Scala analysis: xen09-chalmers-tritriadic-1-5-7
Tritriadic scale built from 1:5:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 35/32 155.139620 septimal neutral second 2: 8/7 231.174094 septimal whole tone 3: 5/4 386.313714 major third 4: 10/7 617.487807 Euler's tritone 5: 49/32 737.651813 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 35/32 155.1396 septimal neutral second 2: 256/245 76.0345 septimal minor semitone 3: 35/32 155.1396 septimal neutral second 4: 8/7 231.1741 septimal whole tone 5: 343/320 120.1640 6: 8/7 231.1741 septimal whole tone 7: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/245 76.034 cents septimal minor semitone 1: 1 343/320 120.164 cents 1: 2 35/32 155.140 cents septimal neutral second 1: 3 8/7 231.174 cents septimal whole tone 2: 2 8/7 231.174 cents septimal whole tone 2: 2 49/40 351.338 cents larger approximation to neutral third 2: 2 5/4 386.314 cents major third 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 3: 1 5/4 386.314 cents major third 3: 2 64/49 462.348 cents 2 septatones or septatonic major third 3: 1 343/256 506.478 cents 3: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 10/7 617.488 cents Euler's tritone 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 10/7 617.488 cents Euler's tritone 4: 1 512/343 693.522 cents 3 septatones or septatonic fifth 4: 2 49/32 737.652 cents 4: 1 8/5 813.686 cents minor sixth 5: 1 49/32 737.652 cents 5: 2 8/5 813.686 cents minor sixth 5: 2 80/49 848.662 cents smaller approximation to neutral sixth 5: 2 7/4 968.826 cents harmonic seventh 6: 3 7/4 968.826 cents harmonic seventh 6: 2 64/35 1044.860 cents septimal neutral seventh 6: 1 640/343 1079.836 cents 6: 1 245/128 1123.966 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 155.1 231.2 386.3 617.5 737.7 968.8 1200.0 155.1 : 76.0 231.2 462.3 582.5 813.7 1044.9 1200.0 231.2 : 155.1 386.3 506.5 737.7 968.8 1124.0 1200.0 386.3 : 231.2 351.3 582.5 813.7 968.8 1044.9 1200.0 617.5 : 120.2 351.3 582.5 737.7 813.7 968.8 1200.0 737.7 : 231.2 462.3 617.5 693.5 848.7 1079.8 1200.0 968.8 : 231.2 386.3 462.3 617.5 848.7 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.0345 .. 231.1741 cents 35/32, 155.1396 cents 256/245, 76.0345 cents 2: 231.1741 .. 462.3482 cents 8/7, 231.1741 cents 1/1, 0.0000 cents 3: 386.3137 .. 617.4878 cents 8/7, 231.1741 cents 245/256,-76.0345 cents 4: 582.5122 .. 813.6863 cents 8/7, 231.1741 cents 49/50,-34.9756 cents 5: 737.6518 .. 968.8259 cents 8/7, 231.1741 cents 245/256,-76.0345 cents 6: 968.8259 .. 1123.9655 cents 35/32, 155.1396 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 256/245, 76.0345 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.254616 Largest / Average step : 1.348516 Largest / Smallest step : 3.040385 Median interval of one step : 35/32, 155.1396 cents, amount: 2 Most common interval of one step : 8/7, 231.1741 cents, amount: 3 Least squares average step : 158.19710 cents, oct.: 1107.37973 cents Scale is not proper Step pattern alph. order: ABACDCC Step pattern size order : CACDBDD Scale is not a Constant Structure Scale diversity : 1.430370 Lumma stability : 0.126724 Lumma impropriety factor : 0.155870 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 : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 50/49, 34.9756 cents Most common intervals : 8/7, 231.1741 cents & inv., amount: 5 Most common triad is 0.0 231.174 968.826 cents, amount: 3 Number of recognisable fifths : 1, average 693.5223 cents Scale contains a complete diamond : 1 7 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 2 and 3 combined -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.022096 Average absolute harmonicity : 0.202496 Specific harmonicity : 0.117925 Fundamental : 1/224, -7.8074 octaves, 1.1680 Hz. Guide tone : 1960, 10.9366 octaves, 512786.108 Hz. Exponens Consonantiae : 4.390400E+05, 18.74399 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 101.5, average 14.50000 Mersenne's string divisions : 5074245 Sum of van Prooijen's expressibility: 6.46853, average 0.92408 Sum of Tenney's harmonic distance : 12.88707, average 1.84101 Vogel's harmonic complexity : 14.85714 Wille's k value : 171 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 109.14734, average 3.89812 Lattice compactness (without 2's) : 41.76998, average 1.49178 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -1.28571 19 1 5: 0 .. 1 0.42857 3 1 7: -1 .. 2 0.28571 6 5 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is weakly epimorphic with val: <7 16 18| Scale is weakly epimorphic with val: <7 17 20| Scale is weakly epimorphic with val: <7 18 22|
FIT/MODE
7: 1 0 1 2 0 2 1 N T3 SD: 48.7636 c. M:-68.2265 c. 8: 1 1 1 1 1 2 1 P M ME S SD: 47.6099 c. M:-81.1741 c. 9: 1 1 1 2 1 1 2 P M ME S SD: 36.8164 c. M:-62.3482 c. 10: 1 1 1 2 1 2 2 N D3 SD: 19.6411 c. M: 35.1396 c. 15: 2 1 2 3 1 3 3 N SD: 13.0116 c. M:-22.5122 c. 16: 2 1 2 3 2 3 3 N SD: 9.9208 c. M: 17.4878 c. 21: 3 1 3 4 2 4 4 N SD: 9.3819 c. M:-16.2890 c. 31: 4 2 4 6 3 6 6 N SD: 1.2671 c. M: 2.1679 c. 78: 10 5 10 15 8 15 15 N SD: 1.1931 c. M: 2.1032 c. 109: 14 7 14 21 11 21 21 N SD: 0.6501 c. M: 1.0112 c. 140: 18 9 18 27 14 27 27 N SD: 0.4775 c. M: 0.8539 c. 171: 22 11 22 33 17 33 33 N SD: 0.4893 c. M: 0.8097 c. 208: 27 13 27 40 21 40 40 N SD: 0.4571 c. M:-0.8097 c. 239: 31 15 31 46 24 46 46 N SD: 0.2985 c. M:-0.5089 c. 270: 35 17 35 52 27 52 52 N SD: 0.2407 c. M:-0.4159 c. 348: 45 22 45 67 35 67 67 N SD: 0.1648 c. M:-0.2792 c. 379: 49 24 49 73 38 73 73 N SD: 0.0478 c. M:-0.0791 c. 789: 102 50 102 152 79 152 152 N SD: 0.0051 c. M: 0.0092 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 17.8484 cents 3 x x 4 x x 5:6 S SD: 46.6888 cents 4 x x 5 x 6:7:8 S SD: 8.9242 cents 5 x x 6:7:8:9:10 S SD: 23.9814 cents 6 x 7:8 x 9:11:12 SD: 29.3385 cents 7 x 8:9:10:11:12:14 S SD: 12.5427 cents 8 x 9:10:11:12:14:16 S SD: 13.3292 cents 9:10 x 11:13:14:16:18 SD: 10.6844 cents 10:11 x 13:14:15:18:20 SD: 16.3162 cents 11:12:13:14:16:17:19:22 SD: 11.1596 cents 12:13:14:15:17:18:21:24 SD: 7.8674 cents 16 x 18:20:23:25:28:32 SD: 7.6066 cents 17:19 x 21:24:26:30:34 SD: 8.2561 cents 19:21:22:24:27:29:33:38 SD: 5.4489 cents 20:22:23:25:29:31:35:40 SD: 5.1942 cents 21:23:24:26:30:32:37:42 SD: 3.1587 cents 28:31:32:35:40:43:49:56 SD: 3.0949 cents 40:44:46:50:57:61:70:80 SD: 2.4014 cents 44:48:50:55:63:67:77:88 SD: 2.1495 cents 51:56:58:64:73:78:89:102 SD: 2.0384 cents 56:61:64:70:80:86:98:112 SD: 1.2416 cents 77:84:88:96:110:118:135:154 SD: 1.0374 cents 84:92:96:105:120:129:147:168 SD: 0.7946 cents 96:105:110:120:137:147:168:192 SD: 0.6929 cents 119:130:136:149:170:182:208:238 SD: 0.6613 cents 128:140:146:160:183:196:224:256 SD: 0.5207 cents 140:153:160:175:200:214:245:280 SD: 0.4778 cents 168:184:192:210:240:257:294:336 SD: 0.4134 cents 203:222:232:254:290:311:355:406 SD: 0.3260 cents 224:245:256:280:320:343:392:448 SD: 0.0000 cents