Scala analysis: raven-JI
a 7-limit JI scale due to John O'Sullivan
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: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 7/6 266.8709 septimal minor third 2: 15/14 119.4428 major diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 21/20 84.4672 minor semitone 7: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 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 2: 1 8/7 231.174 cents septimal whole tone 2: 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: 1 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: 3 4/3 498.045 cents perfect fourth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 10/7 617.488 cents Euler's tritone 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 10/7 617.488 cents Euler's tritone 4: 3 3/2 701.955 cents perfect fifth 4: 1 32/21 729.219 cents wide fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 1 3/2 701.955 cents perfect fifth 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 28/15 1080.557 cents grave major seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 1 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.66667 = 17/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 266.9 386.3 498.0 702.0 884.4 968.8 1200.0 266.9 : 119.4 231.2 435.1 617.5 702.0 933.1 1200.0 386.3 : 111.7 315.6 498.0 582.5 813.7 1080.6 1200.0 498.0 : 203.9 386.3 470.8 702.0 968.8 1088.3 1200.0 702.0 : 182.4 266.9 498.0 764.9 884.4 996.1 1200.0 884.4 : 84.5 315.6 582.5 702.0 813.7 1017.6 1200.0 968.8 : 231.2 498.0 617.5 729.2 933.1 1115.5 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: 231.1741 .. 498.0450 cents 7/6, 266.8709 cents 48/49,-35.6968 cents 3: 435.0841 .. 617.4878 cents 10/9, 182.4037 cents 27/28,-62.9609 cents 4: 582.5122 .. 764.9159 cents 10/9, 182.4037 cents 49/50,-34.9756 cents 5: 701.9550 .. 968.8259 cents 7/6, 266.8709 cents 27/28,-62.9609 cents 6: 933.1291 .. 1115.5328 cents 10/9, 182.4037 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.029528 Largest / Average step : 1.556747 Largest / Smallest step : 3.159462 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 171.25859 cents, oct.: 1198.81012 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : GCBEDAF Scale is not a Constant Structure Scale diversity : 1.570430 Lumma stability : 0.140779 Lumma impropriety factor : 0.193576 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 5.66667 = 17/3 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 6 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval class 4 Scale is differentially coherent in interval class 5 -- Rational properties -- Prime limit : 7 Odd number limit : 21 (O: 21 U: 21) Highest odd numerator or denominator: 7 Scale harmonicity : 0.038433 Average absolute harmonicity : 0.267060 Specific harmonicity : 0.209222 Fundamental : 1/12, -3.5850 octaves, 21.8021 Hz. Guide tone : 420, 8.7142 octaves, 109882.737 Hz. Exponens Consonantiae : 5.040000E+03, 12.29921 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 28.0, average 4.00000 Mersenne's string divisions : 360360 Sum of van Prooijen's expressibility: 4.04238, average 0.57748 Sum of Tenney's harmonic distance : 7.70589, average 1.10084 Vogel's harmonic complexity : 7.14286 Wille's k value : 10 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 63.50619, average 2.26808 Lattice compactness (without 2's) : 36.07837, average 1.28851 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.42857 9 1 3: -1 .. 1 -0.28571 4 2 5: 0 .. 1 0.28571 2 2 7: 0 .. 1 0.28571 2 2 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 12 15 18| Scale is weakly epimorphic with val: <7 12 18 22|
FIT/MODE
7: 2 0 1 1 1 1 1 N T3 SD: 42.2579 c. M:-75.9862 c. 9: 2 1 1 1 2 0 2 N T3 SD: 30.0859 c. M:-48.9746 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 24.2348 c. M: 44.3587 c. 12: 3 1 1 2 2 1 2 N SD: 18.9321 c. M:-33.1291 c. Mela Vagadhisvari, Raga Bhogachayanata, Nandkauns, Ganavaridhi, Chayanata, Bluesy Rock 'n Roll 15: 3 2 1 3 2 1 3 N SD: 15.3878 c. M: 26.8709 c. 19: 4 2 2 3 3 1 4 N SD: 10.8343 c. M: 21.4575 c. 22: 5 2 2 4 3 2 4 N SD: 8.1103 c. M:-12.9923 c. 27: 6 3 2 5 4 2 5 N SD: 8.0683 c. M:-13.6863 c. 31: 7 3 3 5 5 2 6 N SD: 3.9247 c. M:-5.9639 c. 41: 9 4 4 7 6 3 8 N SD: 3.6840 c. M: 6.3099 c. 46: 10 5 4 8 7 3 9 N SD: 3.6281 c. M: 6.0013 c. 53: 12 5 5 9 8 4 10 N SD: 2.6656 c. M:-4.8272 c. 68: 15 7 6 12 10 5 13 N SD: 2.5734 c. M:-3.9274 c. 72: 16 7 7 12 11 5 14 N SD: 1.7841 c. M: 2.9804 c. 99: 22 10 9 17 15 7 19 N SD: 0.9104 c. M:-1.5651 c. 130: 29 13 12 22 20 9 25 N SD: 0.9493 c. M:-1.7951 c. 140: 31 14 13 24 21 10 27 N SD: 0.8980 c. M: 1.5016 c. 171: 38 17 16 29 26 12 33 N SD: 0.2478 c. M: 0.4049 c. 270: 60 27 25 46 41 19 52 N SD: 0.2139 c. M:-0.3530 c. 441: 98 44 41 75 67 31 85 N SD: 0.1049 c. M: 0.2042 c. 612: 136 61 57 104 93 43 118 N SD: 0.1100 c. M: 0.2042 c. 665: 148 66 62 113 101 47 128 N SD: 0.1317 c. M:-0.1968 c. 783: 174 78 73 133 119 55 151 N SD: 0.1310 c. M: 0.2435 c. 836: 186 83 78 142 127 59 161 N SD: 0.1067 c. M: 0.1893 c. 935: 208 93 87 159 142 66 180 N SD: 0.0845 c. M:-0.1581 c. 1106: 246 110 103 188 168 78 213 N SD: 0.0538 c. M: 0.0911 c. 1277: 284 127 119 217 194 90 246 N SD: 0.0522 c. M: 0.0987 c. 1376: 306 137 128 234 209 97 265 N SD: 0.0553 c. M:-0.0799 c. 1407: 313 140 131 239 214 99 271 N SD: 0.0512 c. M:-0.0801 c. 1547: 344 154 144 263 235 109 298 N SD: 0.0393 c. M: 0.0665 c. 1578: 351 157 147 268 240 111 304 N SD: 0.0395 c. M:-0.0539 c. 1718: 382 171 160 292 261 121 331 N SD: 0.0420 c. M: 0.0747 c. 1848: 411 184 172 314 281 130 356 N SD: 0.0293 c. M:-0.0569 c. 2019: 449 201 188 343 307 142 389 N SD: 0.0234 c. M:-0.0395 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 0.0000 cents 5:6 x 7 x 8:9:10 S SD: 25.9895 cents 6:7 x 8:9:10:11:12 S SD: 13.4228 cents 7:8:9 x 11 x 12:14 SD: 21.3666 cents 8:9:10:11:12:13:14:16 S SD: 13.3426 cents 9 x 11:12:14:15:16:18 SD: 13.1456 cents 10:12 x 13:15:17:18:20 SD: 14.7701 cents 11:13:14:15:17:18:19:22 SD: 12.1034 cents 12:14:15:16:18:20:21:24 S SD: 0.0000 cents