Scala analysis: xen15-chalmers-triadic-reversed-diamond-21-16
Triadic reversed diamond for M=21/16, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64/63 27.264092 septimal comma, Archytas' comma 2: 21/16 470.780907 narrow fourth 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 32/21 729.219093 wide fifth 6: 63/32 1172.735908 octave - septimal comma 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 64/63 27.2641 septimal comma, Archytas' comma 1: 64/63 27.2641 septimal comma, Archytas' comma 2: 1323/1024 443.5168 3: 64/63 27.2641 septimal comma, Archytas' comma 4: 9/8 203.9100 major whole tone 5: 64/63 27.2641 septimal comma, Archytas' comma 6: 1323/1024 443.5168 7: 64/63 27.2641 septimal comma, Archytas' comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 9/8 203.910 cents major whole tone 1: 2 1323/1024 443.517 cents 2: 1 4096/3969 54.528 cents two (septimal comma, Archytas' comma) 2: 2 8/7 231.174 cents septimal whole tone 2: 4 21/16 470.781 cents narrow fourth 3: 1 512/441 258.438 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 189/128 674.691 cents 4: 2 256/189 525.309 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 441/256 941.562 cents two (narrow fourth) 5: 4 32/21 729.219 cents wide fifth 5: 2 7/4 968.826 cents harmonic seventh 5: 1 3969/2048 1145.472 cents 6: 2 2048/1323 756.483 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 63/32 1172.736 cents octave - septimal comma 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 : 27.3 470.8 498.0 702.0 729.2 1172.7 1200.0 27.3 : 443.5 470.8 674.7 702.0 1145.5 1172.7 1200.0 470.8 : 27.3 231.2 258.4 702.0 729.2 756.5 1200.0 498.0 : 203.9 231.2 674.7 702.0 729.2 1172.7 1200.0 702.0 : 27.3 470.8 498.0 525.3 968.8 996.1 1200.0 729.2 : 443.5 470.8 498.0 941.6 968.8 1172.7 1200.0 1172.7: 27.3 54.5 498.0 525.3 729.2 756.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 443.5168 cents 83349/65536, 416.2527 cents 64/63, 27.2641 cents 2: 54.5282 .. 470.7809 cents 83349/65536, 416.2527 cents 4194304/5250987,-388.9886 cents 3: 258.4382 .. 674.6909 cents 83349/65536, 416.2527 cents 8192/9261,-212.3427 cents 4: 525.3091 .. 941.5618 cents 83349/65536, 416.2527 cents 32768/35721,-149.3818 cents 5: 729.2191 .. 1145.4718 cents 83349/65536, 416.2527 cents 8192/9261,-212.3427 cents 6: 756.4832 .. 1172.7359 cents 83349/65536, 416.2527 cents 4194304/5250987,-388.9886 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1323/1024, 443.5168 cents Average / Smallest step : 6.287705 Largest / Average step : 2.587181 Largest / Smallest step : 16.267434 Median interval of one step : 64/63, 27.2641 cents, amount: 4 Most common interval of one step : 64/63, 27.2641 cents, amount: 4 Least squares average step : 173.95208 cents, oct.: 1217.66459 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 27.26409 cents Scale diversity : 1.176701 Lumma stability : 0.045440 Lumma impropriety factor : 0.818239 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 : 64/63, 27.2641 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 : 1 3 63 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 : 3969 (O: 3969 U: 3969) Highest odd numerator or denominator: 63 Scale harmonicity : 0.023675 Average absolute harmonicity : 0.242351 Specific harmonicity : 0.128982 Fundamental : 1/2016, -10.9773 octaves, 0.1298 Hz. Guide tone : 4032, 11.9773 octaves, 1054874.279 Hz. Exponens Consonantiae : 8.128512E+06, 22.95456 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 163.5, average 23.35714 Mersenne's string divisions : 496848765 Sum of van Prooijen's expressibility: 7.19736, average 1.02819 Sum of Tenney's harmonic distance : 14.42208, average 2.06030 Vogel's harmonic complexity : 18.57143 Wille's k value : 1984 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 142.91982, average 5.10428 Lattice compactness (without 2's) : 52.73791, average 1.88350 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 6 0.57143 24 1 3: -2 .. 2 0.00000 8 2 7: -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 11 18| Scale is JI-epimorphic with val: <7 11 19| Scale is weakly epimorphic with val: <7 12 19| Scale is weakly epimorphic with val: <7 12 22|
FIT/MODE
7: 0 3 0 1 0 3 0 N T3 I SD: 28.7837 c. M:-43.5048 c. 10: 0 4 0 2 0 4 0 N T3 I SD: 18.1576 c. M:-27.2641 c. 15: 0 6 0 3 0 6 0 N T3 I SD: 18.1576 c. M:-27.2641 c. 26: 1 9 1 4 1 9 1 N T3 I SD: 12.3672 c. M:-18.8898 c. 28: 1 10 1 4 1 10 1 N T3 I SD: 12.0395 c. M:-16.2407 c. 29: 1 10 1 5 1 10 1 N T3 I SD: 11.2770 c. M:-15.6085 c. 31: 1 11 1 5 1 11 1 N T3 I SD: 7.5041 c. M:-11.4456 c. 33: 1 12 1 5 1 12 1 N T3 I SD: 7.7201 c. M:-11.0459 c. 36: 1 13 1 6 1 13 1 N T3 I SD: 4.0562 c. M:-6.0692 c. 41: 1 15 1 7 1 15 1 N T3 I SD: 1.7273 c. M:-2.4882 c. 46: 1 17 1 8 1 17 1 N T3 I SD: 1.5665 c. M: 2.3928 c. 84: 2 31 2 14 2 31 2 N T3 I SD: 1.3039 c. M: 1.9550 c. 87: 2 32 2 15 2 32 2 N T3 I SD: 1.2682 c. M:-1.8154 c. 89: 2 33 2 15 2 33 2 N T3 I SD: 0.7663 c. M: 1.1292 c. 130: 3 48 3 22 3 48 3 N T3 I SD: 0.3194 c. M:-0.4282 c. 176: 4 65 4 30 4 65 4 N T3 I SD: 0.2435 c. M:-0.3264 c. 265: 6 98 6 45 6 98 6 N T3 I SD: 0.1068 c. M:-0.1625 c. 441: 10 163 10 75 10 163 10 N T3 I SD: 0.0567 c. M:-0.0858 c. 571: 13 211 13 97 13 211 13 N T3 I SD: 0.0369 c. M:-0.0564 c. 836: 19 309 19 142 19 309 19 N T3 I SD: 0.0284 c. M:-0.0411 c. 1012: 23 374 23 172 23 374 23 N T3 I SD: 0.0202 c. M: 0.0299 c. 1277: 29 472 29 217 29 472 29 N T3 I SD: 0.0088 c. M:-0.0127 c. 1848: 42 683 42 314 42 683 42 N T3 I SD: 0.0060 c. M:-0.0086 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: 51.7132 cents 4 x 5 x 6 x x 8 S SD: 28.1557 cents 5 x x 7 x 8 x 10 SD: 39.8182 cents 6 x x 8:9 x x 12 S SD: 0.0000 cents 7:8:9 x x 11 x 14 SD: 53.4390 cents 8:9 x 11:12 x x 16 SD: 46.1260 cents 9:10 x 12 x 14 x 18 SD: 39.7984 cents 10:11:13 x 15 x x 20 SD: 34.6832 cents 11:12:14:15 x 17 x 22 SD: 28.4034 cents 12:13 x 16:18 x x 24 SD: 27.8271 cents 13:14:17 x x 20 x 26 SD: 25.6451 cents 14:15:18:19:21 x x 28 SD: 20.6979 cents 15:16 x 20 x 23 x 30 SD: 21.2883 cents 16:17:21 x 24 x x 32 SD: 19.4228 cents 17:18:22:23 x 26:33:34 SD: 13.9555 cents 18:19 x 24:27 x 35:36 SD: 13.9476 cents 19:20:25 x x 29:37:38 SD: 12.9167 cents 20:21:26:27:30 x 39:40 SD: 10.9083 cents 21:22 x 28 x 32:41:42 SD: 11.0398 cents 22:23:29 x 33:34:43:44 SD: 9.5433 cents 23:24:30:31 x 35:45:46 SD: 8.7290 cents 24:25 x 32:36:37:47:48 SD: 8.1231 cents 25:26:33 x x 38:49:50 SD: 8.5483 cents 26:27:34:35:39:40:51:52 SD: 6.5141 cents 27:28:35:36 x 41:53:54 SD: 7.0691 cents 28:29:37 x 42:43:55:56 SD: 6.3598 cents 29:30:38:39 x 44:57:58 SD: 5.9643 cents 30:31:39:40:45:46:59:60 SD: 5.0801 cents 31:32:41 x x 47:61:62 SD: 6.3877 cents 32:33:42:43:48:49:63:64 SD: 4.3544 cents 33:34:43:44 x 50:65:66 SD: 4.8632 cents 34:35 x 45:51:52:67:68 SD: 4.5079 cents 35:36:46:47 x 53:69:70 SD: 4.5438 cents 36:37:47:48:54:55:71:72 SD: 3.2600 cents 37:38 x 49 x 56:73:74 SD: 5.0860 cents 38:39:50:51:57:58:75:76 SD: 3.1559 cents 39:40:51:52 x 59:77:78 SD: 3.7122 cents 40:41 x 53:60:61:79:80 SD: 3.2894 cents 41:42:54:55 x 62:81:82 SD: 3.9710 cents 42:43:55:56:63:64:83:84 SD: 2.2113 cents 48:49:63:64:72:73:95:96 SD: 1.8407 cents 54:55:71:72:81:82:106:108 SD: 1.3688 cents 70:71:92:93:105:107:138:140 SD: 1.3244 cents 74:75:97:99:111:113:146:148 SD: 1.2965 cents 84:85:110:112:126:128:165:168 SD: 1.2520 cents 90:91:118:120:135:137:177:180 SD: 1.2466 cents 102:104:134:136:153:155:201:204 SD: 1.1818 cents 108:110:142:144:162:165:213:216 SD: 1.0988 cents 112:114:147:149:168:171:221:224 SD: 1.0416 cents 114:116:150:152:171:174:224:228 SD: 0.9729 cents 116:118:152:155:174:177:228:232 SD: 0.9141 cents 118:120:155:157:177:180:232:236 SD: 0.7503 cents 122:124:160:163:183:186:240:244 SD: 0.6025 cents 126:128:165:168:189:192:248:252 SD: 0.5649 cents 128:130:168:171:192:195:252:256 SD: 0.4901 cents 132:134:173:176:198:201:260:264 SD: 0.4510 cents 186:189:244:248:279:283:366:372 SD: 0.4196 cents 192:195:252:256:288:293:378:384 SD: 0.3670 cents 198:201:260:264:297:302:390:396 SD: 0.3376 cents 246:250:323:328:369:375:484:492 SD: 0.2289 cents 252:256:331:336:378:384:496:504 SD: 0.1970 cents 378:384:496:504:567:576:744:756 SD: 0.0881 cents 384:390:504:512:576:585:756:768 SD: 0.0854 cents