Scala analysis: xen15-chalmers-triadic-diamond-11-9
Triadic diamond for M=11/9, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/9 347.407941 undecimal neutral third 2: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 44/27 845.452940 neutral sixth 6: 18/11 852.592059 undecimal neutral sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 11/9 347.4079 undecimal neutral third 1: 11/9 347.4079 undecimal neutral third 2: 243/242 7.1391 neutral third comma, rastma 3: 88/81 143.4979 2nd undecimal neutral second 4: 9/8 203.9100 major whole tone 5: 88/81 143.4979 2nd undecimal neutral second 6: 243/242 7.1391 neutral third comma, rastma 7: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 243/242 7.139 cents neutral third comma, rastma 1: 2 88/81 143.498 cents 2nd undecimal neutral second 1: 1 9/8 203.910 cents major whole tone 1: 2 11/9 347.408 cents undecimal neutral third 2: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 121/81 694.816 cents two (undecimal neutral third) 3: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 1 968/729 490.906 cents 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 4: 2 4/3 498.045 cents perfect fourth 4: 2 3/2 701.955 cents perfect fifth 4: 1 729/484 709.094 cents two (neutral third, Zalzal wosta of al-Farabi) 4: 2 44/27 845.453 cents neutral sixth 5: 1 162/121 505.184 cents 5: 2 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 18/11 852.592 cents undecimal neutral sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 81/44 1056.502 cents 2nd undecimal neutral seventh 6: 2 484/243 1192.861 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 347.4 354.5 498.0 702.0 845.5 852.6 1200.0 347.4 : 7.1 150.6 354.5 498.0 505.2 852.6 1200.0 354.5 : 143.5 347.4 490.9 498.0 845.5 1192.9 1200.0 498.0 : 203.9 347.4 354.5 702.0 1049.4 1056.5 1200.0 702.0 : 143.5 150.6 498.0 845.5 852.6 996.1 1200.0 845.5 : 7.1 354.5 702.0 709.1 852.6 1056.5 1200.0 852.6 : 347.4 694.8 702.0 845.5 1049.4 1192.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 7.1391 .. 347.4079 cents 2662/2187, 340.2688 cents 243/242, 7.1391 cents 2: 150.6371 .. 694.8159 cents 1331/972, 544.1788 cents 108/121,-196.7709 cents 3: 354.5471 .. 701.9550 cents 11/9, 347.4079 cents 2187/2662,-340.2688 cents 4: 498.0450 .. 845.4529 cents 11/9, 347.4079 cents 8/9,-203.9100 cents 5: 505.1841 .. 1049.3629 cents 1331/972, 544.1788 cents 2187/2662,-340.2688 cents 6: 852.5921 .. 1192.8609 cents 2662/2187, 340.2688 cents 108/121,-196.7709 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 243/242, 7.1391 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 24.012565 Largest / Average step : 2.026546 Largest / Smallest step : 48.662575 Median interval of one step : 88/81, 143.4979 cents, amount: 2 Least squares average step : 165.00910 cents, oct.: 1155.06371 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DABCBAD Scale is not a Constant Structure Scale diversity : 1.136578 Lumma stability : 0.011899 Lumma impropriety factor : 0.737040 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 243/242, 7.1391 cents Number of recognisable fifths : 6, average 701.9550 cents Scale is a complete diamond : 9 11 27 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 : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.018062 Average absolute harmonicity : 0.234657 Specific harmonicity : 0.097309 Fundamental : 1/594, -9.2143 octaves, 0.4404 Hz. Guide tone : 1188, 10.2143 octaves, 310811.172 Hz. Exponens Consonantiae : 7.056720E+05, 19.42864 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 92.0, average 13.14286 Mersenne's string divisions : 6053460 Sum of van Prooijen's expressibility: 5.89976, average 0.84282 Sum of Tenney's harmonic distance : 12.29927, average 1.75704 Vogel's harmonic complexity : 21.57143 Wille's k value : 445 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 88.60536, average 3.16448 Lattice compactness (without 2's) : 73.03173, average 2.60828 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -3 .. 3 0.00000 12 2 11: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 22| Scale is weakly epimorphic with val: <7 12 25|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 10.9691 c. M:-16.2407 c. 17: 5 0 2 3 2 0 5 N I SD: 3.7271 c. M: 5.5332 c. 24: 7 0 3 4 3 0 7 N I SD: 2.9865 c. M: 4.5471 c. 41: 12 0 5 7 5 0 12 N I SD: 2.7169 c. M: 3.8116 c. 65: 19 0 8 11 8 0 19 N I SD: 2.7121 c. M:-3.7778 c. 87: 25 1 10 15 10 1 25 N I SD: 2.6983 c. M:-4.0736 c. 94: 27 1 11 16 11 1 27 N I SD: 2.1297 c. M:-2.8997 c. 101: 29 1 12 17 12 1 29 N I SD: 1.9004 c. M: 2.8535 c. 111: 32 1 13 19 13 1 32 N I SD: 1.4716 c. M:-2.2097 c. 118: 34 1 14 20 14 1 34 N I SD: 1.1580 c. M: 1.6452 c. 128: 37 1 15 22 15 1 37 N I SD: 1.1405 c. M:-1.7029 c. 135: 39 1 16 23 16 1 39 N I SD: 0.6841 c. M:-1.0085 c. 142: 41 1 17 24 17 1 41 N I SD: 0.6114 c. M: 0.9291 c. 152: 44 1 18 26 18 1 44 N I SD: 0.5270 c. M: 0.7161 c. 159: 46 1 19 27 19 1 46 N I SD: 0.1606 c. M: 0.2381 c. 335: 97 2 40 57 40 2 97 N I SD: 0.0886 c. M:-0.1346 c. 494: 143 3 59 84 59 3 143 N I SD: 0.0721 c. M:-0.1088 c. 518: 150 3 62 88 62 3 150 N I SD: 0.0733 c. M:-0.1069 c. 677: 196 4 81 115 81 4 196 N I SD: 0.0293 c. M:-0.0419 c. 836: 242 5 100 142 100 5 242 N I SD: 0.0305 c. M:-0.0411 c. 1012: 293 6 121 172 121 6 293 N I SD: 0.0167 c. M: 0.0229 c. 1171: 339 7 140 199 140 7 339 N I SD: 0.0143 c. M:-0.0217 c. 1689: 489 10 202 287 202 10 489 N I SD: 0.0130 c. M: 0.0178 c. 1848: 535 11 221 314 221 11 535 N I SD: 0.0048 c. M:-0.0069 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 x 5:6 S SD: 10.5889 cents 4 x 5 x 6 x 7:8 S SD: 30.1241 cents 5:6 x 7 x 8 x 10 S SD: 23.9178 cents 6:7 x 8:9 x 10:12 S SD: 17.3151 cents 7 x x 9 x 11 x 14 SD: 29.6801 cents 8 x 10:11:12:13 x 16 SD: 12.4441 cents 9:11 x 12:14 x 15:18 SD: 14.1042 cents 10:12 x 13:15:16 x 20 SD: 12.5529 cents 11:13:14:15:17 x 18:22 SD: 17.9008 cents 12 x 15:16:18 x 20:24 S SD: 8.9850 cents 13 x 16:17:20:21 x 26 SD: 11.5006 cents 14:17 x 19:21 x 23:28 SD: 6.6728 cents 15:18 x 20:23:24:25:30 SD: 11.1495 cents 16 x 20:21:24:26 x 32 SD: 8.4302 cents 17 x 21:23:26 x 28:34 SD: 8.9962 cents 18:22 x 24:27:29 x 36 SD: 3.9571 cents 19:23 x 25:29:31 x 38 SD: 8.2795 cents 20:24:25:27:30 x 33:40 SD: 8.6397 cents 21 x 26:28:32:34 x 42 SD: 6.6380 cents 22 x 27:29:33 x 36:44 SD: 3.9571 cents 23:28 x 31:35:37:38:46 SD: 7.0631 cents 24:29 x 32:36:39 x 48 SD: 4.0779 cents 25 x 31:33:38 x 41:50 SD: 6.8186 cents 26 x 32:35:39:42:43:52 SD: 4.9110 cents 27:33 x 36:41:44 x 54 SD: 4.2485 cents 28:34 x 37:42 x 46:56 SD: 4.0758 cents 29:35:36:39:44:47 x 58 SD: 6.6075 cents 30 x 37:40:45 x 49:60 SD: 1.8224 cents 31 x 38:41:47 x 51:62 SD: 5.0192 cents 32:39 x 43:48:52 x 64 SD: 3.0334 cents 33:40:41:44:50 x 54:66 SD: 5.1650 cents 34 x 42:45:51:55:56:68 SD: 4.0170 cents 35 x 43:47:53:57 x 70 SD: 4.1267 cents 36:44 x 48:54 x 59:72 SD: 0.5339 cents 37:45 x 49:56:60:61:74 SD: 4.3842 cents 38:46:47:51:57:62 x 76 SD: 4.0520 cents 39 x 48:52:59 x 64:78 SD: 3.2595 cents 40 x 49:53:60:65 x 80 SD: 2.4688 cents 41:50 x 55:62 x 67:82 SD: 3.6197 cents 42:51:52:56:63:68:69:84 SD: 3.2964 cents 43 x 53:57:65:70 x 86 SD: 3.6842 cents 44 x 54:59:66 x 72:88 SD: 1.9617 cents 45:55 x 60:68:73:74:90 SD: 2.8780 cents 46:56 x 61:69:75 x 92 SD: 2.3388 cents 47:57:58:63:71 x 77:94 SD: 3.7629 cents 48 x 59:64:72:78:79:96 SD: 1.9089 cents 49:60 x 65:74:80 x 98 SD: 3.0775 cents 50:61 x 67:75:81:82:100 SD: 2.3835 cents 51:62:63:68:77:83 x 102 SD: 3.0999 cents 52 x 64:69:78 x 85:104 SD: 1.9728 cents 53 x 65:71:80:86:87:106 SD: 2.7414 cents 54:66 x 72:81:88 x 108 SD: 0.0000 cents 55:67:68:73:83 x 90:110 SD: 3.1961 cents 56:68:69:75:84:91:92:112 SD: 2.4947 cents 57 x 70:76:86:93 x 114 SD: 2.0732 cents 58:71 x 77:87 x 95:116 SD: 1.6251 cents 59:72 x 79:89:96:97:118 SD: 2.5226 cents 60:73:74:80:90 x 98:120 SD: 2.0086 cents 61 x 75:81:92:99:100:122 SD: 2.4150 cents 62 x 76:83:93:101 x 124 SD: 1.4591 cents 63:77 x 84:95 x 103:126 SD: 1.8525 cents 65:79:80:87:98:106 x 130 SD: 2.5961 cents 66 x 81:88:99 x 108:132 SD: 0.0000 cents 67:82 x 89:101:109:110:134 SD: 2.1260 cents 68:83 x 91:102:111 x 136 SD: 1.4708 cents 70 x 86:93:105:114:115:140 SD: 1.5811 cents 71 x 87:95:107 x 116:142 SD: 2.1678 cents 72:88 x 96:108:117:118:144 SD: 0.9337 cents 73:89:90:97:110:119 x 146 SD: 2.2275 cents 74:90:91:99:111 x 121:148 SD: 1.8296 cents 75 x 92:100:113:122:123:150 SD: 1.5309 cents 76:93 x 101:114:124 x 152 SD: 1.2823 cents 79 x 97:105:119:129 x 158 SD: 1.9599 cents 80 x 98:107:120:130:131:160 SD: 1.3456 cents 81:99 x 108:122:132:133:162 SD: 1.5427 cents 82:100:101:109:123 x 134:164 SD: 1.5565 cents 84 x 103:112:126:137 x 168 SD: 0.4150 cents 85:104 x 113:128 x 139:170 SD: 1.7507 cents 86:105:106:115:129:140:141:172 SD: 1.4181 cents 87:106:107:116:131:142 x 174 SD: 1.6183 cents 88 x 108:117:132:143:144:176 SD: 1.1609 cents 89:109 x 119:134:145:146:178 SD: 1.6397 cents 90:110 x 120:135 x 147:180 SD: 0.6418 cents 93 x 114:124:140 x 152:186 SD: 1.3702 cents 94:115 x 125:141:153:154:188 SD: 0.9520 cents 95:116:117:127:143:155 x 190 SD: 1.6772 cents 96:117:118:128:144:156:157:192 SD: 1.0752 cents 97 x 119:129:146:158:159:194 SD: 1.3454 cents 98:120 x 131:147:160 x 196 SD: 1.2657 cents 100:122:123:133:150:163:164:200 SD: 1.0917 cents 101:123:124:135:152 x 165:202 SD: 1.6535 cents 102 x 125:136:153:166:167:204 SD: 0.5912 cents 103:126 x 137:155:168:169:206 SD: 1.4472 cents 104:127:128:139:156:169:170:208 SD: 1.2081 cents 105:128:129:140:158:171:172:210 SD: 1.0913 cents 106 x 130:141:159:173 x 212 SD: 0.9983 cents 107:131 x 143:161:174:175:214 SD: 1.3776 cents 108:132:133:144:162:176:177:216 SD: 0.9286 cents 109:133:134:145:164 x 178:218 SD: 1.4261 cents 110:134:135:147:165:179:180:220 SD: 1.0555 cents 111 x 136:148:167:181:182:222 SD: 1.1598 cents 112:137 x 149:168 x 183:224 SD: 0.9713 cents 114:139:140:152:171:186:187:228 SD: 0.9091 cents 115 x 141:153:173:187:188:230 SD: 1.2813 cents 116:142 x 155:174:189:190:232 SD: 0.8183 cents 117:143:144:156:176:191 x 234 SD: 1.2656 cents 118:144:145:157:177:192:193:236 SD: 0.8221 cents 120 x 147:160:180 x 196:240 SD: 0.9076 cents 122:149:150:163:183:199:200:244 SD: 0.8651 cents 124 x 152:165:186:202:203:248 SD: 0.6971 cents 125:153 x 167:188:204:205:250 SD: 1.2980 cents 126:154:155:168:189:205:206:252 SD: 0.7393 cents 128:156:157:171:192:209 x 256 SD: 1.1557 cents 129 x 158:172:194:210:211:258 SD: 1.0000 cents 130:159:160:173:195:212:213:260 SD: 0.9391 cents 132:161:162:176:198:215:216:264 SD: 0.5272 cents 133 x 163:177:200:217:218:266 SD: 1.1528 cents 134:164 x 179:201:218:219:268 SD: 0.9007 cents 135:165:166:180:203:220:221:270 SD: 0.7794 cents 138:169 x 184:207:225:226:276 SD: 0.6315 cents 139:170:171:185:209 x 227:278 SD: 1.2625 cents 140:171:172:187:210:228:229:280 SD: 0.5695 cents 142 x 174:189:213:231:232:284 SD: 0.9620 cents 144:176:177:192:216:235:236:288 SD: 0.6435 cents 147:180 x 196:221:240:241:294 SD: 1.1384 cents 148:181:182:197:222:241:242:296 SD: 0.7163 cents 151 x 185:201:227:246:247:302 SD: 0.9477 cents 152:186:187:203:228:248:249:304 SD: 0.8808 cents 153:187:188:204:230:249:250:306 SD: 0.7861 cents 154:188:189:205:231:251:252:308 SD: 0.4981 cents 156:191 x 208:234:254:255:312 SD: 0.6425 cents 160 x 196:213:240:261:262:320 SD: 0.7823 cents 162:198:199:216:243:264:265:324 SD: 0.2415 cents 169 x 207:225:254:275:277:338 SD: 1.1123 cents 170:208:209:227:255:277:278:340 SD: 0.6440 cents 171:209:210:228:257:279:280:342 SD: 0.6091 cents 176:215:216:235:264:287:288:352 SD: 0.4063 cents 178:218 x 237:267:290:291:356 SD: 0.7679 cents 180:220:221:240:270:293:295:360 SD: 0.4846 cents 184:225:226:245:276:300:301:368 SD: 0.4337 cents 198:242:243:264:297:323:324:396 SD: 0.2554 cents 324:396:398:432:486:528:530:648 SD: 0.2415 cents 330:403:405:440:495:538:540:660 SD: 0.2286 cents 360:440:442:480:540:587:589:720 SD: 0.1776 cents 396:484:486:528:594:645:648:792 SD: 0.1278 cents 432:528:530:576:648:704:707:864 SD: 0.0906 cents 594:726:729:792:891:968:972:1188 SD: 0.0000 cents