Scala analysis: synmav1
First 81/80&135/128 scale Pythagorean
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: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 9/8 203.9100 major whole tone 2: 256/243 90.2250 limma, Pythagorean minor second 3: 9/8 203.9100 major whole tone 4: 9/8 203.9100 major whole tone 5: 9/8 203.9100 major whole tone 6: 256/243 90.2250 limma, Pythagorean minor second 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 5 9/8 203.910 cents major whole tone 2: 4 32/27 294.135 cents Pythagorean minor third 2: 3 81/64 407.820 cents Pythagorean major third 3: 6 4/3 498.045 cents perfect fourth 3: 1 729/512 611.730 cents Pythagorean tritone 4: 1 1024/729 588.270 cents Pythagorean diminished fifth 4: 6 3/2 701.955 cents perfect fifth 5: 3 128/81 792.180 cents Pythagorean minor sixth 5: 4 27/16 905.865 cents Pythagorean major sixth 6: 5 16/9 996.090 cents Pythagorean minor seventh 6: 2 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 294.1 498.0 702.0 905.9 996.1 1200.0 203.9 : 90.2 294.1 498.0 702.0 792.2 996.1 1200.0 294.1 : 203.9 407.8 611.7 702.0 905.9 1109.8 1200.0 498.0 : 203.9 407.8 498.0 702.0 905.9 996.1 1200.0 702.0 : 203.9 294.1 498.0 702.0 792.2 996.1 1200.0 905.9 : 90.2 294.1 498.0 588.3 792.2 996.1 1200.0 996.1 : 203.9 407.8 498.0 702.0 905.9 1109.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 203.9100 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 611.7300 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 4: 588.2700 .. 701.9550 cents 2187/2048, 113.6850 cents 524288/531441,-23.4600 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 6: 996.0900 .. 1109.7750 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.900012 Largest / Average step : 1.189475 Largest / Smallest step : 2.260017 Median interval of one step : 9/8, 203.9100 cents, amount: 5 Most common interval of one step : 9/8, 203.9100 cents, amount: 5 Least squares average step : 171.42857 cents, oct.: 1200.00000 cents Scale is not proper Scale has Myhill's property chromas: 2187/2048, 113.6850 cents and 531441/524288, 23.4600 cents, ratio: 4.845906 generators: 3 of 498.04500 cents and 4 of 701.95500 cents ET pair of linear temperament : 12&41 Scale is distributional even Scale is a mode of a 665-tone equal temperament with octave 2/1 degrees: 113 163 276 389 502 552 665 generators: 276 and 389 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABA Step pattern size order : LSLLLSL Scale is a Constant Structure, by a margin of 23.46001 cents Ratio Whole / Half tone : 2.260017 Scale diversity : 1.288369 Lumma stability : 0.451125 Lumma impropriety factor : 0.019550 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 531441/524288, 23.4600 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 498.045 996.090 cents Most common triad is 0.0 498.045 701.955 cents, amount: 5 Number of recognisable fifths : 6, average 701.9550 cents Scale is Phrygian octave species of abstract tetrachord Scale is Dorian octave species of abstract tetrachord Scale is Hypolydian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best major thirds form a closed circle Best minor thirds form a closed circle Scale is a complete genus musicum : 2^m 3^6 Scale is a complete diamond : 1 3 9 27 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 100.0000% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval class 4 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 3 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.040000 Average absolute harmonicity : 0.267773 Specific harmonicity : 0.221198 Fundamental : 1/432, -8.7549 octaves, 0.6056 Hz. Guide tone : 864, 9.7549 octaves, 226044.488 Hz. Exponens Consonantiae : 3.732480E+05, 18.50978 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 79.5, average 11.35714 Mersenne's string divisions : 22642725 Sum of van Prooijen's expressibility: 5.72546, average 0.81792 Sum of Tenney's harmonic distance : 11.74605, average 1.67801 Vogel's harmonic complexity : 13.57143 Wille's k value : 364 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 128.06604, average 4.57379 Lattice compactness (without 2's) : 68.00000, average 2.42857 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.57143 20 1 3: -3 .. 3 0.00000 12 6 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10| Scale is JI-epimorphic with val: <7 11| = patent Scale is weakly epimorphic with val: <7 12|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.4814 c. M: 48.7221 c. Lebeng 12: 2 1 2 2 2 1 2 P M ME I SD: 3.9100 c. M:-5.8650 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 29: 5 2 5 5 5 2 5 N M DE I SD: 2.9865 c. M: 4.4798 c. 41: 7 3 7 7 7 3 7 N M DE I SD: 0.9680 c. M:-1.4521 c. 53: 9 4 9 9 9 4 9 N M DE I SD: 0.1364 c. M:-0.2046 c. 200: 34 15 34 34 34 15 34 N M DE I SD: 0.0900 c. M:-0.1350 c. 253: 43 19 43 43 43 19 43 N M DE I SD: 0.0426 c. M: 0.0639 c. 306: 52 23 52 52 52 23 52 N M DE I SD: 0.0116 c. M:-0.0174 c. 359: 61 27 61 61 61 27 61 N M DE I SD: 0.0103 c. M:-0.0154 c. 665: 113 50 113 113 113 50 113 N M DE I SD: 0.0002 c. M:-0.0003 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: 7.1688 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 25.7345 cents 6 x 7:8:9:10:11:12 S SD: 10.5986 cents 7:8 x 9:11:12 x 14 SD: 21.8513 cents 8:9 x 11:12 x 14:16 SD: 11.9689 cents 10:11:12:13:15:17:18:20 SD: 9.6077 cents 12 x 14:16:18:20:21:24 S SD: 7.3583 cents 13:15 x 17:20:22:23:26 SD: 11.8630 cents 14:16:17:19:21:24:25:28 SD: 9.3116 cents 15:17:18:20:23:25:27:30 SD: 7.8229 cents 16:18:19:21:24:27:28:32 SD: 5.5293 cents 22:25:26:29:33:37:39:44 SD: 3.9817 cents 26:29:31:35:39:44:46:52 SD: 3.7709 cents 32:36:38:43:48:54:57:64 SD: 2.0421 cents 48:54:57:64:72:81:85:96 SD: 1.0816 cents 54:61:64:72:81:91:96:108 SD: 1.0709 cents 80:90:95:107:120:135:142:160 SD: 0.9889 cents 96:108:114:128:144:162:171:192 SD: 0.6825 cents 135:152:160:180:203:228:240:270 SD: 0.6744 cents 144:162:171:192:216:243:256:288 SD: 0.4826 cents 162:182:192:216:243:273:288:324 SD: 0.4801 cents 198:223:235:264:297:334:352:396 SD: 0.4569 cents 210:236:249:280:315:354:373:420 SD: 0.4451 cents 216:243:256:288:324:365:384:432 SD: 0.3390 cents 270:304:320:360:405:456:480:540 SD: 0.2878 cents 288:324:341:384:432:486:512:576 SD: 0.2416 cents 330:371:391:440:495:557:587:660 SD: 0.2356 cents 336:378:398:448:504:567:597:672 SD: 0.1952 cents 378:425:448:504:567:638:672:756 SD: 0.1533 cents 384:432:455:512:576:648:683:768 SD: 0.1350 cents 432:486:512:576:648:729:768:864 SD: 0.0000 cents