Scala analysis: xen15-chalmers-triadic-reversed-diamond-27-23
Triadic reversed diamond for M=27/23, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92/81 220.454344 2: 27/23 277.590655 vicesimotertial minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 46/27 922.409345 6: 81/46 979.545656 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 92/81 220.4543 1: 92/81 220.4543 2: 2187/2116 57.1363 3: 92/81 220.4543 4: 9/8 203.9100 major whole tone 5: 92/81 220.4543 6: 2187/2116 57.1363 7: 92/81 220.4543
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 2187/2116 57.136 cents 1: 1 9/8 203.910 cents major whole tone 1: 4 92/81 220.454 cents 2: 4 27/23 277.591 cents vicesimotertial minor third 2: 2 23/18 424.364 cents vicesimotertial major third 2: 1 8464/6561 440.909 cents 3: 2 243/184 481.501 cents 3: 4 4/3 498.045 cents perfect fourth 3: 1 1058/729 644.819 cents 4: 1 729/529 555.181 cents two (vicesimotertial minor third) 4: 4 3/2 701.955 cents perfect fifth 4: 2 368/243 718.499 cents 5: 1 6561/4232 759.091 cents 5: 2 36/23 775.636 cents 5: 4 46/27 922.409 cents 6: 4 81/46 979.546 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 4232/2187 1142.864 cents 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 : 220.5 277.6 498.0 702.0 922.4 979.5 1200.0 220.5 : 57.1 277.6 481.5 702.0 759.1 979.5 1200.0 277.6 : 220.5 424.4 644.8 702.0 922.4 1142.9 1200.0 498.0 : 203.9 424.4 481.5 702.0 922.4 979.5 1200.0 702.0 : 220.5 277.6 498.0 718.5 775.6 996.1 1200.0 922.4 : 57.1 277.6 498.0 555.2 775.6 979.5 1200.0 979.5 : 220.5 440.9 498.0 718.5 922.4 1142.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.1363 .. 220.4543 cents 194672/177147, 163.3180 cents 2187/2116, 57.1363 cents 2: 277.5907 .. 440.9087 cents 194672/177147, 163.3180 cents 2187/2116, 57.1363 cents 3: 481.5007 .. 644.8187 cents 194672/177147, 163.3180 cents 1594323/1557376, 40.5920 cents 4: 555.1813 .. 718.4993 cents 194672/177147, 163.3180 cents 531441/559682,-89.6374 cents 5: 759.0913 .. 922.4093 cents 194672/177147, 163.3180 cents 1594323/1557376, 40.5920 cents 6: 979.5457 .. 1142.8637 cents 194672/177147, 163.3180 cents 2187/2116, 57.1363 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 2187/2116, 57.1363 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 92/81, 220.4543 cents Average / Smallest step : 3.000344 Largest / Average step : 1.285984 Largest / Smallest step : 3.858393 Median interval of one step : 92/81, 220.4543 cents, amount: 4 Most common interval of one step : 92/81, 220.4543 cents, amount: 4 Least squares average step : 171.19222 cents, oct.: 1198.34557 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : LSLMLSL Scale is a Constant Structure, by a margin of 40.59197 cents Scale diversity : 1.282457 Lumma stability : 0.258108 Lumma impropriety factor : 0.074698 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 : 736/729, 16.5443 cents Number of recognisable fifths : 6, average 707.4698 cents Number of appreciable 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 : 23 27 81 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 : 23 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.009216 Average absolute harmonicity : 0.223345 Specific harmonicity : 0.049404 Fundamental : 1/3726, -11.8634 octaves, 0.0702 Hz. Guide tone : 7452, 12.8634 octaves, 1949633.713 Hz. Exponens Consonantiae : 2.776615E+07, 24.72682 octaves Euler's gradus suavitatis : 64 Sum of Mann's harmonic distance : 219.0, average 31.28571 Mersenne's string divisions : 1684077150 Sum of van Prooijen's expressibility: 7.63394, average 1.09056 Sum of Tenney's harmonic distance : 15.48909, average 2.21273 Vogel's harmonic complexity : 36.57143 Wille's k value : 3280 Wilson's harmonic complexity : 70 Rectangular lattice diameter : 10 Triangular lattice diameter : 8 Lattice compactness : 107.84138, average 3.85148 Lattice compactness (without 2's) : 95.51346, average 3.41120 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -4 .. 4 0.00000 16 2 23: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is weakly epimorphic with val: <7 10 31| Scale is weakly epimorphic with val: <7 10 32| Scale is JI-epimorphic with val: <7 11 31| Scale is weakly epimorphic with val: <7 11 32| = patent Scale is weakly epimorphic with val: <7 12 30| Scale is weakly epimorphic with val: <7 12 33|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 44.4876 c. M: 65.2665 c. Lebeng 9: 2 0 2 1 2 0 2 N T3 I SD: 31.6236 c. M: 46.2123 c. 10: 2 0 2 2 2 0 2 N M DE I SD: 24.6154 c. M: 37.5907 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 16.2514 c. M: 22.4093 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 17: 3 1 3 3 3 1 3 N M DE I SD: 5.6974 c. M: 8.6896 c. Supra-7 22: 4 1 4 4 4 1 4 N M DE I SD: 4.7731 c. M:-7.1359 c. Supra-7 39: 7 2 7 7 7 2 7 N M DE I SD: 4.1080 c. M:-5.7373 c. Supra-7 43: 8 2 8 7 8 2 8 N T3 I SD: 2.8465 c. M:-4.2806 c. 60: 11 3 11 10 11 3 11 N T3 I SD: 1.6762 c. M: 2.4093 c. 65: 12 3 12 11 12 3 12 N T3 I SD: 0.7160 c. M:-1.0841 c. 82: 15 4 15 14 15 4 15 N T3 I SD: 0.6169 c. M:-0.9421 c. 147: 27 7 27 25 27 7 27 N T3 I SD: 0.0562 c. M: 0.0858 c. 947: 174 45 174 161 174 45 174 N T3 I SD: 0.0547 c. M: 0.0827 c. 1007: 185 48 185 171 185 48 185 N T3 I SD: 0.0507 c. M:-0.0682 c. 1154: 212 55 212 196 212 55 212 N T3 I SD: 0.0382 c. M: 0.0523 c. 1301: 239 62 239 221 239 62 239 N T3 I SD: 0.0290 c. M: 0.0419 c. 1448: 266 69 266 246 266 69 266 N T3 I SD: 0.0223 c. M: 0.0337 c. 1595: 293 76 293 271 293 76 293 N T3 I SD: 0.0177 c. M: 0.0269 c. 1742: 320 83 320 296 320 83 320 N T3 I SD: 0.0150 c. M: 0.0213 c. 1889: 347 90 347 321 347 90 347 N T3 I SD: 0.0141 c. M:-0.0203 c. 1954: 359 93 359 332 359 93 359 N T3 I SD: 0.0109 c. M:-0.0165 c. 2101: 386 100 386 357 386 100 386 N T3 I SD: 0.0081 c. M: 0.0121 c. 2248: 413 107 413 382 413 107 413 N T3 I SD: 0.0073 c. M: 0.0106 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: 12.6835 cents 4 x 5 x 6 x 7:8 S SD: 27.3126 cents 5 x 6:7 x x 9:10 SD: 25.0380 cents 6 x 7:8:9:10:11:12 S SD: 13.3720 cents 7:8 x 9:11:12 x 14 SD: 20.6689 cents 8:9 x 11:12 x 14:16 SD: 11.3607 cents 11 x 13:15:17:19 x 22 SD: 13.9793 cents 12 x 14:16:18:20:21:24 S SD: 6.8266 cents 13:15 x 17:20:22:23:26 SD: 10.5384 cents 14:16 x 19:21:24:25:28 SD: 6.9863 cents 15:17:18:20:23 x 26:30 SD: 10.0754 cents 16:18:19:21:24:27:28:32 SD: 6.0652 cents 19 x 22:25:29:32:33:38 SD: 9.0689 cents 20:23 x 27:30:34:35:40 SD: 5.4113 cents 22:25:26:29:33:37:39:44 SD: 4.8723 cents 24:27:28:32:36:41:42:48 SD: 3.2752 cents 30:34:35:40:45:51:53:60 SD: 1.8935 cents 51:58:60:68:77:87:90:102 SD: 1.8372 cents 58:66:68:77:87:99:102:116 SD: 1.3304 cents 74:84:87:99:111:126:130:148 SD: 1.1001 cents 80:91:94:107:120:136:141:160 SD: 1.0613 cents 88:100:103:117:132:150:155:176 SD: 1.0306 cents 96:109:113:128:144:164:169:192 SD: 0.9521 cents 102:116:120:136:153:174:180:204 SD: 0.8827 cents 104:118:122:139:156:177:183:208 SD: 0.7406 cents 126:143:148:168:189:215:222:252 SD: 0.4758 cents 138:157:162:184:207:235:243:276 SD: 0.4251 cents 162:184:190:216:243:276:285:324 SD: 0.3200 cents 258:293:303:344:387:440:454:516 SD: 0.3198 cents 264:300:310:352:396:450:465:528 SD: 0.1987 cents 294:334:345:392:441:501:518:588 SD: 0.1894 cents 368:418:432:491:552:627:648:736 SD: 0.1692 cents 414:470:486:552:621:705:729:828 SD: 0.1653 cents 426:484:500:568:639:726:750:852 SD: 0.1231 cents 552:627:648:736:828:940:972:1104 SD: 0.1178 cents