Scala analysis: xen09-chalmers-tritriadic-1-7-9
Tritriadic scale built from 1:7:9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 81/64 407.820003 Pythagorean major third 3: 14/9 764.915905 septimal minor sixth 4: 7/4 968.825906 harmonic seventh 5: 16/9 996.089998 Pythagorean minor seventh 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: 9/8 203.9100 major whole tone 2: 9/8 203.9100 major whole tone 3: 896/729 357.0959 4: 9/8 203.9100 major whole tone 5: 64/63 27.2641 septimal comma, Archytas' comma 6: 567/512 176.6459 7: 64/63 27.2641 septimal comma, Archytas' comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 567/512 176.646 cents 1: 3 9/8 203.910 cents major whole tone 1: 1 896/729 357.096 cents 2: 2 9/8 203.910 cents major whole tone 2: 2 8/7 231.174 cents septimal whole tone 2: 1 81/64 407.820 cents Pythagorean major third 2: 2 112/81 561.006 cents 3: 1 8/7 231.174 cents septimal whole tone 3: 2 81/64 407.820 cents Pythagorean major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 1 1024/729 588.270 cents Pythagorean diminished fifth 3: 2 14/9 764.916 cents septimal minor sixth 4: 2 9/7 435.084 cents septimal major third, BP third 4: 1 729/512 611.730 cents Pythagorean tritone 4: 1 14/9 764.916 cents septimal minor sixth 4: 2 128/81 792.180 cents Pythagorean minor sixth 4: 1 7/4 968.826 cents harmonic seventh 5: 2 81/56 638.994 cents 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 7/4 968.826 cents harmonic seventh 5: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 729/448 842.904 cents 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 1024/567 1023.354 cents 6: 2 63/32 1172.736 cents octave - septimal comma Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 407.8 764.9 968.8 996.1 1172.7 1200.0 203.9 : 203.9 561.0 764.9 792.2 968.8 996.1 1200.0 407.8 : 357.1 561.0 588.3 764.9 792.2 996.1 1200.0 764.9 : 203.9 231.2 407.8 435.1 639.0 842.9 1200.0 968.8 : 27.3 203.9 231.2 435.1 639.0 996.1 1200.0 996.1 : 176.6 203.9 407.8 611.7 968.8 1172.7 1200.0 1172.7: 27.3 231.2 435.1 792.2 996.1 1023.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 357.0959 cents 98/81, 329.8318 cents 64/63, 27.2641 cents 2: 203.9100 .. 561.0059 cents 896/729, 357.0959 cents 6561/7168,-153.1859 cents 3: 231.1741 .. 764.9159 cents 49/36, 533.7418 cents 81/98,-329.8318 cents 4: 435.0841 .. 968.8259 cents 49/36, 533.7418 cents 81/98,-329.8318 cents 5: 638.9941 .. 996.0900 cents 896/729, 357.0959 cents 81/98,-329.8318 cents 6: 842.9041 .. 1172.7359 cents 98/81, 329.8318 cents 6561/7168,-153.1859 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 : 896/729, 357.0959 cents Average / Smallest step : 6.287705 Largest / Average step : 2.083059 Largest / Smallest step : 13.097664 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 197.18905 cents, oct.: 1380.32334 cents Scale is not proper Step pattern alph. order: AABACDC Step pattern size order : CCDCABA Scale is not a Constant Structure Scale diversity : 1.271941 Lumma stability : 0.045440 Lumma impropriety factor : 0.660150 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 531441/524288, 23.4600 cents Most common intervals : 9/8, 203.9100 cents & inv., amount: 5 Most common triad is 0.0 203.910 996.090 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 1 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 7 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 81 Scale harmonicity : 0.027559 Average absolute harmonicity : 0.211029 Specific harmonicity : 0.142342 Fundamental : 1/576, -9.1699 octaves, 0.4542 Hz. Guide tone : 9072, 13.1472 octaves, 2373467.128 Hz. Exponens Consonantiae : 5.225472E+06, 22.31713 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 159.5, average 22.78571 Mersenne's string divisions : 177738825 Sum of van Prooijen's expressibility: 7.41565, average 1.05938 Sum of Tenney's harmonic distance : 14.88341, average 2.12620 Vogel's harmonic complexity : 15.28571 Wille's k value : 364 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 6 Lattice compactness : 139.50759, average 4.98241 Lattice compactness (without 2's) : 74.10456, average 2.64659 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 4 -1.42857 22 1 3: -2 .. 4 0.57143 12 3 7: 0 .. 1 0.42857 3 3 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 11 18| Scale is weakly epimorphic with val: <7 12 19|
FIT/MODE
7: 1 1 2 2 0 1 0 N SD: 49.1587 c. M: 79.2016 c. 8: 1 2 2 1 1 1 0 N SD: 43.5801 c. M: 68.8259 c. 10: 2 1 3 2 0 2 0 N SD: 33.2316 c. M: 47.8200 c. 11: 2 2 3 2 0 2 0 N SD: 17.4678 c. M:-28.5436 c. 17: 3 3 5 3 0 3 0 N SD: 15.2303 c. M:-27.2641 c. 24: 4 4 7 4 1 3 1 N SD: 13.0140 c. M: 22.7359 c. 29: 5 5 8 5 1 4 1 N SD: 11.6421 c. M: 20.0883 c. 30: 5 5 9 5 1 4 1 N SD: 7.1314 c. M: 12.7359 c. 35: 6 6 10 6 1 5 1 N SD: 6.0914 c. M: 10.6302 c. 36: 6 6 11 6 1 5 1 N SD: 4.4125 c. M: 7.8200 c. 41: 7 7 12 7 1 6 1 N SD: 2.2039 c. M: 3.9403 c. 47: 8 8 14 8 1 7 1 N SD: 0.9801 c. M:-1.7322 c. 88: 15 15 26 15 2 13 2 N SD: 0.7995 c. M: 1.2795 c. 135: 23 23 40 23 3 20 3 N SD: 0.5728 c. M:-1.0689 c. 171: 29 29 51 29 4 25 4 N SD: 0.5042 c. M: 0.8061 c. 218: 37 37 65 37 5 32 5 N SD: 0.2572 c. M: 0.4806 c. 265: 45 45 79 45 6 39 6 N SD: 0.2099 c. M:-0.3671 c. 306: 52 52 91 52 7 45 7 N SD: 0.1305 c. M: 0.2100 c. 353: 60 60 105 60 8 52 8 N SD: 0.0604 c. M:-0.1120 c. 877: 149 149 261 149 20 129 20 N SD: 0.0573 c. M: 0.1019 c. 924: 157 157 275 157 21 136 21 N SD: 0.0153 c. M: 0.0278 c. 1277: 217 217 380 217 29 188 29 N SD: 0.0075 c. M:-0.0127 c. 2201: 374 374 655 374 50 324 50 N SD: 0.0051 c. M:-0.0091 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 31.4805 cents 3 x 4 x 5 x x 6 S SD: 41.1977 cents 4 x 5:6:7 x x 8 S SD: 16.6332 cents 5 x 6:8 x 9 x 10 S SD: 26.6200 cents 6:7:8:9 x 11 x 12 SD: 27.5003 cents 7:8:9:11:12 x x 14 SD: 11.0812 cents 8:9:10:12:14 x x 16 S SD: 13.3065 cents 9:10:11:14 x 16 x 18 SD: 12.8252 cents 10:11:13:16 x 18 x 20 SD: 16.1334 cents 11:12:14:17:19:20 x 22 SD: 11.8847 cents 12:14:15:19:21 x x 24 SD: 14.6500 cents 13:15:16:20 x 23 x 26 SD: 13.7029 cents 14:16:18:22 x 25 x 28 SD: 8.6141 cents 15:17:19:23:26:27 x 30 SD: 6.5038 cents 16:18:20:25:28 x x 32 SD: 4.5694 cents 17:19:22:26 x 30:33:34 SD: 9.4794 cents 18:20:23:28 x 32:35:36 SD: 5.7705 cents 21:24:27:33:37 x 41:42 SD: 7.7141 cents 22:25:28:34 x 39:43:44 SD: 4.4260 cents 23:26:29:36:40:41:45:46 SD: 3.1356 cents 25:28:32:39:44 x 49:50 SD: 4.1598 cents 26:29:33:40 x 46:51:52 SD: 4.4753 cents 27:30:34:42:47:48:53:54 SD: 3.6395 cents 30:34:38:47 x 53:59:60 SD: 3.4892 cents 31:35:39:48:54:55:61:62 SD: 2.4195 cents 34:38:43:53 x 60:67:68 SD: 2.9322 cents 39:44:49:61:68:69:77:78 SD: 2.8874 cents 40:45:51:62:70:71:79:80 SD: 2.2087 cents 41:46:52:64:72:73:81:82 SD: 1.7560 cents 49:55:62:76:86:87:96:98 SD: 1.7058 cents 56:63:71:87:98:100:110:112 SD: 1.3485 cents 63:71:80:98:110:112:124:126 SD: 1.0889 cents 72:81:91:112:126:128:142:144 SD: 0.5524 cents 128:144:162:199:224:228:252:256 SD: 0.5019 cents 135:152:171:210:236:240:266:270 SD: 0.4391 cents 184:207:233:286:322:327:362:368 SD: 0.3012 cents 225:253:285:350:394:400:443:450 SD: 0.2851 cents 248:279:314:386:434:441:488:496 SD: 0.2234 cents 256:288:324:398:448:455:504:512 SD: 0.1507 cents 320:360:405:498:560:569:630:640 SD: 0.1205 cents 504:567:638:784:882:896:992:1008 SD: 0.0789 cents 576:648:729:896:1008:1024:1134:1152 SD: 0.0000 cents