Scala analysis: 400_D6
Diatonic tetrachord 15/14 * 8/7 * 49/45
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: 60/49 350.616902 smaller approximation to neutral third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 49/45 147.4281 BP minor semitone 1: 15/14 119.4428 major diatonic semitone 2: 8/7 231.1741 septimal whole tone 3: 49/45 147.4281 BP minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 49/45 147.428 cents BP minor semitone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 60/49 350.617 cents smaller approximation to neutral third 2: 1 56/45 378.602 cents septimal narrow 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 : 119.4 350.6 498.0 119.4: 231.2 378.6 498.0 350.6: 147.4 266.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 231.1741 cents 16/15, 111.7313 cents 15/14, 119.4428 cents 2: 266.8709 .. 378.6022 cents 16/15, 111.7313 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 15/14, 119.4428 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.389912 Largest / Average step : 1.392489 Largest / Smallest step : 1.935438 Median interval of one step : 49/45, 147.4281 cents, amount: 1 Least squares average step : 165.34369 cents, oct.: 496.03106 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2135-tone equal temperament with octave 4/3 degrees: 512 1503 2135 Least number of segments generator : 1068 of 249.139 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1849 of 431.328 cents and inv. generated superset size: 48 = 45 more = 1600.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.281600 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.551321 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 : 686/675, 27.9853 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best minor thirds form a closed circle 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 49 Scale harmonicity : 0.028325 Average absolute harmonicity : 0.098342 Specific harmonicity : 0.125720 Fundamental : 1/294, -8.1997 octaves, 0.8899 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 1.764000E+04, 14.10656 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 72.5, average 24.16667 Mersenne's string divisions : 22127 Sum of van Prooijen's expressibility: 3.34341, average 1.11447 Sum of Tenney's harmonic distance : 6.86975, average 2.28992 Vogel's harmonic complexity : 16.33333 Wille's k value : 157 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 17.43361, average 2.90560 Lattice compactness (without 2's) : 11.63103, average 1.93851 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 7: -2 .. 0 -1.00000 3 2 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 19 19| Scale is weakly epimorphic with val: <6 10 19 20| Scale is weakly epimorphic with val: <6 11 17 19| Scale is weakly epimorphic with val: <7 10 19 19| Scale is weakly epimorphic with val: <7 10 19 20| Scale is weakly epimorphic with val: <7 11 17 19| Scale is JI-epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 12 15 19| Scale is weakly epimorphic with val: <7 12 18 20| Scale is weakly epimorphic with val: <8 12 15 20| Scale is weakly epimorphic with val: <8 12 18 19|
FIT/MODE
3: 1 1 1 SP B ME I SD: 28.9508 c. M:-46.5722 c. 4: 1 2 1 P M ME I SD: 13.5508 c. M:-22.9168 c. 7: 2 3 2 SP M ME I SD: 13.5240 c. M:-22.8558 c. 9: 2 4 3 SP T3 SD: 11.8648 c. M: 18.5869 c. 10: 2 5 3 P T3 SD: 11.5083 c. M: 19.8338 c. 11: 3 5 3 SP M DE I SD: 11.5911 c. M:-16.3876 c. 12: 3 5 4 SP T3 SD: 11.1230 c. M: 18.5869 c. 13: 3 6 4 SP T3 SD: 4.2492 c. M: 5.8165 c. 17: 4 8 5 SP T3 SD: 1.4119 c. M: 2.2557 c. 37: 9 17 11 SP T3 SD: 1.0504 c. M:-1.7033 c. 54: 13 25 16 SP T3 SD: 0.2760 c. M:-0.4569 c. 71: 17 33 21 SP T3 SD: 0.1307 c. M: 0.1926 c. 125: 30 58 37 SP T3 SD: 0.0510 c. M:-0.0880 c. 196: 47 91 58 SP T3 SD: 0.0285 c. M:-0.0474 c. 321: 77 149 95 SP T3 SD: 0.0236 c. M:-0.0316 c. 517: 124 240 153 SP T3 SD: 0.0226 c. M:-0.0376 c. 838: 201 389 248 SP T3 SD: 0.0225 c. M:-0.0353 c. 1172: 281 544 347 SP T3 SD: 0.0252 c. M: 0.0310 c. 1226: 294 569 363 SP T3 SD: 0.0212 c. M: 0.0355 c. 1297: 311 602 384 SP T3 SD: 0.0192 c. M: 0.0270 c. 1351: 324 627 400 SP T3 SD: 0.0182 c. M: 0.0316 c. 1422: 341 660 421 SP T3 SD: 0.0151 c. M: 0.0240 c. 1493: 358 693 442 SP T3 SD: 0.0147 c. M: 0.0188 c. 1547: 371 718 458 SP T3 SD: 0.0125 c. M: 0.0216 c. 1618: 388 751 479 SP T3 SD: 0.0108 c. M: 0.0154 c. 1743: 418 809 516 SP T3 SD: 0.0082 c. M: 0.0138 c. 1814: 435 842 537 SP T3 SD: 0.0080 c. M: 0.0108 c. 1868: 448 867 553 SP T3 SD: 0.0073 c. M: 0.0124 c. 1939: 465 900 574 SP T3 SD: 0.0051 c. M: 0.0076 c. 2064: 495 958 611 SP T3 SD: 0.0039 c. M: 0.0067 c. 2135: 512 991 632 SP T3 SD: 0.0034 c. M: 0.0053 c. 2260: 542 1049 669 SP T3 SD: 0.0012 c. M: 0.0020 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 5 x S SD: 35.6968 cents 5 x 6:7 S SD: 45.7111 cents 6 x 7:8 S SD: 41.8730 cents 7:8 x 9 S SD: 64.1248 cents 8:9:10:11 H SD: 35.3506 cents 9:10:11:12 H SD: 21.0142 cents 12:13:15:16 SD: 13.4999 cents 13:14:16:17 S SD: 11.9581 cents 14:15:17:19 SD: 11.2981 cents 18:19:22:24 SD: 8.6794 cents 26:28:32:35 SD: 6.9226 cents 27:29:33:36 SD: 1.7803 cents 72:77:88:96 SD: 1.5127 cents 84:90:103:112 SD: 0.8009 cents 111:119:136:148 SD: 0.4900 cents 183:196:224:244 SD: 0.2974 cents 267:286:327:356 SD: 0.1801 cents 294:315:360:392 SD: 0.0000 cents