Scala analysis: semimaj1
First 16/15&648/625 scale = smithgw_star transposed cluster8f
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 6/5 315.641287 minor third 3: 5/4 386.313714 major third 4: 36/25 631.282574 classic diminished fifth 5: 3/2 701.955001 perfect fifth 6: 5/3 884.358713 major sixth, BP sixth 7: 9/5 1017.596288 just minor seventh, BP seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 144/125 244.9689 classic diminished third 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 144/125 244.9689 classic diminished third 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 10/9 182.4037 minor whole tone 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 2 10/9 182.404 cents minor whole tone 1: 2 144/125 244.969 cents classic diminished third 2: 2 125/108 253.076 cents semi-augmented whole tone 2: 6 6/5 315.641 cents minor third 3: 4 5/4 386.314 cents major third 3: 3 4/3 498.045 cents perfect fourth 3: 1 864/625 560.610 cents 4: 4 25/18 568.717 cents classic augmented fourth 4: 4 36/25 631.283 cents classic diminished fifth 5: 1 625/432 639.390 cents 5: 3 3/2 701.955 cents perfect fifth 5: 4 8/5 813.686 cents minor sixth 6: 6 5/3 884.359 cents major sixth, BP sixth 6: 2 216/125 946.924 cents semi-augmented sixth 7: 2 125/72 955.031 cents classic augmented sixth 7: 2 9/5 1017.596 cents just minor seventh, BP seventh 7: 1 50/27 1066.762 cents grave major seventh 7: 3 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 2.85714 = 20/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 70.7 315.6 386.3 631.3 702.0 884.4 1017.6 1200.0 70.7 : 245.0 315.6 560.6 631.3 813.7 946.9 1129.3 1200.0 315.6 : 70.7 315.6 386.3 568.7 702.0 884.4 955.0 1200.0 386.3 : 245.0 315.6 498.0 631.3 813.7 884.4 1129.3 1200.0 631.3 : 70.7 253.1 386.3 568.7 639.4 884.4 955.0 1200.0 702.0 : 182.4 315.6 498.0 568.7 813.7 884.4 1129.3 1200.0 884.4 : 133.2 315.6 386.3 631.3 702.0 946.9 1017.6 1200.0 1017.6: 182.4 253.1 498.0 568.7 813.7 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 244.9689 cents 3456/3125, 174.2964 cents 25/24, 70.6724 cents 2: 253.0761 .. 315.6413 cents 648/625, 62.5651 cents 15625/15552, 8.1073 cents 3: 386.3137 .. 560.6101 cents 3456/3125, 174.2964 cents 25/24, 70.6724 cents 4: 568.7174 .. 631.2826 cents 648/625, 62.5651 cents 15625/15552, 8.1073 cents 5: 639.3899 .. 813.6863 cents 3456/3125, 174.2964 cents 15625/15552, 8.1073 cents 6: 884.3587 .. 946.9239 cents 648/625, 62.5651 cents 25/24, 70.6724 cents 7: 955.0311 .. 1129.3276 cents 3456/3125, 174.2964 cents 15625/15552, 8.1073 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 144/125, 244.9689 cents Average / Smallest step : 2.122469 Largest / Average step : 1.633126 Largest / Smallest step : 3.466258 Median interval of one step : 157.82064 cents, amount: 0 Most common interval of one step : 25/24, 70.6724 cents, amount: 3 Least squares average step : 146.69180 cents, oct.: 1173.53442 cents Scale is strictly proper Step pattern alph. order: ABABACDC Step pattern size order : ADADACBC Scale is a Constant Structure, by a margin of 8.10728 cents Scale diversity : 1.359277 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.262599 Rothenberg efficiency : 0.546429 redundancy: 0.453571 Efficiency x scale size : 4.371429 Number of different interval sizes : 20 = 2.85714 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 2.85714 = 20/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 15625/15552, 8.1073 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 6 Most common triad is 0.0 315.641 884.359 cents, amount: 4 Number of recognisable fifths : 3, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 3 5 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 37.5000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is 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 classes 5 and 6 combined Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 6-7 -- Rational properties -- Prime limit : 5 Odd number limit : 625 (O: 625 U: 625) Highest odd numerator or denominator: 25 Scale harmonicity : 0.025907 Average absolute harmonicity : 0.223806 Specific harmonicity : 0.153758 Fundamental : 1/600, -9.2288 octaves, 0.4360 Hz. Guide tone : 900, 9.8138 octaves, 235463.009 Hz. Exponens Consonantiae : 5.400000E+05, 19.04260 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 80.0, average 10.00000 Mersenne's string divisions : 11836440 Sum of van Prooijen's expressibility: 6.32415, average 0.79052 Sum of Tenney's harmonic distance : 12.41903, average 1.55238 Vogel's harmonic complexity : 17.25000 Wille's k value : 312 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 105.22247, average 2.92285 Lattice compactness (without 2's) : 74.41026, average 2.06695 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.25000 10 1 3: -1 .. 2 0.50000 8 1 5: -2 .. 2 0.00000 8 6 Average exponent except 2's : 4 / 8 = 0.50000 Average absolute exponent except 2's: 16 / 8 = 2.00000 Scale is JI-epimorphic with val: <8 13 19| = patent Scale is weakly epimorphic with val: <8 13 20|
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 43.5532 c. M:-79.3276 c. 10: 1 2 0 2 1 1 1 2 N D3 SD: 38.2141 c. M: 57.5963 c. 12: 1 2 1 2 1 2 1 2 SP B ME SD: 18.8042 c. M: 31.2826 c. Octatonic, Messiaen mode 2, Dominant Diminished, Diminished Blues, Half-Whole step scale 15: 1 3 1 3 1 2 2 2 P D3 SD: 12.3281 c. M:-22.4037 c. 19: 1 4 1 4 1 3 2 3 P SD: 5.1593 c. M: 7.5145 c. 34: 2 7 2 7 2 5 4 5 P SD: 3.1318 c. M:-5.9331 c. 53: 3 11 3 11 3 8 6 8 P SD: 1.6555 c. M: 2.7479 c. 84: 5 17 5 17 5 13 9 13 SP SD: 1.8282 c. M: 3.3106 c. 99: 6 20 6 20 6 15 11 15 SP SD: 1.0960 c. M:-2.0548 c. 118: 7 24 7 24 7 18 13 18 SP SD: 0.4563 c. M: 0.7741 c. 152: 9 31 9 31 9 23 17 23 SP SD: 0.4601 c. M:-0.8248 c. 171: 10 35 10 35 10 26 19 26 SP SD: 0.2606 c. M: 0.4970 c. 270: 16 55 16 55 16 41 30 41 SP SD: 0.2412 c. M:-0.4387 c. 289: 17 59 17 59 17 44 32 44 SP SD: 0.1575 c. M: 0.2952 c. 441: 26 90 26 90 26 67 49 67 SP SD: 0.0592 c. M:-0.0908 c. 612: 36 125 36 125 36 93 68 93 SP SD: 0.0541 c. M:-0.0900 c. 730: 43 149 43 149 43 111 81 111 SP SD: 0.0340 c. M: 0.0620 c. 1171: 69 239 69 239 69 178 130 178 SP SD: 0.0195 c. M:-0.0364 c. 1342: 79 274 79 274 79 204 149 204 SP SD: 0.0170 c. M: 0.0316 c. 1783: 105 364 105 364 105 271 198 271 SP SD: 0.0083 c. M:-0.0145 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x x 5 x 6 S SD: 37.2438 cents 4 x x 5 x 6 x 7:8 S SD: 12.1926 cents 5 x 6 x 7 x 8:9:10 S SD: 17.1734 cents 6 x 7:8 x 9:10:11:12 S SD: 20.9971 cents 7 x 8:9:10:11:12:13:14 S SD: 20.9449 cents 8 x x 10 x 12:13:14:16 S SD: 13.1144 cents 9:10:11 x 13:14:15:16:18 SD: 19.1386 cents 10:11:12:13:14:15:17:18:20 SD: 16.3281 cents 11:12:13:14:16:17:18:20:22 S SD: 13.8923 cents 12:13:14:15:17:18:20:22:24 SD: 11.7247 cents 13:14 x 16:19:20:22:23:26 SD: 12.9462 cents 14:15:17:18:20:21:23:25:28 SD: 9.8250 cents 15:16:18:19:22:23:25:27:30 SD: 8.5409 cents 16:17:19:20:23:24:27:29:32 SD: 5.7542 cents 20:21:24:25:29:30:33:36:40 SD: 3.1538 cents 40:42:48:50:58:60:67:72:80 SD: 2.5261 cents 44:46:53:55:63:66:73:79:88 SD: 2.0195 cents 48:50:58:60:69:72:80:86:96 SD: 1.8419 cents 64:67:77:80:92:96:107:115:128 SD: 1.4901 cents 70:73:84:88:101:105:117:126:140 SD: 1.4652 cents 72:75:86:90:104:108:120:130:144 SD: 1.3776 cents 75:78:90:94:108:113:125:135:150 SD: 1.1718 cents 80:83:96:100:115:120:133:144:160 SD: 1.0896 cents 95:99:114:119:137:143:158:171:190 SD: 1.0478 cents 96:100:115:120:138:144:160:173:192 SD: 0.5878 cents 100:104:120:125:144:150:167:180:200 SD: 0.5541 cents 120:125:144:150:173:180:200:216:240 SD: 0.2503 cents 216:225:259:270:311:324:360:389:432 SD: 0.2026 cents 264:275:317:330:380:396:440:475:528 SD: 0.1878 cents 336:350:403:420:484:504:560:605:672 SD: 0.1475 cents 384:400:461:480:553:576:640:691:768 SD: 0.1140 cents 480:500:576:600:691:720:800:864:960 SD: 0.0626 cents 600:625:720:750:864:900:1000:1080:1200 SD: 0.0000 cents