Scala analysis: xen15-chalmers-triadic-reversed-diamond-26-21
Triadic reversed diamond for M=26/21, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 26/21 369.746754 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 21/13 830.253246 6: 13/7 1071.701755 16/3-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 14/13 128.2982 2/3-tone 1: 14/13 128.2982 2/3-tone 2: 169/147 241.4485 3: 14/13 128.2982 2/3-tone 4: 9/8 203.9100 major whole tone 5: 14/13 128.2982 2/3-tone 6: 169/147 241.4485 7: 14/13 128.2982 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 14/13 128.298 cents 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 169/147 241.449 cents 2: 1 196/169 256.596 cents two (2/3-tone) 2: 2 63/52 332.208 cents 2: 4 26/21 369.747 cents 3: 1 441/338 460.506 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 39/28 573.657 cents 4: 2 56/39 626.343 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 676/441 739.494 cents 5: 4 21/13 830.253 cents 5: 2 104/63 867.792 cents 5: 1 169/98 943.404 cents 6: 2 294/169 958.551 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 13/7 1071.702 cents 16/3-tone 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 4 5 6 7 0.0 : 128.3 369.7 498.0 702.0 830.3 1071.7 1200.0 128.3 : 241.4 369.7 573.7 702.0 943.4 1071.7 1200.0 369.7 : 128.3 332.2 460.5 702.0 830.3 958.6 1200.0 498.0 : 203.9 332.2 573.7 702.0 830.3 1071.7 1200.0 702.0 : 128.3 369.7 498.0 626.3 867.8 996.1 1200.0 830.3 : 241.4 369.7 498.0 739.5 867.8 1071.7 1200.0 1071.7: 128.3 256.6 498.0 626.3 830.3 958.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 241.4485 cents 2197/2058, 113.1503 cents 14/13, 128.2982 cents 2: 256.5965 .. 369.7468 cents 2197/2058, 113.1503 cents 28812/28561, 15.1480 cents 3: 460.5065 .. 573.6568 cents 2197/2058, 113.1503 cents 9261/8788, 90.7597 cents 4: 626.3432 .. 739.4935 cents 2197/2058, 113.1503 cents 1568/1521, 52.6865 cents 5: 830.2532 .. 943.4035 cents 2197/2058, 113.1503 cents 9261/8788, 90.7597 cents 6: 958.5515 .. 1071.7018 cents 2197/2058, 113.1503 cents 28812/28561, 15.1480 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 14/13, 128.2982 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 169/147, 241.4485 cents Average / Smallest step : 1.336172 Largest / Average step : 1.408450 Largest / Smallest step : 1.881932 Median interval of one step : 14/13, 128.2982 cents, amount: 4 Most common interval of one step : 14/13, 128.2982 cents, amount: 4 Least squares average step : 172.50874 cents, oct.: 1207.56118 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 15.14798 cents Scale diversity : 1.394949 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.434249 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 Number of different interval sizes : 18 = 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 : 28812/28561, 15.1480 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best minor thirds form a closed circle Scale is a complete diamond : 7 13 21 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 100.0000% Scale is differentially coherent in interval classes 3 and 4 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 13 Odd number limit : 441 (O: 441 U: 441) Highest odd numerator or denominator: 21 Scale harmonicity : 0.013659 Average absolute harmonicity : 0.229132 Specific harmonicity : 0.073348 Fundamental : 1/546, -9.0928 octaves, 0.4792 Hz. Guide tone : 1092, 10.0928 octaves, 285695.117 Hz. Exponens Consonantiae : 5.962320E+05, 19.18551 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 71.5, average 10.21429 Mersenne's string divisions : 3020220 Sum of van Prooijen's expressibility: 5.82657, average 0.83237 Sum of Tenney's harmonic distance : 11.55083, average 1.65012 Vogel's harmonic complexity : 24.57143 Wille's k value : 409 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 60.17688, average 2.14917 Lattice compactness (without 2's) : 47.53320, average 1.69761 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 6 1 3: -1 .. 1 0.00000 4 2 7: -1 .. 1 0.00000 4 13: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 10 18 27| Scale is weakly epimorphic with val: <7 10 19 27| Scale is weakly epimorphic with val: <7 10 19 28| Scale is weakly epimorphic with val: <7 10 20 28| Scale is weakly epimorphic with val: <7 10 20 29| Scale is weakly epimorphic with val: <7 10 21 29| Scale is weakly epimorphic with val: <7 10 22 24| Scale is JI-epimorphic with val: <7 11 18 24| Scale is weakly epimorphic with val: <7 11 19 24| Scale is JI-epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 20 25| Scale is JI-epimorphic with val: <7 11 20 26| = patent Scale is weakly epimorphic with val: <7 11 21 26| Scale is JI-epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 11 22 27| Scale is JI-epimorphic with val: <7 11 22 28| Scale is weakly epimorphic with val: <7 12 18 26| Scale is weakly epimorphic with val: <7 12 18 29| Scale is weakly epimorphic with val: <7 12 19 27| Scale is weakly epimorphic with val: <7 12 20 24| Scale is weakly epimorphic with val: <7 12 20 28| Scale is weakly epimorphic with val: <7 12 21 25| Scale is weakly epimorphic with val: <7 12 21 29| Scale is weakly epimorphic with val: <7 12 22 26|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 28.5209 c. M: 43.1303 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 24.9907 c. M:-35.2883 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 11.8259 c. M:-18.0450 c. 17: 2 3 2 3 2 3 2 SP M ME I SD: 11.5102 c. M: 16.8056 c. Neutral Dorian, Maqamic-7 19: 2 4 2 3 2 4 2 P T3 I SD: 6.3400 c. M: 9.2006 c. 29: 3 6 3 5 3 6 3 P T3 I SD: 2.7595 c. M:-4.1603 c. 55: 6 11 6 9 6 11 6 SP T3 I SD: 2.5301 c. M:-3.7732 c. 65: 7 13 7 11 7 13 7 SP T3 I SD: 0.6116 c. M:-0.9325 c. 94: 10 19 10 16 10 19 10 SP T3 I SD: 0.4326 c. M: 0.6387 c. 159: 17 32 17 27 17 32 17 SP T3 I SD: 0.0502 c. M:-0.0682 c. 1188: 127 239 127 202 127 239 127 SP T3 I SD: 0.0446 c. M: 0.0652 c. 1347: 144 271 144 229 144 271 144 SP T3 I SD: 0.0335 c. M:-0.0495 c. 1506: 161 303 161 256 161 303 161 SP T3 I SD: 0.0248 c. M: 0.0370 c. 1665: 178 335 178 283 178 335 178 SP T3 I SD: 0.0179 c. M: 0.0270 c. 1824: 195 367 195 310 195 367 195 SP T3 I SD: 0.0122 c. M: 0.0187 c. 1983: 212 399 212 337 212 399 212 SP T3 I SD: 0.0078 c. M:-0.0117 c. 2142: 229 431 229 364 229 431 229 SP T3 I SD: 0.0049 c. M:-0.0069 c. 2301: 246 463 246 391 246 463 246 SP T3 I SD: 0.0045 c. M:-0.0062 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: 18.0352 cents 4 x 5 x 6 x 7:8 S SD: 26.0503 cents 5 x 6:7 x 8:9:10 S SD: 23.0339 cents 6 x 7:8:9:10:11:12 S SD: 19.7272 cents 7:8 x 9 x 11:13:14 SD: 25.9451 cents 8:9:10:11:12:13:15:16 SD: 13.7095 cents 10:11:12:13:15:16:19:20 SD: 12.8018 cents 12:13:15:16:18:19:22:24 SD: 6.5197 cents 16:17:20:21:24:26:30:32 SD: 6.2966 cents 21:23:26:28:32:34:39:42 SD: 5.7340 cents 24:26:30:32:36:39:45:48 SD: 3.9384 cents 26:28:32:35:39:42:48:52 SD: 3.1480 cents 36:39:45:48:54:58:67:72 SD: 2.9092 cents 38:41:47:51:57:61:71:76 SD: 2.7509 cents 42:45:52:56:63:68:78:84 SD: 1.3835 cents 54:58:67:72:81:87:100:108 SD: 1.2787 cents 76:82:94:101:114:123:141:152 SD: 1.1050 cents 92:99:114:123:138:149:171:184 SD: 0.9907 cents 102:110:126:136:153:165:189:204 SD: 0.9313 cents 104:112:129:139:156:168:193:208 SD: 0.7713 cents 114:123:141:152:171:184:212:228 SD: 0.6576 cents 130:140:161:173:195:210:241:260 SD: 0.6520 cents 156:168:193:208:234:252:290:312 SD: 0.3048 cents 210:226:260:280:315:339:390:420 SD: 0.2380 cents 286:308:354:381:429:462:531:572 SD: 0.2359 cents 336:362:416:448:504:543:624:672 SD: 0.1487 cents 390:420:483:520:585:630:724:780 SD: 0.1220 cents 504:543:624:672:756:814:936:1008 SD: 0.1151 cents 546:588:676:728:819:882:1014:1092 SD: 0.0000 cents