Scala analysis: xen11-chalmers-tetrachordal-04-04
Iasti-Aiolikai, a Kithara tuning: Tonic Diatonic and Ditonic 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: 27/16 905.865003 Pythagorean major 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: 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: 9/8 203.9100 major whole tone 6: 256/243 90.2250 limma, Pythagorean minor second 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: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 4 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 3 32/27 294.135 cents Pythagorean minor third 2: 2 81/64 407.820 cents Pythagorean major third 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 896/729 357.096 cents 3: 4 4/3 498.045 cents perfect fourth 3: 1 729/512 611.730 cents Pythagorean tritone 3: 1 81/56 638.994 cents 4: 1 112/81 561.006 cents 4: 1 1024/729 588.270 cents Pythagorean diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 729/448 842.904 cents 5: 1 14/9 764.916 cents septimal minor sixth 5: 2 128/81 792.180 cents Pythagorean minor sixth 5: 3 27/16 905.865 cents Pythagorean major sixth 5: 1 12/7 933.129 cents septimal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 4 16/9 996.090 cents Pythagorean minor seventh 6: 1 243/128 1109.775 cents Pythagorean major seventh 6: 1 27/14 1137.039 cents septimal major seventh 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 : 63.0 294.1 498.0 702.0 905.9 996.1 1200.0 63.0 : 231.2 435.1 639.0 842.9 933.1 1137.0 1200.0 294.1 : 203.9 407.8 611.7 702.0 905.9 968.8 1200.0 498.0 : 203.9 407.8 498.0 702.0 764.9 996.1 1200.0 702.0 : 203.9 294.1 498.0 561.0 792.2 996.1 1200.0 905.9 : 90.2 294.1 357.1 588.3 792.2 996.1 1200.0 996.1 : 203.9 266.9 498.0 702.0 905.9 1109.8 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: 357.0959 .. 638.9941 cents 59049/50176, 281.8982 cents 6272/6561,-77.9882 cents 4: 561.0059 .. 842.9041 cents 59049/50176, 281.8982 cents 6272/6561,-77.9882 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 6272/6561,-77.9882 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: 4 Most common interval of one step : 9/8, 203.9100 cents, amount: 4 Least squares average step : 170.42179 cents, oct.: 1192.95255 cents Scale is not proper Step pattern alph. order: ABCCCDC Step pattern size order : ADCCCBC Scale is a Constant Structure, by a margin of 23.46001 cents Scale diversity : 1.530732 Lumma stability : 0.164430 Lumma impropriety factor : 0.194970 Rothenberg efficiency : 0.439456 redundancy: 0.560544 Efficiency x scale size : 3.076190 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 : 531441/524288, 23.4600 cents Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 71.4286% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 168.2132 cents: 6 -- Rational properties -- Prime limit : 7 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.028340 Average absolute harmonicity : 0.257672 Specific harmonicity : 0.182336 Fundamental : 1/432, -8.7549 octaves, 0.6056 Hz. Guide tone : 6048, 12.5622 octaves, 1582311.419 Hz. Exponens Consonantiae : 2.612736E+06, 21.31713 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 98.5, average 14.07143 Mersenne's string divisions : 14651175 Sum of van Prooijen's expressibility: 6.20258, average 0.88608 Sum of Tenney's harmonic distance : 12.76724, average 1.82389 Vogel's harmonic complexity : 13.14286 Wille's k value : 364 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 6 Lattice compactness : 121.56002, average 4.34143 Lattice compactness (without 2's) : 71.18071, average 2.54217 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 1.28571 19 1 3: -3 .. 3 -0.71429 13 5 7: 0 .. 1 0.14286 1 1 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 22| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 12 18|
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 38.3487 c. M: 62.9609 c. 9: 0 2 2 1 2 0 2 N SD: 41.2346 c. M: 62.9609 c. 11: 0 2 2 2 2 1 2 N SD: 49.4065 c. M: 75.9532 c. 12: 1 2 2 2 2 1 2 P D3 S SD: 14.4599 c. M:-37.0391 c. Mela Natakapriya, Jazz Minor inverse, Phrygian-Mixolydian, Dorian flat 2, Raga Natabharanam, Motaki, Ahiri Todi 13: 1 2 2 3 2 1 2 N SD: 25.3306 c. M:-36.5065 c. 15: 1 3 2 3 2 1 3 N SD: 22.6213 c. M: 36.0900 c. 16: 1 3 3 2 3 1 3 N SD: 17.3686 c. M:-26.9550 c. 17: 1 3 3 3 3 1 3 N D3 S SD: 7.8226 c. M: 11.7821 c. 24: 1 5 4 4 4 2 4 N SD: 6.0911 c. M: 12.9609 c. 36: 2 7 6 6 6 3 6 N SD: 3.8815 c. M:-5.8650 c. 41: 2 8 7 7 7 3 7 N SD: 1.8973 c. M: 4.4243 c. 53: 3 10 9 9 9 4 9 N SD: 1.8803 c. M:-4.9636 c. 77: 4 15 13 13 13 6 13 N SD: 1.2379 c. M:-1.9689 c. 94: 5 18 16 16 16 7 16 N SD: 0.4583 c. M:-0.8689 c. 135: 7 26 23 23 23 10 23 N SD: 0.5681 c. M:-0.8017 c. 171: 9 33 29 29 29 13 29 N SD: 0.3789 c. M: 0.6018 c. 212: 11 41 36 36 36 16 36 N SD: 0.2921 c. M: 0.6968 c. 265: 14 51 45 45 45 20 45 N SD: 0.2074 c. M:-0.4353 c. 306: 16 59 52 52 52 23 52 N SD: 0.0823 c. M: 0.2158 c. 400: 21 77 68 68 68 30 68 N SD: 0.0846 c. M:-0.1350 c. 571: 30 110 97 97 97 43 97 N SD: 0.0621 c. M:-0.0864 c. 706: 37 136 120 120 120 53 120 N SD: 0.0584 c. M:-0.0840 c. 877: 46 169 149 149 149 66 149 N SD: 0.0315 c. M:-0.0497 c. 971: 51 187 165 165 165 73 165 N SD: 0.0255 c. M:-0.0669 c. 1277: 67 246 217 217 217 96 217 N SD: 0.0050 c. M:-0.0081 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: 7.1688 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 25.7345 cents 6 x 7:8:9:10:11:12 S SD: 10.5986 cents 7 x 8:9:11:12 x 14 SD: 24.6233 cents 8 x 9:11:12 x 14:16 SD: 21.6535 cents 9 x 11:12:14:15:16:18 SD: 14.2054 cents 12:13:14:16:18:20:21:24 S SD: 12.5082 cents 14:15:17:19:21:24:25:28 SD: 11.6894 cents 15:16:18:20:23:25:27:30 SD: 10.3154 cents 16:17:19:21:24:27:28:32 SD: 8.1586 cents 18:19:21:24:27:30:32:36 SD: 6.6160 cents 20:21:24:27:30:34:36:40 SD: 6.4100 cents 21:22:25:28:32:35:37:42 SD: 6.0867 cents 22:23:26:29:33:37:39:44 SD: 3.6977 cents 26:27:31:35:39:44:46:52 SD: 3.1350 cents 32:33:38:43:48:54:57:64 SD: 2.4669 cents 48:50:57:64:72:81:85:96 SD: 1.5439 cents 54:56:64:72:81:91:96:108 SD: 0.3395 cents 216:224:256:288:324:365:384:432 SD: 0.3390 cents 270:280:320:360:405:456:480:540 SD: 0.2035 cents 324:336:384:432:486:547:576:648 SD: 0.1131 cents 378:392:448:504:567:638:672:756 SD: 0.0485 cents 432:448:512:576:648:729:768:864 SD: 0.0000 cents