Scala analysis: xen15-chalmers-triadic-reversed-diamond-23-20-tetrachord
Tetrachord 23/20 * 1600/1587 * 23/20 of triadic reversed diamond for M=23/20, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/20 241.960633 2: 80/69 256.084366 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 23/20 241.9606 1: 23/20 241.9606 2: 1600/1587 14.1237 3: 23/20 241.9606
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1600/1587 14.124 cents 1: 2 23/20 241.961 cents 2: 2 80/69 256.084 cents 2: 1 529/400 483.921 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 242.0 256.1 498.0 242.0: 14.1 256.1 498.0 256.1: 242.0 483.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.1237 .. 241.9606 cents 36501/32000, 227.8369 cents 1600/1587, 14.1237 cents 2: 256.0844 .. 483.9213 cents 36501/32000, 227.8369 cents 1600/1587, 14.1237 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 1600/1587, 14.1237 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/20, 241.9606 cents Average / Smallest step : 11.754329 Largest / Average step : 1.457462 Largest / Smallest step : 17.131494 Median interval of one step : 23/20, 241.9606 cents, amount: 2 Most common interval of one step : 23/20, 241.9606 cents, amount: 2 Least squares average step : 160.59031 cents, oct.: 481.77093 cents Scale is strictly proper Scale has Myhill's property chromas: 36501/32000, 227.8369 cents and 57927087/51200000, 213.7132 cents, ratio: 1.066087 generators: 1 of 241.96063 cents and 2 of 256.08437 cents ET pair of linear temperament : 70&494 Scale is distributional even Scale is a mode of a 247-tone equal temperament with octave 4/3 degrees: 120 127 247 generators: 120 and 127 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : LSL Scale is a Constant Structure, by a margin of 14.12373 cents Scale diversity : 0.286511 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.085075 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 1600/1587, 14.1237 cents Most common intervals : 23/20, 241.9606 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 483.9213 cents Number of appreciable fourths : 0 Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 23 Odd number limit : 1587 (O: 529 U: 1587) Highest odd numerator or denominator: 69 Scale harmonicity : 0.009466 Average absolute harmonicity : 0.084074 Specific harmonicity : 0.049753 Fundamental : 1/1380, -10.4305 octaves, 0.1896 Hz. Guide tone : 1840, 10.8455 octaves, 481391.040 Hz. Exponens Consonantiae : 2.539200E+06, 21.27594 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 99.5, average 33.16667 Mersenne's string divisions : 44849 Sum of van Prooijen's expressibility: 3.67770, average 1.22590 Sum of Tenney's harmonic distance : 7.48388, average 2.49463 Vogel's harmonic complexity : 32.33333 Wille's k value : 793 Wilson's harmonic complexity : 59 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 22.56105, average 3.76017 Lattice compactness (without 2's) : 10.29253, average 1.71542 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.33333 8 3: -1 .. 0 -0.66667 2 1 5: -1 .. 1 0.00000 2 23: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is JI-epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 15 31| Scale is weakly epimorphic with val: <7 11 15 33| Scale is weakly epimorphic with val: <7 11 15 34| Scale is weakly epimorphic with val: <7 11 15 36| Scale is JI-epimorphic with val: <7 11 16 31| Scale is weakly epimorphic with val: <7 11 16 32| Scale is weakly epimorphic with val: <7 11 16 34| Scale is weakly epimorphic with val: <7 11 16 35| Scale is weakly epimorphic with val: <7 11 17 30| Scale is JI-epimorphic with val: <7 11 17 32| Scale is weakly epimorphic with val: <7 11 17 33| = patent Scale is weakly epimorphic with val: <7 11 17 35| Scale is weakly epimorphic with val: <7 11 17 36| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 31| Scale is JI-epimorphic with val: <7 11 18 33| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 18 36| Scale is weakly epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 11 19 32| Scale is JI-epimorphic with val: <7 11 19 34| Scale is weakly epimorphic with val: <7 11 19 35|
FIT/MODE
3: 1 0 2 N G T3 SD: 68.0202 c. M: 90.0694 c. 4: 2 0 2 P M DE I SD: 5.7660 c. M:-7.0619 c. 19: 9 1 9 SP M DE I SD: 4.9354 c. M: 6.0446 c. 21: 10 1 10 SP M DE I SD: 3.9162 c. M: 4.7963 c. 23: 11 1 11 SP M DE I SD: 3.0743 c. M:-3.7652 c. 25: 12 1 12 SP M DE I SD: 2.3671 c. M: 2.8990 c. 27: 13 1 13 SP M DE I SD: 1.7646 c. M: 2.1612 c. 29: 14 1 14 SP M DE I SD: 1.2453 c. M: 1.5251 c. 31: 15 1 15 SP M DE I SD: 0.7929 c. M:-0.9711 c. 33: 16 1 16 SP M DE I SD: 0.3954 c. M: 0.4843 c. 35: 17 1 17 SP M DE I SD: 0.0433 c. M:-0.0531 c. 142: 69 4 69 SP M DE I SD: 0.0385 c. M:-0.0471 c. 177: 86 5 86 SP M DE I SD: 0.0223 c. M:-0.0273 c. 212: 103 6 103 SP M DE I SD: 0.0115 c. M: 0.0141 c. 247: 120 7 120 SP M DE I SD: 0.0037 c. M:-0.0045 c. 282: 137 8 137 SP M DE I SD: 0.0021 c. M: 0.0026 c. 529: 257 15 257 SP M DE I SD: 0.0006 c. M:-0.0007 c. 811: 394 23 394 SP M DE I SD: 0.0003 c. M: 0.0004 c. 1340: 651 38 651 SP M DE I SD: 0.0000 c. M: 0.0000 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 x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 51.6762 cents 6 x 7:8 S SD: 5.3933 cents 7:8 x 9 S SD: 31.9391 cents 8:9 x 11 SD: 32.7332 cents 9:10 x 12 S SD: 29.7785 cents 10 x 12:13 S SD: 36.9736 cents 11 x 13:15 SD: 25.5487 cents 12 x 14:16 S SD: 5.3933 cents 13:15 x 17 SD: 17.0553 cents 14:16 x 19 SD: 16.2426 cents 15:17 x 20 SD: 12.6370 cents 17 x 20:23 SD: 17.8714 cents 18 x 21:24 S SD: 5.3933 cents 19 x 22:25 SD: 11.5218 cents 20:23 x 27 SD: 10.7531 cents 21:24 x 28 S SD: 5.3933 cents 24 x 28:32 S SD: 5.3933 cents 25 x 29:33 SD: 8.7105 cents 26:30 x 35 SD: 8.7732 cents 27:31 x 36 SD: 1.3950 cents 28:32 x 37 SD: 9.4529 cents 30 x 35:40 S SD: 5.3933 cents 31 x 36:41 SD: 7.1466 cents 32 x 37:43 SD: 7.1412 cents 33:38 x 44 SD: 1.1397 cents 34:39 x 45 SD: 6.7620 cents 36:41:42:48 SD: 6.6572 cents 37 x 43:49 SD: 6.2146 cents 38 x 44:51 SD: 5.7895 cents 39:45 x 52 SD: 2.8902 cents 40:46 x 53 SD: 5.4271 cents 42:48:49:56 S SD: 5.0848 cents 44 x 51:59 SD: 4.9105 cents 45 x 52:60 SD: 2.8902 cents 46:53 x 61 SD: 4.9925 cents 47:54 x 63 SD: 4.6615 cents 48:55:56:64 SD: 4.1612 cents 50 x 58:67 SD: 4.3389 cents 51 x 59:68 SD: 1.9116 cents 52:60 x 69 SD: 5.0750 cents 53:61 x 71 SD: 4.1349 cents 54:62:63:72 SD: 3.7138 cents 57 x 66:76 SD: 1.1397 cents 58 x 67:77 SD: 4.9068 cents 59:68 x 79 SD: 4.1292 cents 60:69:70:80 SD: 3.5955 cents 61:70:71:81 SD: 3.4887 cents 64 x 74:85 SD: 4.1347 cents 65:75 x 87 SD: 4.4040 cents 66:76:77:88 SD: 3.6749 cents 67:77:78:89 SD: 3.2221 cents 68:78:79:91 SD: 2.8333 cents 69:79:80:92 SD: 2.5510 cents 70 x 81:93 SD: 3.5339 cents 71 x 82:95 SD: 4.5323 cents 72:83 x 96 SD: 2.0883 cents 75:86:87:100 SD: 1.6998 cents 77 x 89:103 SD: 3.8760 cents 78:90 x 104 SD: 2.8902 cents 80:92:93:107 SD: 2.3634 cents 81:93:94:108 SD: 1.0725 cents 84 x 97:112 SD: 3.4849 cents 85:98:99:113 SD: 3.4571 cents 86:99:100:115 SD: 2.4397 cents 87:100:101:116 SD: 0.7996 cents 90 x 104:120 SD: 2.8902 cents 92:106:107:123 SD: 2.6234 cents 93:107:108:124 SD: 0.9683 cents 97:112 x 129 SD: 4.1394 cents 98:113:114:131 SD: 2.8575 cents 99:114:115:132 SD: 1.3303 cents 113:130:131:151 SD: 1.2961 cents 114:131:132:152 SD: 0.8782 cents 120:138:139:160 SD: 0.5413 cents 126:145:146:168 SD: 0.5259 cents 201:231:233:268 SD: 0.3898 cents 207:238:240:276 SD: 0.1212 cents 420:483:487:560 SD: 0.0515 cents