Scala analysis: unknown
Is this scale known?
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 10/9 182.4037 minor whole tone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 11/10 165.0042 Ptolemy's second, 4/5-tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 2: 2 6/5 315.641 cents minor third 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 5/4 386.314 cents major third 3: 2 72/55 466.278 cents undecimal semi-diminished fourth 3: 2 4/3 498.045 cents perfect fourth 3: 2 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 25/18 568.717 cents classic augmented fourth 4: 1 36/25 631.283 cents classic diminished fifth 4: 2 16/11 648.682 cents undecimal semi-diminished fifth 4: 2 3/2 701.955 cents perfect fifth 4: 2 55/36 733.722 cents undecimal semi-augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 121/72 898.726 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 20/11 1034.996 cents large minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 150.6 315.6 498.0 702.0 884.4 1049.4 1200.0 150.6 : 165.0 347.4 551.3 733.7 898.7 1049.4 1200.0 315.6 : 182.4 386.3 568.7 733.7 884.4 1035.0 1200.0 498.0 : 203.9 386.3 551.3 702.0 852.6 1017.6 1200.0 702.0 : 182.4 347.4 498.0 648.7 813.7 996.1 1200.0 884.4 : 165.0 315.6 466.3 631.3 813.7 1017.6 1200.0 1049.4: 150.6 301.3 466.3 648.7 852.6 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 203.9100 cents 33/32, 53.2729 cents 12/11, 150.6371 cents 2: 301.2741 .. 386.3137 cents 605/576, 85.0396 cents 128/121, 97.3641 cents 3: 466.2783 .. 568.7174 cents 1375/1296, 102.4391 cents 288/275, 79.9646 cents 4: 631.2826 .. 733.7217 cents 1375/1296, 102.4391 cents 648/625, 62.5651 cents 5: 813.6863 .. 898.7259 cents 605/576, 85.0396 cents 288/275, 79.9646 cents 6: 996.0900 .. 1049.3629 cents 33/32, 53.2729 cents 128/121, 97.3641 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.138024 Largest / Average step : 1.189475 Largest / Smallest step : 1.353651 Median interval of one step : 11/10, 165.0042 cents, amount: 2 Least squares average step : 172.87033 cents, oct.: 1210.09229 cents Scale is strictly proper Step pattern alph. order: ABCDCBA Step pattern size order : ABCDCBA Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.387678 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.598747 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 24 = 4.00000 / 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 : 121/120, 14.3672 cents Number of recognisable fifths : 2, average 701.9550 cents Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 4 at degree 3 Length of longest subharmonic part : 4 at degree 0 Formal octave complements present : 7 = 100.0000% Scale is differentially coherent in interval class 1 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 11 Odd number limit : 121 (O: 121 U: 121) Highest odd numerator or denominator: 11 Scale harmonicity : 0.017392 Average absolute harmonicity : 0.255168 Specific harmonicity : 0.137887 Fundamental : 1/330, -8.3663 octaves, 0.7928 Hz. Guide tone : 660, 9.3663 octaves, 172672.873 Hz. Exponens Consonantiae : 2.178000E+05, 17.73264 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 37.0, average 5.28571 Mersenne's string divisions : 3612840 Sum of van Prooijen's expressibility: 4.43497, average 0.63357 Sum of Tenney's harmonic distance : 8.75169, average 1.25024 Vogel's harmonic complexity : 20.57143 Wille's k value : 302 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 63.64129, average 2.27290 Lattice compactness (without 2's) : 43.64224, average 1.55865 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -1 .. 1 0.00000 6 2 5: -1 .. 1 0.00000 2 2 11: -1 .. 1 0.00000 2 2 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 10 15 23| Scale is weakly epimorphic with val: <7 10 15 25| Scale is weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 10 16 26| Scale is weakly epimorphic with val: <7 10 18 22| Scale is weakly epimorphic with val: <7 10 18 26| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 11 16 26| Scale is weakly epimorphic with val: <7 11 17 23| Scale is weakly epimorphic with val: <7 12 15 25| Scale is weakly epimorphic with val: <7 12 16 25| Scale is weakly epimorphic with val: <7 12 18 22| Scale is weakly epimorphic with val: <7 12 18 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 20.2608 c. M: 27.2159 c. Lebeng 15: 2 2 2 3 2 2 2 SP M ME I SD: 11.1135 c. M:-18.0450 c. Miller's Porcupine-7 22: 3 3 3 4 3 3 3 SP M ME I SD: 10.0739 c. M:-12.9993 c. Minor quasi-equal Heptatonic, Miller's Porcupine-7 24: 3 3 4 4 4 3 3 P I SD: 8.4326 c. M: 15.6413 c. 26: 3 4 4 4 4 4 3 SP D3 I SD: 9.2056 c. M:-12.1755 c. 31: 4 4 5 5 5 4 4 SP I SD: 4.7828 c. M: 5.9639 c. 41: 5 6 6 7 6 6 5 SP I SD: 4.0884 c. M:-6.3099 c. 46: 6 6 7 8 7 6 6 SP I SD: 3.6685 c. M:-5.8847 c. 56: 7 8 8 10 8 8 7 SP I SD: 4.1683 c. M: 5.7873 c. 65: 8 9 10 11 10 9 8 SP I SD: 1.8568 c. M:-2.9448 c. 72: 9 10 11 12 11 10 9 SP I SD: 1.2282 c. M: 1.9550 c. 87: 11 12 13 15 13 12 11 SP I SD: 1.3062 c. M:-1.6001 c. 111: 14 15 17 19 17 15 14 SP I SD: 1.2645 c. M: 2.1278 c. 118: 15 16 18 20 18 16 15 SP I SD: 1.0485 c. M:-1.9053 c. 152: 19 21 23 26 23 21 19 SP I SD: 0.5030 c. M: 0.6766 c. 224: 28 31 34 38 34 31 28 SP I SD: 0.4207 c. M:-0.6371 c. 270: 34 37 41 46 41 37 34 SP I SD: 0.2945 c. M:-0.4741 c. 335: 42 46 51 57 51 46 42 SP I SD: 0.2553 c. M: 0.4174 c. 342: 43 47 52 58 52 47 43 SP I SD: 0.1851 c. M:-0.2401 c. 494: 62 68 75 84 75 68 62 SP I SD: 0.0889 c. M: 0.1482 c. 677: 85 93 103 115 103 93 85 SP I SD: 0.0743 c. M:-0.1317 c. 829: 104 114 126 141 126 114 104 SP I SD: 0.0837 c. M: 0.0957 c. 901: 113 124 137 153 137 124 113 SP I SD: 0.0822 c. M:-0.1376 c. 1019: 128 140 155 173 155 140 128 SP I SD: 0.0744 c. M:-0.0990 c. 1171: 147 161 178 199 178 161 147 SP I SD: 0.0090 c. M: 0.0136 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 26.7871 cents 5 x 6:7 x 8:9:10 S SD: 22.9246 cents 6 x 7:8:9:10:11:12 S SD: 8.1284 cents 7:8 x 9:11:12:13:14 SD: 23.4604 cents 8:9:10:11:12:13:15:16 SD: 16.9666 cents 9:10:11:12:14:15:17:18 SD: 13.2891 cents 10:11:12:13:15:17:18:20 SD: 9.3809 cents 12:13:14:16:18:20:22:24 S SD: 7.1772 cents 18:20:22:24:27:30:33:36 S SD: 6.4178 cents 20:22:24:27:30:33:37:40 SD: 4.9839 cents 24:26:29:32:36:40:44:48 SD: 2.4290 cents 30:33:36:40:45:50:55:60 S SD: 2.0525 cents 54:59:65:72:81:90:99:108 SD: 0.8522 cents 66:72:79:88:99:110:121:132 SD: 0.6253 cents 90:98:108:120:135:150:165:180 SD: 0.4584 cents 120:131:144:160:180:200:220:240 SD: 0.1717 cents 210:229:252:280:315:350:385:420 SD: 0.0982 cents 330:360:396:440:495:550:605:660 S SD: 0.0000 cents