Scala analysis: xen09-chalmers-tritriadic-22-28-33
Tritriadic scale built from 22:28:33
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: 14/11 417.507964 undecimal diminished fourth or major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 56/33 915.552963 6: 21/11 1119.462965 undecimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 9/8 203.9100 major whole tone 2: 112/99 213.5980 3: 22/21 80.5370 undecimal minor semitone 4: 9/8 203.9100 major whole tone 5: 112/99 213.5980 6: 9/8 203.9100 major whole tone 7: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 3 9/8 203.910 cents major whole tone 1: 2 112/99 213.598 cents 2: 3 33/28 284.447 cents undecimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 297/224 488.357 cents 3: 5 4/3 498.045 cents perfect fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 448/297 711.643 cents 5: 3 11/7 782.492 cents undecimal augmented fifth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 3 56/33 915.553 cents 6: 2 99/56 986.402 cents 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 21/11 1119.463 cents undecimal major seventh 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 : 203.9 417.5 498.0 702.0 915.6 1119.5 1200.0 203.9 : 213.6 294.1 498.0 711.6 915.6 996.1 1200.0 417.5 : 80.5 284.4 498.0 702.0 782.5 986.4 1200.0 498.0 : 203.9 417.5 621.4 702.0 905.9 1119.5 1200.0 702.0 : 213.6 417.5 498.0 702.0 915.6 996.1 1200.0 915.6 : 203.9 284.4 488.4 702.0 782.5 986.4 1200.0 1119.5: 80.5 284.4 498.0 578.6 782.5 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 213.5980 cents 392/363, 133.0609 cents 22/21, 80.5370 cents 2: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 3267/3136, 70.8491 cents 3: 488.3570 .. 621.4180 cents 392/363, 133.0609 cents 3267/3136, 70.8491 cents 4: 578.5820 .. 711.6430 cents 392/363, 133.0609 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 915.5530 cents 392/363, 133.0609 cents 3267/3136, 70.8491 cents 6: 986.4020 .. 1119.4630 cents 392/363, 133.0609 cents 3267/3136, 70.8491 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 112/99, 213.5980 cents Average / Smallest step : 2.128568 Largest / Average step : 1.245988 Largest / Smallest step : 2.652171 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 : 178.82445 cents, oct.: 1251.77118 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : MLSMLMS Scale is a Constant Structure, by a margin of 42.83593 cents Scale diversity : 1.324962 Lumma stability : 0.370392 Lumma impropriety factor : 0.035697 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 : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 896/891, 9.6880 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 417.508 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 6, average 703.5697 cents Scale is Lydian octave species of abstract tetrachord Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 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 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 133.0609 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 297 (O: 297 U: 297) Highest odd numerator or denominator: 33 Scale harmonicity : 0.023547 Average absolute harmonicity : 0.243194 Specific harmonicity : 0.110596 Fundamental : 1/264, -8.0444 octaves, 0.9910 Hz. Guide tone : 504, 8.9773 octaves, 131859.285 Hz. Exponens Consonantiae : 1.330560E+05, 17.02167 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 89.0, average 12.71429 Mersenne's string divisions : 25418400 Sum of van Prooijen's expressibility: 5.79061, average 0.82723 Sum of Tenney's harmonic distance : 11.83353, average 1.69050 Vogel's harmonic complexity : 16.57143 Wille's k value : 148 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 79.26754, average 2.83098 Lattice compactness (without 2's) : 46.44630, average 1.65880 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.42857 11 1 3: -1 .. 2 0.28571 6 3 7: 0 .. 1 0.42857 3 11: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 20 22| Scale is weakly epimorphic with val: <7 10 21 23| Scale is weakly epimorphic with val: <7 10 22 24| Scale is JI-epimorphic with val: <7 11 18 23| Scale is JI-epimorphic with val: <7 11 19 24| Scale is JI-epimorphic with val: <7 11 20 25| Scale is JI-epimorphic with val: <7 11 21 26| Scale is weakly epimorphic with val: <7 12 18 26| Scale is weakly epimorphic with val: <7 12 21 22| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 51.8629 c. M: 90.8915 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 37.4910 c. M:-62.7567 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 35.4436 c. M: 57.5080 c. Pseudo Rast 11: 2 2 1 1 2 2 1 P D3 S SD: 33.1747 c. M:-47.4095 c. 12: 2 2 1 2 2 2 1 P M ME S SD: 11.6506 c. M: 19.4630 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 17: 3 3 1 3 3 3 1 N M DE S SD: 5.7590 c. M:-9.9488 c. Seventeen-tone Major 29: 5 5 2 5 5 5 2 N M DE S SD: 2.9091 c. M: 5.2081 c. Twenty-nine tone Major 46: 8 8 3 8 8 8 3 N M DE S SD: 2.5592 c. M:-4.7857 c. 60: 10 11 4 10 11 10 4 N T3 SD: 2.6513 c. M:-4.4470 c. 72: 12 13 5 12 13 12 5 N T3 SD: 2.1613 c. M: 3.9100 c. 77: 13 14 5 13 14 13 5 N T3 SD: 2.2535 c. M:-3.9276 c. 89: 15 16 6 15 16 15 6 N T3 SD: 0.9405 c. M: 1.6628 c. 106: 18 19 7 18 19 18 7 N T3 SD: 0.8933 c. M:-1.4282 c. 118: 20 21 8 20 21 20 8 N T3 SD: 0.4595 c. M: 0.8189 c. 135: 23 24 9 23 24 23 9 N T3 SD: 0.3359 c. M:-0.5370 c. 224: 38 40 15 38 40 38 15 N T3 SD: 0.2916 c. M:-0.5185 c. 253: 43 45 17 43 45 43 17 N T3 SD: 0.0797 c. M: 0.1379 c. 730: 124 130 49 124 130 124 49 N T3 SD: 0.0433 c. M: 0.0744 c. 865: 147 154 58 147 154 147 58 N T3 SD: 0.0435 c. M:-0.0746 c. 983: 167 175 66 167 175 167 66 N T3 SD: 0.0247 c. M: 0.0443 c. 1118: 190 199 75 190 199 190 75 N T3 SD: 0.0205 c. M:-0.0361 c. 1371: 233 244 92 233 244 233 92 N T3 SD: 0.0154 c. M:-0.0287 c. 2101: 357 374 141 357 374 357 141 N T3 SD: 0.0062 c. M:-0.0111 c. 2354: 400 419 158 400 419 400 158 N T3 SD: 0.0039 c. M: 0.0067 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: 10.3981 cents 4 x 5 x 6:7 x 8 S SD: 15.4335 cents 5 x 6:7 x 8 x 10 S SD: 41.7495 cents 6:7 x 8:9:10:11:12 S SD: 16.5422 cents 7:8:9 x 11:12:13:14 SD: 16.7734 cents 8:9:10:11:12:14:15:16 S SD: 12.4722 cents 10:11:13 x 15:17:19:20 SD: 9.0351 cents 13:15 x 17:20:22:25:26 SD: 11.9662 cents 14:16:18:19:21:24:27:28 SD: 7.2970 cents 16:18:20:21:24:27:31:32 SD: 7.0916 cents 18:20:23:24:27:31:34:36 SD: 5.5378 cents 22:25:28:29:33:37:42:44 SD: 4.3690 cents 24:27:31:32:36:41:46:48 SD: 4.1268 cents 26:29:33:35:39:44:50:52 SD: 3.7806 cents 30:34:38:40:45:51:57:60 SD: 2.5127 cents 40:45:51:53:60:68:76:80 SD: 2.0463 cents 48:54:61:64:72:81:92:96 SD: 1.7351 cents 54:61:69:72:81:92:103:108 SD: 1.7315 cents 56:63:71:75:84:95:107:112 SD: 1.4707 cents 66:74:84:88:99:112:126:132 SD: 0.8341 cents 96:108:122:128:144:163:183:192 SD: 0.5388 cents 144:162:183:192:216:244:275:288 SD: 0.5272 cents 162:182:206:216:243:275:309:324 SD: 0.4660 cents 168:189:214:224:252:285:321:336 SD: 0.3076 cents 198:223:252:264:297:336:378:396 SD: 0.2774 cents 264:297:336:352:396:448:504:528 SD: 0.0000 cents