Scala analysis: xen15-chalmers-triadic-reversed-diamond-40-33
Triadic reversed diamond for M=40/33, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 40/33 333.040771 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 33/20 866.959229 6: 20/11 1034.995772 large minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 11/10 165.0042 Ptolemy's second, 4/5-tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 400/363 168.0365 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 9/8 203.9100 major whole tone 5: 11/10 165.0042 Ptolemy's second, 4/5-tone 6: 400/363 168.0365 7: 11/10 165.0042 Ptolemy's second, 4/5-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 400/363 168.037 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 121/100 330.008 cents two (Ptolemy's second, 4/5-tone) 2: 4 40/33 333.041 cents 2: 2 99/80 368.914 cents 3: 4 4/3 498.045 cents perfect fourth 3: 1 1089/800 533.918 cents 3: 2 15/11 536.951 cents undecimal augmented fourth 4: 2 22/15 663.049 cents undecimal diminished fifth 4: 1 1600/1089 666.082 cents 4: 4 3/2 701.955 cents perfect fifth 5: 2 160/99 831.086 cents 5: 4 33/20 866.959 cents 5: 1 200/121 869.992 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 363/200 1031.963 cents 6: 4 20/11 1034.996 cents large minor 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 : 165.0 333.0 498.0 702.0 867.0 1035.0 1200.0 165.0 : 168.0 333.0 537.0 702.0 870.0 1035.0 1200.0 333.0 : 165.0 368.9 533.9 702.0 867.0 1032.0 1200.0 498.0 : 203.9 368.9 537.0 702.0 867.0 1035.0 1200.0 702.0 : 165.0 333.0 498.0 663.0 831.1 996.1 1200.0 867.0 : 168.0 333.0 498.0 666.1 831.1 1035.0 1200.0 1035.0: 165.0 330.0 498.0 663.0 867.0 1032.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 165.0042 .. 203.9100 cents 45/44, 38.9058 cents 11/10, 165.0042 cents 2: 330.0085 .. 368.9142 cents 45/44, 38.9058 cents 242/225, 126.0985 cents 3: 498.0450 .. 536.9508 cents 45/44, 38.9058 cents 320/297, 129.1308 cents 4: 663.0492 .. 701.9550 cents 45/44, 38.9058 cents 242/225, 126.0985 cents 5: 831.0858 .. 869.9915 cents 45/44, 38.9058 cents 320/297, 129.1308 cents 6: 996.0900 .. 1034.9958 cents 45/44, 38.9058 cents 242/225, 126.0985 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 11/10, 165.0042 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.038934 Largest / Average step : 1.189475 Largest / Smallest step : 1.235787 Median interval of one step : 11/10, 165.0042 cents, amount: 4 Most common interval of one step : 11/10, 165.0042 cents, amount: 4 Least squares average step : 171.98437 cents, oct.: 1203.89058 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : SMSLSMS Scale is a Constant Structure, by a margin of 126.09846 cents Scale diversity : 1.185866 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.805471 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 : 4000/3993, 3.0323 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 Best major thirds form a closed circle Best minor thirds form a closed circle Scale is a complete diamond : 5 11 33 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 : 11 Odd number limit : 1089 (O: 1089 U: 1089) Highest odd numerator or denominator: 33 Scale harmonicity : 0.016808 Average absolute harmonicity : 0.232996 Specific harmonicity : 0.089640 Fundamental : 1/660, -9.3663 octaves, 0.3964 Hz. Guide tone : 1320, 10.3663 octaves, 345345.746 Hz. Exponens Consonantiae : 8.712000E+05, 19.73264 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 96.5, average 13.78571 Mersenne's string divisions : 12593595 Sum of van Prooijen's expressibility: 6.07406, average 0.86772 Sum of Tenney's harmonic distance : 12.48230, average 1.78319 Vogel's harmonic complexity : 21.57143 Wille's k value : 544 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 78.76043, average 2.81287 Lattice compactness (without 2's) : 47.53320, average 1.69761 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 12 1 3: -1 .. 1 0.00000 4 2 5: -1 .. 1 0.00000 4 11: -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 16 22| Scale is weakly epimorphic with val: <7 10 17 22| Scale is weakly epimorphic with val: <7 10 17 23| Scale is weakly epimorphic with val: <7 10 18 23| Scale is weakly epimorphic with val: <7 10 18 24| Scale is JI-epimorphic with val: <7 11 15 23| Scale is weakly epimorphic with val: <7 11 15 24| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 11 16 25| Scale is JI-epimorphic with val: <7 11 17 25| Scale is weakly epimorphic with val: <7 11 17 26| Scale is JI-epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 12 15 25| Scale is weakly epimorphic with val: <7 12 16 22| Scale is weakly epimorphic with val: <7 12 16 26| Scale is weakly epimorphic with val: <7 12 17 23| Scale is weakly epimorphic with val: <7 12 18 24|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 10.7091 c. M:-16.2407 c. Lebeng 22: 3 3 3 4 3 3 3 SP M ME I SD: 4.9588 c. M:-7.1359 c. Minor quasi-equal Heptatonic, Miller's Porcupine-7 29: 4 4 4 5 4 4 4 SP M ME I SD: 1.3647 c. M:-2.0063 c. Miller's Porcupine-7 36: 5 5 5 6 5 5 5 SP M ME I SD: 1.3806 c. M: 1.9550 c. Equal Diatonic Dorian 65: 9 9 9 11 9 9 9 SP M DE I SD: 0.7621 c. M: 1.1496 c. 94: 13 13 13 16 13 13 13 SP M DE I SD: 0.7939 c. M: 1.1259 c. 159: 22 22 22 27 22 22 22 SP M DE I SD: 0.7568 c. M: 1.0335 c. 205: 28 29 28 35 28 29 28 SP T3 I SD: 0.7231 c. M: 1.1018 c. 212: 29 30 29 36 29 30 29 SP T3 I SD: 0.6723 c. M:-0.9215 c. 234: 32 33 32 40 32 33 32 SP T3 I SD: 0.6023 c. M: 0.9017 c. 241: 33 34 33 41 33 34 33 SP T3 I SD: 0.4819 c. M: 0.6889 c. 270: 37 38 37 46 37 38 37 SP T3 I SD: 0.3666 c. M: 0.5598 c. 277: 38 39 38 47 38 39 38 SP T3 I SD: 0.3601 c. M:-0.5332 c. 299: 41 42 41 51 41 42 41 SP T3 I SD: 0.3214 c. M: 0.4557 c. 306: 42 43 42 52 42 43 42 SP T3 I SD: 0.2234 c. M: 0.2983 c. 335: 46 47 46 57 46 47 46 SP T3 I SD: 0.1501 c. M: 0.2281 c. 371: 51 52 51 63 51 52 51 SP T3 I SD: 0.0744 c. M:-0.1129 c. 400: 55 56 55 68 55 56 55 SP T3 I SD: 0.0325 c. M:-0.0450 c. 771: 106 108 106 131 106 108 106 SP T3 I SD: 0.0224 c. M:-0.0332 c. 1171: 161 164 161 199 161 164 161 SP T3 I SD: 0.0112 c. M: 0.0170 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: 5.7998 cents 4 x 5 x 6 x 7:8 S SD: 21.2374 cents 5 x 6:7 x 8:9:10 S SD: 20.5701 cents 6 x 7:8:9:10:11:12 S SD: 11.6519 cents 7:8 x 9:11:12:13:14 SD: 23.8947 cents 8:9:10:11:12:13:15:16 SD: 14.7954 cents 9:10:11:12:14:15:16:18 S SD: 11.3296 cents 10:11:12:13:15:17:18:20 SD: 10.2993 cents 12:13:15:16:18:20:22:24 SD: 9.0866 cents 17:19:21:23:26:28:31:34 SD: 8.6169 cents 18:20:22:24:27:30:33:36 S SD: 4.5587 cents 28:31:34:37:42:46:51:56 SD: 3.0039 cents 32:35:39:43:48:53:58:64 SD: 2.9972 cents 38:42:46:51:57:63:69:76 SD: 2.3727 cents 42:46:51:56:63:69:76:84 SD: 1.9725 cents 48:53:58:64:72:79:87:96 SD: 1.5696 cents 60:66:73:80:90:99:109:120 SD: 0.9484 cents 100:110:121:133:150:165:182:200 SD: 0.7950 cents 108:119:131:144:162:178:196:216 SD: 0.6999 cents 132:145:160:176:198:218:240:264 SD: 0.4096 cents 160:176:194:213:240:264:291:320 SD: 0.4019 cents 180:198:218:240:270:297:327:360 SD: 0.2916 cents 240:264:291:320:360:396:436:480 SD: 0.2202 cents 340:374:412:453:510:561:618:680 SD: 0.2090 cents 372:409:451:496:558:614:676:744 SD: 0.2032 cents 400:440:485:533:600:660:727:800 SD: 0.1962 cents 420:462:509:560:630:693:764:840 SD: 0.1258 cents 480:528:582:640:720:792:873:960 SD: 0.1093 cents 528:581:640:704:792:871:960:1056 SD: 0.1023 cents 600:660:727:800:900:990:1091:1200 SD: 0.0950 cents