Scala analysis: xen10-chalmers-tritriadic-5-27-9
Tritriadic scale built from 5:27:9
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: 243/200 337.147577 acute minor third 3: 27/20 519.551289 acute fourth 4: 3/2 701.955001 perfect 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: 2187/2000 154.7439 Gorgo limma 3: 10/9 182.4037 minor whole tone 4: 10/9 182.4037 minor whole tone 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 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 : 182.4 337.1 519.6 702.0 835.2 1017.6 1200.0 182.4 : 154.7 337.1 519.6 652.8 835.2 1017.6 1200.0 337.1 : 182.4 364.8 498.0 680.4 862.9 1045.3 1200.0 519.6 : 182.4 315.6 498.0 680.4 862.9 1017.6 1200.0 702.0 : 133.2 315.6 498.0 680.4 835.2 1017.6 1200.0 835.2 : 182.4 364.8 547.2 702.0 884.4 1066.8 1200.0 1017.6: 182.4 364.8 519.6 702.0 884.4 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 : 170.74795 cents, oct.: 1195.23567 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : LMLLSLL 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 0.0 519.551 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: 2 3 Limited inverse transpositions with margin 49.1661 cents: 1 2 6 -- Rational properties -- Prime limit : 5 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 243 Scale harmonicity : 0.023885 Average absolute harmonicity : 0.224665 Specific harmonicity : 0.132872 Fundamental : 1/1800, -10.8138 octaves, 0.1453 Hz. Guide tone : 2430, 11.2467 octaves, 635750.124 Hz. Exponens Consonantiae : 4.374000E+06, 22.06052 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 331.0, average 47.28571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.11106, average 1.15872 Sum of Tenney's harmonic distance : 15.71312, average 2.24473 Vogel's harmonic complexity : 20.28571 Wille's k value : 1093 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 10 Triangular lattice diameter : 7 Lattice compactness : 102.71524, average 3.66840 Lattice compactness (without 2's) : 87.10358, average 3.11084 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.71429 9 1 3: -2 .. 5 1.85714 17 1 5: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 8 / 7 = 1.14286 Average absolute exponent except 2's: 24 / 7 = 3.42857 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: 12.2288 c. M:-21.9503 c. Lebeng 19: 3 2 3 3 2 3 3 SP M ME S SD: 12.0257 c. M: 21.3581 c. Nineteen-tone Natural Minor, Aeolian 24: 4 3 3 4 3 3 4 SP D3 I SD: 14.0904 c. M: 19.5513 c. Miha'il Musaqa's mode: Egypt, Neutral Diatonic Hypodorian, Dastgah-e Sehgah, Maqam Nairuz 25: 4 3 4 4 2 4 4 SP T3 SD: 11.6549 c. M: 19.1926 c. 26: 4 3 4 4 3 4 4 SP M ME S SD: 8.1156 c. M: 14.0707 c. Twenty-six tone Natural Minor 32: 5 4 5 5 3 5 5 SP T3 SD: 6.5120 c. M:-10.5450 c. 33: 5 4 5 5 4 5 5 SP M ME S SD: 6.8765 c. M: 11.0459 c. 39: 6 5 6 6 4 6 6 SP T3 SD: 3.3042 c. M:-5.7373 c. 46: 7 6 7 7 5 7 7 SP T3 SD: 1.4489 c. M:-2.3928 c. 99: 15 13 15 15 11 15 15 SP T3 SD: 1.2546 c. M:-2.2464 c. 118: 18 15 18 18 13 18 18 SP T3 SD: 0.9118 c. M: 1.5544 c. 125: 19 16 19 19 14 19 19 SP T3 SD: 0.7537 c. M: 1.1550 c. 164: 25 21 25 25 18 25 25 SP T3 SD: 0.5598 c. M: 1.0462 c. 171: 26 22 26 26 19 26 26 SP T3 SD: 0.1749 c. M: 0.3055 c. 388: 59 50 59 59 43 59 59 SP T3 SD: 0.0790 c. M: 0.1410 c. 559: 85 72 85 85 62 85 85 SP T3 SD: 0.0774 c. M: 0.1300 c. 612: 93 79 93 93 68 93 93 SP T3 SD: 0.0657 c. M:-0.1073 c. 783: 119 101 119 119 87 119 119 SP T3 SD: 0.0310 c. M:-0.0565 c. 1000: 152 129 152 152 111 152 152 SP T3 SD: 0.0321 c. M:-0.0524 c. 1171: 178 151 178 178 130 178 178 SP T3 SD: 0.0057 c. M:-0.0091 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: 17.8880 cents 4 x 5 x 6 x 7:8 S SD: 17.3130 cents 5 x 6:7 x 8:9:10 S SD: 13.9844 cents 6 x 7:8:9:10:11:12 S SD: 15.6594 cents 7:8 x 9 x 11:13:14 SD: 24.6723 cents 8:9:10:11:12:13:14:16 S SD: 11.3353 cents 10:11:12:14:15:16:18:20 S SD: 10.2935 cents 14:16:17:19:21:23:25:28 SD: 8.1337 cents 16:18:19:22:24:26:29:32 SD: 8.0996 cents 18:20:22:24:27:29:32:36 SD: 4.7832 cents 24:27:29:32:36:39:43:48 SD: 4.7569 cents 26:29:32:35:39:42:47:52 SD: 3.6305 cents 28:31:34:38:42:45:50:56 SD: 3.2054 cents 34:38:41:46:51:55:61:68 SD: 2.5786 cents 42:47:51:57:63:68:76:84 SD: 2.5588 cents 46:51:56:62:69:75:83:92 SD: 1.8875 cents 52:58:63:70:78:84:94:104 SD: 1.8728 cents 56:62:68:76:84:91:101:112 SD: 1.8245 cents 60:67:73:81:90:97:108:120 SD: 1.3770 cents 74:82:90:100:111:120:133:148 SD: 0.8774 cents 106:118:129:143:159:172:191:212 SD: 0.7994 cents 108:120:131:146:162:175:194:216 SD: 0.7415 cents 116:129:141:157:174:188:209:232 SD: 0.7223 cents 126:140:153:170:189:204:227:252 SD: 0.3331 cents 200:222:243:270:300:324:360:400 SD: 0.2474 cents 260:289:316:351:390:421:468:520 SD: 0.1702 cents 386:429:469:521:579:625:695:772 SD: 0.1658 cents 414:460:503:559:621:671:745:828 SD: 0.1425 cents 460:511:559:621:690:745:828:920 SD: 0.0962 cents 540:600:656:729:810:875:972:1080 SD: 0.0680 cents