Scala analysis: xen09-chalmers-tritriadic-1-3-7
Tritriadic scale built from 1:3:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 21/16 470.780907 narrow fourth 3: 3/2 701.955001 perfect fifth 4: 49/32 737.651813 5: 12/7 933.129094 septimal major sixth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 8/7 231.1741 septimal whole tone 2: 147/128 239.6068 3: 8/7 231.1741 septimal whole tone 4: 49/48 35.6968 slendro diesis, septimal 1/6-tone 5: 384/343 195.4773 6: 49/48 35.6968 slendro diesis, septimal 1/6-tone 7: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 384/343 195.477 cents 1: 3 8/7 231.174 cents septimal whole tone 1: 1 147/128 239.607 cents 2: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 2: 2 21/16 470.781 cents narrow fourth 3: 1 7/6 266.871 cents septimal minor third 3: 2 64/49 462.348 cents 2 septatones or septatonic major third 3: 1 4/3 498.045 cents perfect fourth 3: 1 343/256 506.478 cents 3: 2 3/2 701.955 cents perfect fifth 4: 2 4/3 498.045 cents perfect fourth 4: 1 512/343 693.522 cents 3 septatones or septatonic fifth 4: 1 3/2 701.955 cents perfect fifth 4: 2 49/32 737.652 cents 4: 1 12/7 933.129 cents septimal major sixth 5: 2 32/21 729.219 cents wide fifth 5: 1 49/32 737.652 cents 5: 2 12/7 933.129 cents septimal major sixth 5: 2 7/4 968.826 cents harmonic seventh 6: 1 256/147 960.393 cents 6: 3 7/4 968.826 cents harmonic seventh 6: 1 343/192 1004.523 cents 6: 2 96/49 1164.303 cents 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 : 231.2 470.8 702.0 737.7 933.1 968.8 1200.0 231.2 : 239.6 470.8 506.5 702.0 737.7 968.8 1200.0 470.8 : 231.2 266.9 462.3 498.0 729.2 960.4 1200.0 702.0 : 35.7 231.2 266.9 498.0 729.2 968.8 1200.0 737.7 : 195.5 231.2 462.3 693.5 933.1 1164.3 1200.0 933.1 : 35.7 266.9 498.0 737.7 968.8 1004.5 1200.0 968.8 : 231.2 462.3 702.0 933.1 968.8 1164.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 239.6068 cents 9/8, 203.9100 cents 49/48, 35.6968 cents 2: 231.1741 .. 470.7809 cents 147/128, 239.6068 cents 1024/1029,-8.4327 cents 3: 266.8709 .. 701.9550 cents 9/7, 435.0841 cents 8/9,-203.9100 cents 4: 498.0450 .. 933.1291 cents 9/7, 435.0841 cents 8/9,-203.9100 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 8/9,-203.9100 cents 6: 960.3932 .. 1164.3032 cents 9/8, 203.9100 cents 1024/1029,-8.4327 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 147/128, 239.6068 cents Average / Smallest step : 4.802350 Largest / Average step : 1.397706 Largest / Smallest step : 6.712275 Median interval of one step : 8/7, 231.1741 cents, amount: 3 Most common interval of one step : 8/7, 231.1741 cents, amount: 3 Least squares average step : 179.34149 cents, oct.: 1255.39045 cents Scale is not proper Step pattern alph. order: ABACDCA Step pattern size order : CDCABAC Scale is not a Constant Structure Scale diversity : 1.095086 Lumma stability : 0.059495 Lumma impropriety factor : 0.523830 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 : 1029/1024, 8.4327 cents Most common intervals : 8/7, 231.1741 cents & inv., amount: 5 Most common triad is 0.0 231.174 968.826 cents, amount: 3 Number of recognisable fifths : 4, average 699.8468 cents Scale contains a complete diamond : 1 7 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 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 435.0841 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.024083 Average absolute harmonicity : 0.227766 Specific harmonicity : 0.131764 Fundamental : 1/224, -7.8074 octaves, 1.1680 Hz. Guide tone : 1176, 10.1997 octaves, 307671.665 Hz. Exponens Consonantiae : 2.634240E+05, 18.00703 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 85.5, average 12.21429 Mersenne's string divisions : 3131865 Sum of van Prooijen's expressibility: 6.02483, average 0.86069 Sum of Tenney's harmonic distance : 11.92049, average 1.70293 Vogel's harmonic complexity : 14.42857 Wille's k value : 171 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 106.06937, average 3.78819 Lattice compactness (without 2's) : 41.76998, average 1.49178 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -0.85714 18 1 3: 0 .. 1 0.42857 3 1 7: -1 .. 2 0.28571 6 5 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is weakly epimorphic with val: <7 10 20| Scale is weakly epimorphic with val: <7 11 22|
FIT/MODE
7: 1 1 2 0 1 0 2 N T3 S SD: 76.6647 c. M: 127.9238 c. 8: 2 1 2 0 1 0 2 N SD: 43.8572 c. M:-68.8259 c. 10: 2 2 2 0 2 0 2 N D3 S SD: 15.1188 c. M:-26.8709 c. 21: 4 4 4 1 3 1 4 N G S SD: 10.9901 c. M: 18.8434 c. 26: 5 5 5 1 4 1 5 N G S SD: 6.3305 c. M: 10.0522 c. 31: 6 6 6 1 5 1 6 N G S SD: 3.5841 c. M: 6.2648 c. 36: 7 7 7 1 6 1 7 N G S SD: 2.6394 c. M: 4.3185 c. 67: 13 13 13 2 11 2 13 N G S SD: 2.8722 c. M: 5.1093 c. 77: 15 15 15 2 13 2 15 N G S SD: 2.8042 c. M: 5.1843 c. 89: 17 18 17 3 14 3 17 N SD: 2.1655 c. M:-3.9212 c. 94: 18 19 18 3 15 3 18 N SD: 1.4869 c. M:-2.7737 c. 99: 19 20 19 3 16 3 19 N SD: 1.1673 c. M:-1.9464 c. 125: 24 25 24 4 20 4 24 N SD: 1.1210 c. M: 1.9291 c. 130: 25 26 25 4 21 4 25 N SD: 0.5116 c. M: 0.8214 c. 135: 26 27 26 4 22 4 26 N SD: 0.1874 c. M:-0.3302 c. 436: 84 87 84 13 71 13 84 N SD: 0.0811 c. M: 0.1387 c. 571: 110 114 110 17 93 17 110 N SD: 0.0187 c. M: 0.0293 c. 1277: 246 255 246 38 208 38 246 N SD: 0.0080 c. M:-0.0146 c. 1848: 356 369 356 55 301 55 356 N SD: 0.0072 c. M: 0.0122 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: 0.0000 cents 3 x 4 x x 5 x 6 S SD: 18.6246 cents 4 x 5:6 x x 7:8 S SD: 21.1168 cents 5:6:7 x 8 x 9:10 S SD: 33.3337 cents 6:7:8:9 x 10:11:12 S SD: 17.3864 cents 7:8:9 x 11:12 x 14 SD: 11.4628 cents 8:9:11:12 x x 14:16 SD: 17.0053 cents 9:10:12 x 14:15:16:18 S SD: 13.9315 cents 10:11:13:15 x 17:18:20 SD: 14.1827 cents 11:13:14 x 17:19 x 22 SD: 16.2879 cents 12:14:16:18 x x 21:24 S SD: 8.9835 cents 13:15:17 x 20:22:23:26 SD: 5.8642 cents 14:16:18:21 x 24:25:28 SD: 8.3293 cents 15:17:20 x 23 x 26:30 SD: 7.0234 cents 17:19:22 x 26:29:30:34 SD: 8.1207 cents 19:22:25 x 29 x 33:38 SD: 5.4143 cents 20:23:26:30:31:34:35:40 SD: 4.6173 cents 21:24:28 x 32:36:37:42 SD: 5.1430 cents 22:25:29:33:34:38:39:44 SD: 4.6915 cents 23:26:30 x 35:39:40:46 SD: 5.4392 cents 25:29:33 x 38:43:44:50 SD: 5.4139 cents 26:30:34:39:40:45:46:52 SD: 4.5478 cents 27:31:35 x 41:46:47:54 SD: 5.0954 cents 28:32:37:42:43:48:49:56 SD: 1.8248 cents 29:33:38 x 44:50:51:58 SD: 3.6817 cents 31:35:41 x 47:53:54:62 SD: 5.2711 cents 32:37:42:48:49:55:56:64 SD: 2.9523 cents 36:41:47:54:55:62:63:72 SD: 2.0203 cents 48:55:63:72:74:82:84:96 SD: 1.9913 cents 56:64:74:84:86:96:98:112 SD: 1.8248 cents 60:69:79:90:92:103:105:120 SD: 1.7944 cents 64:73:84:96:98:110:112:128 SD: 0.8047 cents 92:105:121:138:141:158:161:184 SD: 0.7894 cents 112:128:147:168:172:192:196:224 SD: 0.7200 cents 128:146:168:192:196:219:224:256 SD: 0.6838 cents 132:151:173:198:202:226:231:264 SD: 0.5508 cents 140:160:184:210:214:240:245:280 SD: 0.5482 cents 154:176:202:231:236:264:270:308 SD: 0.5217 cents 160:183:210:240:245:274:280:320 SD: 0.3221 cents 196:224:257:294:300:336:343:392 SD: 0.2616 cents 224:256:294:336:343:384:392:448 SD: 0.0000 cents