Scala analysis: synpor3
Third 81/80&250/243 scale = inverse synpor2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 40/27 680.448711 grave fifth 5: 81/50 835.192576 acute minor sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 10/9 182.4037 minor whole tone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 10/9 182.4037 minor whole tone 4: 10/9 182.4037 minor whole tone 5: 2187/2000 154.7439 Gorgo limma 6: 10/9 182.4037 minor whole tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 2187/2000 154.744 cents Gorgo limma 1: 5 10/9 182.404 cents minor whole tone 2: 2 6/5 315.641 cents minor third 2: 2 243/200 337.148 cents acute minor third 2: 3 100/81 364.807 cents grave major third 3: 3 4/3 498.045 cents perfect fourth 3: 3 27/20 519.551 cents acute fourth 3: 1 1000/729 547.211 cents 4: 1 729/500 652.789 cents 4: 3 40/27 680.449 cents grave fifth 4: 3 3/2 701.955 cents perfect fifth 5: 3 81/50 835.193 cents acute minor sixth 5: 2 400/243 862.852 cents grave major sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 6: 5 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 4000/2187 1045.256 cents 6: 1 50/27 1066.762 cents grave 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 : 182.4 315.6 498.0 680.4 835.2 1017.6 1200.0 182.4 : 133.2 315.6 498.0 652.8 835.2 1017.6 1200.0 315.6 : 182.4 364.8 519.6 702.0 884.4 1066.8 1200.0 498.0 : 182.4 337.1 519.6 702.0 884.4 1017.6 1200.0 680.4 : 154.7 337.1 519.6 702.0 835.2 1017.6 1200.0 835.2 : 182.4 364.8 547.2 680.4 862.9 1045.3 1200.0 1017.6: 182.4 364.8 498.0 680.4 862.9 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 182.4037 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 2: 315.6413 .. 364.8074 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 3: 498.0450 .. 547.2111 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 4: 652.7889 .. 701.9550 cents 250/243, 49.1661 cents 531441/500000, 105.5777 cents 5: 835.1926 .. 884.3587 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 6: 1017.5963 .. 1066.7624 cents 250/243, 49.1661 cents 27/25, 133.2376 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.286638 Largest / Average step : 1.064022 Largest / Smallest step : 1.369011 Median interval of one step : 10/9, 182.4037 cents, amount: 5 Most common interval of one step : 10/9, 182.4037 cents, amount: 5 Least squares average step : 169.36541 cents, oct.: 1185.55784 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : LSLLMLL Scale is a Constant Structure, by a margin of 105.57773 cents Scale diversity : 1.255905 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.754169 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 : 81/80, 21.5063 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 498.045 1017.596 cents Most common triad is 0.0 182.404 1017.596 cents, amount: 3 Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 5 9 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 n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited transpositions with margin 49.1661 cents: 4 Limited inverse transpositions with margin 49.1661 cents: 3 5 6 -- Rational properties -- Prime limit : 5 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 81 Scale harmonicity : 0.023885 Average absolute harmonicity : 0.225104 Specific harmonicity : 0.139555 Fundamental : 1/1350, -10.3987 octaves, 0.1938 Hz. Guide tone : 3240, 11.6618 octaves, 847666.832 Hz. Exponens Consonantiae : 4.374000E+06, 22.06052 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 126.0, average 18.00000 Mersenne's string divisions : 77044506 Sum of van Prooijen's expressibility: 6.42443, average 0.91778 Sum of Tenney's harmonic distance : 13.10567, average 1.87224 Vogel's harmonic complexity : 20.00000 Wille's k value : 1093 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 10 Triangular lattice diameter : 7 Lattice compactness : 95.98215, average 3.42793 Lattice compactness (without 2's) : 83.13263, average 2.96902 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.00000 9 1 3: -3 .. 4 0.14286 13 1 5: -2 .. 1 -0.28571 6 5 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 15.8336 c. M:-27.2159 c. Lebeng 19: 3 2 3 3 2 3 3 SP M ME S SD: 8.9137 c. M:-14.2881 c. Nineteen-tone Natural Minor, Aeolian 26: 4 3 4 4 3 4 4 SP M ME S SD: 6.7437 c. M:-11.8590 c. Twenty-six tone Natural Minor 33: 5 4 5 5 4 5 5 SP M ME S SD: 7.2583 c. M:-11.6314 c. 34: 5 4 5 5 5 5 5 SP M ME S SD: 6.8441 c. M:-11.8662 c. 39: 6 4 6 6 5 6 6 SP T3 SD: 4.4382 c. M: 7.9490 c. 46: 7 5 7 7 6 7 7 SP T3 SD: 1.5817 c. M: 2.5978 c. 53: 8 6 8 8 7 8 8 SP T3 SD: 1.3602 c. M:-2.5433 c. 99: 15 11 15 15 13 15 15 SP T3 SD: 0.9420 c. M: 1.6608 c. 118: 18 13 18 18 15 18 18 SP T3 SD: 0.7125 c. M: 1.2943 c. 125: 19 14 19 19 16 19 19 SP T3 SD: 0.7561 c. M:-1.1587 c. 164: 25 18 25 25 21 25 25 SP T3 SD: 0.6428 c. M: 1.0462 c. 171: 26 19 26 26 22 26 26 SP T3 SD: 0.1428 c. M:-0.2530 c. 388: 59 43 59 59 50 59 59 SP T3 SD: 0.1028 c. M: 0.1774 c. 559: 85 62 85 85 72 85 85 SP T3 SD: 0.0700 c. M: 0.1300 c. 612: 93 68 93 93 79 93 93 SP T3 SD: 0.0544 c. M:-0.1015 c. 783: 119 87 119 119 101 119 119 SP T3 SD: 0.0397 c. M:-0.0675 c. 1000: 152 111 152 152 129 152 152 SP T3 SD: 0.0297 c. M: 0.0487 c. 1171: 178 130 178 178 151 178 178 SP T3 SD: 0.0077 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: 10.7531 cents 3 x x 4 x 5 x 6 S SD: 16.3887 cents 4 x 5 x 6 x 7:8 S SD: 22.1298 cents 5 x 6:7 x 8:9:10 S SD: 17.4324 cents 6 x 7:8:9:10:11:12 S SD: 13.1946 cents 7:8 x 9:10:11:13:14 SD: 21.0894 cents 8:9:10:11:12:13:14:16 S SD: 15.0947 cents 9:10:11:12:13:15:16:18 SD: 10.8892 cents 10:11:12:13:15:16:18:20 SD: 8.0165 cents 15:17:18:20:22:24:27:30 SD: 6.2932 cents 19:21:23:25:28:31:34:38 SD: 4.9000 cents 21:23:25:28:31:34:38:42 SD: 4.3652 cents 27:30:32:36:40:44:49:54 SD: 3.9620 cents 29:32:35:39:43:47:52:58 SD: 3.2253 cents 35:39:42:47:52:57:63:70 SD: 2.4078 cents 44:49:53:59:65:71:79:88 SD: 2.2331 cents 45:50:54:60:67:73:81:90 SD: 1.2793 cents 71:79:85:95:105:115:128:142 SD: 1.2474 cents 79:88:95:105:117:128:142:158 SD: 1.1857 cents 81:90:97:108:120:131:146:162 SD: 0.7394 cents 90:100:108:120:133:146:162:180 SD: 0.7058 cents 126:140:151:168:187:204:227:252 SD: 0.6087 cents 135:150:162:180:200:219:243:270 SD: 0.3390 cents 189:210:227:252:280:306:340:378 SD: 0.2997 cents 216:240:259:288:320:350:389:432 SD: 0.2363 cents 270:300:324:360:400:437:486:540 SD: 0.2263 cents 324:360:389:432:480:525:583:648 SD: 0.1630 cents 405:450:486:540:600:656:729:810 SD: 0.0377 cents