Scala analysis: xen11-chalmers-tetrachordal-04-05
Iastia or Lydia, Kithara tunings: Intense Diatonic and Tonic Diatonic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 8/7 231.1741 septimal whole tone 3: 9/8 203.9100 major whole tone 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 280/243 245.365 cents 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 1 81/64 407.820 cents Pythagorean major third 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 1 320/243 476.539 cents grave fourth 3: 2 4/3 498.045 cents perfect fourth 3: 2 27/20 519.551 cents acute fourth 3: 1 81/56 638.994 cents 4: 1 112/81 561.006 cents 4: 2 40/27 680.449 cents grave fifth 4: 2 3/2 701.955 cents perfect fifth 4: 1 243/160 723.461 cents acute fifth 4: 1 54/35 750.725 cents septimal semi-augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 243/140 954.635 cents 6: 1 7/4 968.826 cents harmonic seventh 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 1 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.33333 = 16/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 294.1 498.0 702.0 813.7 1017.6 1200.0 63.0 : 231.2 435.1 639.0 750.7 954.6 1137.0 1200.0 294.1 : 203.9 407.8 519.6 723.5 905.9 968.8 1200.0 498.0 : 203.9 315.6 519.6 702.0 764.9 996.1 1200.0 702.0 : 111.7 315.6 498.0 561.0 792.2 996.1 1200.0 813.7 : 203.9 386.3 449.3 680.4 884.4 1088.3 1200.0 1017.6: 182.4 245.4 476.5 680.4 884.4 996.1 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: 245.3646 .. 435.0841 cents 2187/1960, 189.7195 cents 245/243, 14.1905 cents 3: 449.2746 .. 638.9941 cents 2187/1960, 189.7195 cents 245/243, 14.1905 cents 4: 561.0059 .. 750.7254 cents 2187/1960, 189.7195 cents 6272/6561,-77.9882 cents 5: 764.9159 .. 954.6354 cents 2187/1960, 189.7195 cents 245/243, 14.1905 cents 6: 968.8259 .. 1137.0391 cents 54/49, 168.2132 cents 245/243, 14.1905 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: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 168.05139 cents, oct.: 1176.35975 cents Scale is not proper Step pattern alph. order: ABCCDCE Step pattern size order : AEDDBDC Scale is a Constant Structure, by a margin of 14.19052 cents Scale diversity : 1.661086 Lumma stability : 0.152237 Lumma impropriety factor : 0.064990 Rothenberg efficiency : 0.355102 redundancy: 0.644898 Efficiency x scale size : 2.485714 Number of different interval sizes : 32 = 5.33333 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.33333 = 16/3 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 245/243, 14.1905 cents Most common intervals : 9/8, 203.9100 cents & inv., amount: 3 Number of recognisable fifths : 2, 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 : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.027763 Average absolute harmonicity : 0.257834 Specific harmonicity : 0.174165 Fundamental : 1/270, -8.0768 octaves, 0.9690 Hz. Guide tone : 2016, 10.9773 octaves, 527437.140 Hz. Exponens Consonantiae : 5.443200E+05, 19.05410 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 78.0, average 11.14286 Mersenne's string divisions : 1771770 Sum of van Prooijen's expressibility: 5.47018, average 0.78145 Sum of Tenney's harmonic distance : 11.22867, average 1.60410 Vogel's harmonic complexity : 14.57143 Wille's k value : 202 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 96.16217, average 3.43436 Lattice compactness (without 2's) : 64.33486, average 2.29767 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 5 1.71429 14 1 3: -3 .. 2 -0.57143 10 3 5: -1 .. 0 -0.28571 2 2 7: 0 .. 1 0.14286 1 1 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is JI-epimorphic with val: <7 11 16 20| = patent
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 35.6057 c. M: 62.9609 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 16.5222 c. M:-37.0391 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 13: 1 2 2 3 1 2 2 N T3 SD: 24.2595 c. M:-36.5065 c. 15: 1 3 2 3 1 3 2 N T3 SD: 18.1258 c. M:-25.8650 c. 17: 1 3 3 3 1 3 3 N M DE S SD: 18.8032 c. M: 37.2157 c. 18: 1 3 3 3 2 3 3 P T3 SD: 22.3449 c. M: 35.2883 c. 19: 1 4 3 3 2 3 3 N SD: 9.8373 c. M:-21.6545 c. 21: 1 4 4 3 2 4 3 N SD: 11.5885 c. M:-16.2407 c. 24: 1 5 4 4 2 4 4 N SD: 10.0497 c. M: 17.5963 c. 31: 2 6 5 5 3 5 5 N SD: 9.4801 c. M:-15.5424 c. 32: 2 6 5 6 3 5 5 N SD: 8.9099 c. M:-12.0391 c. 33: 2 6 6 5 3 6 5 N SD: 8.7625 c. M: 13.6863 c. 34: 2 6 6 6 3 6 5 N SD: 6.1729 c. M: 11.7821 c. 38: 2 7 7 6 4 6 6 N SD: 6.6223 c. M: 9.9245 c. 41: 2 8 7 7 4 7 6 N SD: 3.8219 c. M:-6.7940 c. 53: 3 10 9 9 5 9 8 N SD: 2.0103 c. M:-4.9636 c. 74: 4 14 13 12 7 13 11 N SD: 3.3062 c. M:-4.6577 c. 77: 4 15 13 13 7 13 12 N SD: 2.3065 c. M: 4.6093 c. 91: 5 17 16 15 9 15 14 N SD: 3.0182 c. M: 4.0251 c. 94: 5 18 16 16 9 16 14 N SD: 1.9179 c. M:-3.6803 c. 97: 5 19 16 17 9 16 15 N SD: 2.5988 c. M:-3.1996 c. 99: 5 19 17 17 9 17 15 N SD: 1.7344 c. M: 3.2259 c. 111: 6 21 19 19 10 19 17 N SD: 1.6881 c. M: 2.8755 c. 118: 6 23 20 20 11 20 18 N SD: 0.8416 c. M: 1.9440 c. 171: 9 33 29 29 16 29 26 N SD: 0.2942 c. M:-0.6018 c. 441: 23 85 75 75 41 75 67 N SD: 0.1840 c. M: 0.3759 c. 494: 26 95 84 84 46 84 75 N SD: 0.1440 c. M:-0.2175 c. 612: 32 118 104 104 57 104 93 N SD: 0.0854 c. M: 0.2158 c. 665: 35 128 113 113 62 113 101 N SD: 0.1087 c. M:-0.1970 c. 783: 41 151 133 133 73 133 119 N SD: 0.0802 c. M: 0.1257 c. 1106: 58 213 188 188 103 188 168 N SD: 0.0684 c. M:-0.1252 c. 1277: 67 246 217 217 119 217 194 N SD: 0.0529 c. M:-0.1014 c. 1677: 88 323 285 285 156 285 255 N SD: 0.0452 c. M: 0.0906 c. 1848: 97 356 314 314 172 314 281 N SD: 0.0333 c. M: 0.0638 c. 2289: 120 441 389 389 213 389 348 N SD: 0.0343 c. M: 0.0559 c. 2342: 123 451 398 398 218 398 356 N SD: 0.0276 c. M:-0.0622 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: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 26.0714 cents 5 x 6:7 x 8:9:10 S SD: 17.4324 cents 6 x 7:8:9:10:11:12 S SD: 13.6901 cents 7 x 8:9 x 11:13:14 SD: 21.7519 cents 8 x 9:11:12:13:14:16 SD: 19.7748 cents 9 x 11:12 x 14:16:18 SD: 15.0719 cents 12:13:14:16:18:19:22:24 SD: 12.6154 cents 14:15:17:19:21:22:25:28 SD: 12.0001 cents 15:16:18:20:23:24:27:30 SD: 9.3557 cents 16:17:19:21:24:26:29:32 SD: 8.3082 cents 18:19:21:24:27:29:32:36 SD: 6.8338 cents 20:21:24:27:30:32:36:40 S SD: 5.3214 cents 22:23:26:29:33:35:40:44 SD: 4.5438 cents 26:27:31:35:39:42:47:52 SD: 3.8244 cents 28:29:33:37:42:45:50:56 SD: 3.4688 cents 30:31:36:40:45:48:54:60 SD: 3.1972 cents 32:33:38:43:48:51:58:64 SD: 3.1175 cents 44:46:52:59:66:70:79:88 SD: 2.9720 cents 48:50:57:64:72:77:86:96 SD: 1.7825 cents 54:56:64:72:81:86:97:108 SD: 1.2556 cents 60:62:71:80:90:96:108:120 SD: 0.9657 cents 80:83:95:107:120:128:144:160 SD: 0.9168 cents 102:106:121:136:153:163:184:204 SD: 0.8383 cents 108:112:128:144:162:173:194:216 SD: 0.5842 cents 140:145:166:187:210:224:252:280 SD: 0.5536 cents 162:168:192:216:243:259:292:324 SD: 0.3891 cents 190:197:225:253:285:304:342:380 SD: 0.3868 cents 210:218:249:280:315:336:378:420 SD: 0.2753 cents 270:280:320:360:405:432:486:540 S SD: 0.0000 cents