Scala analysis: xen15-chalmers-triadic-reversed-diamond-34-27
Triadic reversed diamond for M=34/27, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 18/17 98.954592 Arabic lute index finger 2: 34/27 399.090407 septendecimal major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 27/17 800.909593 septendecimal minor sixth 6: 17/9 1101.045408 septendecimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 18/17 98.9546 Arabic lute index finger 1: 18/17 98.9546 Arabic lute index finger 2: 289/243 300.1358 3: 18/17 98.9546 Arabic lute index finger 4: 9/8 203.9100 major whole tone 5: 18/17 98.9546 Arabic lute index finger 6: 289/243 300.1358 7: 18/17 98.9546 Arabic lute index finger
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 18/17 98.955 cents Arabic lute index finger 1: 1 9/8 203.910 cents major whole tone 1: 2 289/243 300.136 cents 2: 1 324/289 197.909 cents two (Arabic lute index finger) 2: 2 81/68 302.865 cents Persian wosta 2: 4 34/27 399.090 cents septendecimal major third 3: 1 729/578 401.819 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 17/12 603.000 cents 2nd septendecimal tritone 4: 2 24/17 597.000 cents 1st septendecimal tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 1156/729 798.181 cents two (septendecimal major third) 5: 4 27/17 800.910 cents septendecimal minor sixth 5: 2 136/81 897.135 cents 5: 1 289/162 1002.091 cents 6: 2 486/289 899.864 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 17/9 1101.045 cents septendecimal 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 : 99.0 399.1 498.0 702.0 800.9 1101.0 1200.0 99.0 : 300.1 399.1 603.0 702.0 1002.1 1101.0 1200.0 399.1 : 99.0 302.9 401.8 702.0 800.9 899.9 1200.0 498.0 : 203.9 302.9 603.0 702.0 800.9 1101.0 1200.0 702.0 : 99.0 399.1 498.0 597.0 897.1 996.1 1200.0 800.9 : 300.1 399.1 498.0 798.2 897.1 1101.0 1200.0 1101.0: 99.0 197.9 498.0 597.0 800.9 899.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.9546 .. 300.1358 cents 4913/4374, 201.1812 cents 18/17, 98.9546 cents 2: 197.9092 .. 399.0904 cents 4913/4374, 201.1812 cents 78732/83521,-102.2266 cents 3: 401.8192 .. 603.0004 cents 4913/4374, 201.1812 cents 19683/19652, 2.7288 cents 4: 596.9996 .. 798.1808 cents 4913/4374, 201.1812 cents 288/289,-6.0008 cents 5: 800.9096 .. 1002.0908 cents 4913/4374, 201.1812 cents 19683/19652, 2.7288 cents 6: 899.8642 .. 1101.0454 cents 4913/4374, 201.1812 cents 78732/83521,-102.2266 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 18/17, 98.9546 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 289/243, 300.1358 cents Average / Smallest step : 1.732396 Largest / Average step : 1.750792 Largest / Smallest step : 3.033066 Median interval of one step : 18/17, 98.9546 cents, amount: 4 Most common interval of one step : 18/17, 98.9546 cents, amount: 4 Least squares average step : 172.92793 cents, oct.: 1210.49554 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2195-tone equal temperament with octave 2/1 degrees: 181 730 911 1284 1465 2014 2195 Least number of segments generator : 1098 of 600.273 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2012 of 1099.954 cents and inv. generated superset size: 87 = 80 more = 1242.857% 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 2.72878 cents Scale diversity : 1.301341 Lumma stability : 0.169472 Lumma impropriety factor : 0.175378 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 : 19683/19652, 2.7288 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 : 9 17 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 differentially coherent in interval classes 3 and 4 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 17 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.012621 Average absolute harmonicity : 0.227779 Specific harmonicity : 0.068511 Fundamental : 1/918, -9.8424 octaves, 0.2850 Hz. Guide tone : 1836, 10.8424 octaves, 480344.538 Hz. Exponens Consonantiae : 1.685448E+06, 20.68470 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 90.5, average 12.92857 Mersenne's string divisions : 3663660 Sum of van Prooijen's expressibility: 6.27787, average 0.89684 Sum of Tenney's harmonic distance : 12.45343, average 1.77906 Vogel's harmonic complexity : 27.57143 Wille's k value : 688 Wilson's harmonic complexity : 52 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 84.41585, average 3.01485 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 6 1 3: -3 .. 3 0.00000 12 2 17: -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 28| Scale is weakly epimorphic with val: <7 10 29| Scale is weakly epimorphic with val: <7 11 27| Scale is JI-epimorphic with val: <7 11 28| Scale is weakly epimorphic with val: <7 12 28| Scale is weakly epimorphic with val: <7 12 32|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 49.7951 c. M: 72.4740 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 26.3384 c. M:-35.2883 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 25.6158 c. M:-39.0904 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 1.2809 c. M: 1.9550 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 111: 9 28 9 19 9 28 9 N T3 I SD: 1.0867 c. M: 1.6573 c. 123: 10 31 10 21 10 31 10 N T3 I SD: 0.9264 c. M:-1.3936 c. 135: 11 34 11 23 11 34 11 N T3 I SD: 0.8078 c. M: 1.1768 c. 147: 12 37 12 25 12 37 12 N T3 I SD: 0.7222 c. M: 0.9954 c. 159: 13 40 13 27 13 40 13 N T3 I SD: 0.6633 c. M:-0.9096 c. 171: 14 43 14 29 14 43 14 N T3 I SD: 0.6257 c. M:-0.9096 c. 183: 15 46 15 31 15 46 15 N T3 I SD: 0.6047 c. M:-0.9096 c. 195: 16 49 16 33 16 49 16 N T3 I SD: 0.5962 c. M:-0.9096 c. 229: 19 57 19 39 19 57 19 N T3 I SD: 0.5666 c. M:-0.8371 c. 241: 20 60 20 41 20 60 20 N T3 I SD: 0.5277 c. M: 0.7502 c. 253: 21 63 21 43 21 63 21 N T3 I SD: 0.4997 c. M: 0.6714 c. 265: 22 66 22 45 22 66 22 N T3 I SD: 0.4813 c. M: 0.6680 c. 277: 23 69 23 47 23 69 23 N T3 I SD: 0.4710 c. M:-0.6844 c. 289: 24 72 24 49 24 72 24 N T3 I SD: 0.4675 c. M:-0.6994 c. 304: 25 76 25 52 25 76 25 N T3 I SD: 0.4459 c. M: 0.6766 c. 316: 26 79 26 54 26 79 26 N T3 I SD: 0.3810 c. M:-0.5766 c. 328: 27 82 27 56 27 82 27 N T3 I SD: 0.3210 c. M:-0.4840 c. 340: 28 85 28 58 28 85 28 N T3 I SD: 0.2655 c. M:-0.3979 c. 352: 29 88 29 60 29 88 29 N T3 I SD: 0.2142 c. M:-0.3177 c. 364: 30 91 30 62 30 91 30 N T3 I SD: 0.1670 c. M:-0.2428 c. 376: 31 94 31 64 31 94 31 N T3 I SD: 0.1241 c. M:-0.1727 c. 388: 32 97 32 66 32 97 32 N T3 I SD: 0.0868 c. M: 0.1213 c. 400: 33 100 33 68 33 100 33 N T3 I SD: 0.0592 c. M:-0.0904 c. 412: 34 103 34 70 34 103 34 N T3 I SD: 0.0521 c. M: 0.0745 c. 1224: 101 306 101 208 101 306 101 N T3 I SD: 0.0515 c. M:-0.0708 c. 1347: 111 337 111 229 111 337 111 N T3 I SD: 0.0461 c. M: 0.0682 c. 1359: 112 340 112 231 112 340 112 N T3 I SD: 0.0382 c. M: 0.0583 c. 1371: 113 343 113 233 113 343 113 N T3 I SD: 0.0328 c. M: 0.0487 c. 1383: 114 346 114 235 114 346 114 N T3 I SD: 0.0307 c. M:-0.0419 c. 1759: 145 440 145 299 145 440 145 N T3 I SD: 0.0263 c. M: 0.0348 c. 1771: 146 443 146 301 146 443 146 N T3 I SD: 0.0188 c. M: 0.0274 c. 1783: 147 446 147 303 147 446 147 N T3 I SD: 0.0133 c. M: 0.0202 c. 1795: 148 449 148 305 148 449 148 N T3 I SD: 0.0123 c. M:-0.0182 c. 2183: 180 546 180 371 180 546 180 N T3 I SD: 0.0097 c. M: 0.0148 c. 2195: 181 549 181 373 181 549 181 N T3 I SD: 0.0026 c. M:-0.0040 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: 27.8164 cents 4 x 5 x 6 x x 8 S SD: 4.2589 cents 5 x 6:7 x 8:9:10 S SD: 29.1379 cents 6 x x 8:9:10:11:12 S SD: 19.6314 cents 7:8:9 x x 11:13:14 SD: 28.2686 cents 8:9:10:11:12:13:15:16 SD: 17.9283 cents 9:10:11:12 x 14:17:18 SD: 17.4247 cents 10:11 x 13:15:16:19:20 SD: 13.4887 cents 11:12:14:15 x 17:21:22 SD: 14.0414 cents 12:13:15:16:18:19:23:24 SD: 6.9989 cents 15:16:19:20:23:24:28:30 SD: 6.8470 cents 16:17:20:21:24:25:30:32 SD: 6.2363 cents 18:19:23:24:27:29:34:36 SD: 5.1117 cents 20:21:25:27:30:32:38:40 SD: 4.7423 cents 27:29:34:36:41:43:51:54 SD: 4.7093 cents 30:32:38:40:45:48:57:60 SD: 3.2972 cents 34:36:43:45:51:54:64:68 SD: 2.2816 cents 36:38:45:48:54:57:68:72 SD: 2.1214 cents 46:49:58:61:69:73:87:92 SD: 2.0671 cents 51:54:64:68:77:81:96:102 SD: 2.0164 cents 54:57:68:72:81:86:102:108 SD: 1.0216 cents 66:70:83:88:99:105:125:132 SD: 0.9443 cents 100:106:126:133:150:159:189:200 SD: 0.7592 cents 116:123:146:155:174:184:219:232 SD: 0.7355 cents 120:127:151:160:180:191:227:240 SD: 0.6806 cents 134:142:169:179:201:213:253:268 SD: 0.6727 cents 136:144:171:181:204:216:257:272 SD: 0.5991 cents 138:146:174:184:207:219:261:276 SD: 0.5284 cents 150:159:189:200:225:238:283:300 SD: 0.4910 cents 170:180:214:227:255:270:321:340 SD: 0.3831 cents 204:216:257:272:306:324:385:408 SD: 0.2393 cents 270:286:340:360:405:429:510:540 SD: 0.1439 cents 444:470:559:592:666:705:839:888 SD: 0.1405 cents 474:502:597:632:711:753:895:948 SD: 0.1316 cents 510:540:642:680:765:810:963:1020 SD: 0.1210 cents 594:629:748:792:891:943:1122:1188 SD: 0.1104 cents