Scala analysis: xen07-harrison-thoughts-7
Slendro with steps 5/4, 16/15, 9/8, 81/64, 256/243
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 243/128 1109.775004 Pythagorean major seventh 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 5/4 386.3137 major third 2: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 81/64 407.8200 Pythagorean major third 5: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 1 5/4 386.314 cents major third 1: 1 81/64 407.820 cents Pythagorean major third 2: 1 6/5 315.641 cents minor third 2: 1 320/243 476.539 cents grave fourth 2: 2 4/3 498.045 cents perfect fourth 2: 1 729/512 611.730 cents Pythagorean tritone 3: 1 1024/729 588.270 cents Pythagorean diminished fifth 3: 2 3/2 701.955 cents perfect fifth 3: 1 243/160 723.461 cents acute fifth 3: 1 5/3 884.359 cents major sixth, BP sixth 4: 1 128/81 792.180 cents Pythagorean minor sixth 4: 1 8/5 813.686 cents minor sixth 4: 1 16/9 996.090 cents Pythagorean minor seventh 4: 1 15/8 1088.269 cents classic major seventh 4: 1 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.50000 = 9/2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 386.3 498.0 702.0 1109.8 1200.0 386.3 : 111.7 315.6 723.5 813.7 1200.0 498.0 : 203.9 611.7 702.0 1088.3 1200.0 702.0 : 407.8 498.0 884.4 996.1 1200.0 1109.8: 90.2 476.5 588.3 792.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 407.8200 cents 19683/16384, 317.5950 cents 256/243, 90.2250 cents 2: 315.6413 .. 611.7300 cents 1215/1024, 296.0887 cents 128/135,-92.1787 cents 3: 588.2700 .. 884.3587 cents 1215/1024, 296.0887 cents 524288/531441,-23.4600 cents 4: 792.1800 .. 1109.7750 cents 19683/16384, 317.5950 cents 128/135,-92.1787 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 81/64, 407.8200 cents Average / Smallest step : 2.660017 Largest / Average step : 1.699250 Largest / Smallest step : 4.520034 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 253.22489 cents, oct.: 1266.12443 cents Scale is not proper Step pattern alph. order: ABCDE Step pattern size order : DBCEA Scale is a Constant Structure, by a margin of 23.46001 cents Scale diversity : 1.674357 Lumma stability : 0.150375 Lumma impropriety factor : 0.173181 Rothenberg efficiency : 0.440000 redundancy: 0.560000 Efficiency x scale size : 2.200000 Number of different interval sizes : 18 = 4.50000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.50000 = 9/2 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 81/80, 21.5063 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 2 Most common triad is 0.0 498.045 701.955 cents, amount: 1 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 : 1 at degree 0 Formal octave complements present : 3 = 60.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 243 Scale harmonicity : 0.031847 Average absolute harmonicity : 0.331048 Specific harmonicity : 0.205714 Fundamental : 1/384, -8.5850 octaves, 0.6813 Hz. Guide tone : 4860, 12.2467 octaves, 1271500.247 Hz. Exponens Consonantiae : 1.866240E+06, 20.83170 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 197.5, average 39.50000 Mersenne's string divisions : 16695 Sum of van Prooijen's expressibility: 4.03882, average 0.80776 Sum of Tenney's harmonic distance : 7.95221, average 1.59044 Vogel's harmonic complexity : 12.60000 Wille's k value : 364 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 6 Lattice compactness : 66.48464, average 4.43231 Lattice compactness (without 2's) : 35.92745, average 2.39516 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 2 -1.40000 13 1 3: -1 .. 5 1.00000 7 3 5: 0 .. 1 0.20000 1 1 Average exponent except 2's : 6 / 5 = 1.20000 Average absolute exponent except 2's: 8 / 5 = 1.60000
FIT/MODE
5: 2 0 1 2 0 N T3 SD: 59.2772 c. M:-93.6863 c. 7: 2 1 1 2 1 P M ME S SD: 42.4500 c. M: 81.2036 c. Thai mode 6 9: 3 1 1 3 1 N M DE S SD: 30.1203 c. M: 43.1083 c. Pelog Pancanada: Sunda 10: 3 1 2 3 1 P T3 SD: 21.1197 c. M: 29.7750 c. Pelog Degung: Sunda 12: 4 1 2 4 1 N T3 SD: 7.6225 c. M:-13.6863 c. Ionian Pentatonic, Raga Gambhiranata, Pelog Degung Modern, Ryukyu: Japan, Vong co: Vietnam, Batti Major: Ethiopia 29: 9 3 5 10 2 N SD: 7.1192 c. M: 13.8999 c. 31: 10 3 5 11 2 N SD: 6.6073 c. M:-12.8056 c. 37: 12 3 7 12 3 N T3 SD: 8.0683 c. M:-11.5585 c. 38: 12 4 6 13 3 N SD: 5.9804 c. M: 7.3663 c. 41: 13 4 7 14 3 N SD: 2.8378 c. M: 5.8259 c. 53: 17 5 9 18 4 N SD: 0.6493 c. M: 1.4081 c. 118: 38 11 20 40 9 N SD: 0.6070 c. M: 1.3004 c. 171: 55 16 29 58 13 N SD: 0.4916 c. M: 1.0031 c. 224: 72 21 38 76 17 N SD: 0.4760 c. M: 0.8464 c. 255: 82 24 43 87 19 N SD: 0.6418 c. M:-0.8132 c. 267: 86 25 45 91 20 N SD: 0.5545 c. M:-0.8314 c. 277: 89 26 47 94 21 N SD: 0.4849 c. M: 0.7541 c. 304: 98 28 52 103 23 N SD: 0.5502 c. M: 0.6766 c. 308: 99 29 52 105 23 N SD: 0.5654 c. M:-0.6563 c. 320: 103 30 54 109 24 N SD: 0.4580 c. M:-0.7050 c. 335: 108 31 57 114 25 N SD: 0.3984 c. M:-0.6728 c. 345: 111 32 59 117 26 N SD: 0.4359 c. M:-0.6537 c. 357: 115 33 61 121 27 N SD: 0.4430 c. M:-0.5660 c. 373: 120 35 63 127 28 N SD: 0.4101 c. M:-0.6145 c. 376: 121 35 64 128 28 N SD: 0.4063 c. M:-0.8633 c. 388: 125 36 66 132 29 N SD: 0.2790 c. M:-0.5343 c. 410: 132 38 70 139 31 N SD: 0.3811 c. M: 0.5067 c. 429: 138 40 73 146 32 N SD: 0.3581 c. M:-0.7145 c. 441: 142 41 75 150 33 N SD: 0.2027 c. M:-0.4291 c. 453: 146 42 77 154 34 N SD: 0.2107 c. M:-0.4413 c. 494: 159 46 84 168 37 N SD: 0.1648 c. M:-0.3465 c. 506: 163 47 86 172 38 N SD: 0.1213 c. M:-0.2476 c. 559: 180 52 95 190 42 N SD: 0.0503 c. M:-0.0906 c. 612: 197 57 104 208 46 N SD: 0.0221 c. M: 0.0392 c. 1171: 377 109 199 398 88 N SD: 0.0235 c. M:-0.0457 c. 1783: 574 166 303 606 134 N SD: 0.0186 c. M:-0.0399 c. 2395: 771 223 407 814 180 N SD: 0.0177 c. M:-0.0371 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 4:5 x 6 S SD: 60.8012 cents 4:5 x 6 x 8 S SD: 0.0000 cents 5:6:7:8 x 10 S SD: 39.2215 cents 6 x 8:9:11:12 SD: 15.1030 cents 7:9 x 11:13:14 SD: 25.3899 cents 8:10:11:12:15:16 S SD: 11.4900 cents 10 x 13:15:19:20 SD: 10.9635 cents 12:15:16:18:23:24 SD: 3.3089 cents 28:35:37:42:53:56 SD: 3.2684 cents 32:40:43:48:61:64 SD: 3.0467 cents 36:45:48:54:68:72 SD: 1.7459 cents 48:60:64:72:91:96 SD: 0.4753 cents 60:75:80:90:114:120 SD: 0.2849 cents 108:135:144:162:205:216 SD: 0.0528 cents 276:345:368:414:524:552 SD: 0.0206 cents 384:480:512:576:729:768 SD: 0.0000 cents