Scala analysis: genggong
Genggong polos scale, harmonics 5 through 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6/5 315.641287 minor third 2: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 3: 8/5 813.686286 minor sixth 4: 9/5 1017.596288 just minor seventh, BP seventh 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 6/5 315.6413 minor third 2: 7/6 266.8709 septimal minor third 3: 8/7 231.1741 septimal whole tone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 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 5/4 386.314 cents major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 2 4/3 498.045 cents perfect fourth 2: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 10/7 617.488 cents Euler's tritone 3: 2 3/2 701.955 cents perfect fifth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 8/5 813.686 cents minor sixth 4: 1 5/3 884.359 cents major sixth, BP sixth 4: 1 12/7 933.129 cents septimal major sixth 4: 1 7/4 968.826 cents harmonic seventh 4: 1 16/9 996.090 cents Pythagorean minor seventh 4: 1 9/5 1017.596 cents just minor seventh, BP 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 : 315.6 582.5 813.7 1017.6 1200.0 315.6 : 266.9 498.0 702.0 884.4 1200.0 582.5 : 231.2 435.1 617.5 933.1 1200.0 813.7 : 203.9 386.3 702.0 968.8 1200.0 1017.6: 182.4 498.0 764.9 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 182.4037 .. 315.6413 cents 27/25, 133.2376 cents 10/9, 182.4037 cents 2: 386.3137 .. 582.5122 cents 28/25, 196.1985 cents 25/24, 70.6724 cents 3: 617.4878 .. 813.6863 cents 28/25, 196.1985 cents 50/49, 34.9756 cents 4: 884.3587 .. 1017.5963 cents 27/25, 133.2376 cents 25/24, 70.6724 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 10/9, 182.4037 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 1.315763 Largest / Average step : 1.315172 Largest / Smallest step : 1.730454 Median interval of one step : 8/7, 231.1741 cents, amount: 1 Least squares average step : 254.40199 cents, oct.: 1272.00997 cents Scale is strictly proper Step pattern alph. order: ABCDE Step pattern size order : EDCBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.573508 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.450940 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 Best fifths form a closed circle All steps are superparticular (epimoric) Steps are strictly decreasing Scale is harmonic, base degree is : 0 Length of longest subharmonic part : 1 at degree 0 Scale is an arithmetic sequence and a class 1 isoharmonic scale Formal octave complements present : 1 = 20.0000% Scale is differentially coherent -- Rational properties -- Prime limit : 7 Odd number limit : 9 (O: 9 U: 9) Highest odd numerator or denominator: 9 Scale harmonicity : 0.039970 Average absolute harmonicity : 0.270175 Specific harmonicity : 0.230333 Fundamental : 1/5, -2.3219 octaves, 52.3251 Hz. Guide tone : 504, 8.9773 octaves, 131859.285 Hz. Exponens Consonantiae : 2.520000E+03, 11.29921 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 26.5, average 5.30000 Mersenne's string divisions : 12012 Sum of van Prooijen's expressibility: 3.19728, average 0.63946 Sum of Tenney's harmonic distance : 6.57749, average 1.31550 Vogel's harmonic complexity : 5.20000 Wille's k value : 4 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 31.76266, average 2.11751 Lattice compactness (without 2's) : 20.77927, average 1.38528 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.00000 5 1 3: 0 .. 2 0.60000 3 5: -1 .. 0 -0.80000 4 3 7: 0 .. 1 0.20000 1 1 Average exponent except 2's : 0 / 5 = 0.00000 Average absolute exponent except 2's: 8 / 5 = 1.60000 Scale is weakly epimorphic with val: <5 7 11 13| Scale is JI-epimorphic with val: <5 8 12 14| = patent
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 75.2659 c. M: 102.5122 c. 6: 2 1 1 1 1 P M ME S SD: 39.7974 c. M:-84.3587 c. 7: 2 1 2 1 1 P M ME S SD: 38.4824 c. M: 68.2265 c. Thai mode 3 8: 2 2 1 2 1 P M ME S SD: 33.6346 c. M: 63.6863 c. Father-5 10: 3 2 2 2 1 P T3 SD: 37.0409 c. M:-62.4037 c. 11: 3 2 2 2 2 SP M ME S SD: 32.5381 c. M: 50.0499 c. 12: 3 3 2 2 2 P D3 S SD: 14.4735 c. M: 17.5963 c. Raga Harikauns, Chin: China 19: 5 4 4 3 3 SP SD: 7.7824 c. M: 14.0911 c. 27: 7 6 5 5 4 SP SD: 7.0944 c. M: 13.6863 c. 31: 8 7 6 5 5 SP SD: 5.7249 c. M: 11.1447 c. 35: 9 8 7 6 5 SP SD: 7.1367 c. M:-10.9751 c. 37: 10 8 7 6 6 SP SD: 6.8396 c. M: 12.1909 c. 41: 11 9 8 7 6 SP SD: 5.0608 c. M:-6.7940 c. 46: 12 10 9 8 7 SP SD: 4.5966 c. M: 8.5991 c. 53: 14 12 10 9 8 SP SD: 2.9471 c. M:-6.1671 c. 68: 18 15 13 12 10 SP SD: 2.9306 c. M:-5.9331 c. 72: 19 16 14 12 11 SP SD: 1.5148 c. M:-2.9804 c. 99: 26 22 19 17 15 SP SD: 0.8383 c. M: 1.5651 c. 159: 42 35 31 27 24 SP SD: 1.2083 c. M:-1.4081 c. 171: 45 38 33 29 26 SP SD: 0.1729 c. M:-0.3488 c. 441: 116 98 85 75 67 SP SD: 0.1044 c. M: 0.1993 c. 612: 161 136 118 104 93 SP SD: 0.0794 c. M: 0.1593 c. 783: 206 174 151 133 119 SP SD: 0.0842 c. M: 0.1367 c. 1106: 291 246 213 188 168 SP SD: 0.0934 c. M:-0.1280 c. 1205: 317 268 232 205 183 SP SD: 0.0871 c. M:-0.1630 c. 1236: 325 275 238 210 188 SP SD: 0.0837 c. M: 0.1206 c. 1277: 336 284 246 217 194 SP SD: 0.0894 c. M:-0.1033 c. 1308: 344 291 252 222 199 SP SD: 0.0873 c. M: 0.1651 c. 1376: 362 306 265 234 209 SP SD: 0.0699 c. M:-0.1363 c. 1407: 370 313 271 239 214 SP SD: 0.0633 c. M: 0.1123 c. 1547: 407 344 298 263 235 SP SD: 0.0621 c. M:-0.1154 c. 1578: 415 351 304 268 240 SP SD: 0.0527 c. M: 0.1058 c. 1677: 441 373 323 285 255 SP SD: 0.0638 c. M: 0.0906 c. 1718: 452 382 331 292 261 SP SD: 0.0609 c. M:-0.0987 c. 1749: 460 389 337 297 266 SP SD: 0.0500 c. M: 0.1006 c. 1848: 486 411 356 314 281 SP SD: 0.0486 c. M: 0.0638 c. 2019: 531 449 389 343 307 SP SD: 0.0396 c. M: 0.0629 c. 2190: 576 487 422 372 333 SP SD: 0.0368 c. M: 0.0620 c. 2342: 616 521 451 398 356 SP SD: 0.0322 c. M:-0.0668 c. 2361: 621 525 455 401 359 SP SD: 0.0387 c. M: 0.0613 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 55.8656 cents 3 x 4:5 x 6 S SD: 36.7110 cents 4:5 x 6:7:8 S SD: 35.2287 cents 5:6:7:8:9:10 H SD: 0.0000 cents