Scala analysis: xen11-chalmers-tetrachordal-08-04
Transposition and Inversion by 3/2, 7 tones, Psi-Dorian
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: 16/15 111.731285 minor diatonic semitone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 15/8 1088.268715 classic major seventh 6: 27/14 1137.039096 septimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 5/4 386.3137 major third 4: 9/8 203.9100 major whole tone 5: 5/4 386.3137 major third 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 5/4 386.314 cents major third 2: 2 16/15 111.731 cents minor diatonic semitone 2: 1 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 2 9/7 435.084 cents septimal major third, BP third 2: 2 45/32 590.224 cents diatonic tritone 3: 2 448/405 174.692 cents 3: 2 4/3 498.045 cents perfect fourth 3: 2 81/56 638.994 cents 3: 1 225/128 976.537 cents augmented sixth 4: 1 256/225 223.463 cents Neapolitan diminished third 4: 2 112/81 561.006 cents 4: 2 3/2 701.955 cents perfect fifth 4: 2 405/224 1025.308 cents 5: 2 64/45 609.776 cents 2nd tritone 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 729/392 1074.078 cents 5: 2 15/8 1088.269 cents classic major seventh 6: 2 8/5 813.686 cents minor sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 111.7 498.0 702.0 1088.3 1137.0 1200.0 63.0 : 48.8 435.1 639.0 1025.3 1074.1 1137.0 1200.0 111.7 : 386.3 590.2 976.5 1025.3 1088.3 1151.2 1200.0 498.0 : 203.9 590.2 639.0 702.0 764.9 813.7 1200.0 702.0 : 386.3 435.1 498.0 561.0 609.8 996.1 1200.0 1088.3: 48.8 111.7 174.7 223.5 609.8 813.7 1200.0 1137.0: 63.0 125.9 174.7 561.0 764.9 1151.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 111.7313 .. 590.2237 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 3: 174.6922 .. 976.5374 cents 91125/57344, 801.8452 cents 14336/18225,-415.5315 cents 4: 223.4626 .. 1025.3078 cents 91125/57344, 801.8452 cents 32768/50625,-753.0749 cents 5: 609.7763 .. 1088.2687 cents 675/512, 478.4924 cents 14336/18225,-415.5315 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.515014 Largest / Average step : 2.253497 Largest / Smallest step : 7.921072 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 180.37112 cents, oct.: 1262.59783 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : BADCDAB Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.406363 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 24 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 245/243, 14.1905 cents 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 : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 100.0000% Scale is differentially coherent in interval class 1 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 7 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.017739 Average absolute harmonicity : 0.249652 Specific harmonicity : 0.138448 Fundamental : 1/7560, -12.8842 octaves, 0.0346 Hz. Guide tone : 15120, 13.8842 octaves, 3955778.547 Hz. Exponens Consonantiae : 1.143072E+08, 26.76834 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 82.5, average 11.78571 Mersenne's string divisions : 33764115 Sum of van Prooijen's expressibility: 6.16915, average 0.88131 Sum of Tenney's harmonic distance : 12.07377, average 1.72482 Vogel's harmonic complexity : 24.57143 Wille's k value : 7087 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 105.22724, average 3.75812 Lattice compactness (without 2's) : 66.03369, average 2.35835 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.57143 14 1 3: -3 .. 3 0.00000 10 2 5: -1 .. 1 0.00000 2 2 7: -1 .. 1 0.00000 2 2 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 10 17 18| Scale is weakly epimorphic with val: <7 10 17 21| Scale is weakly epimorphic with val: <7 11 15 18| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 12 15 18| Scale is weakly epimorphic with val: <7 12 15 19| Scale is weakly epimorphic with val: <7 12 17 18| Scale is weakly epimorphic with val: <7 12 17 19|
FIT/MODE
7: 0 1 2 1 2 1 0 N I SD: 47.1823 c. M:-62.9609 c. 10: 1 0 3 2 3 0 1 N I SD: 32.2820 c. M:-57.0391 c. 12: 1 0 4 2 4 0 1 N I SD: 20.7938 c. M: 37.0391 c. 14: 1 0 5 2 5 0 1 N I SD: 20.4126 c. M: 26.0170 c. 17: 1 1 5 3 5 1 1 N I SD: 16.3935 c. M:-29.4452 c. 19: 1 1 6 3 6 1 1 N I SD: 8.6989 c. M: 14.5845 c. 22: 1 1 7 4 7 1 1 N I SD: 6.0642 c. M:-8.4154 c. 34: 2 1 11 6 11 1 2 N I SD: 5.5500 c. M:-7.6273 c. 41: 2 2 13 7 13 2 2 N I SD: 3.7166 c. M:-5.3419 c. 53: 3 2 17 9 17 2 3 N I SD: 2.7683 c. M:-4.9636 c. 55: 3 2 18 9 18 2 3 N I SD: 2.7993 c. M:-3.7732 c. 75: 4 3 24 13 24 3 4 N I SD: 1.2345 c. M:-2.0450 c. 96: 5 4 31 16 31 4 5 N I SD: 1.1496 c. M: 1.9550 c. 118: 6 5 38 20 38 5 6 N I SD: 1.0508 c. M:-1.9440 c. 130: 7 5 42 22 42 5 7 N I SD: 1.0469 c. M:-1.6545 c. 149: 8 6 48 25 48 6 8 N I SD: 1.1767 c. M: 1.4686 c. 152: 8 6 49 26 49 6 8 N I SD: 0.7461 c. M: 1.2050 c. 171: 9 7 55 29 55 7 9 N I SD: 0.3299 c. M:-0.5494 c. 246: 13 10 79 42 79 10 13 N I SD: 0.4327 c. M:-0.4840 c. 248: 13 10 80 42 80 10 13 N I SD: 0.2999 c. M:-0.4410 c. 323: 17 13 104 55 104 13 17 N I SD: 0.2139 c. M:-0.2762 c. 419: 22 17 135 71 135 17 22 N I SD: 0.1552 c. M:-0.2844 c. 494: 26 20 159 84 159 20 26 N I SD: 0.1117 c. M:-0.1970 c. 742: 39 30 239 126 239 30 39 N I SD: 0.1029 c. M:-0.1410 c. 913: 48 37 294 155 294 37 48 N I SD: 0.0847 c. M: 0.1278 c. 935: 49 38 301 159 301 38 49 N I SD: 0.0691 c. M:-0.0771 c. 1106: 58 45 356 188 356 45 58 N I SD: 0.0276 c. M: 0.0341 c. 1848: 97 75 595 314 595 75 97 N I SD: 0.0271 c. M:-0.0430 c. 2019: 106 82 650 343 650 82 106 N I SD: 0.0253 c. M: 0.0406 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 4:5 x x 6 S SD: 60.8012 cents 4 x x 5:6 x x 8 S SD: 37.2438 cents 5 x x 7:8:9 x 10 SD: 39.2215 cents 6 x 7:8:9:11 x 12 SD: 31.9887 cents 7 x 8:9:11:13 x 14 SD: 31.6173 cents 8 x 9:11:12:15 x 16 SD: 21.2931 cents 9 x 10:12:14:17 x 18 SD: 19.1017 cents 10 x 11:13:15:19 x 20 SD: 14.5396 cents 11 x 12:15:17 x 21:22 SD: 15.5014 cents 12 x 13:16:18 x 23:24 SD: 5.7806 cents 13 x 14:17:20:24:25:26 SD: 10.6335 cents 14 x 15:19:21:26:27:28 SD: 5.9462 cents 15 x 16:20:23:28:29:30 SD: 6.5097 cents 16 x 17:21:24:30:31:32 SD: 4.8682 cents 17 x 18:23:26:32:33:34 SD: 7.6472 cents 18 x 19:24:27:34:35:36 SD: 4.3883 cents 19 x 20:25:29:36:37:38 SD: 8.4472 cents 20:21 x 27:30:38:39:40 SD: 7.1040 cents 21:22 x 28:32:39:41:42 SD: 7.0276 cents 22:23 x 29:33:41:42:44 SD: 5.2890 cents 24:25:26:32:36:45:46:48 SD: 4.2734 cents 26:27:28:35:39:49:50:52 SD: 3.6628 cents 28:29:30:37:42:53:54:56 SD: 3.4248 cents 30:31:32:40:45:56:58:60 SD: 1.5390 cents 58:60:62:77:87:109:112:116 SD: 1.4896 cents 72:75:77:96:108:135:139:144 SD: 1.3008 cents 78:81:83:104:117:146:150:156 SD: 1.0707 cents 102:106:109:136:153:191:197:204 SD: 0.8421 cents 108:112:115:144:162:203:208:216 SD: 0.8197 cents 132:137:141:176:198:248:255:264 SD: 0.7653 cents 134:139:143:179:201:251:258:268 SD: 0.6777 cents 136:141:145:181:204:255:262:272 SD: 0.5449 cents 138:143:147:184:207:259:266:276 SD: 0.4740 cents 168:174:179:224:252:315:324:336 SD: 0.4194 cents 192:199:205:256:288:360:370:384 SD: 0.3373 cents 210:218:224:280:315:394:405:420 SD: 0.2971 cents 240:249:256:320:360:450:463:480 SD: 0.1342 cents 432:448:461:576:648:810:833:864 SD: 0.1154 cents 570:591:608:760:855:1069:1099:1140 SD: 0.0982 cents 600:622:640:800:900:1125:1157:1200 SD: 0.0935 cents