Scala analysis: xen18-secor-neutral-third-mos-1-just
MOS generated by a neutral third, just
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 13/8 840.527662 tridecimal neutral sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 13/12 138.5727 tridecimal 2/3-tone 2: 44/39 208.8353 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 9/8 203.9100 major whole tone 5: 13/12 138.5727 tridecimal 2/3-tone 6: 44/39 208.8353 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 44/39 208.835 cents 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 2 16/13 359.472 cents tridecimal neutral third 3: 1 117/88 493.120 cents tridecimal gentle fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 18/13 563.382 cents tridecimal augmented fourth 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 176/117 706.880 cents 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 1 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 1 22/13 910.790 cents tridecimal major sixth 6: 2 39/22 991.165 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 24/13 1061.427 cents tridecimal neutral seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 138.6 347.4 498.0 702.0 840.5 1049.4 1200.0 138.6 : 208.8 359.5 563.4 702.0 910.8 1061.4 1200.0 347.4 : 150.6 354.5 493.1 702.0 852.6 991.2 1200.0 498.0 : 203.9 342.5 551.3 702.0 840.5 1049.4 1200.0 702.0 : 138.6 347.4 498.0 636.6 845.5 996.1 1200.0 840.5 : 208.8 359.5 498.0 706.9 857.5 1061.4 1200.0 1049.4: 150.6 289.2 498.0 648.7 852.6 991.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 208.8353 cents 176/169, 70.2626 cents 13/12, 138.5727 cents 2: 289.2097 .. 359.4723 cents 176/169, 70.2626 cents 507/484, 80.3744 cents 3: 493.1197 .. 563.3823 cents 176/169, 70.2626 cents 1521/1408, 133.6474 cents 4: 636.6177 .. 706.8803 cents 176/169, 70.2626 cents 169/162, 73.2353 cents 5: 840.5277 .. 910.7903 cents 176/169, 70.2626 cents 1521/1408, 133.6474 cents 6: 991.1647 .. 1061.4273 cents 176/169, 70.2626 cents 507/484, 80.3744 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 44/39, 208.8353 cents Average / Smallest step : 1.237102 Largest / Average step : 1.218206 Largest / Smallest step : 1.507045 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Least squares average step : 171.67257 cents, oct.: 1201.70798 cents Scale is strictly proper Step pattern alph. order: ABCDABC Step pattern size order : ADBCADB Scale is a Constant Structure, by a margin of 73.23532 cents Scale diversity : 1.320222 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.648687 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 : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 352/351, 4.9253 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 5, average 702.9401 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 117 U: 117) Highest odd numerator or denominator: 13 Scale harmonicity : 0.018749 Average absolute harmonicity : 0.236049 Specific harmonicity : 0.103555 Fundamental : 1/72, -6.1699 octaves, 3.6337 Hz. Guide tone : 1716, 10.7448 octaves, 448949.470 Hz. Exponens Consonantiae : 1.235520E+05, 16.91476 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 49.0, average 7.00000 Mersenne's string divisions : 35700 Sum of van Prooijen's expressibility: 5.26491, average 0.75213 Sum of Tenney's harmonic distance : 10.18370, average 1.45481 Vogel's harmonic complexity : 13.57143 Wille's k value : 58 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 72.93237, average 2.60473 Lattice compactness (without 2's) : 41.33385, average 1.47621 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.57143 10 1 3: -2 .. 1 -0.57143 6 2 11: 0 .. 1 0.28571 2 2 13: 0 .. 1 0.28571 2 2 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 10 26 29| Scale is weakly epimorphic with val: <7 11 23 27| Scale is JI-epimorphic with val: <7 11 24 26| = patent Scale is weakly epimorphic with val: <7 12 23 29|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 18.2682 c. M:-32.8559 c. Lebeng 10: 1 2 1 2 1 2 1 P M ME I SD: 17.2943 c. M:-30.6371 c. 16: 2 3 2 2 2 3 2 SP M ME I SD: 19.2226 c. M:-27.5921 c. Armodue-7, Antidorian 17: 2 3 2 3 2 3 2 SP M ME I SD: 5.3506 c. M:-9.4606 c. Neutral Dorian, Maqamic-7 41: 5 7 5 7 5 7 5 SP M DE I SD: 4.8094 c. M:-8.2528 c. Maqamic-7 53: 6 9 7 9 6 9 7 SP T3 SD: 4.4322 c. M: 7.8535 c. 58: 7 10 7 10 7 10 7 SP M DE I SD: 4.7207 c. M:-7.7482 c. 60: 7 10 8 10 7 10 8 SP T3 SD: 4.6675 c. M: 9.3629 c. 61: 7 11 7 11 7 10 8 SP SD: 5.3149 c. M: 6.7400 c. 62: 7 11 8 10 7 11 8 SP SD: 4.6325 c. M: 8.2696 c. 63: 7 11 8 11 7 11 8 SP T3 SD: 3.2266 c. M: 5.2393 c. 70: 8 12 9 12 8 12 9 SP T3 SD: 2.3291 c. M: 4.5508 c. 80: 9 14 10 14 9 14 10 SP T3 SD: 2.3235 c. M: 3.5727 c. 87: 10 15 11 15 10 15 11 SP T3 SD: 1.3855 c. M: 2.5804 c. 104: 12 18 13 18 12 18 13 SP T3 SD: 1.3262 c. M:-1.8912 c. 137: 16 24 17 23 16 24 17 SP SD: 1.5740 c. M:-2.9570 c. 159: 18 28 20 27 18 28 20 SP SD: 1.4819 c. M: 2.7918 c. 166: 19 29 21 28 19 29 21 SP SD: 1.0732 c. M: 1.9734 c. 183: 21 32 23 31 21 32 23 SP SD: 0.5860 c. M: 1.1834 c. 190: 22 33 24 32 22 33 24 SP SD: 0.6476 c. M: 0.9419 c. 200: 23 35 25 34 23 35 25 SP SD: 0.4419 c. M:-0.6371 c. 207: 24 36 26 35 24 36 26 SP SD: 0.3794 c. M:-0.5578 c. 287: 33 50 36 49 33 50 36 SP SD: 0.3747 c. M: 0.5936 c. 294: 34 51 37 50 34 51 37 SP SD: 0.2689 c. M: 0.4692 c. 407: 47 71 51 69 47 71 51 SP SD: 0.2647 c. M:-0.5036 c. 477: 55 83 60 81 55 83 60 SP SD: 0.1997 c. M: 0.3063 c. 494: 57 86 62 84 57 86 62 SP SD: 0.0611 c. M: 0.1111 c. 701: 81 122 88 119 81 122 88 SP SD: 0.0727 c. M:-0.1005 c. 1195: 138 208 150 203 138 208 150 SP SD: 0.0244 c. M:-0.0398 c. 1689: 195 294 212 287 195 294 212 SP SD: 0.0181 c. M: 0.0303 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: 14.6104 cents 4 x 5 x 6 x 7:8 S SD: 22.3605 cents 5 x 6:7 x 8:9:10 S SD: 19.8730 cents 6 x 7:8:9:10:11:12 S SD: 15.2820 cents 7:8 x 9 x 11:13:14 SD: 25.6174 cents 8:9:10:11:12:13:15:16 SD: 14.3813 cents 10:11:12:13:15:16:18:20 SD: 10.4574 cents 12:13:15:16:18:20:22:24 SD: 8.3725 cents 14:15:17:19:21:23:26:28 SD: 6.8350 cents 18:20:22:24:27:29:33:36 SD: 6.6117 cents 21:23:26:28:32:34:39:42 SD: 6.6082 cents 22:24:27:29:33:36:40:44 SD: 4.3798 cents 24:26:29:32:36:39:44:48 SD: 2.8265 cents 36:39:44:48:54:59:66:72 SD: 2.1049 cents 48:52:59:64:72:78:88:96 SD: 1.4012 cents 72:78:88:96:108:117:132:144 SD: 0.0000 cents