Scala analysis: 423_D9
Diatonic tetrachord 27/26 * 26/23 * 92/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/26 65.337341 tridecimal comma 2: 27/23 277.590655 vicesimotertial minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 92/81 220.4543 1: 27/26 65.3373 tridecimal comma 2: 26/23 212.2533 3: 92/81 220.4543
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 27/26 65.337 cents tridecimal comma 1: 1 26/23 212.253 cents 1: 1 92/81 220.454 cents 2: 1 27/23 277.591 cents vicesimotertial minor third 2: 1 46/39 285.792 cents 2: 1 104/81 432.708 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 65.3 277.6 498.0 65.3 : 212.3 432.7 498.0 277.6: 220.5 285.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 65.3373 .. 220.4543 cents 2392/2187, 155.1170 cents 27/26, 65.3373 cents 2: 277.5907 .. 432.7077 cents 2392/2187, 155.1170 cents 2187/2116, 57.1363 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 27/26, 65.3373 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 92/81, 220.4543 cents Average / Smallest step : 2.540890 Largest / Average step : 1.327918 Largest / Smallest step : 3.374094 Median interval of one step : 26/23, 212.2533 cents, amount: 1 Least squares average step : 151.04669 cents, oct.: 453.14007 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 57.13631 cents Scale diversity : 0.809665 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.377096 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1058/1053, 8.2010 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 146.9160 cents: 1 -- Rational properties -- Prime limit : 23 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.012836 Average absolute harmonicity : 0.088783 Specific harmonicity : 0.066191 Fundamental : 1/1794, -10.8090 octaves, 0.1458 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 1.937520E+05, 17.56385 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 55.0, average 18.33333 Mersenne's string divisions : 18550 Sum of van Prooijen's expressibility: 3.33985, average 1.11328 Sum of Tenney's harmonic distance : 6.71861, average 2.23954 Vogel's harmonic complexity : 33.33333 Wille's k value : 931 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 20.12862, average 3.35477 Lattice compactness (without 2's) : 16.98498, average 2.83083 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 3 1.66667 7 1 13: -1 .. 0 -0.33333 1 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 11 25 30| Scale is weakly epimorphic with val: <6 11 28 30| Scale is JI-epimorphic with val: <7 11 25 31| Scale is weakly epimorphic with val: <7 11 25 34| Scale is weakly epimorphic with val: <7 11 27 32| Scale is weakly epimorphic with val: <7 11 27 35| Scale is weakly epimorphic with val: <7 11 28 31| Scale is weakly epimorphic with val: <7 11 28 34| Scale is weakly epimorphic with val: <7 11 30 32| Scale is weakly epimorphic with val: <7 11 30 35| Scale is weakly epimorphic with val: <7 12 25 33| Scale is weakly epimorphic with val: <7 12 26 32| Scale is weakly epimorphic with val: <7 12 26 35| Scale is weakly epimorphic with val: <7 12 28 33| Scale is weakly epimorphic with val: <8 11 27 30| Scale is weakly epimorphic with val: <8 11 30 30| Scale is weakly epimorphic with val: <8 12 25 31| Scale is weakly epimorphic with val: <8 12 25 34| Scale is weakly epimorphic with val: <8 12 26 33| Scale is weakly epimorphic with val: <8 12 29 33|
FIT/MODE
3: 0 2 1 N G T3 SD: 49.1006 c. M: 65.3373 c. 4: 0 2 2 P M DE S SD: 41.1708 c. M: 65.3373 c. 5: 1 2 2 SP M ME S SD: 23.2775 c. M:-34.2717 c. 6: 1 2 3 P T3 SD: 19.3939 c. M: 28.5682 c. 7: 1 3 3 SP M DE S SD: 5.2558 c. M:-7.0065 c. 16: 2 7 7 SP M DE S SD: 2.3129 c. M: 3.0817 c. 23: 3 10 10 SP M DE S SD: 2.2695 c. M:-3.9130 c. 31: 4 13 14 SP T3 SD: 2.6537 c. M: 4.4692 c. 36: 5 15 16 SP T3 SD: 2.2745 c. M:-3.8356 c. 38: 5 16 17 SP T3 SD: 1.3645 c. M: 2.3553 c. 45: 6 19 20 SP T3 SD: 0.8063 c. M:-1.0687 c. 54: 7 23 24 SP T3 SD: 0.6856 c. M: 0.8990 c. 61: 8 26 27 SP T3 SD: 0.0125 c. M: 0.0200 c. 1509: 198 643 668 SP T3 SD: 0.0131 c. M: 0.0189 c. 1570: 206 669 695 SP T3 SD: 0.0122 c. M: 0.0178 c. 1631: 214 695 722 SP T3 SD: 0.0113 c. M: 0.0168 c. 1692: 222 721 749 SP T3 SD: 0.0106 c. M: 0.0159 c. 1753: 230 747 776 SP T3 SD: 0.0099 c. M: 0.0151 c. 1814: 238 773 803 SP T3 SD: 0.0092 c. M: 0.0143 c. 1875: 246 799 830 SP T3 SD: 0.0086 c. M: 0.0136 c. 1936: 254 825 857 SP T3 SD: 0.0081 c. M: 0.0129 c. 1997: 262 851 884 SP T3 SD: 0.0075 c. M: 0.0122 c. 2058: 270 877 911 SP T3 SD: 0.0071 c. M: 0.0116 c. 2119: 278 903 938 SP T3 SD: 0.0066 c. M: 0.0111 c. 2180: 286 929 965 SP T3 SD: 0.0062 c. M: 0.0105 c. 2241: 294 955 992 SP T3 SD: 0.0059 c. M: 0.0100 c. 2302: 302 981 1019 SP T3 SD: 0.0056 c. M: 0.0095 c. 2363: 310 1007 1046 SP T3 SD: 0.0053 c. M: 0.0091 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x 5 x S SD: 108.7231 cents 5 x 6:7 S SD: 46.3210 cents 6 x 7:8 S SD: 5.3599 cents 7 x 8:9 S SD: 39.1107 cents 8 x 9:11 SD: 45.4611 cents 9 x 11:12 SD: 34.9086 cents 11:12:13:15 SD: 31.4902 cents 12:13:14:16 S SD: 24.6719 cents 15:16:18:20 S SD: 20.0007 cents 16:17:19:21 SD: 17.3520 cents 17:18:20:23 SD: 14.0755 cents 18:19:21:24 SD: 10.0767 cents 21:22:25:28 SD: 9.5416 cents 22:23:26:29 SD: 8.5731 cents 23:24:27:31 SD: 6.8306 cents 24:25:28:32 SD: 3.9913 cents 45:47:53:60 SD: 3.8194 cents 51:53:60:68 SD: 1.3239 cents 75:78:88:100 SD: 0.9006 cents 126:131:148:168 SD: 0.7582 cents 132:137:155:176 SD: 0.3621 cents 207:215:243:276 SD: 0.1032 cents 339:352:398:452 SD: 0.0892 cents 546:567:641:728 SD: 0.0391 cents