Scala analysis: ch9_5
Four tetrads five
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 7/6 266.870906 septimal minor third 3: 49/40 351.338099 larger approximation to neutral third 4: 5/4 386.313714 major third 5: 21/16 470.780907 narrow fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 7/4 968.825906 harmonic seventh 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 21/20 84.4672 minor semitone 2: 10/9 182.4037 minor whole tone 3: 21/20 84.4672 minor semitone 4: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 5: 21/20 84.4672 minor semitone 6: 16/15 111.7313 minor diatonic semitone 7: 15/14 119.4428 major diatonic semitone 8: 7/6 266.8709 septimal minor third 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 : 84.5 266.9 351.3 386.3 470.8 582.5 702.0 968.8 1200.0 84.5 : 182.4 266.9 301.8 386.3 498.0 617.5 884.4 1115.5 1200.0 266.9 : 84.5 119.4 203.9 315.6 435.1 702.0 933.1 1017.6 1200.0 351.3 : 35.0 119.4 231.2 350.6 617.5 848.7 933.1 1115.5 1200.0 386.3 : 84.5 196.2 315.6 582.5 813.7 898.2 1080.6 1165.0 1200.0 470.8 : 111.7 231.2 498.0 729.2 813.7 996.1 1080.6 1115.5 1200.0 582.5 : 119.4 386.3 617.5 702.0 884.4 968.8 1003.8 1088.3 1200.0 702.0 : 266.9 498.0 582.5 764.9 849.4 884.4 968.8 1080.6 1200.0 968.8 : 231.2 315.6 498.0 582.5 617.5 702.0 813.7 933.1 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 : 114.14298 cents, oct.: 1027.28678 cents Scale is not proper Step pattern alph. order: ABACADEFG Step pattern size order : BEBABCDGF 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 7 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 1 = 11.1111% 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 Scale is n-1 differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 49 Scale harmonicity : 0.022881 Average absolute harmonicity : 0.193773 Specific harmonicity : 0.144628 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 1470, 10.5216 octaves, 384589.581 Hz. Exponens Consonantiae : 3.528000E+05, 18.42849 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 110.0, average 12.22222 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.04602, average 0.89400 Sum of Tenney's harmonic distance : 15.43653, average 1.71517 Vogel's harmonic complexity : 15.44444 Wille's k value : 157 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 111.98845, average 2.48863 Lattice compactness (without 2's) : 67.24531, average 1.49434 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.55556 16 1 3: -1 .. 1 0.22222 4 1 5: -1 .. 1 -0.22222 4 1 7: 0 .. 2 0.77778 7 6 Average exponent except 2's : 7 / 9 = 0.77778 Average absolute exponent except 2's: 15 / 9 = 1.66667
FIT/MODE
9: 0 2 0 0 1 1 1 2 2 N SD: 65.4496 c. M: 119.6470 c. 10: 1 1 1 0 1 1 1 2 2 N S SD: 19.8506 c. M:-35.5328 c. 15: 1 2 1 1 1 1 2 3 3 N SD: 17.9713 c. M: 31.3381 c. 17: 1 3 1 0 2 1 2 4 3 N SD: 17.6460 c. M: 33.3725 c. 19: 1 3 1 1 1 2 2 4 4 N SD: 19.7433 c. M: 35.5486 c. 20: 1 3 2 0 2 2 2 4 4 N SD: 17.8962 c. M: 26.8709 c. 21: 1 4 1 1 1 2 2 5 4 N SD: 14.6830 c. M: 27.3243 c. 25: 2 4 1 1 2 2 3 5 5 N SD: 12.2519 c. M:-21.1291 c. 26: 2 4 2 0 2 3 2 6 5 N SD: 11.8273 c. M:-17.8927 c. 27: 2 4 2 1 2 2 3 6 5 N SD: 9.0614 c. M:-18.1080 c. 28: 2 4 2 1 2 3 2 7 5 N SD: 10.6651 c. M:-17.4878 c. 31: 2 5 2 1 2 3 3 7 6 N SD: 4.0349 c. M: 7.0478 c. 41: 3 6 3 1 3 4 4 9 8 N SD: 2.9897 c. M: 5.8259 c. 68: 5 10 5 2 5 6 7 15 13 N SD: 2.9074 c. M:-5.6897 c. 72: 5 11 5 2 5 7 7 16 14 N SD: 2.0571 c. M: 4.1142 c. 99: 7 15 7 3 7 9 10 22 19 N SD: 0.9918 c. M:-1.9464 c. 130: 9 20 9 4 9 12 13 29 25 N SD: 0.8244 c. M: 1.3903 c. 140: 10 21 10 4 10 13 14 31 27 N SD: 0.7209 c. M:-1.2471 c. 171: 12 26 12 5 12 16 17 38 33 N SD: 0.3359 c. M: 0.6055 c. 270: 19 41 19 8 19 25 27 60 52 N SD: 0.2326 c. M:-0.3530 c. 441: 31 67 31 13 31 41 44 98 85 N SD: 0.1578 c. M: 0.3177 c. 612: 43 93 43 18 43 57 61 136 118 N SD: 0.1816 c. M: 0.3577 c. 711: 50 108 50 21 50 66 71 158 137 N SD: 0.1681 c. M: 0.2832 c. 867: 61 132 61 25 61 81 86 193 167 N SD: 0.1710 c. M:-0.2571 c. 935: 66 142 66 27 66 87 93 208 180 N SD: 0.1758 c. M:-0.3197 c. 966: 68 147 68 28 68 90 96 215 186 N SD: 0.1169 c. M:-0.2147 c. 1065: 75 162 75 31 75 99 106 237 205 N SD: 0.1418 c. M:-0.2112 c. 1106: 78 168 78 32 78 103 110 246 213 N SD: 0.1076 c. M:-0.1990 c. 1137: 80 173 80 33 80 106 113 253 219 N SD: 0.0818 c. M:-0.1476 c. 1236: 87 188 87 36 87 115 123 275 238 N SD: 0.0798 c. M:-0.1194 c. 1277: 90 194 90 37 90 119 127 284 246 N SD: 0.0696 c. M:-0.1106 c. 1407: 99 214 99 41 99 131 140 313 271 N SD: 0.0404 c. M:-0.0801 c. 1578: 111 240 111 46 111 147 157 351 304 N SD: 0.0366 c. M: 0.0585 c. 1718: 121 261 121 50 121 160 171 382 331 N SD: 0.0321 c. M: 0.0506 c. 1848: 130 281 130 54 130 172 184 411 356 N SD: 0.0315 c. M: 0.0516 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x 4 S SD: 0.0000 cents 3 x x x x 4 x x 5:6 S SD: 29.5861 cents 4 x x x 5 x x 6:7:8 S SD: 0.0000 cents 5 x x 6 x x 7:8:9:10 S SD: 25.4061 cents 6 x 7 x x 8 x 9:11:12 SD: 17.0053 cents 7 x 8 x x 9:10:11:12:14 S SD: 17.8981 cents 8 x 9 x 10 x 11:12:14:16 S SD: 11.7108 cents 9 x x 11 x 12:13:14:16:18 SD: 15.2694 cents 10:11 x 12 x 13:14:15:18:20 S SD: 14.5781 cents 11:12:13 x 14 x 15:17:19:22 SD: 15.0575 cents 12:13:14 x 15:16:17:18:21:24 S SD: 7.9946 cents 13:14:15:16 x 17:18:20:23:26 SD: 8.8730 cents 14:15:16:17 x 18:20:21:25:28 SD: 10.0388 cents 15:16 x 18:19:20:21:23:26:30 SD: 8.8468 cents 16:17:19 x 20:21:22:24:28:32 SD: 6.0361 cents 17:18:20:21 x 22:24:26:30:34 SD: 6.5857 cents 18:19:21:22:23:24:25:27:32:36 SD: 6.3086 cents 19:20:22:23:24:25:27:29:33:38 SD: 5.7792 cents 20:21:23 x 25:26:28:30:35:40 SD: 3.7395 cents 21:22:25 x 26:28:29:32:37:42 SD: 7.6035 cents 22:23:26:27:28:29:31:33:39:44 SD: 5.2344 cents 23:24:27:28:29:30:32:35:40:46 SD: 4.3629 cents 25:26:29 x 31:33:35:38:44:50 SD: 4.4838 cents 28:29:33:34:35:37:39:42:49:56 SD: 4.0351 cents 29:30:34 x 36:38:41:44:51:58 SD: 5.0626 cents 30:32:35:37:38:39:42:45:53:60 SD: 4.9074 cents 31:33:36:38:39:41:43:47:54:62 SD: 4.4353 cents 32:34:37:39:40:42:45:48:56:64 SD: 3.1402 cents 35:37:41:43:44:46:49:53:61:70 SD: 2.8003 cents 36:38:42:44:45:47:50:54:63:72 SD: 2.1475 cents 48:50:56:59:60:63:67:72:84:96 SD: 1.7620 cents 60:63:70:74:75:79:84:90:105:120 SD: 1.4396 cents 76:80:89:93:95:100:106:114:133:152 SD: 1.2459 cents 80:84:93:98:100:105:112:120:140:160 SD: 0.6882 cents 120:126:140:147:150:158:168:180:210:240 SD: 0.6097 cents 156:164:182:191:195:205:218:234:273:312 SD: 0.4947 cents 160:168:187:196:200:210:224:240:280:320 SD: 0.3432 cents 240:252:280:294:300:315:336:360:420:480 S SD: 0.0000 cents