Scala analysis: morphable-06-tritavium
Sevish: Tritavium, Morphable
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 5/4 386.313714 major third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave 8: 9/4 1403.910002 major ninth 9: 5/2 1586.313714 major 10th 10: 11/4 1751.317942 undecimal semi-augmented fourth +1 octave 11: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 10/9 182.4037 minor whole tone 6: 21/20 84.4672 minor semitone 7: 8/7 231.1741 septimal whole tone 8: 9/8 203.9100 major whole tone 9: 10/9 182.4037 minor whole tone 10: 11/10 165.0042 Ptolemy's second, 4/5-tone 11: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 3 10/9 182.404 cents minor whole tone 1: 2 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 6/5 315.641 cents minor third 2: 1 40/33 333.041 cents 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 5/4 386.314 cents major third 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 4 4/3 498.045 cents perfect fourth 3: 2 27/20 519.551 cents acute fourth 3: 1 15/11 536.951 cents undecimal augmented fourth 3: 2 11/8 551.318 cents undecimal semi-augmented 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 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 40/27 680.449 cents grave fifth 4: 7 3/2 701.955 cents perfect fifth 4: 1 11/7 782.492 cents undecimal augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 2 33/20 866.959 cents 5: 3 5/3 884.359 cents major sixth, BP sixth 5: 1 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: 1 16/9 996.090 cents Pythagorean minor seventh 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 20/11 1034.996 cents large minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 15/8 1088.269 cents classic major seventh 6: 1 27/14 1137.039 cents septimal major seventh 7: 1 21/11 1119.463 cents undecimal major seventh 7: 7 2/1 1200.000 cents octave 7: 1 81/40 1221.506 cents syntonic comma, Didymus comma +1 octave 7: 1 33/16 1253.273 cents undecimal comma, al-Farabi's 1/4-tone +1 octave 7: 1 15/7 1319.443 cents septimal minor ninth, BP ninth 8: 1 21/10 1284.467 cents minor semitone +1 octave 8: 2 24/11 1350.637 cents undecimal neutral second, 3/4-tone +1 octave 8: 1 11/5 1365.004 cents neutral ninth 8: 2 20/9 1382.404 cents small ninth 8: 4 9/4 1403.910 cents major ninth 8: 1 33/14 1484.447 cents undecimal minor third +1 octave 9: 1 7/3 1466.871 cents minimal tenth, BP tenth 9: 2 12/5 1515.641 cents minor 10th 9: 1 22/9 1547.408 cents undecimal neutral third +1 octave 9: 2 27/11 1554.547 cents neutral third, Zalzal wosta of al-Farabi +1 octave 9: 1 99/40 1568.914 cents 9: 3 5/2 1586.314 cents major 10th 9: 1 18/7 1635.084 cents septimal major 10th 10: 1 21/8 1670.781 cents narrow fourth +1 octave 10: 2 8/3 1698.045 cents perfect 11th 10: 3 27/10 1719.551 cents acute fourth +1 octave 10: 2 30/11 1736.951 cents undecimal augmented fourth +1 octave 10: 2 11/4 1751.318 cents undecimal semi-augmented fourth +1 octave 10: 1 20/7 1817.488 cents Euler's tritone +1 octave Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.20000 = 31/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 203.9 386.3 551.3 702.0 884.4 968.8 1200.0 1403.9 1586.3 1751.3 1902.0 203.9 : 182.4 347.4 498.0 680.4 764.9 996.1 1200.0 1382.4 1547.4 1698.0 1902.0 386.3 : 165.0 315.6 498.0 582.5 813.7 1017.6 1200.0 1365.0 1515.6 1719.6 1902.0 551.3 : 150.6 333.0 417.5 648.7 852.6 1035.0 1200.0 1350.6 1554.5 1737.0 1902.0 702.0 : 182.4 266.9 498.0 702.0 884.4 1049.4 1200.0 1403.9 1586.3 1751.3 1902.0 884.4 : 84.5 315.6 519.6 702.0 867.0 1017.6 1221.5 1403.9 1568.9 1719.6 1902.0 968.8 : 231.2 435.1 617.5 782.5 933.1 1137.0 1319.4 1484.4 1635.1 1817.5 1902.0 1200.0: 203.9 386.3 551.3 702.0 905.9 1088.3 1253.3 1403.9 1586.3 1670.8 1902.0 1403.9: 182.4 347.4 498.0 702.0 884.4 1049.4 1200.0 1382.4 1466.9 1698.0 1902.0 1586.3: 165.0 315.6 519.6 702.0 867.0 1017.6 1200.0 1284.5 1515.6 1719.6 1902.0 1751.3: 150.6 354.5 537.0 702.0 852.6 1035.0 1119.5 1350.6 1554.5 1737.0 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 231.1741 cents 160/147, 146.7069 cents 21/20, 84.4672 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 417.5080 .. 617.4878 cents 55/49, 199.9798 cents 98/99,-17.5761 cents 4: 582.5122 .. 782.4920 cents 55/49, 199.9798 cents 49/50,-34.9756 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 98/99,-17.5761 cents 6: 968.8259 .. 1137.0391 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 7: 1119.4630 .. 1319.4428 cents 55/49, 199.9798 cents 98/99,-17.5761 cents 8: 1284.4672 .. 1484.4470 cents 55/49, 199.9798 cents 49/50,-34.9756 cents 9: 1466.8709 .. 1635.0841 cents 54/49, 168.2132 cents 98/99,-17.5761 cents 10: 1670.7809 .. 1817.4878 cents 160/147, 146.7069 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 172.9050 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.047008 Largest / Average step : 1.337001 Largest / Smallest step : 2.736851 Median interval of one step : 10/9, 182.4037 cents, amount: 3 Most common interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 173.94436 cents, oct.: 1913.38800 cents Scale is not proper Step pattern alph. order: ABCDBEFABCD Step pattern size order : EDCBDAFEDCB Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 0.366388 Lumma stability : 0.145127 Lumma impropriety factor : 0.073743 Rothenberg efficiency : 0.312121 redundancy: 0.687879 Efficiency x scale size : 3.433333 Number of different interval sizes : 62 = 6.20000 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 6.20000 = 31/5 Median interval variety : 5.5 Lowest interval variety : 5 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 3/2, 701.9550 cents & inv., amount: 7 Most common triad is 0.0 701.955 1200.000 cents, amount: 4 Number of recognisable fifths : 7, average 701.9550 cents Number of recognisable fourths : 4, average 498.0450 cents Scale contains two identical disjunct tetrachords All steps are superparticular (epimoric) Length of longest harmonic part : 5 at degree 6 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 27.2727% 2/1 octave complements present : 1 = 9.0909% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval classes 6 and 7 combined Scale is n-1 differentially coherent in interval classes 7 and 8 combined -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 33) Highest odd numerator or denominator: 11 Scale harmonicity : 0.021337 Average absolute harmonicity : 0.222429 Specific harmonicity : 0.157105 Fundamental : 1/24, -4.5850 octaves, 10.9011 Hz. Guide tone : 6930, 12.7586 octaves, 1813065.168 Hz. Exponens Consonantiae : 1.663200E+05, 17.34360 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 55.5, average 5.04545 Mersenne's string divisions : 116396280 Sum of van Prooijen's expressibility: 7.88752, average 0.71705 Sum of Tenney's harmonic distance : 13.48215, average 1.22565 Vogel's harmonic complexity : 10.00000 Wille's k value : 16 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 149.36281, average 2.26307 Lattice compactness (without 2's) : 94.63779, average 1.43391 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.36364 17 1 3: -1 .. 2 0.45455 7 4 5: 0 .. 1 0.27273 3 3 7: 0 .. 1 0.09091 1 1 11: 0 .. 1 0.18182 2 2 Average exponent except 2's : 11 / 11 = 1.00000 Average absolute exponent except 2's: 13 / 11 = 1.18182 Scale is JI-epimorphic with val: <7 11 16 20 24| Scale is weakly epimorphic with val: <7 11 17 19 23|
FIT/MODE
11: 1 1 1 1 1 0 2 1 1 1 1 N T3 SD: 39.2935 c. M: 104.3009 c. 12: 1 1 1 1 1 1 1 2 1 1 1 P M ME S SD: 56.2181 c. M: 91.8775 c. 13: 1 2 1 1 1 1 1 2 1 1 1 P M ME S SD: 38.2927 c. M:-59.1323 c. 14: 2 1 1 1 2 0 2 1 2 1 1 N D3 SD: 37.0547 c. M:-67.7979 c. 16: 2 1 2 1 1 1 2 2 1 2 1 N D3 SD: 30.7180 c. M: 52.2534 c. 17: 2 2 1 1 2 1 2 2 1 2 1 P D3 SD: 33.1764 c. M:-61.2051 c. 18: 2 2 1 2 1 1 2 2 2 2 1 N SD: 29.4349 c. M:-44.9729 c. 19: 2 2 2 1 2 1 2 2 2 2 1 P D3 SD: 24.7760 c. M:-50.5342 c. 20: 2 2 2 1 2 1 3 2 2 1 2 N SD: 25.8490 c. M: 39.5584 c. 22: 2 2 2 2 2 1 3 2 2 2 2 P T3 SD: 24.1654 c. M: 40.5037 c. 24: 3 2 2 2 2 1 3 3 2 2 2 N SD: 15.2549 c. M:-33.8344 c. 28: 3 3 2 2 3 1 4 3 2 3 2 N SD: 16.9665 c. M: 23.9935 c. 30: 3 3 3 2 3 1 4 3 3 3 2 N SD: 12.1316 c. M:-23.8401 c. 35: 4 3 3 3 3 2 4 4 3 3 3 P SD: 9.3896 c. M: 14.8936 c. 49: 5 5 4 4 5 2 6 5 5 4 4 N SD: 5.6204 c. M: 9.8330 c. 65: 7 6 6 5 6 3 8 7 6 6 5 N SD: 3.9149 c. M: 6.5333 c. 73: 8 7 6 6 7 3 9 8 7 6 6 N SD: 3.5492 c. M: 5.6880 c. 84: 9 8 7 7 8 4 10 9 8 7 7 N SD: 3.7259 c. M: 7.9022 c. 92: 10 9 8 7 9 4 11 10 9 8 7 N SD: 4.2354 c. M:-6.8645 c. 103: 11 10 9 8 10 4 13 11 10 9 8 N SD: 3.0128 c. M: 8.6156 c. 114: 12 11 10 9 11 5 14 12 11 10 9 N SD: 1.7464 c. M: 3.7042 c. 149: 16 14 13 12 14 7 18 16 14 13 12 N SD: 2.1439 c. M: 3.5876 c. 176: 19 17 15 14 17 8 21 19 17 15 14 N SD: 1.7482 c. M:-3.7647 c. 187: 20 18 16 15 18 8 23 20 18 16 15 N SD: 1.1913 c. M: 2.5921 c. 241: 26 23 21 19 23 11 29 26 23 21 19 N SD: 0.8720 c. M:-1.8814 c. 290: 31 28 25 23 28 13 35 31 28 25 23 N SD: 0.7575 c. M:-1.8270 c. 344: 37 33 30 27 33 15 42 37 33 30 27 N SD: 0.8237 c. M:-1.5760 c. 355: 38 34 31 28 34 16 43 38 34 31 28 N SD: 0.4569 c. M:-0.9033 c. 428: 46 41 37 34 41 19 52 46 41 37 34 N SD: 0.2739 c. M:-0.5057 c. 542: 58 52 47 43 52 24 66 58 52 47 43 N SD: 0.2477 c. M: 0.3826 c. 783: 84 75 68 62 75 35 95 84 75 68 62 N SD: 0.1454 c. M:-0.3696 c. 970: 104 93 84 77 93 43 118 104 93 84 77 N SD: 0.1593 c. M: 0.3429 c. 1176: 126 113 102 93 113 52 143 126 113 102 93 N SD: 0.1740 c. M:-0.3091 c. 1211: 130 116 105 96 116 54 147 130 116 105 96 N SD: 0.1359 c. M:-0.2635 c. 1325: 142 127 115 105 127 59 161 142 127 115 105 N SD: 0.1007 c. M: 0.1810 c. 1753: 188 168 152 139 168 78 213 188 168 152 139 N SD: 0.0885 c. M: 0.1740 c. 1959: 210 188 170 155 188 87 238 210 188 170 155 N SD: 0.0904 c. M:-0.1506 c. 2146: 230 206 186 170 206 95 261 230 206 186 170 N SD: 0.0823 c. M:-0.1479 c. 2387: 256 229 207 189 229 106 290 256 229 207 189 N SD: 0.0725 c. M:-0.1329 c.
FIT/HARMONIC
1 x x x x x x 2 x x x 3 S SD: 0.0000 cents 2 x x x 3 x x 4 x 5 x 6 S SD: 0.0000 cents 3 x x 4 x 5 x 6:7 x 8:9 S SD: 16.3640 cents 4 x 5 x 6 x 7:8:9:10:11:12 S SD: 0.0000 cents 5 x 6:7 x 8:9:10:11:13:14:15 SD: 15.8846 cents 6:7 x 8:9:10:11:12:14:15:17:18 SD: 14.1150 cents 7:8:9:10:11 x 12:14:16:18:19:21 SD: 13.7459 cents 8:9:10:11:12:13:14:16:18:20:22:24 S SD: 3.9846 cents 16:18:20:22:24:27:28:32:36:40:44:48 S SD: 1.9551 cents 24:27:30:33:36:40:42:48:54:60:66:72 S SD: 0.0000 cents