Scala analysis: xen09-chalmers-tritriadic-10-13-18
Tritriadic scale built from 10:13:18
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: 117/100 271.810236 3: 13/10 454.213948 tridecimal semi-diminished fourth 4: 13/9 636.617660 tridecimal diminished 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: 1053/1000 89.4065 3: 10/9 182.4037 minor whole tone 4: 10/9 182.4037 minor whole tone 5: 729/650 198.5749 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 1053/1000 89.407 cents 1: 5 10/9 182.404 cents minor whole tone 1: 1 729/650 198.575 cents 2: 2 117/100 271.810 cents 2: 3 100/81 364.807 cents grave major third 2: 2 81/65 380.979 cents 3: 3 13/10 454.214 cents tridecimal semi-diminished fourth 3: 1 1000/729 547.211 cents 3: 3 18/13 563.382 cents tridecimal augmented fourth 4: 3 13/9 636.618 cents tridecimal diminished fifth 4: 1 729/500 652.789 cents 4: 3 20/13 745.786 cents tridecimal semi-augmented fifth 5: 2 130/81 819.021 cents 5: 3 81/50 835.193 cents acute minor sixth 5: 2 200/117 928.190 cents 6: 1 1300/729 1001.425 cents 6: 5 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 2000/1053 1110.593 cents 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 : 182.4 271.8 454.2 636.6 835.2 1017.6 1200.0 182.4 : 89.4 271.8 454.2 652.8 835.2 1017.6 1200.0 271.8 : 182.4 364.8 563.4 745.8 928.2 1110.6 1200.0 454.2 : 182.4 381.0 563.4 745.8 928.2 1017.6 1200.0 636.6 : 198.6 381.0 563.4 745.8 835.2 1017.6 1200.0 835.2 : 182.4 364.8 547.2 636.6 819.0 1001.4 1200.0 1017.6: 182.4 364.8 454.2 636.6 819.0 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.4065 .. 198.5749 cents 180/169, 109.1684 cents 1053/1000, 89.4065 cents 2: 271.8102 .. 380.9786 cents 180/169, 109.1684 cents 169/162, 73.2353 cents 3: 454.2139 .. 563.3823 cents 180/169, 109.1684 cents 169/162, 73.2353 cents 4: 636.6177 .. 745.7861 cents 180/169, 109.1684 cents 169/162, 73.2353 cents 5: 819.0214 .. 928.1898 cents 180/169, 109.1684 cents 169/162, 73.2353 cents 6: 1001.4251 .. 1110.5935 cents 180/169, 109.1684 cents 169/162, 73.2353 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1053/1000, 89.4065 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 729/650, 198.5749 cents Average / Smallest step : 1.917406 Largest / Average step : 1.158354 Largest / Smallest step : 2.221034 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 : 166.54769 cents, oct.: 1165.83386 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : MSMMLMM Scale is a Constant Structure, by a margin of 73.23532 cents Scale diversity : 1.390251 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.454158 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 : 6561/6500, 16.1712 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 454.214 1017.596 cents Most common triad is 0.0 182.404 1017.596 cents, amount: 3 Number of recognisable fifths : 0 Best fifths 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% Limited inverse transpositions with margin 109.1684 cents: 3 -- Rational properties -- Prime limit : 13 Odd number limit : 1053 (O: 1053 U: 1053) Highest odd numerator or denominator: 117 Scale harmonicity : 0.016569 Average absolute harmonicity : 0.185499 Specific harmonicity : 0.082940 Fundamental : 1/900, -9.8138 octaves, 0.2907 Hz. Guide tone : 10530, 13.3622 octaves, 2754917.203 Hz. Exponens Consonantiae : 9.477000E+06, 23.17600 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 214.5, average 30.64286 Mersenne's string divisions : 819891534 Sum of van Prooijen's expressibility: 8.11304, average 1.15901 Sum of Tenney's harmonic distance : 15.76626, average 2.25232 Vogel's harmonic complexity : 21.42857 Wille's k value : 526 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 93.96616, average 3.35593 Lattice compactness (without 2's) : 83.83777, average 2.99421 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.28571 6 1 3: -2 .. 4 0.57143 12 5: -2 .. 1 -0.71429 7 3 13: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 Scale is weakly epimorphic with val: <7 10 15 28| Scale is weakly epimorphic with val: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 17 29| Scale is weakly epimorphic with val: <7 10 18 26| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 12 16 27| Scale is JI-epimorphic with val: <7 12 18 28|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 41.0391 c. M:-71.0469 c. Lebeng 8: 1 1 1 1 2 1 1 P M ME S SD: 34.7507 c. M:-64.8074 c. 10: 1 1 2 1 2 1 2 P M ME S SD: 38.2703 c. M: 62.4037 c. 11: 2 1 1 2 2 1 2 P D3 S SD: 33.1342 c. M:-55.4625 c. 13: 2 1 2 2 2 2 2 SP M ME S SD: 5.3463 c. M:-9.5362 c. Tamashian 40: 6 3 6 6 7 6 6 SP T3 SD: 3.7701 c. M: 6.6177 c. 53: 8 4 8 8 9 8 8 SP T3 SD: 1.6336 c. M: 2.6554 c. 66: 10 5 10 10 11 10 10 SP T3 SD: 0.6625 c. M:-1.1711 c. 145: 22 11 22 22 24 22 22 SP T3 SD: 0.7223 c. M:-1.2932 c. 164: 25 12 25 25 27 25 25 SP T3 SD: 0.6670 c. M: 1.0785 c. 211: 32 16 32 32 35 32 32 SP T3 SD: 0.6665 c. M:-1.1755 c. 217: 33 16 33 33 36 33 33 SP T3 SD: 0.5043 c. M: 0.8425 c. 230: 35 17 35 35 38 35 35 SP T3 SD: 0.2947 c. M: 0.5059 c. 296: 45 22 45 45 49 45 45 SP T3 SD: 0.1091 c. M: 0.1886 c. 362: 55 27 55 55 60 55 55 SP T3 SD: 0.1002 c. M:-0.1665 c. 605: 92 45 92 92 100 92 92 SP T3 SD: 0.0809 c. M: 0.1513 c. 658: 100 49 100 100 109 100 100 SP T3 SD: 0.0805 c. M: 0.1435 c. 671: 102 50 102 102 111 102 102 SP T3 SD: 0.0247 c. M:-0.0440 c. 967: 147 72 147 147 160 147 147 SP T3 SD: 0.0241 c. M: 0.0419 c. 1033: 157 77 157 157 171 157 157 SP T3 SD: 0.0239 c. M:-0.0446 c. 1638: 249 122 249 249 271 249 249 SP T3 SD: 0.0149 c. M: 0.0277 c. 1704: 259 127 259 259 282 259 259 SP T3 SD: 0.0125 c. M:-0.0208 c. 2000: 304 149 304 304 331 304 304 SP T3 SD: 0.0100 c. M: 0.0177 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: 32.6687 cents 3 x x 4 x 5 x 6 S SD: 21.9557 cents 4 x x 5:6 x 7:8 S SD: 26.5259 cents 5 x 6 x 7:8:9:10 S SD: 14.5754 cents 6 x 7:8:9:10:11:12 S SD: 16.3647 cents 7 x 8:9:10:11:13:14 SD: 14.9888 cents 8:9 x 10:12:13:14:16 S SD: 18.0654 cents 9:10:11:12:13:15:16:18 SD: 14.6497 cents 10:11:12:13:14:16:18:20 S SD: 10.7036 cents 11:12:13:14:16:18:20:22 S SD: 8.3424 cents 14 x 16:18:20:23:25:28 SD: 9.3717 cents 16:18:19:21:23:26:29:32 SD: 5.7839 cents 18:20:21:23:26:29:32:36 SD: 5.4747 cents 24:27:28:31:35:39:43:48 SD: 4.4683 cents 27:30:32:35:39:44:49:54 SD: 4.1143 cents 29:32:34:38:42:47:52:58 SD: 2.8937 cents 34:38:40:44:49:55:61:68 SD: 2.5142 cents 36:40:42:47:52:58:65:72 SD: 2.0107 cents 47:52:55:61:68:76:85:94 SD: 1.7350 cents 63:70:74:82:91:102:113:126 SD: 1.3487 cents 70:78:82:91:101:113:126:140 SD: 1.1944 cents 81:90:95:105:117:131:146:162 SD: 1.0698 cents 90:100:105:117:130:146:162:180 SD: 0.7828 cents 106:118:124:138:153:172:191:212 SD: 0.7806 cents 124:138:145:161:179:201:223:248 SD: 0.6052 cents 153:170:179:199:221:248:275:306 SD: 0.4054 cents 171:190:200:222:247:277:308:342 SD: 0.3810 cents 200:222:234:260:289:324:360:400 SD: 0.2651 cents 270:300:316:351:390:437:486:540 SD: 0.2394 cents 306:340:358:398:442:496:551:612 SD: 0.2079 cents 324:360:379:421:468:525:583:648 SD: 0.1641 cents 360:400:421:468:520:583:648:720 SD: 0.1449 cents 513:570:600:667:741:831:923:1026 SD: 0.1438 cents 524:582:613:681:757:849:943:1048 SD: 0.1433 cents 540:600:632:702:780:875:972:1080 SD: 0.0966 cents 576:640:674:749:832:933:1037:1152 SD: 0.0923 cents