Scala analysis: xen15-chalmers-triadic-reversed-diamond-81-64
Triadic reversed diamond for M=81/64, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 81/64 407.820003 Pythagorean major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 128/81 792.179997 Pythagorean minor sixth 6: 243/128 1109.775004 Pythagorean major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 256/243 90.2250 limma, Pythagorean minor second 2: 19683/16384 317.5950 Pythagorean augmented second 3: 256/243 90.2250 limma, Pythagorean minor second 4: 9/8 203.9100 major whole tone 5: 256/243 90.2250 limma, Pythagorean minor second 6: 19683/16384 317.5950 Pythagorean augmented second 7: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 256/243 90.225 cents limma, Pythagorean minor second 1: 1 9/8 203.910 cents major whole tone 1: 2 19683/16384 317.595 cents Pythagorean augmented second 2: 1 65536/59049 180.450 cents Pythagorean diminished third 2: 2 32/27 294.135 cents Pythagorean minor third 2: 4 81/64 407.820 cents Pythagorean major third 3: 1 8192/6561 384.360 cents Pythagorean diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 2 729/512 611.730 cents Pythagorean tritone 4: 2 1024/729 588.270 cents Pythagorean diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 6561/4096 815.640 cents Pythagorean augmented fifth 5: 4 128/81 792.180 cents Pythagorean minor sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 1 59049/32768 1019.550 cents Pythagorean augmented sixth 6: 2 32768/19683 882.405 cents Pythagorean diminished seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 243/128 1109.775 cents Pythagorean major seventh 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 : 90.2 407.8 498.0 702.0 792.2 1109.8 1200.0 90.2 : 317.6 407.8 611.7 702.0 1019.6 1109.8 1200.0 407.8 : 90.2 294.1 384.4 702.0 792.2 882.4 1200.0 498.0 : 203.9 294.1 611.7 702.0 792.2 1109.8 1200.0 702.0 : 90.2 407.8 498.0 588.3 905.9 996.1 1200.0 792.2 : 317.6 407.8 498.0 815.6 905.9 1109.8 1200.0 1109.8: 90.2 180.4 498.0 588.3 792.2 882.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 317.5950 cents 4782969/4194304, 227.3700 cents 256/243, 90.2250 cents 2: 180.4500 .. 407.8200 cents 4782969/4194304, 227.3700 cents 1073741824/1162261467,-137.1450 cents 3: 384.3600 .. 611.7300 cents 4782969/4194304, 227.3700 cents 524288/531441,-23.4600 cents 4: 588.2700 .. 815.6400 cents 4782969/4194304, 227.3700 cents 524288/531441,-23.4600 cents 5: 792.1800 .. 1019.5500 cents 4782969/4194304, 227.3700 cents 524288/531441,-23.4600 cents 6: 882.4050 .. 1109.7750 cents 4782969/4194304, 227.3700 cents 1073741824/1162261467,-137.1450 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 19683/16384, 317.5950 cents Average / Smallest step : 1.900012 Largest / Average step : 1.852638 Largest / Smallest step : 3.520034 Median interval of one step : 256/243, 90.2250 cents, amount: 4 Most common interval of one step : 256/243, 90.2250 cents, amount: 4 Least squares average step : 173.05264 cents, oct.: 1211.36850 cents Scale is not proper Scale has trivalence property Scale is a mode of a 665-tone equal temperament with octave 2/1 degrees: 50 226 276 389 439 615 665 Least number of segments generator : 333 of 600.902 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 389 of 701.955 cents and inv. generated superset size: 11 = 4 more = 157.143% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 23.46001 cents Scale diversity : 1.401536 Lumma stability : 0.150375 Lumma impropriety factor : 0.287225 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 : 531441/524288, 23.4600 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale is a complete diamond : 1 3 243 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 : 3 Odd number limit : 59049 (O: 59049 U: 59049) Highest odd numerator or denominator: 243 Scale harmonicity : 0.024000 Average absolute harmonicity : 0.242810 Specific harmonicity : 0.130790 Fundamental : 1/31104, -14.9248 octaves, 0.0084 Hz. Guide tone : 62208, 15.9248 octaves, 16275203.166 Hz. Exponens Consonantiae : 1.934918E+09, 30.84963 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 619.5, average 88.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.54243, average 1.36320 Sum of Tenney's harmonic distance : 19.17538, average 2.73934 Vogel's harmonic complexity : 22.57143 Wille's k value : 29524 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 10 Triangular lattice diameter : 10 Lattice compactness : 214.51798, average 7.66136 Lattice compactness (without 2's) : 116.00000, average 4.14286 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: -7 .. 8 0.57143 32 1 3: -5 .. 5 0.00000 20 6 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is weakly epimorphic with val: <7 10| Scale is JI-epimorphic with val: <7 11| = patent Scale is weakly epimorphic with val: <7 12|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 56.2595 c. M: 81.2036 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 30.0701 c. M: 43.1083 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 6.7723 c. M: 9.7750 c. Double Harmonic Major, Major Gipsy, Bhairav That, Mela Mayamalavagaula, Raga Paraj, Kalingada, Gaulipantu, Lalitapancamam, Gandhakriya, Kalingda, Manjiri, Chromatic 2nd Byzantine Liturgical, Hitzazkiar: Greece, Maqam Zengule, Hijaz Kar, Suzidil 26: 2 7 2 4 2 7 2 N T3 I SD: 6.6468 c. M:-9.6473 c. 27: 2 7 2 5 2 7 2 N T3 I SD: 6.4757 c. M: 9.1561 c. 29: 2 8 2 5 2 8 2 N T3 I SD: 5.1729 c. M: 7.4664 c. 38: 3 10 3 6 3 10 3 N T3 I SD: 4.7744 c. M:-7.2182 c. 41: 3 11 3 7 3 11 3 N T3 I SD: 1.6767 c. M: 2.4201 c. 53: 4 14 4 9 4 14 4 N T3 I SD: 0.2363 c. M: 0.3410 c. 200: 15 53 15 34 15 53 15 N T3 I SD: 0.1559 c. M: 0.2250 c. 253: 19 67 19 43 19 67 19 N T3 I SD: 0.0737 c. M: 0.1064 c. 306: 23 81 23 52 23 81 23 N T3 I SD: 0.0200 c. M: 0.0289 c. 359: 27 95 27 61 27 95 27 N T3 I SD: 0.0178 c. M: 0.0257 c. 665: 50 176 50 113 50 176 50 N T3 I SD: 0.0004 c. M: 0.0006 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: 30.7262 cents 4 x 5 x 6 x x 8 S SD: 7.1688 cents 5 x 6:7 x 8 x 10 S SD: 31.7157 cents 6 x x 8:9 x 11:12 SD: 15.1030 cents 7:8:9 x x 11:13:14 SD: 29.7680 cents 8:9:10:11:12:13:15:16 SD: 19.7044 cents 9:10:11:12 x 14:17:18 SD: 18.9781 cents 10:11 x 13:15:16:19:20 SD: 14.8863 cents 11:12:14:15 x 17:21:22 SD: 13.7805 cents 12:13:15:16:18:19:23:24 SD: 7.9349 cents 16:17:20:21:24:25:30:32 SD: 6.8029 cents 18:19:23:24:27:28:34:36 SD: 4.7481 cents 22:23:28:29:33:35:42:44 SD: 4.2637 cents 30:32:38:40:45:47:57:60 SD: 3.7521 cents 33:35:42:44:50:52:63:66 SD: 3.6428 cents 34:36:43:45:51:54:65:68 SD: 3.0769 cents 36:38:46:48:54:57:68:72 SD: 2.7581 cents 38:40:48:51:57:60:72:76 SD: 1.7829 cents 57:60:72:76:86:90:108:114 SD: 1.6212 cents 60:63:76:80:90:95:114:120 SD: 0.9961 cents 72:76:91:96:108:114:137:144 SD: 0.9487 cents 90:95:114:120:135:142:171:180 SD: 0.6821 cents 128:135:162:171:192:202:243:256 SD: 0.6490 cents 132:139:167:176:198:209:251:264 SD: 0.6434 cents 148:156:187:197:222:234:281:296 SD: 0.6166 cents 150:158:190:200:225:237:285:300 SD: 0.2929 cents 264:278:334:352:396:417:501:528 SD: 0.2031 cents 336:354:425:448:504:531:638:672 SD: 0.1552 cents 372:392:471:496:558:588:706:744 SD: 0.1528 cents 414:436:524:552:621:654:786:828 SD: 0.1206 cents 486:512:615:648:729:768:923:972 SD: 0.1034 cents