Scala analysis: xen15-chalmers-triadic-reversed-diamond-24-19
Triadic reversed diamond for M=24/19, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/18 93.603014 undevicesimal semitone 2: 24/19 404.441985 smaller undevicesimal major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 19/12 795.558015 undevicesimal minor sixth 6: 36/19 1106.396986 smaller undevicesimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 19/18 93.6030 undevicesimal semitone 1: 19/18 93.6030 undevicesimal semitone 2: 432/361 310.8390 3: 19/18 93.6030 undevicesimal semitone 4: 9/8 203.9100 major whole tone 5: 19/18 93.6030 undevicesimal semitone 6: 432/361 310.8390 7: 19/18 93.6030 undevicesimal semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 19/18 93.603 cents undevicesimal semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 432/361 310.839 cents 2: 1 361/324 187.206 cents two (undevicesimal semitone) 2: 2 19/16 297.513 cents 19th harmonic 2: 4 24/19 404.442 cents smaller undevicesimal major third 3: 1 361/288 391.116 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 27/19 608.352 cents 4: 2 38/27 591.648 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 576/361 808.884 cents two (smaller undevicesimal major third) 5: 4 19/12 795.558 cents undevicesimal minor sixth 5: 2 32/19 902.487 cents 19th subharmonic 5: 1 648/361 1012.794 cents 6: 2 361/216 889.161 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 36/19 1106.397 cents smaller undevicesimal 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 : 93.6 404.4 498.0 702.0 795.6 1106.4 1200.0 93.6 : 310.8 404.4 608.4 702.0 1012.8 1106.4 1200.0 404.4 : 93.6 297.5 391.1 702.0 795.6 889.2 1200.0 498.0 : 203.9 297.5 608.4 702.0 795.6 1106.4 1200.0 702.0 : 93.6 404.4 498.0 591.6 902.5 996.1 1200.0 795.6 : 310.8 404.4 498.0 808.9 902.5 1106.4 1200.0 1106.4: 93.6 187.2 498.0 591.6 795.6 889.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6030 .. 310.8390 cents 7776/6859, 217.2360 cents 19/18, 93.6030 cents 2: 187.2060 .. 404.4420 cents 7776/6859, 217.2360 cents 130321/139968,-123.6329 cents 3: 391.1160 .. 608.3520 cents 7776/6859, 217.2360 cents 6859/6912,-13.3260 cents 4: 591.6480 .. 808.8840 cents 7776/6859, 217.2360 cents 722/729,-16.7040 cents 5: 795.5580 .. 1012.7940 cents 7776/6859, 217.2360 cents 6859/6912,-13.3260 cents 6: 889.1610 .. 1106.3970 cents 7776/6859, 217.2360 cents 130321/139968,-123.6329 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 19/18, 93.6030 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 432/361, 310.8390 cents Average / Smallest step : 1.831443 Largest / Average step : 1.813227 Largest / Smallest step : 3.320822 Median interval of one step : 19/18, 93.6030 cents, amount: 4 Most common interval of one step : 19/18, 93.6030 cents, amount: 4 Least squares average step : 173.00439 cents, oct.: 1211.03070 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 13.32595 cents Scale diversity : 1.360248 Lumma stability : 0.156005 Lumma impropriety factor : 0.242185 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 : 6912/6859, 13.3260 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 : 3 9 19 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 : 19 Odd number limit : 361 (O: 361 U: 361) Highest odd numerator or denominator: 19 Scale harmonicity : 0.011922 Average absolute harmonicity : 0.226687 Specific harmonicity : 0.064266 Fundamental : 1/684, -9.4179 octaves, 0.3825 Hz. Guide tone : 1368, 10.4179 octaves, 357903.773 Hz. Exponens Consonantiae : 9.357120E+05, 19.83571 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 90.5, average 12.92857 Mersenne's string divisions : 56965755 Sum of van Prooijen's expressibility: 6.06926, average 0.86704 Sum of Tenney's harmonic distance : 12.54434, average 1.79205 Vogel's harmonic complexity : 27.57143 Wille's k value : 541 Wilson's harmonic complexity : 50 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 85.16880, average 3.04174 Lattice compactness (without 2's) : 52.73791, average 1.88350 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 12 1 3: -2 .. 2 0.00000 8 2 19: -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 32| Scale is weakly epimorphic with val: <7 10 33| Scale is JI-epimorphic with val: <7 11 30| = patent Scale is weakly epimorphic with val: <7 11 31| Scale is weakly epimorphic with val: <7 12 27| Scale is weakly epimorphic with val: <7 12 30|
FIT/MODE
7: 0 2 0 2 0 2 1 N T3 SD: 88.6596 c. M: 155.1879 c. 8: 0 2 1 1 1 2 1 N D3 SD: 73.3182 c. M: 104.4420 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 28.5031 c. M: 39.7303 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 4.2920 c. M: 6.3970 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 39: 3 10 3 7 3 10 3 N T3 I SD: 3.9398 c. M:-5.7373 c. 50: 4 13 4 8 4 13 4 N T3 I SD: 3.9231 c. M:-5.9550 c. 51: 4 13 4 9 4 13 4 N T3 I SD: 3.1812 c. M:-4.4420 c. 53: 4 14 4 9 4 14 4 N T3 I SD: 2.3219 c. M:-3.1052 c. 65: 5 17 5 11 5 17 5 N T3 I SD: 1.1689 c. M:-1.7119 c. 77: 6 20 6 13 6 20 6 N T3 I SD: 0.5363 c. M:-0.7528 c. 166: 13 43 13 28 13 43 13 N T3 I SD: 0.4911 c. M:-0.7502 c. 193: 15 50 15 33 15 50 15 N T3 I SD: 0.4164 c. M:-0.6357 c. 205: 16 53 16 35 16 53 16 N T3 I SD: 0.3886 c. M:-0.5395 c. 258: 20 67 20 44 20 67 20 N T3 I SD: 0.3844 c. M: 0.5798 c. 270: 21 70 21 46 21 70 21 N T3 I SD: 0.2029 c. M:-0.2697 c. 282: 22 73 22 48 22 73 22 N T3 I SD: 0.1361 c. M:-0.1867 c. 359: 28 93 28 61 28 93 28 N T3 I SD: 0.0099 c. M:-0.0148 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: 29.6002 cents 4 x 5 x 6 x x 8 S SD: 6.0428 cents 5 x 6:7 x 8:9:10 S SD: 30.4857 cents 6 x x 8:9:10:11:12 S SD: 21.1078 cents 7:8:9 x x 11:13:14 SD: 29.1474 cents 8:9:10:11:12:13:15:16 SD: 18.9979 cents 9:10:11:12 x 14:17:18 SD: 18.3379 cents 10:11 x 13:15:16:19:20 SD: 14.3091 cents 11:12:14:15 x 17:21:22 SD: 13.8095 cents 12:13:15:16:18:19:23:24 SD: 7.4885 cents 16:17:20:21:24:25:30:32 SD: 6.4765 cents 18:19:23:24:27:29:34:36 SD: 5.2140 cents 20:21:25:27:30:32:38:40 SD: 5.0027 cents 22:23:28:29:33:35:42:44 SD: 4.6911 cents 30:32:38:40:45:48:57:60 SD: 3.7888 cents 34:36:43:45:51:54:64:68 SD: 2.6874 cents 38:40:48:51:57:60:72:76 SD: 1.8898 cents 54:57:68:72:81:86:102:108 SD: 1.8024 cents 56:59:71:75:84:89:106:112 SD: 1.7875 cents 57:60:72:76:86:90:108:114 SD: 1.7381 cents 58:61:73:77:87:92:110:116 SD: 1.7319 cents 60:63:76:80:90:95:114:120 SD: 1.6262 cents 68:72:86:91:102:108:129:136 SD: 1.4752 cents 72:76:91:96:108:114:136:144 SD: 0.7778 cents 106:112:134:141:159:168:201:212 SD: 0.7329 cents 126:133:159:168:189:200:239:252 SD: 0.7195 cents 132:139:167:176:198:209:250:264 SD: 0.7169 cents 144:152:182:192:216:228:273:288 SD: 0.2024 cents 324:342:409:432:486:513:614:648 SD: 0.1646 cents 360:380:455:480:540:570:682:720 SD: 0.1481 cents 396:418:500:528:594:627:750:792 SD: 0.1472 cents 468:494:591:624:702:741:887:936 SD: 0.0987 cents 540:570:682:720:810:855:1023:1080 SD: 0.0540 cents