Scala analysis: porchrome6
Sixth 25/24&250/243 scale = transposed liu_minor inverse porchrome7
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: 25/18 568.717426 classic augmented fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP 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: 125/108 253.0761 semi-augmented whole tone 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 10/9 182.4037 minor whole tone 6: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 3 10/9 182.404 cents minor whole tone 1: 1 125/108 253.076 cents semi-augmented whole tone 2: 4 6/5 315.641 cents minor third 2: 1 100/81 364.807 cents grave major third 2: 2 5/4 386.314 cents major third 3: 1 162/125 448.879 cents 3: 3 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 2 25/18 568.717 cents classic augmented fourth 4: 2 36/25 631.283 cents classic diminished fifth 4: 1 40/27 680.449 cents grave fifth 4: 3 3/2 701.955 cents perfect fifth 4: 1 125/81 751.121 cents 5: 2 8/5 813.686 cents minor sixth 5: 1 81/50 835.193 cents acute minor sixth 5: 4 5/3 884.359 cents major sixth, BP sixth 6: 1 216/125 946.924 cents semi-augmented sixth 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 3 50/27 1066.762 cents grave major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 315.6 568.7 702.0 884.4 1017.6 1200.0 182.4 : 133.2 386.3 519.6 702.0 835.2 1017.6 1200.0 315.6 : 253.1 386.3 568.7 702.0 884.4 1066.8 1200.0 568.7 : 133.2 315.6 448.9 631.3 813.7 946.9 1200.0 702.0 : 182.4 315.6 498.0 680.4 813.7 1066.8 1200.0 884.4 : 133.2 315.6 498.0 631.3 884.4 1017.6 1200.0 1017.6: 182.4 364.8 498.0 751.1 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 253.0761 cents 3125/2916, 119.8386 cents 27/25, 133.2376 cents 2: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 648/625, 62.5651 cents 3: 448.8789 .. 568.7174 cents 3125/2916, 119.8386 cents 648/625, 62.5651 cents 4: 631.2826 .. 751.1211 cents 3125/2916, 119.8386 cents 648/625, 62.5651 cents 5: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 648/625, 62.5651 cents 6: 946.9239 .. 1066.7624 cents 3125/2916, 119.8386 cents 648/625, 62.5651 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 : 125/108, 253.0761 cents Average / Smallest step : 1.286638 Largest / Average step : 1.476277 Largest / Smallest step : 1.899435 Median interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 173.25021 cents, oct.: 1212.75149 cents Scale is strictly proper Step pattern alph. order: ABCBABA Step pattern size order : MSLSMSM Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.446675 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.482751 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 3.266667 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 4 Most common triad is 0.0 315.641 884.359 cents, amount: 2 Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle 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 : 5 = 71.4286% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 125 (O: 125 U: 125) Highest odd numerator or denominator: 25 Scale harmonicity : 0.031381 Average absolute harmonicity : 0.242626 Specific harmonicity : 0.170545 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 450, 8.8138 octaves, 117731.504 Hz. Exponens Consonantiae : 4.050000E+04, 15.30563 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 51.5, average 7.35714 Mersenne's string divisions : 7549080 Sum of van Prooijen's expressibility: 5.18149, average 0.74021 Sum of Tenney's harmonic distance : 9.99306, average 1.42758 Vogel's harmonic complexity : 13.14286 Wille's k value : 67 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 71.92250, average 2.56866 Lattice compactness (without 2's) : 61.84461, average 2.20874 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.14286 5 1 3: -2 .. 2 -0.14286 9 1 5: -1 .. 2 0.28571 6 5 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 15 / 7 = 2.14286 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: 26.5892 c. M: 54.4317 c. Lebeng 8: 1 1 2 1 1 1 1 P M ME S SD: 28.9734 c. M:-48.0450 c. 11: 2 1 2 1 2 1 2 P M ME I SD: 28.3336 c. M: 47.4095 c. Superkleismic-7 12: 2 1 3 1 2 1 2 P D3 SD: 17.2833 c. M:-31.2826 c. Mela Hemavati, Raga Desisimharavam, Maqam Nakriz, Tunisian, Dorian sharp 4, Misheberekh: Jewish, Nigriz, Pimenikos, Souzinak (Peiraiotikos Minor): Greece, Ukrainian Dorian, Ukrainian Minor, Kaffa, Gnossiennes 15: 2 2 3 2 2 2 2 SP M ME S SD: 14.3600 c. M: 22.4037 c. 19: 3 2 4 2 3 2 3 SP D3 SD: 4.6630 c. M: 7.2182 c. 34: 5 4 7 4 5 4 5 SP SD: 3.9635 c. M: 5.9331 c. 46: 7 5 10 5 7 5 7 SP SD: 2.5719 c. M:-5.1956 c. 53: 8 6 11 6 8 6 8 SP SD: 1.4147 c. M: 2.6797 c. 72: 11 8 15 8 11 8 11 SP SD: 1.3016 c. M: 2.0508 c. 99: 15 11 21 11 15 11 15 SP SD: 0.6847 c. M:-1.0753 c. 118: 18 13 25 13 18 13 18 SP SD: 0.5077 c. M:-0.7741 c. 171: 26 19 36 19 26 19 26 SP SD: 0.1592 c. M: 0.2964 c. 270: 41 30 57 30 41 30 41 SP SD: 0.1610 c. M:-0.2672 c. 441: 67 49 93 49 67 49 67 SP SD: 0.0586 c. M: 0.0908 c. 612: 93 68 129 68 93 68 93 SP SD: 0.0498 c. M: 0.0900 c. 730: 111 81 154 81 111 81 111 SP SD: 0.0427 c. M: 0.0620 c. 901: 137 100 190 100 137 100 137 SP SD: 0.0419 c. M: 0.0682 c. 1000: 152 111 211 111 152 111 152 SP SD: 0.0419 c. M:-0.0826 c. 1171: 178 130 247 130 178 130 178 SP SD: 0.0133 c. M:-0.0272 c. 1342: 204 149 283 149 204 149 204 SP SD: 0.0109 c. M: 0.0176 c. 1783: 271 198 376 198 271 198 271 SP SD: 0.0103 c. M: 0.0145 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: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 21.4668 cents 5 x 6:7 x 8:9:10 S SD: 14.4012 cents 6 x 7:8:9:10:11:12 S SD: 15.2591 cents 7:8 x 10:11:12:13:14 S SD: 21.4407 cents 8:9:10:11:12:13:14:16 S SD: 14.3282 cents 9:10:11 x 14:15:16:18 SD: 12.2879 cents 10:11:12:14:15:17:18:20 SD: 5.8351 cents 18:20:22:25:27:30:32:36 SD: 5.4803 cents 20:22:24:28:30:33:36:40 S SD: 4.0299 cents 26:29:31:36:39:43:47:52 SD: 2.9617 cents 34:38:41:47:51:57:61:68 SD: 2.7726 cents 36:40:43:50:54:60:65:72 SD: 1.3777 cents 54:60:65:75:81:90:97:108 SD: 0.9167 cents 80:89:96:111:120:133:144:160 SD: 0.7348 cents 90:100:108:125:135:150:162:180 SD: 0.0000 cents