Scala analysis: xen15-chalmers-triadic-reversed-diamond-64-51
Triadic reversed diamond for M=64/51, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 64/51 393.089590 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 51/32 806.910410 6: 32/17 1095.044590 17th subharmonic 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 17/16 104.9554 17th harmonic 1: 17/16 104.9554 17th harmonic 2: 1024/867 288.1342 3: 17/16 104.9554 17th harmonic 4: 9/8 203.9100 major whole tone 5: 17/16 104.9554 17th harmonic 6: 1024/867 288.1342 7: 17/16 104.9554 17th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 17/16 104.955 cents 17th harmonic 1: 1 9/8 203.910 cents major whole tone 1: 2 1024/867 288.134 cents 2: 1 289/256 209.911 cents two (17th harmonic) 2: 2 153/128 308.865 cents 2: 4 64/51 393.090 cents 3: 1 2601/2048 413.821 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 24/17 597.000 cents 1st septendecimal tritone 4: 2 17/12 603.000 cents 2nd septendecimal tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 4096/2601 786.179 cents 5: 4 51/32 806.910 cents 5: 2 256/153 891.135 cents 5: 1 512/289 990.089 cents 6: 2 867/512 911.866 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 32/17 1095.045 cents 17th subharmonic 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 : 105.0 393.1 498.0 702.0 806.9 1095.0 1200.0 105.0 : 288.1 393.1 597.0 702.0 990.1 1095.0 1200.0 393.1 : 105.0 308.9 413.8 702.0 806.9 911.9 1200.0 498.0 : 203.9 308.9 597.0 702.0 806.9 1095.0 1200.0 702.0 : 105.0 393.1 498.0 603.0 891.1 996.1 1200.0 806.9 : 288.1 393.1 498.0 786.2 891.1 1095.0 1200.0 1095.0: 105.0 209.9 498.0 603.0 806.9 911.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.9554 .. 288.1342 cents 16384/14739, 183.1788 cents 17/16, 104.9554 cents 2: 209.9108 .. 393.0896 cents 16384/14739, 183.1788 cents 250563/262144,-78.2234 cents 3: 413.8208 .. 596.9996 cents 16384/14739, 183.1788 cents 132651/131072, 20.7312 cents 4: 603.0004 .. 786.1792 cents 16384/14739, 183.1788 cents 289/288, 6.0008 cents 5: 806.9104 .. 990.0892 cents 16384/14739, 183.1788 cents 132651/131072, 20.7312 cents 6: 911.8658 .. 1095.0446 cents 16384/14739, 183.1788 cents 250563/262144,-78.2234 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 17/16, 104.9554 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1024/867, 288.1342 cents Average / Smallest step : 1.633347 Largest / Average step : 1.680783 Largest / Smallest step : 2.745301 Median interval of one step : 17/16, 104.9554 cents, amount: 4 Most common interval of one step : 17/16, 104.9554 cents, amount: 4 Least squares average step : 172.84221 cents, oct.: 1209.89546 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1795-tone equal temperament with octave 2/1 degrees: 157 588 745 1050 1207 1638 1795 Least number of segments generator : 898 of 600.334 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1753 of 1171.922 cents and inv. generated superset size: 79 = 72 more = 1128.571% 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 6.00082 cents Scale diversity : 1.352315 Lumma stability : 0.214478 Lumma impropriety factor : 0.130372 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 : 289/288, 6.0008 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 Scale is a complete diamond : 1 3 51 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 : 2601 (O: 2601 U: 2601) Highest odd numerator or denominator: 51 Scale harmonicity : 0.013060 Average absolute harmonicity : 0.228149 Specific harmonicity : 0.069654 Fundamental : 1/1632, -10.6724 octaves, 0.1603 Hz. Guide tone : 3264, 11.6724 octaves, 853945.845 Hz. Exponens Consonantiae : 5.326848E+06, 22.34485 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 147.5, average 21.07143 Mersenne's string divisions : 15434265 Sum of van Prooijen's expressibility: 6.83028, average 0.97575 Sum of Tenney's harmonic distance : 14.05500, average 2.00786 Vogel's harmonic complexity : 25.57143 Wille's k value : 1300 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 138.87641, average 4.95987 Lattice compactness (without 2's) : 39.08641, average 1.39594 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 6 0.57143 24 1 3: -1 .. 1 0.00000 4 2 17: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 10 26| Scale is weakly epimorphic with val: <7 10 27| Scale is JI-epimorphic with val: <7 11 29| = patent Scale is weakly epimorphic with val: <7 11 30| Scale is weakly epimorphic with val: <7 12 27| Scale is weakly epimorphic with val: <7 12 31|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 45.3738 c. M: 66.4732 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 24.4851 c. M:-35.2883 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 21.6919 c. M:-33.0896 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 4.6639 c. M: 6.9104 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 34: 3 8 3 6 3 8 3 N T3 I SD: 3.3742 c. M:-4.8543 c. 46: 4 11 4 8 4 11 4 N T3 I SD: 1.6285 c. M: 2.3928 c. 58: 5 14 5 10 5 14 5 N T3 I SD: 1.1341 c. M: 1.5071 c. 113: 10 27 10 19 10 27 10 N T3 I SD: 0.8798 c. M:-1.2393 c. 125: 11 30 11 21 11 30 11 N T3 I SD: 0.7578 c. M:-1.1550 c. 159: 14 38 14 27 14 38 14 N T3 I SD: 0.5091 c. M:-0.7050 c. 171: 15 41 15 29 15 41 15 N T3 I SD: 0.2045 c. M: 0.3077 c. 229: 20 55 20 39 20 55 20 N T3 I SD: 0.1522 c. M: 0.2284 c. 400: 35 96 35 68 35 96 35 N T3 I SD: 0.0587 c. M: 0.0896 c. 583: 51 140 51 99 51 140 51 N T3 I SD: 0.0461 c. M:-0.0682 c. 812: 71 195 71 138 71 195 71 N T3 I SD: 0.0192 c. M:-0.0293 c. 1212: 106 291 106 206 106 291 106 N T3 I SD: 0.0175 c. M:-0.0252 c. 1795: 157 431 157 305 157 431 157 N T3 I SD: 0.0034 c. M:-0.0051 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: 25.8161 cents 4 x 5 x 6 x x 8 S SD: 2.2586 cents 5 x 6:7 x 8:9:10 S SD: 27.6963 cents 6 x x 8:9:10:11:12 S SD: 17.9834 cents 7:8:9 x x 11:13:14 SD: 27.4487 cents 8:9:10:11:12:13:15:16 SD: 16.8135 cents 9:10:11:12 x 14:17:18 SD: 16.5702 cents 10:11 x 13:15:16:19:20 SD: 12.7300 cents 12:13:15:16:18:19:23:24 SD: 6.8259 cents 15:16:19:20:23:24:28:30 SD: 6.4056 cents 16:17:20:21:24:26:30:32 SD: 6.3331 cents 18:19:23:24:27:29:34:36 SD: 5.5233 cents 20:21:25:27:30:32:38:40 SD: 5.0205 cents 27:29:34:36:41:43:51:54 SD: 4.2298 cents 28:30:35:37:42:45:53:56 SD: 4.0396 cents 30:32:38:40:45:48:56:60 SD: 3.3887 cents 32:34:40:43:48:51:60:64 SD: 2.3619 cents 44:47:55:59:66:70:83:88 SD: 2.2610 cents 48:51:60:64:72:77:90:96 SD: 2.1142 cents 50:53:63:67:75:80:94:100 SD: 1.9746 cents 52:55:65:69:78:83:98:104 SD: 1.9603 cents 60:64:75:80:90:96:113:120 SD: 1.6815 cents 62:66:78:83:93:99:117:124 SD: 1.4850 cents 66:70:83:88:99:105:124:132 SD: 0.9414 cents 78:83:98:104:117:124:147:156 SD: 0.8384 cents 94:100:118:125:141:150:177:188 SD: 0.7992 cents 110:117:138:147:165:175:207:220 SD: 0.7679 cents 114:121:143:152:171:182:215:228 SD: 0.6935 cents 126:134:158:168:189:201:237:252 SD: 0.4175 cents 180:191:226:240:270:287:339:360 SD: 0.3866 cents 192:204:241:256:288:306:361:384 SD: 0.2883 cents 270:287:339:360:405:430:508:540 SD: 0.2713 cents 290:308:364:387:435:462:546:580 SD: 0.2669 cents 306:325:384:408:459:488:576:612 SD: 0.1848 cents 384:408:482:512:576:612:723:768 SD: 0.0854 cents 510:542:640:680:765:813:960:1020 SD: 0.0807 cents