Scala analysis: neutr_pent2
Quasi-Neutral Pentatonic 2, 15/13 x 52/45 in each trichord, after Dudon
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/13 247.741053 tridecimal 5/4-tone 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 45/26 949.696054 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 52/45 250.3039 1: 15/13 247.7411 tridecimal 5/4-tone 2: 52/45 250.3039 3: 9/8 203.9100 major whole tone 4: 15/13 247.7411 tridecimal 5/4-tone 5: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 9/8 203.910 cents major whole tone 1: 2 15/13 247.741 cents tridecimal 5/4-tone 1: 2 52/45 250.304 cents 2: 1 135/104 451.651 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 2: 3 4/3 498.045 cents perfect fourth 3: 3 3/2 701.955 cents perfect fifth 3: 1 20/13 745.786 cents tridecimal semi-augmented fifth 3: 1 208/135 748.349 cents 4: 2 45/26 949.696 cents 4: 2 26/15 952.259 cents tridecimal semi-augmented sixth 4: 1 16/9 996.090 cents Pythagorean minor seventh 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 4 5 0.0 : 247.7 498.0 702.0 949.7 1200.0 247.7 : 250.3 454.2 702.0 952.3 1200.0 498.0 : 203.9 451.7 702.0 949.7 1200.0 702.0 : 247.7 498.0 745.8 996.1 1200.0 949.7 : 250.3 498.0 748.3 952.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 203.9100 .. 250.3039 cents 416/405, 46.3939 cents 9/8, 203.9100 cents 2: 451.6511 .. 498.0450 cents 416/405, 46.3939 cents 6075/5408, 201.3471 cents 3: 701.9550 .. 748.3489 cents 416/405, 46.3939 cents 9/8, 203.9100 cents 4: 949.6961 .. 996.0900 cents 416/405, 46.3939 cents 6075/5408, 201.3471 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 9/8, 203.9100 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 1.176990 Largest / Average step : 1.042933 Largest / Smallest step : 1.227522 Median interval of one step : 15/13, 247.7411 cents, amount: 2 Least squares average step : 239.06328 cents, oct.: 1195.31639 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCAB Step pattern size order : MLSML Scale is a Constant Structure, by a margin of 201.34711 cents Scale diversity : 1.185893 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.845354 Rothenberg efficiency : 0.580000 redundancy: 0.420000 Efficiency x scale size : 2.900000 Number of different interval sizes : 12 = 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 Most common intervals : 4/3, 498.0450 cents & inv., amount: 3 Scale is a chain of 2 triads 0.0 247.741 498.045 cents Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 60.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.025282 Average absolute harmonicity : 0.309541 Specific harmonicity : 0.119961 Fundamental : 1/78, -6.2854 octaves, 3.3542 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 1.404000E+04, 13.77726 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 57.0, average 11.40000 Mersenne's string divisions : 29820 Sum of van Prooijen's expressibility: 3.78355, average 0.75671 Sum of Tenney's harmonic distance : 7.51658, average 1.50332 Vogel's harmonic complexity : 15.80000 Wille's k value : 67 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 33.95892, average 2.26393 Lattice compactness (without 2's) : 24.27546, average 1.61836 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.20000 5 1 3: -1 .. 2 0.60000 5 2 5: 0 .. 1 0.40000 2 13: -1 .. 0 -0.40000 2 2 Average exponent except 2's : 3 / 5 = 0.60000 Average absolute exponent except 2's: 9 / 5 = 1.80000 Scale is weakly epimorphic with val: <5 7 11 19| Scale is weakly epimorphic with val: <5 7 12 20| Scale is weakly epimorphic with val: <5 7 13 21| Scale is JI-epimorphic with val: <5 8 11 18| Scale is JI-epimorphic with val: <5 8 12 19| = patent Scale is JI-epimorphic with val: <5 8 13 20| Scale is weakly epimorphic with val: <5 9 11 17| Scale is weakly epimorphic with val: <5 9 12 18| Scale is weakly epimorphic with val: <5 9 13 19|
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 12.7855 c. M:-18.0450 c. 14: 3 3 2 3 3 SP M ME I SD: 11.5125 c. M:-16.2407 c. Semaphore-5 19: 4 4 3 4 4 SP M ME I SD: 5.1680 c. M:-7.2182 c. Quasi-equal Pentatonic, Semaphore-5 24: 5 5 4 5 5 SP M ME I SD: 1.6025 c. M:-2.2589 c. Quasi-equal Pentatonic, Semaphore-5 29: 6 6 5 6 6 SP M ME I SD: 1.3311 c. M:-2.0281 c. Quasi-equal Pentatonic, Semaphore-5 53: 11 11 9 11 11 SP M DE I SD: 0.8119 c. M:-1.3156 c. 248: 51 52 42 51 52 SP T3 SD: 0.7592 c. M: 1.3090 c. 253: 52 53 43 52 53 SP T3 SD: 0.6896 c. M: 1.1007 c. 272: 56 57 46 56 57 SP T3 SD: 0.6776 c. M: 1.1666 c. 277: 57 58 47 57 58 SP T3 SD: 0.5694 c. M: 0.9596 c. 282: 58 59 48 58 59 SP T3 SD: 0.5489 c. M: 0.9325 c. 301: 62 63 51 62 63 SP T3 SD: 0.4959 c. M: 0.8588 c. 306: 63 64 52 63 64 SP T3 SD: 0.4297 c. M: 0.6822 c. 330: 68 69 56 68 69 SP T3 SD: 0.3530 c. M: 0.6051 c. 335: 69 70 57 69 70 SP T3 SD: 0.3360 c. M: 0.5769 c. 354: 73 74 60 73 74 SP T3 SD: 0.3197 c. M: 0.5435 c. 359: 74 75 61 74 75 SP T3 SD: 0.2466 c. M: 0.3924 c. 383: 79 80 65 79 80 SP T3 SD: 0.2016 c. M: 0.3488 c. 388: 80 81 66 80 81 SP T3 SD: 0.1838 c. M: 0.3184 c. 407: 84 85 69 84 85 SP T3 SD: 0.2061 c. M: 0.3103 c. 412: 85 86 70 85 86 SP T3 SD: 0.1110 c. M: 0.1815 c. 436: 90 91 74 90 91 SP T3 SD: 0.1039 c. M: 0.1548 c. 441: 91 92 75 91 92 SP T3 SD: 0.0786 c. M: 0.1220 c. 465: 96 97 79 96 97 SP T3 SD: 0.0149 c. M:-0.0195 c. 1424: 294 297 242 294 297 SP T3 SD: 0.0136 c. M:-0.0230 c. 1889: 390 394 321 390 394 SP T3 SD: 0.0074 c. M:-0.0128 c. 2354: 486 491 400 486 491 SP T3 SD: 0.0045 c. M:-0.0075 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 0.0000 cents 3 x 4 x 5:6 S SD: 21.7791 cents 4 x 5:6:7:8 S SD: 28.3393 cents 6:7:8:9:10:12 S SD: 13.6160 cents 12:14:16:18:21:24 S SD: 5.4107 cents 18:21:24:27:31:36 SD: 4.1924 cents 26:30:35:39:45:52 SD: 3.3134 cents 38:44:51:57:66:76 SD: 2.8455 cents 40:46:53:60:69:80 SD: 2.7176 cents 44:51:59:66:76:88 SD: 2.6085 cents 46:53:61:69:80:92 SD: 2.5685 cents 48:55:64:72:83:96 SD: 2.4341 cents 52:60:69:78:90:104 SD: 1.6687 cents 60:69:80:90:104:120 SD: 1.2646 cents 66:76:88:99:114:132 SD: 0.9902 cents 78:90:104:117:135:156 SD: 0.0000 cents