Scala analysis: xen11-chalmers-tetrachordal-04-03
Metabolika, another Lyra tuning: Soft Diatonic and Tonic Diatonic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 14/9 764.915905 septimal minor sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 21/20 84.4672 minor semitone 2: 10/9 182.4037 minor whole tone 3: 8/7 231.1741 septimal whole tone 4: 9/8 203.9100 major whole tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 8/7 231.1741 septimal whole tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 21/20 84.467 cents minor semitone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 189/160 288.377 cents 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 80/63 413.578 cents wide major third 2: 2 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute 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 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 32/21 729.219 cents wide fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 63/40 786.422 cents narrow minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 320/189 911.623 cents 5: 2 12/7 933.129 cents septimal major sixth 6: 2 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 40/21 1115.533 cents acute major seventh 6: 1 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 84.5 266.9 498.0 702.0 764.9 996.1 1200.0 84.5 : 182.4 413.6 617.5 680.4 911.6 1115.5 1200.0 266.9 : 231.2 435.1 498.0 729.2 933.1 1017.6 1200.0 498.0 : 203.9 266.9 498.0 702.0 786.4 968.8 1200.0 702.0 : 63.0 294.1 498.0 582.5 764.9 996.1 1200.0 764.9 : 231.2 435.1 519.6 702.0 933.1 1137.0 1200.0 996.1 : 203.9 288.4 470.8 702.0 905.9 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 231.1741 cents 54/49, 168.2132 cents 28/27, 62.9609 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 470.7809 .. 617.4878 cents 160/147, 146.7069 cents 49/48, 35.6968 cents 4: 582.5122 .. 729.2191 cents 160/147, 146.7069 cents 49/50,-34.9756 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 6: 968.8259 .. 1137.0391 cents 54/49, 168.2132 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.722778 Largest / Average step : 1.348516 Largest / Smallest step : 3.671709 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 165.15203 cents, oct.: 1156.06418 cents Scale is not proper Step pattern alph. order: ABCDECD Step pattern size order : BCEDAED Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.501290 Lumma stability : 0.223924 Lumma impropriety factor : 0.029146 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 5120/5103, 5.7578 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 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 2 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 168.2132 cents: 5 -- Rational properties -- Prime limit : 7 Odd number limit : 189 (O: 189 U: 189) Highest odd numerator or denominator: 21 Scale harmonicity : 0.032588 Average absolute harmonicity : 0.253261 Specific harmonicity : 0.173088 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 336, 8.3923 octaves, 87906.190 Hz. Exponens Consonantiae : 6.048000E+04, 15.88417 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 58.5, average 8.35714 Mersenne's string divisions : 6435975 Sum of van Prooijen's expressibility: 5.03004, average 0.71858 Sum of Tenney's harmonic distance : 10.66359, average 1.52337 Vogel's harmonic complexity : 14.14286 Wille's k value : 94 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 84.58083, average 3.02074 Lattice compactness (without 2's) : 48.57011, average 1.73465 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 0.57143 12 1 3: -2 .. 1 -0.57143 8 3 5: -1 .. 0 -0.14286 1 7: 0 .. 1 0.42857 3 3 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 17 19| Scale is JI-epimorphic with val: <7 11 16 20| = patent
FIT/MODE
7: 0 1 2 1 0 2 1 N T3 SD: 58.6751 c. M: 95.4423 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 37.8866 c. M: 62.7567 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 2 0 2 2 P D3 S SD: 29.1690 c. M: 44.9159 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 19.2452 c. M:-35.0841 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 14: 1 2 3 2 1 3 2 P T3 SD: 15.6806 c. M:-32.4814 c. 17: 1 3 3 3 1 3 3 N M DE S SD: 9.6981 c. M:-15.4820 c. 27: 2 4 5 5 1 5 5 N SD: 9.3367 c. M: 18.3122 c. 29: 2 4 6 5 1 6 5 N SD: 10.4582 c. M: 20.0883 c. 31: 2 5 6 5 2 6 5 N T3 SD: 6.6930 c. M:-10.3616 c. 36: 3 5 7 6 2 7 6 P SD: 6.1795 c. M:-15.5328 c. 41: 3 6 8 7 2 8 7 N SD: 2.3910 c. M: 3.9403 c. 58: 4 9 11 10 3 11 10 N SD: 1.7340 c. M: 2.9865 c. 94: 7 14 18 16 5 18 16 N SD: 1.9528 c. M:-4.8945 c. 99: 7 15 19 17 5 19 17 N SD: 1.1188 c. M: 2.1506 c. 113: 8 17 22 19 6 22 19 N SD: 1.1416 c. M:-2.1401 c. 130: 9 20 25 22 7 25 22 N SD: 0.8603 c. M: 1.3903 c. 171: 12 26 33 29 9 33 29 N SD: 0.2233 c. M:-0.4012 c. 400: 28 61 77 68 21 77 68 N SD: 0.1905 c. M: 0.4672 c. 441: 31 67 85 75 23 85 75 N SD: 0.1616 c. M: 0.2901 c. 571: 40 87 110 97 30 110 97 N SD: 0.1569 c. M: 0.4041 c. 612: 43 93 118 104 32 118 104 N SD: 0.1251 c. M: 0.2100 c. 783: 55 119 151 133 41 151 133 N SD: 0.1249 c. M: 0.2042 c. 836: 59 127 161 142 44 161 142 N SD: 0.1176 c. M:-0.2218 c. 1007: 71 153 194 171 53 194 171 N SD: 0.0985 c. M:-0.1406 c. 1065: 75 162 205 181 56 205 181 N SD: 0.0899 c. M:-0.1713 c. 1106: 78 168 213 188 58 213 188 N SD: 0.0703 c. M:-0.1621 c. 1236: 87 188 238 210 65 238 210 N SD: 0.0686 c. M:-0.1326 c. 1277: 90 194 246 217 67 246 217 N SD: 0.0402 c. M:-0.1060 c. 1448: 102 220 279 246 76 279 246 N SD: 0.0319 c. M:-0.0632 c. 1677: 118 255 323 285 88 323 285 N SD: 0.0226 c. M:-0.0343 c. 1848: 130 281 356 314 97 356 314 N SD: 0.0223 c. M: 0.0516 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 x 5:6 S SD: 37.2438 cents 4 x x 5:6 x 7:8 S SD: 28.7524 cents 5 x 6:7 x 8:9:10 S SD: 22.2300 cents 6 x 7:8:9 x 11:12 SD: 10.6546 cents 7 x 8:9 x 11:12:14 SD: 19.5052 cents 8 x 9:11:12 x 14:16 SD: 17.3729 cents 9 x 11:12 x 14:16:18 SD: 16.1074 cents 11:12:13:15 x 17:20:22 SD: 14.9369 cents 12:13:14:16:18:19:21:24 SD: 9.6992 cents 13:14:15:17 x 20:23:26 SD: 10.3451 cents 14:15:16:19:21:22:25:28 SD: 8.8120 cents 15:16:18:20 x 23:27:30 SD: 10.8076 cents 16:17:19:21:24:25:28:32 SD: 7.6995 cents 17:18:20:23 x 26:30:34 SD: 7.6063 cents 18:19:21:24:27:28:32:36 SD: 1.3051 cents 60:63:70:80:90:93:107:120 SD: 1.1741 cents 78:82:91:104:117:121:139:156 SD: 0.9522 cents 96:101:112:128:144:149:171:192 SD: 0.8824 cents 102:107:119:136:153:159:181:204 SD: 0.7279 cents 120:126:140:160:180:187:213:240 SD: 0.5867 cents 126:132:147:168:189:196:224:252 SD: 0.5615 cents 138:145:161:184:207:215:245:276 SD: 0.5380 cents 144:151:168:192:216:224:256:288 SD: 0.3274 cents 162:170:189:216:243:252:288:324 SD: 0.1454 cents 180:189:210:240:270:280:320:360 S SD: 0.0000 cents