is weakly epimorphic with val: <7 11 17 27 27| Scale is weakly epimorphic with val: <7 11 17 27 30| = patent Scale is weakly epimorphic with val: <7 11 17 27 33| Scale is weakly epimorphic with val: <7 11 17 29 31| Scale is weakly epimorphic with val: <7 11 17 30 30| Scale is weakly epimorphic with val: <7 11 17 30 33| Scale is weakly epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 25 33| Scale is JI-epimorphic with val: <7 11 18 27 28| Scale is weakly epimorphic with val: <7 11 18 27 31| Scale is weakly epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 28 33| Scale is weakly epimorphic with val: <7 11 18 30 31| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 26 27| Scale is weakly epimorphic with val: <7 11 19 26 30| Scale is weakly epimorphic with val: <7 11 19 26 33| Scale is JI-epimorphic with val: <7 11 19 28 28| Scale is weakly epimorphic with val: <7 11 19 28 31| Scale is weakly epimorphic with val: <7 11 19 29 30| Scale is weakly epimorphic with val: <7 11 19 29 33| Scale is weakly epimorphic with val: <7 12 15 26 28| Scale is weakly epimorphic with val: <7 12 16 25 27| Scale is weakly epimorphic with val: <7 12 16 25 30| Scale is weakly epimorphic with val: <7 12 16 25 33| Scale is weakly epimorphic with val: <7 12 16 27 28| Scale is weakly epimorphic with val: <7 12 17 25 28| Scale is weakly epimorphic with val: <7 12 17 26 27| Scale is weakly epimorphic with val: <7 12 17 26 30| Scale is weakly epimorphic with val: <7 12 17 26 33| Scale is weakly epimorphic with val: <7 12 17 28 28| Scale is weakly epimorphic with val: <7 12 18 26 28| Scale is weakly epimorphic with val: <7 12 18 27 27| Scale is weakly epimorphic with val: <7 12 18 27 30| Scale is weakly epimorphic with val: <7 12 18 27 33| Scale is weakly epimorphic with val: <7 12 19 27 28| Scale is weakly epimorphic with val: <7 12 19 28 30| Scale is weakly epimorphic with val: <7 12 19 28 33| Scale is weakly epimorphic with val: <8 11 15 25 27| Scale is weakly epimorphic with val: <8 11 16 26 27| Scale is weakly epimorphic with val: <8 11 17 25 29| Scale is weakly epimorphic with val: <8 11 17 25 32| Scale is weakly epimorphic with val: <8 11 17 27 27| Scale is weakly epimorphic with val: <8 11 18 25 27| Scale is weakly epimorphic with val: <8 11 18 26 29| Scale is weakly epimorphic with val: <8 11 18 26 32| Scale is weakly epimorphic with val: <8 11 19 26 27| Scale is weakly epimorphic with val: <8 11 19 27 29| Scale is weakly epimorphic with val: <8 11 19 27 32| Scale is weakly epimorphic with val: <8 12 15 25 29| Scale is weakly epimorphic with val: <8 12 15 28 29| Scale is weakly epimorphic with val: <8 12 16 25 27| Scale is weakly epimorphic with val: <8 12 16 25 30| Scale is weakly epimorphic with val: <8 12 16 25 33| Scale is weakly epimorphic with val: <8 12 16 26 29| Scale is weakly epimorphic with val: <8 12 16 29 29| Scale is weakly epimorphic with val: <8 12 17 26 27| Scale is weakly epimorphic with val: <8 12 17 26 30| Scale is weakly epimorphic with val: <8 12 17 26 33| Scale is weakly epimorphic with val: <8 12 17 27 29| Scale is weakly epimorphic with val: <8 12 18 25 29| Scale is weakly epimorphic with val: <8 12 18 27 27| Scale is weakly epimorphic with val: <8 12 18 27 30| Scale is weakly epimorphic with val: <8 12 18 27 33| Scale is weakly epimorphic with val: <8 12 18 28 29| Scale is weakly epimorphic with val: <8 12 19 26 29| Scale is weakly epimorphic with val: <8 12 19 28 30| Scale is weakly epimorphic with val: <8 12 19 28 33| Scale is weakly epimorphic with val: <8 12 19 29 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 74.0971 c. M: 98.9546 c. 4: 1 1 2 P M ME S SD: 14.7737 c. M:-25.5567 c. 6: 1 2 3 P T3 SD: 9.2367 c. M: 15.9471 c. 10: 2 3 5 P T3 SD: 0.8307 c. M:-1.2814 c. 86: 17 26 43 P T3 SD: 0.7950 c. M:-1.2814 c. 96: 19 29 48 P T3 SD: 0.7722 c. M:-1.2814 c. 101: 20 30 51 N T3 SD: 0.7100 c. M: 1.1841 c. 105: 21 31 53 N T3 SD: 0.7341 c. M: 1.0902 c. 111: 22 33 56 N T3 SD: 0.5729 c. M: 0.9620 c. 115: 23 34 58 N T3 SD: 0.6350 c. M: 0.8840 c. 121: 24 36 61 N T3 SD: 0.4588 c. M: 0.7766 c. 125: 25 37 63 N T3 SD: 0.5578 c. M: 0.7107 c. 131: 26 39 66 N T3 SD: 0.3629 c. M: 0.6195 c. 141: 28 42 71 N T3 SD: 0.2814 c. M: 0.4847 c. 151: 30 45 76 N T3 SD: 0.2123 c. M: 0.3677 c. 161: 32 48 81 N T3 SD: 0.1545 c. M: 0.2653 c. 171: 34 51 86 N T3 SD: 0.1091 c. M: 0.1748 c. 181: 36 54 91 N T3 SD: 0.0811 c. M:-0.1041 c. 191: 38 57 96 N T3 SD: 0.0778 c. M:-0.1329 c. 372: 74 111 187 N T3 SD: 0.0762 c. M:-0.1189 c. 378: 75 113 190 N T3 SD: 0.0813 c. M: 0.1361 c. 388: 77 116 195 N T3 SD: 0.0668 c. M: 0.1158 c. 398: 79 119 200 N T3 SD: 0.0583 c. M: 0.0964 c. 408: 81 122 205 N T3 SD: 0.0571 c. M: 0.0780 c. 549: 109 164 276 N T3 SD: 0.0616 c. M: 0.0793 c. 559: 111 167 281 N T3 SD: 0.0463 c. M: 0.0584 c. 569: 113 170 286 N T3 SD: 0.0321 c. M: 0.0458 c. 579: 115 173 291 N T3 SD: 0.0201 c. M: 0.0337 c. 589: 117 176 296 N T3 SD: 0.0148 c. M: 0.0221 c. 760: 151 227 382 N T3 SD: 0.0169 c. M: 0.0292 c. 770: 153 230 387 N T3 SD: 0.0083 c. M: 0.0122 c. 780: 155 233 392 N T3 SD: 0.0095 c. M:-0.0159 c. 1349: 268 403 678 N T3 SD: 0.0085 c. M: 0.0107 c. 1359: 270 406 683 N T3 SD: 0.0031 c. M: 0.0053 c. 2129: 423 636 1070 N T3 SD: 0.0030 c. M: 0.0052 c. 2139: 425 639 1075 N T3 SD: 0.0015 c. M:-0.0025 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 54.1875 cents 6 x 7:8 S SD: 9.5649 cents 7 x 8:9 S SD: 32.5520 cents 8 x 9:11 SD: 34.4934 cents 9 x 10:12 S SD: 32.6687 cents 11:12:13:15 SD: 25.6133 cents 12:13:14:16 S SD: 14.6649 cents 14:15:16:19 SD: 13.4708 cents 15:16:17:20 SD: 11.1933 cents 18:19:21:24 SD: 6.6214 cents 32:34:37:43 SD: 5.0608 cents 33:35:38:44 SD: 1.5179 cents 51:54:59:68 SD: 1.5067 cents 84:89:97:112 SD: 0.5960 cents 117:124:135:156 SD: 0.5478 cents 189:200:218:252 SD: 0.3957 cents 222:235:256:296 SD: 0.3756 cents 240:254:277:320 SD: 0.3116 cents 273:289:315:364 SD: 0.1174 cents 357:378:412:476 SD: 0.1078 cents 390:413:450:520 SD: 0.0822 cents