Scala analysis: xen15-chalmers-triadic-reversed-diamond-9-7
Triadic reversed diamond for M=9/7, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 9/7 435.084095 septimal major third, BP third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 14/9 764.915905 septimal minor sixth 6: 27/14 1137.039096 septimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 243/196 372.1232 3: 28/27 62.9609 Archytas' 1/3-tone 4: 9/8 203.9100 major whole tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 243/196 372.1232 7: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 243/196 372.123 cents 2: 1 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 2 7/6 266.871 cents septimal minor third 2: 4 9/7 435.084 cents septimal major third, BP third 3: 1 98/81 329.832 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 81/56 638.994 cents 4: 2 112/81 561.006 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 81/49 870.168 cents two (septimal major third, BP third) 5: 4 14/9 764.916 cents septimal minor sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 729/392 1074.078 cents 6: 2 392/243 827.877 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 27/14 1137.039 cents septimal 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 : 63.0 435.1 498.0 702.0 764.9 1137.0 1200.0 63.0 : 372.1 435.1 639.0 702.0 1074.1 1137.0 1200.0 435.1 : 63.0 266.9 329.8 702.0 764.9 827.9 1200.0 498.0 : 203.9 266.9 639.0 702.0 764.9 1137.0 1200.0 702.0 : 63.0 435.1 498.0 561.0 933.1 996.1 1200.0 764.9 : 372.1 435.1 498.0 870.2 933.1 1137.0 1200.0 1137.0: 63.0 125.9 498.0 561.0 764.9 827.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 372.1232 cents 6561/5488, 309.1623 cents 28/27, 62.9609 cents 2: 125.9218 .. 435.0841 cents 6561/5488, 309.1623 cents 153664/177147,-246.2014 cents 3: 329.8318 .. 638.9941 cents 6561/5488, 309.1623 cents 686/729,-105.2523 cents 4: 561.0059 .. 870.1682 cents 6561/5488, 309.1623 cents 6272/6561,-77.9882 cents 5: 764.9159 .. 1074.0782 cents 6561/5488, 309.1623 cents 686/729,-105.2523 cents 6: 827.8768 .. 1137.0391 cents 6561/5488, 309.1623 cents 153664/177147,-246.2014 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 243/196, 372.1232 cents Average / Smallest step : 2.722778 Largest / Average step : 2.170719 Largest / Smallest step : 5.910385 Median interval of one step : 28/27, 62.9609 cents, amount: 4 Most common interval of one step : 28/27, 62.9609 cents, amount: 4 Least squares average step : 173.44213 cents, oct.: 1214.09491 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1277-tone equal temperament with octave 2/1 degrees: 67 463 530 747 814 1210 1277 Least number of segments generator : 639 of 600.470 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 680 of 638.998 cents and inv. generated superset size: 71 = 64 more = 1014.286% 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 42.29138 cents Scale diversity : 1.502863 Lumma stability : 0.104935 Lumma impropriety factor : 0.580261 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 : 19683/19208, 42.2914 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 : 7 9 27 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 n-1 differentially coherent in interval classes 2 and 3 combined 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 : 7 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.025271 Average absolute harmonicity : 0.244622 Specific harmonicity : 0.136696 Fundamental : 1/378, -8.5622 octaves, 0.6921 Hz. Guide tone : 756, 9.5622 octaves, 197788.927 Hz. Exponens Consonantiae : 2.857680E+05, 18.12448 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 75.0, average 10.71429 Mersenne's string divisions : 17426640 Sum of van Prooijen's expressibility: 5.72546, average 0.81792 Sum of Tenney's harmonic distance : 11.51409, average 1.64487 Vogel's harmonic complexity : 17.57143 Wille's k value : 364 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 86.91151, average 3.10398 Lattice compactness (without 2's) : 73.03173, average 2.60828 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -3 .. 3 0.00000 12 2 7: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 21| Scale is weakly epimorphic with val: <7 10 22| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 11 21| Scale is weakly epimorphic with val: <7 12 18| Scale is weakly epimorphic with val: <7 12 21|
FIT/MODE
7: 0 3 0 1 0 3 0 N T3 I SD: 54.7742 c. M: 79.2016 c. 8: 0 3 0 2 0 3 0 N T3 I SD: 43.0776 c. M:-62.9609 c. 11: 0 4 0 2 1 3 1 N SD: 41.6578 c. M: 62.9609 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 27.2900 c. M: 37.0391 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 14: 1 4 1 2 1 4 1 N T3 I SD: 15.3427 c. M: 22.7534 c. 17: 1 5 1 3 1 5 1 N T3 I SD: 7.6925 c. M: 11.5547 c. 19: 1 6 1 3 1 6 1 N T3 I SD: 5.3835 c. M:-7.2182 c. 36: 2 11 2 6 2 11 2 N T3 I SD: 2.4272 c. M: 3.7058 c. 58: 3 18 3 10 3 18 3 N T3 I SD: 0.9837 c. M: 1.4933 c. 77: 4 24 4 13 4 24 4 N T3 I SD: 0.8377 c. M: 1.2795 c. 94: 5 29 5 16 5 29 5 N T3 I SD: 0.7309 c. M: 1.0415 c. 113: 6 35 6 19 6 35 6 N T3 I SD: 0.7201 c. M:-1.0700 c. 135: 7 42 7 23 7 42 7 N T3 I SD: 0.4897 c. M:-0.7387 c. 171: 9 53 9 29 9 53 9 N T3 I SD: 0.1503 c. M:-0.2006 c. 400: 21 124 21 68 21 124 21 N T3 I SD: 0.0551 c. M: 0.0841 c. 706: 37 219 37 120 37 219 37 N T3 I SD: 0.0471 c. M:-0.0714 c. 877: 46 272 46 149 46 272 46 N T3 I SD: 0.0233 c. M: 0.0356 c. 1106: 58 343 58 188 58 343 58 N T3 I SD: 0.0248 c. M: 0.0341 c. 1277: 67 396 67 217 67 396 67 N T3 I SD: 0.0018 c. M:-0.0027 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: 39.8143 cents 4 x 5 x 6 x x 8 S SD: 16.2568 cents 5 x 6:7 x 8 x 10 S SD: 38.5518 cents 6 x x 8:9 x x 12 S SD: 0.0000 cents 7:8:9 x x 11 x 14 SD: 42.2822 cents 8:9:10:11:12 x 15:16 S SD: 27.6193 cents 9:10 x 12 x 14:17:18 SD: 24.9497 cents 10:11:13 x 15:16:19:20 SD: 19.5967 cents 11:12:14:15 x 17:21:22 SD: 16.6214 cents 12:13:15:16:18:19:23:24 SD: 13.6647 cents 13:14:17 x x 20:25:26 SD: 14.8598 cents 14:15:18:19:21:22:27:28 SD: 9.5170 cents 15:16:19:20 x 23:29:30 SD: 10.1174 cents 16:17 x 21:24:25:31:32 SD: 8.5477 cents 17:18:22:23 x 26:33:34 SD: 9.2041 cents 18:19:23:24:27:28:35:36 SD: 5.0613 cents 24:25:31:32:36:37:46:48 SD: 3.1279 cents 32:33:41:43:48:50:62:64 SD: 2.9797 cents 42:44:54:56:63:65:81:84 SD: 2.8116 cents 45:47:58:60:68:70:87:90 SD: 2.6785 cents 48:50:62:64:72:75:93:96 SD: 2.2444 cents 50:52:64:67:75:78:96:100 SD: 2.2236 cents 52:54:67:69:78:81:100:104 SD: 1.5581 cents 56:58:72:75:84:87:108:112 SD: 1.1887 cents 81:84:104:108:122:126:156:162 SD: 1.1234 cents 84:87:108:112:126:131:162:168 SD: 0.7048 cents 108:112:139:144:162:168:208:216 SD: 0.4242 cents 186:193:239:248:279:289:359:372 SD: 0.4027 cents 192:199:247:256:288:299:370:384 SD: 0.3900 cents 210:218:270:280:315:327:405:420 SD: 0.3567 cents 238:247:306:317:357:370:459:476 SD: 0.3522 cents 252:261:324:336:378:392:486:504 SD: 0.3157 cents 266:276:342:355:399:414:513:532 SD: 0.2987 cents 270:280:347:360:405:420:521:540 SD: 0.1696 cents 378:392:486:504:567:588:729:756 SD: 0.0000 cents