Scala analysis: hjelm
Paul Hjelmstad's "blues" scale tuning@yahoo May 27, 2005
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 4/3 498.044999 perfect fourth 3: 49/36 533.741811 Arabic lute acute fourth 4: 3/2 701.955001 perfect fifth 5: 7/4 968.825906 harmonic seventh 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 7/6 266.8709 septimal minor third 2: 8/7 231.1741 septimal whole tone 3: 49/48 35.6968 slendro diesis, septimal 1/6-tone 4: 54/49 168.2132 Zalzal's mujannab 5: 7/6 266.8709 septimal minor third 6: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 54/49 168.213 cents Zalzal's mujannab 1: 2 8/7 231.174 cents septimal whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 3 4/3 498.045 cents perfect fourth 3: 1 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 3: 1 49/36 533.742 cents Arabic lute acute fourth 3: 1 72/49 666.258 cents Arabic lute grave fifth 3: 1 32/21 729.219 cents wide fifth 3: 1 14/9 764.916 cents septimal minor sixth 4: 3 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 4: 1 12/7 933.129 cents septimal major sixth 4: 1 16/9 996.090 cents Pythagorean minor seventh 5: 2 12/7 933.129 cents septimal major sixth 5: 2 7/4 968.826 cents harmonic seventh 5: 1 49/27 1031.787 cents 5: 1 96/49 1164.303 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.40000 = 22/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 266.9 498.0 533.7 702.0 968.8 1200.0 266.9 : 231.2 266.9 435.1 702.0 933.1 1200.0 498.0 : 35.7 203.9 470.8 702.0 968.8 1200.0 533.7 : 168.2 435.1 666.3 933.1 1164.3 1200.0 702.0 : 266.9 498.0 764.9 996.1 1031.8 1200.0 968.8 : 231.2 498.0 729.2 764.9 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 266.8709 cents 8/7, 231.1741 cents 49/48, 35.6968 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 27/28,-62.9609 cents 3: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 27/28,-62.9609 cents 4: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 27/28,-62.9609 cents 5: 933.1291 .. 1164.3032 cents 8/7, 231.1741 cents 27/28,-62.9609 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 5.602741 Largest / Average step : 1.334355 Largest / Smallest step : 7.476043 Median interval of one step : 8/7, 231.1741 cents, amount: 2 Least squares average step : 194.68281 cents, oct.: 1168.09687 cents Scale is not proper Step pattern alph. order: ABCDAB Step pattern size order : DCABDC Scale is not a Constant Structure Scale diversity : 1.364118 Lumma stability : 0.059495 Lumma impropriety factor : 0.209870 Rothenberg efficiency : 0.477778 redundancy: 0.522222 Efficiency x scale size : 2.866667 Number of different interval sizes : 18 = 3.60000 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.40000 = 22/5 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 64/63, 27.2641 cents Number of recognisable fifths : 3, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 3 = 50.0000% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 49 Scale harmonicity : 0.030702 Average absolute harmonicity : 0.279319 Specific harmonicity : 0.170646 Fundamental : 1/36, -5.1699 octaves, 7.2674 Hz. Guide tone : 588, 9.1997 octaves, 153835.832 Hz. Exponens Consonantiae : 2.116800E+04, 14.36960 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 62.0, average 10.33333 Mersenne's string divisions : 255255 Sum of van Prooijen's expressibility: 4.33463, average 0.72244 Sum of Tenney's harmonic distance : 8.47527, average 1.41254 Vogel's harmonic complexity : 10.66667 Wille's k value : 31 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 54.15281, average 2.57871 Lattice compactness (without 2's) : 33.04168, average 1.57341 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.50000 9 1 3: -2 .. 1 -0.50000 5 2 7: 0 .. 2 0.66667 4 3 Average exponent except 2's : 1 / 6 = 0.16667 Average absolute exponent except 2's: 9 / 6 = 1.50000 Scale is weakly epimorphic with val: <6 11 15|
FIT/MODE
6: 1 1 0 1 1 2 N D3 SD: 108.6803 c. M: 168.8259 c. 7: 2 1 0 1 2 1 N SD: 41.3310 c. M:-75.9862 c. 9: 2 2 0 1 2 2 N G SD: 25.0015 c. M: 35.4926 c. 10: 2 2 0 2 2 2 P M DE SD: 26.8929 c. M: 53.7418 c. 12: 3 2 0 2 3 2 N SD: 23.1499 c. M: 33.7418 c. 14: 3 3 0 2 3 3 N G SD: 16.7086 c. M: 25.9688 c. 17: 4 3 1 2 4 3 N SD: 16.3607 c. M:-30.9641 c. 19: 4 4 0 3 4 4 N G SD: 16.2194 c. M: 28.4787 c. 20: 4 4 1 3 4 4 P SD: 15.7605 c. M: 26.8709 c. 21: 5 4 0 3 5 4 N SD: 14.5368 c. M: 19.4561 c. 22: 5 4 1 3 5 4 N SD: 8.5842 c. M:-12.9923 c. 27: 6 5 1 4 6 5 N SD: 6.4293 c. M: 9.1561 c. 31: 7 6 1 4 7 6 N SD: 4.8093 c. M:-8.1937 c. 36: 8 7 1 5 8 7 N SD: 1.4442 c. M: 2.1592 c. 94: 21 18 3 13 21 18 N SD: 1.2486 c. M:-2.4284 c. 99: 22 19 3 14 22 19 N SD: 0.7394 c. M:-1.0753 c. 130: 29 25 4 18 29 25 N SD: 0.8046 c. M:-1.6428 c. 135: 30 26 4 19 30 26 N SD: 0.2434 c. M: 0.4085 c. 171: 38 33 5 24 38 33 N SD: 0.2748 c. M: 0.4085 c. 306: 68 59 9 43 68 59 N SD: 0.2033 c. M: 0.4085 c. 364: 81 70 11 51 81 70 N SD: 0.2624 c. M:-0.4049 c. 400: 89 77 12 56 89 77 N SD: 0.1401 c. M:-0.2582 c. 436: 97 84 13 61 97 84 N SD: 0.1160 c. M:-0.2031 c. 535: 119 103 16 75 119 103 N SD: 0.0930 c. M:-0.1461 c. 571: 127 110 17 80 127 110 N SD: 0.0314 c. M:-0.0585 c. 706: 157 136 21 99 157 136 N SD: 0.0220 c. M: 0.0308 c. 1277: 284 246 38 179 284 246 N SD: 0.0054 c. M:-0.0092 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: 28.1557 cents 4 x 5 x 6:7:8 S SD: 27.9328 cents 5:6 x 7:8:9:10 S SD: 28.0139 cents 6:7:8 x 9:11:12 SD: 16.1074 cents 8:9 x 11:12:14:16 SD: 13.0736 cents 9:11:12 x 14:16:18 SD: 21.1600 cents 10:12:13:14:15:18:20 S SD: 15.8612 cents 11:13 x 15:17:19:22 SD: 12.1533 cents 12:14:16 x 18:21:24 S SD: 0.0000 cents 14:16 x 19:21:25:28 SD: 10.0461 cents 15:18:20 x 23:26:30 SD: 12.8076 cents 16:19:21:22:24:28:32 SD: 7.4371 cents 17:20 x 23:26:30:34 SD: 8.1450 cents 18:21:24:25:27:32:36 SD: 7.3911 cents 19:22:25:26:29:33:38 SD: 7.1876 cents 20:23 x 27:30:35:40 SD: 5.7337 cents 23:27 x 31:35:40:46 SD: 6.7531 cents 24:28:32:33:36:42:48 S SD: 2.9294 cents 26:30:35 x 39:46:52 SD: 6.3195 cents 27:32:36:37:41:47:54 SD: 6.2731 cents 28:33:37:38:42:49:56 SD: 3.9985 cents 29:34:39 x 44:51:58 SD: 5.5029 cents 30:35:40:41:45:53:60 SD: 2.9768 cents 36:42:48:49:54:63:72 SD: 0.0000 cents