Scala analysis: dwarf6_7
Dwarf(<6 10 14 17|)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 5/4 386.313714 major third 3: 10/7 617.487807 Euler's tritone 4: 3/2 701.955001 perfect fifth 5: 12/7 933.129094 septimal major sixth 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 8/7 231.1741 septimal whole tone 2: 35/32 155.1396 septimal neutral second 3: 8/7 231.1741 septimal whole tone 4: 21/20 84.4672 minor semitone 5: 8/7 231.1741 septimal whole tone 6: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 1 35/32 155.140 cents septimal neutral second 1: 3 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 2 4/3 498.045 cents perfect fourth 3: 1 21/16 470.781 cents narrow fourth 3: 1 48/35 546.815 cents septimal semi-augmented fourth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 10/7 617.488 cents Euler's tritone 3: 1 35/24 653.185 cents septimal semi-diminished fifth 3: 1 32/21 729.219 cents wide fifth 4: 2 3/2 701.955 cents perfect fifth 4: 2 8/5 813.686 cents minor sixth 4: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 3 7/4 968.826 cents harmonic seventh 5: 1 64/35 1044.860 cents septimal neutral seventh 5: 1 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 231.2 386.3 617.5 702.0 933.1 1200.0 231.2 : 155.1 386.3 470.8 702.0 968.8 1200.0 386.3 : 231.2 315.6 546.8 813.7 1044.9 1200.0 617.5 : 84.5 315.6 582.5 813.7 968.8 1200.0 702.0 : 231.2 498.0 729.2 884.4 1115.5 1200.0 933.1 : 266.9 498.0 653.2 884.4 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 266.8709 cents 10/9, 182.4037 cents 21/20, 84.4672 cents 2: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 36/35, 48.7704 cents 3: 470.7809 .. 729.2191 cents 512/441, 258.4382 cents 63/64,-27.2641 cents 4: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 63/64,-27.2641 cents 5: 933.1291 .. 1115.5328 cents 10/9, 182.4037 cents 36/35, 48.7704 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.367783 Largest / Average step : 1.334355 Largest / Smallest step : 3.159462 Median interval of one step : 8/7, 231.1741 cents, amount: 3 Most common interval of one step : 8/7, 231.1741 cents, amount: 3 Least squares average step : 192.63440 cents, oct.: 1155.80640 cents Scale is not proper Step pattern alph. order: ABACAD Step pattern size order : CBCACD Scale is a Constant Structure, by a margin of 27.26409 cents Scale diversity : 1.631581 Lumma stability : 0.222063 Lumma impropriety factor : 0.045440 Rothenberg efficiency : 0.450000 redundancy: 0.550000 Efficiency x scale size : 2.700000 Number of different interval sizes : 20 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.00000 = 4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 64/63, 27.2641 cents Most common intervals : 8/7, 231.1741 cents & inv., amount: 3 Most common triad is 0.0 231.174 1115.533 cents, amount: 1 Number of recognisable fifths : 2, average 701.9550 cents Length of longest harmonic part : 2 at degree 5 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 1 = 16.6667% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval class 4 -- Rational properties -- Prime limit : 7 Odd number limit : 35 (O: 35 U: 35) Highest odd numerator or denominator: 7 Scale harmonicity : 0.041064 Average absolute harmonicity : 0.265077 Specific harmonicity : 0.189852 Fundamental : 1/28, -4.8074 octaves, 9.3438 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 3.360000E+03, 11.71425 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 34.0, average 5.66667 Mersenne's string divisions : 14535 Sum of van Prooijen's expressibility: 3.71139, average 0.61856 Sum of Tenney's harmonic distance : 7.89778, average 1.31630 Vogel's harmonic complexity : 8.83333 Wille's k value : 17 Wilson's harmonic complexity : 15 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 52.65716, average 2.50748 Lattice compactness (without 2's) : 24.77781, average 1.17990 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.66667 10 1 3: 0 .. 1 0.33333 2 1 5: 0 .. 1 0.33333 2 1 7: -1 .. 0 -0.50000 3 3 Average exponent except 2's : 1 / 6 = 0.16667 Average absolute exponent except 2's: 7 / 6 = 1.16667 Scale is weakly epimorphic with val: <6 10 14 15| Scale is JI-epimorphic with val: <6 10 14 17| = patent Scale is weakly epimorphic with val: <6 10 14 19| Scale is weakly epimorphic with val: <6 11 13 15|
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 50.9076 c. M:-98.0450 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 1 1 1 1 2 P M ME SD: 60.7541 c. M: 103.2021 c. 9: 2 1 2 0 2 2 N SD: 29.1859 c. M:-49.1789 c. 10: 2 1 2 1 2 2 P D3 SD: 18.8140 c. M:-26.8709 c. 12: 2 2 2 1 2 3 P T3 SD: 20.6814 c. M: 33.1291 c. Raga Yamuna Kalyani, Kalyani Keseri, Airavati, Ancient Chinese 15: 3 2 3 1 3 3 P SD: 17.4149 c. M:-26.8709 c. 19: 4 2 4 1 4 4 N SD: 12.7024 c. M:-21.4575 c. 21: 4 3 4 1 4 5 N SD: 12.4885 c. M: 18.8434 c. 22: 4 3 4 2 4 5 P SD: 9.8324 c. M: 17.4878 c. 26: 5 3 5 2 5 6 N SD: 11.4886 c. M: 17.4878 c. 27: 5 4 5 2 5 6 P SD: 7.8924 c. M:-13.6863 c. 31: 6 4 6 2 6 7 N SD: 2.8548 c. M: 5.1808 c. 68: 13 9 13 5 13 15 N SD: 2.1188 c. M:-3.9274 c. 72: 14 9 14 5 14 16 N SD: 1.7360 c. M: 2.9804 c. 99: 19 13 19 7 19 22 N SD: 0.9026 c. M:-1.5651 c. 130: 25 17 25 9 25 29 N SD: 0.8022 c. M:-1.3786 c. 140: 27 18 27 10 27 31 N SD: 0.6702 c. M:-1.1566 c. 171: 33 22 33 12 33 38 N SD: 0.2486 c. M:-0.4049 c. 270: 52 35 52 19 52 60 N SD: 0.2330 c. M:-0.3530 c. 441: 85 57 85 31 85 98 N SD: 0.1350 c. M:-0.2042 c. 612: 118 79 118 43 118 136 N SD: 0.1342 c. M:-0.2042 c. 935: 180 121 180 66 180 208 N SD: 0.1030 c. M: 0.1616 c. 1106: 213 143 213 78 213 246 N SD: 0.0673 c. M: 0.1280 c. 1236: 238 160 238 87 238 275 N SD: 0.0760 c. M: 0.1194 c. 1277: 246 165 246 90 246 284 N SD: 0.0577 c. M: 0.1033 c. 1376: 265 178 265 97 265 306 N SD: 0.0483 c. M:-0.0799 c. 1407: 271 182 271 99 271 313 N SD: 0.0434 c. M: 0.0801 c. 1547: 298 200 298 109 298 344 N SD: 0.0295 c. M:-0.0489 c. 1578: 304 204 304 111 304 351 N SD: 0.0299 c. M: 0.0539 c. 1848: 356 239 356 130 356 411 N SD: 0.0280 c. M:-0.0499 c. 2019: 389 261 389 142 389 449 N SD: 0.0251 c. M:-0.0456 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 0.0000 cents 3 x 4 x x 5:6 S SD: 40.6372 cents 4 x 5 x 6:7:8 S SD: 8.9242 cents 5 x 6:7:8:9:10 S SD: 32.1475 cents 6:7:8 x 9:10:12 S SD: 25.4061 cents 7:8:9:10:11:12:14 S SD: 15.6921 cents 8:9:10:11:12:14:16 S SD: 13.3292 cents 12:14:15:17:18:21:24 SD: 8.7534 cents 14:16:18:20:21:24:28 S SD: 8.1284 cents 16:18:20:23:24:27:32 SD: 6.6729 cents 20:23:25:29:30:34:40 SD: 5.2457 cents 24:27:30:34:36:41:48 SD: 5.2427 cents 28:32:35:40:42:48:56 SD: 0.0000 cents