Scala analysis: ch9_6
Four tetrads six
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 10/7 617.487807 Euler's tritone 6: 3/2 701.955001 perfect fifth 7: 5/3 884.358713 major sixth, BP sixth 8: 7/4 968.825906 harmonic seventh 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 7/6 266.8709 septimal minor third 2: 15/14 119.4428 major diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 21/20 84.4672 minor semitone 5: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 6: 21/20 84.4672 minor semitone 7: 10/9 182.4037 minor whole tone 8: 21/20 84.4672 minor semitone 9: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 3 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 2 15/14 119.443 cents major diatonic semitone 2: 1 28/25 196.198 cents middle second 2: 1 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 1 4/3 498.045 cents perfect fourth 3: 1 9/8 203.910 cents major whole tone 3: 1 8/7 231.174 cents septimal whole tone 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 1 6/5 315.641 cents minor third 3: 1 49/40 351.338 cents larger approximation to neutral third 3: 2 4/3 498.045 cents perfect fourth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 10/7 617.488 cents Euler's tritone 4: 1 6/5 315.641 cents minor third 4: 1 60/49 350.617 cents smaller approximation to neutral third 4: 2 5/4 386.314 cents major third 4: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 3/2 701.955 cents perfect fifth 4: 1 32/21 729.219 cents wide fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 1 9/7 435.084 cents septimal major third, BP third 5: 1 21/16 470.781 cents narrow fourth 5: 1 4/3 498.045 cents perfect fourth 5: 2 10/7 617.488 cents Euler's tritone 5: 2 8/5 813.686 cents minor sixth 5: 1 49/30 849.383 cents larger approximation to neutral sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 10/7 617.488 cents Euler's tritone 6: 2 3/2 701.955 cents perfect fifth 6: 1 80/49 848.662 cents smaller approximation to neutral sixth 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 42/25 898.153 cents quasi-equal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 7: 1 3/2 701.955 cents perfect fifth 7: 1 8/5 813.686 cents minor sixth 7: 1 5/3 884.359 cents major sixth, BP sixth 7: 2 12/7 933.129 cents septimal major sixth 7: 1 7/4 968.826 cents harmonic seventh 7: 1 25/14 1003.802 cents middle minor seventh 7: 2 28/15 1080.557 cents grave major seventh 8: 1 12/7 933.129 cents septimal major sixth 8: 1 7/4 968.826 cents harmonic seventh 8: 1 9/5 1017.596 cents just minor seventh, BP seventh 8: 1 28/15 1080.557 cents grave major seventh 8: 1 15/8 1088.269 cents classic major seventh 8: 3 40/21 1115.533 cents acute major seventh 8: 1 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 7.25000 = 29/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 266.9 386.3 498.0 582.5 617.5 702.0 884.4 968.8 1200.0 266.9 : 119.4 231.2 315.6 350.6 435.1 617.5 702.0 933.1 1200.0 386.3 : 111.7 196.2 231.2 315.6 498.0 582.5 813.7 1080.6 1200.0 498.0 : 84.5 119.4 203.9 386.3 470.8 702.0 968.8 1088.3 1200.0 582.5 : 35.0 119.4 301.8 386.3 617.5 884.4 1003.8 1115.5 1200.0 617.5 : 84.5 266.9 351.3 582.5 849.4 968.8 1080.6 1165.0 1200.0 702.0 : 182.4 266.9 498.0 764.9 884.4 996.1 1080.6 1115.5 1200.0 884.4 : 84.5 315.6 582.5 702.0 813.7 898.2 933.1 1017.6 1200.0 968.8 : 231.2 498.0 617.5 729.2 813.7 848.7 933.1 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 266.8709 cents 343/300, 231.8953 cents 50/49, 34.9756 cents 2: 119.4428 .. 498.0450 cents 56/45, 378.6022 cents 45/49,-147.4281 cents 3: 203.9100 .. 617.4878 cents 80/63, 413.5778 cents 27/32,-294.1350 cents 4: 315.6413 .. 764.9159 cents 35/27, 449.2746 cents 21/25,-301.8465 cents 5: 435.0841 .. 884.3587 cents 35/27, 449.2746 cents 81/98,-329.8318 cents 6: 582.5122 .. 996.0900 cents 80/63, 413.5778 cents 21/25,-301.8465 cents 7: 701.9550 .. 1080.5572 cents 56/45, 378.6022 cents 27/32,-294.1350 cents 8: 933.1291 .. 1165.0244 cents 343/300, 231.8953 cents 45/49,-147.4281 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 3.812180 Largest / Average step : 2.001532 Largest / Smallest step : 7.630199 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Most common interval of one step : 21/20, 84.4672 cents, amount: 3 Least squares average step : 129.48761 cents, oct.: 1165.38851 cents Scale is not proper Step pattern alph. order: ABCDEDFDG Step pattern size order : GDCBABEBF Scale is not a Constant Structure Scale diversity : 1.499259 Lumma stability : 0.058293 Lumma impropriety factor : 0.800929 Rothenberg efficiency : 0.343034 redundancy: 0.656966 Efficiency x scale size : 3.087302 Number of different interval sizes : 36 = 4.50000 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 7.25000 = 29/4 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 2401/2400, 0.7212 cents Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 8 Formal octave complements present : 5 = 55.5556% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 7 Scale harmonicity : 0.023417 Average absolute harmonicity : 0.220655 Specific harmonicity : 0.153711 Fundamental : 1/420, -8.7142 octaves, 0.6229 Hz. Guide tone : 420, 8.7142 octaves, 109882.737 Hz. Exponens Consonantiae : 1.764000E+05, 17.42849 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 42.5, average 4.72222 Mersenne's string divisions : 6126120 Sum of van Prooijen's expressibility: 5.73257, average 0.63695 Sum of Tenney's harmonic distance : 11.09506, average 1.23278 Vogel's harmonic complexity : 18.77778 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 103.30610, average 2.29569 Lattice compactness (without 2's) : 65.69140, average 1.45981 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.22222 10 1 3: -1 .. 1 -0.22222 4 2 5: -1 .. 1 0.22222 4 2 7: -1 .. 1 0.22222 4 4 Average exponent except 2's : 2 / 9 = 0.22222 Average absolute exponent except 2's: 12 / 9 = 1.33333
FIT/MODE
9: 2 1 1 0 1 0 2 0 2 N SD: 35.2345 c. M:-49.1789 c. 10: 2 1 1 1 0 1 1 1 2 N I SD: 22.9079 c. M: 44.3587 c. 12: 3 1 1 1 0 1 2 1 2 N SD: 18.6208 c. M:-33.1291 c. 15: 3 2 1 1 1 1 2 1 3 N SD: 17.2276 c. M: 26.8709 c. 19: 4 2 2 1 1 1 3 1 4 N SD: 11.6371 c. M: 21.4575 c. 22: 5 2 2 2 0 2 3 2 4 N SD: 10.9142 c. M:-17.4878 c. 27: 6 3 2 2 1 2 4 2 5 N SD: 7.4574 c. M:-13.6863 c. 31: 7 3 3 2 1 2 5 2 6 N SD: 3.5714 c. M:-5.9639 c. 41: 9 4 4 3 1 3 6 3 8 N SD: 3.5165 c. M: 6.3099 c. 68: 15 7 6 5 2 5 10 5 13 N SD: 2.2708 c. M:-3.9274 c. 72: 16 7 7 5 2 5 11 5 14 N SD: 1.6204 c. M: 2.9804 c. 99: 22 10 9 7 3 7 15 7 19 N SD: 0.8670 c. M:-1.5651 c. 140: 31 14 13 10 4 10 21 10 27 N SD: 0.8084 c. M: 1.5016 c. 171: 38 17 16 12 5 12 26 12 33 N SD: 0.2201 c. M: 0.4049 c. 270: 60 27 25 19 8 19 41 19 52 N SD: 0.2330 c. M:-0.3530 c. 441: 98 44 41 31 13 31 67 31 85 N SD: 0.1318 c. M: 0.2042 c. 612: 136 61 57 43 18 43 93 43 118 N SD: 0.1227 c. M: 0.2042 c. 935: 208 93 87 66 27 66 142 66 180 N SD: 0.1065 c. M:-0.1616 c. 966: 215 96 90 68 28 68 147 68 186 N SD: 0.1089 c. M:-0.2098 c. 1065: 237 106 99 75 31 75 162 75 205 N SD: 0.1134 c. M:-0.1882 c. 1106: 246 110 103 78 32 78 168 78 213 N SD: 0.0768 c. M:-0.1280 c. 1236: 275 123 115 87 36 87 188 87 238 N SD: 0.0719 c. M:-0.1194 c. 1277: 284 127 119 90 37 90 194 90 246 N SD: 0.0670 c. M:-0.1033 c. 1376: 306 137 128 97 40 97 209 97 265 N SD: 0.0534 c. M:-0.0799 c. 1407: 313 140 131 99 41 99 214 99 271 N SD: 0.0452 c. M:-0.0801 c. 1547: 344 154 144 109 45 109 235 109 298 N SD: 0.0383 c. M: 0.0665 c. 1578: 351 157 147 111 46 111 240 111 304 N SD: 0.0349 c. M:-0.0539 c. 1718: 382 171 160 121 50 121 261 121 331 N SD: 0.0389 c. M: 0.0747 c. 1848: 411 184 172 130 54 130 281 130 356 N SD: 0.0333 c. M:-0.0569 c. 2019: 449 201 188 142 59 142 307 142 389 N SD: 0.0298 c. M:-0.0456 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x x x 5 x 6 S SD: 0.0000 cents 4 x 5 x x x 6 x 7:8 S SD: 0.0000 cents 5:6 x x 7 x x 8:9:10 S SD: 19.7501 cents 6:7 x 8 x x 9:10:11:12 S SD: 13.4228 cents 7:8:9 x x 10:11 x 12:14 S SD: 17.8055 cents 8:9:10 x 11 x 12:13:14:16 S SD: 11.8307 cents 9 x 11:12 x 13:14:15:16:18 SD: 11.5943 cents 10:12 x 13:14 x 15:17:18:20 SD: 12.6601 cents 11:13:14:15 x 16:17:18:19:22 SD: 11.2855 cents 12:14:15:16 x 17:18:20:21:24 S SD: 1.8109 cents 14:16:18:19 x 20:21:23:25:28 SD: 10.0277 cents 15:18:19:20:21 x 23:25:26:30 SD: 8.5025 cents 16:19:20:21:22:23:24:27:28:32 SD: 6.3189 cents 17:20:21:23:24 x 26:28:30:34 SD: 7.1130 cents 18:21:23:24:25:26:27:30:32:36 SD: 5.8240 cents 19:22:24:25 x 27:29:32:33:38 SD: 6.2682 cents 20:23:25:27:28:29:30:33:35:40 SD: 5.0310 cents 22:26:28:29:31 x 33:37:39:44 SD: 6.5355 cents 23:27:29:31:32:33:35:38:40:46 SD: 4.7507 cents 24:28:30:32 x 34:36:40:42:48 S SD: 1.8109 cents 29:34:36:39:41 x 44:48:51:58 SD: 4.5625 cents 30:35:38:40:42:43:45:50:53:60 SD: 3.1978 cents 32:37:40:43:45:46:48:53:56:64 SD: 2.9736 cents 36:42:45:48:50:51:54:60:63:72 S SD: 2.2227 cents 40:47:50:53:56:57:60:67:70:80 SD: 2.1169 cents 48:56:60:64:67:69:72:80:84:96 SD: 1.3286 cents 60:70:75:80:84:86:90:100:105:120 SD: 0.6401 cents 72:84:90:96:101:103:108:120:126:144 SD: 0.4655 cents 108:126:135:144:151:154:162:180:189:216 SD: 0.4381 cents 156:182:195:208:218:223:234:260:273:312 SD: 0.3736 cents 168:196:210:224:235:240:252:280:294:336 SD: 0.1636 cents 180:210:225:240:252:257:270:300:315:360 SD: 0.1069 cents 240:280:300:320:336:343:360:400:420:480 SD: 0.0801 cents 420:490:525:560:588:600:630:700:735:840 S SD: 0.0000 cents