Scala analysis: hjelmconv
convex closure in breed plane of hjelm.scl
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: 49/40 351.338099 larger approximation to neutral third 3: 4/3 498.044999 perfect fourth 4: 49/36 533.741811 Arabic lute acute fourth 5: 10/7 617.487807 Euler's tritone 6: 3/2 701.955001 perfect fifth 7: 49/30 849.383098 larger approximation to neutral sixth 8: 7/4 968.825906 harmonic seventh 9: 40/21 1115.532807 acute major seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21/20 84.4672 minor semitone 1: 7/6 266.8709 septimal minor third 2: 21/20 84.4672 minor semitone 3: 160/147 146.7069 4: 49/48 35.6968 slendro diesis, septimal 1/6-tone 5: 360/343 83.7460 6: 21/20 84.4672 minor semitone 7: 49/45 147.4281 BP minor semitone 8: 15/14 119.4428 major diatonic semitone 9: 160/147 146.7069 10: 21/20 84.4672 minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 360/343 83.746 cents 1: 3 21/20 84.467 cents minor semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 2 160/147 146.707 cents 1: 1 49/45 147.428 cents BP minor semitone 1: 1 7/6 266.871 cents septimal minor third 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 54/49 168.213 cents Zalzal's mujannab 2: 1 10/9 182.404 cents minor whole tone 2: 2 8/7 231.174 cents septimal whole tone 2: 1 343/300 231.895 cents 2: 1 400/343 266.150 cents 2: 1 7/6 266.871 cents septimal minor third 2: 2 49/40 351.338 cents larger approximation to neutral third 3: 1 9/8 203.910 cents major whole tone 3: 1 400/343 266.150 cents 3: 1 7/6 266.871 cents septimal minor third 3: 1 6/5 315.641 cents minor third 3: 1 60/49 350.617 cents smaller approximation to neutral third 3: 1 49/40 351.338 cents larger approximation to neutral third 3: 1 80/63 413.578 cents wide major third 3: 1 1029/800 435.805 cents 3: 2 4/3 498.045 cents perfect fourth 4: 2 60/49 350.617 cents smaller approximation to neutral third 4: 1 49/40 351.338 cents larger approximation to neutral third 4: 1 9/7 435.084 cents septimal major third, BP third 4: 2 4/3 498.045 cents perfect fourth 4: 1 49/36 533.742 cents Arabic lute acute fourth 4: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 10/7 617.488 cents Euler's tritone 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: 1 480/343 581.791 cents 5: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 1 10/7 617.488 cents Euler's tritone 5: 1 343/240 618.209 cents 5: 1 3/2 701.955 cents perfect fifth 5: 1 32/21 729.219 cents wide fifth 5: 1 14/9 764.916 cents septimal minor sixth 6: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 2 10/7 617.488 cents Euler's tritone 6: 1 72/49 666.258 cents Arabic lute grave fifth 6: 2 3/2 701.955 cents perfect fifth 6: 1 14/9 764.916 cents septimal minor sixth 6: 1 80/49 848.662 cents smaller approximation to neutral sixth 6: 2 49/30 849.383 cents larger approximation to neutral sixth 7: 2 3/2 701.955 cents perfect fifth 7: 1 1600/1029 764.195 cents 7: 1 63/40 786.422 cents narrow minor sixth 7: 1 80/49 848.662 cents smaller approximation to neutral sixth 7: 1 49/30 849.383 cents larger approximation to neutral sixth 7: 1 5/3 884.359 cents major sixth, BP sixth 7: 1 12/7 933.129 cents septimal major sixth 7: 1 343/200 933.850 cents 7: 1 16/9 996.090 cents Pythagorean minor seventh 8: 2 80/49 848.662 cents smaller approximation to neutral sixth 8: 1 12/7 933.129 cents septimal major sixth 8: 1 343/200 933.850 cents 8: 1 600/343 968.105 cents 8: 2 7/4 968.826 cents harmonic seventh 8: 1 9/5 1017.596 cents just minor seventh, BP seventh 8: 1 49/27 1031.787 cents 8: 1 28/15 1080.557 cents grave major seventh 9: 1 12/7 933.129 cents septimal major sixth 9: 1 90/49 1052.572 cents 9: 2 147/80 1053.293 cents 9: 1 28/15 1080.557 cents grave major seventh 9: 3 40/21 1115.533 cents acute major seventh 9: 1 343/180 1116.254 cents 9: 1 96/49 1164.303 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 8.00000 = 8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 266.9 351.3 498.0 533.7 617.5 702.0 849.4 968.8 1115.5 1200.0 266.9 : 84.5 231.2 266.9 350.6 435.1 582.5 702.0 848.7 933.1 1200.0 351.3 : 146.7 182.4 266.1 350.6 498.0 617.5 764.2 848.7 1115.5 1200.0 498.0 : 35.7 119.4 203.9 351.3 470.8 617.5 702.0 968.8 1053.3 1200.0 533.7 : 83.7 168.2 315.6 435.1 581.8 666.3 933.1 1017.6 1164.3 1200.0 617.5 : 84.5 231.9 351.3 498.0 582.5 849.4 933.9 1080.6 1116.3 1200.0 702.0 : 147.4 266.9 413.6 498.0 764.9 849.4 996.1 1031.8 1115.5 1200.0 849.4 : 119.4 266.1 350.6 617.5 702.0 848.7 884.4 968.1 1052.6 1200.0 968.8 : 146.7 231.2 498.0 582.5 729.2 764.9 848.7 933.1 1080.6 1200.0 1115.5: 84.5 351.3 435.8 582.5 618.2 702.0 786.4 933.9 1053.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 266.8709 cents 8/7, 231.1741 cents 49/48, 35.6968 cents 2: 119.4428 .. 351.3381 cents 343/300, 231.8953 cents 45/49,-147.4281 cents 3: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 45/49,-147.4281 cents 4: 350.6169 .. 617.4878 cents 7/6, 266.8709 cents 45/49,-147.4281 cents 5: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 9/10,-182.4037 cents 6: 582.5122 .. 849.3831 cents 7/6, 266.8709 cents 9/10,-182.4037 cents 7: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 45/49,-147.4281 cents 8: 848.6619 .. 1080.5572 cents 343/300, 231.8953 cents 45/49,-147.4281 cents 9: 933.1291 .. 1164.3032 cents 8/7, 231.1741 cents 45/49,-147.4281 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 3.361645 Largest / Average step : 2.223924 Largest / Smallest step : 7.476043 Median interval of one step : 101.95500 cents, amount: 0 Most common interval of one step : 21/20, 84.4672 cents, amount: 3 Least squares average step : 123.72442 cents, oct.: 1237.24422 cents Scale is not proper Step pattern alph. order: ABCDEBFGCB Step pattern size order : GCEABCFDEC Scale is not a Constant Structure Scale diversity : 1.501972 Lumma stability : 0.059495 Lumma impropriety factor : 0.800929 Rothenberg efficiency : 0.308571 redundancy: 0.691429 Efficiency x scale size : 3.085714 Number of different interval sizes : 48 = 5.33333 / class Number of one step interval sizes : 7 Highest interval variety : 10 Mean interval variety : 8.00000 = 8 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 30.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 7 Odd number limit : 1029 (O: 1029 U: 1029) Highest odd numerator or denominator: 49 Scale harmonicity : 0.017344 Average absolute harmonicity : 0.184320 Specific harmonicity : 0.098831 Fundamental : 1/2520, -11.2992 octaves, 0.1038 Hz. Guide tone : 5880, 12.5216 octaves, 1538358.324 Hz. Exponens Consonantiae : 1.481760E+07, 23.82081 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 185.0, average 18.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.88234, average 0.98823 Sum of Tenney's harmonic distance : 19.70422, average 1.97042 Vogel's harmonic complexity : 23.40000 Wille's k value : 1543 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 170.46094, average 3.09929 Lattice compactness (without 2's) : 109.23480, average 1.98609 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 -0.30000 17 1 3: -2 .. 1 -0.50000 7 2 5: -1 .. 1 0.00000 4 7: -1 .. 2 0.60000 10 7 Average exponent except 2's : 1 / 10 = 0.10000 Average absolute exponent except 2's: 21 / 10 = 2.10000
FIT/MODE
10: 2 1 1 0 1 1 1 1 1 1 N T3 SD: 24.6391 c. M: 53.7418 c. 11: 2 1 2 0 1 0 2 1 1 1 N SD: 32.0556 c. M: 48.6891 c. 13: 3 1 2 0 1 1 1 2 1 1 N SD: 29.4436 c. M:-55.8012 c. 14: 3 1 2 0 1 1 2 1 2 1 N SD: 14.5416 c. M: 25.9688 c. 17: 4 1 2 1 1 1 2 2 2 1 N SD: 14.5729 c. M:-30.9641 c. 22: 5 1 3 1 1 2 3 2 2 2 N SD: 15.7428 c. M: 24.6237 c. 23: 5 2 3 0 2 1 3 3 2 2 N SD: 16.3804 c. M:-23.6941 c. 24: 5 2 3 1 1 2 3 2 3 2 N SD: 12.0842 c. M: 18.8259 c. 27: 6 2 3 1 2 2 3 3 3 2 N SD: 5.7633 c. M: 9.1561 c. 31: 7 2 4 1 2 2 4 3 4 2 N SD: 4.5345 c. M:-8.1937 c. 41: 9 3 5 1 3 3 5 4 5 3 N SD: 2.9781 c. M: 6.9125 c. 58: 13 4 7 2 4 4 7 6 7 4 N SD: 2.3198 c. M:-4.1892 c. 72: 16 5 9 2 5 5 9 7 9 5 N SD: 1.2902 c. M: 2.1592 c. 99: 22 7 12 3 7 7 12 10 12 7 N SD: 0.6888 c. M:-1.0753 c. 171: 38 12 21 5 12 12 21 17 21 12 N SD: 0.2832 c. M: 0.4609 c. 270: 60 19 33 8 19 19 33 27 33 19 N SD: 0.2712 c. M: 0.4942 c. 441: 98 31 54 13 31 31 54 44 54 31 N SD: 0.2353 c. M: 0.4085 c. 571: 127 40 70 17 40 40 70 57 70 40 N SD: 0.2389 c. M:-0.4041 c. 612: 136 43 75 18 43 43 75 61 75 43 N SD: 0.2360 c. M: 0.4085 c. 742: 165 52 91 22 52 52 91 74 91 52 N SD: 0.2262 c. M: 0.3947 c. 836: 186 59 102 25 58 59 103 83 102 59 N SD: 0.2119 c. M:-0.3777 c. 894: 199 63 109 27 62 63 110 89 109 63 N SD: 0.2447 c. M:-0.4864 c. 908: 202 64 111 27 63 64 112 90 111 64 N SD: 0.2077 c. M:-0.3966 c. 935: 208 66 114 28 65 66 115 93 114 66 N SD: 0.1771 c. M:-0.3197 c. 966: 215 68 118 29 67 68 119 96 118 68 N SD: 0.2001 c. M:-0.4197 c. 976: 217 69 119 29 68 69 120 97 119 69 N SD: 0.1966 c. M: 0.3689 c. 1007: 224 71 123 30 70 71 124 100 123 71 N SD: 0.1428 c. M:-0.2693 c. 1065: 237 75 130 32 74 75 131 106 130 75 N SD: 0.1635 c. M:-0.3427 c. 1106: 246 78 135 33 77 78 136 110 135 78 N SD: 0.1112 c. M:-0.1990 c. 1178: 262 83 144 35 82 83 145 117 144 83 N SD: 0.1029 c. M:-0.1925 c. 1236: 275 87 151 37 86 87 152 123 151 87 N SD: 0.1069 c. M:-0.2388 c. 1277: 284 90 156 38 89 90 157 127 156 90 N SD: 0.0678 c. M:-0.1106 c. 1407: 313 99 172 42 98 99 173 140 172 99 N SD: 0.0685 c. M:-0.1601 c. 1448: 322 102 177 43 101 102 178 144 177 102 N SD: 0.0467 c. M: 0.0845 c. 1547: 344 109 189 46 108 109 190 154 189 109 N SD: 0.0458 c. M: 0.0835 c. 1578: 351 111 193 47 110 111 194 157 193 111 N SD: 0.0483 c. M:-0.0985 c. 1619: 360 114 198 48 113 114 199 161 198 114 N SD: 0.0491 c. M: 0.0798 c. 1677: 373 118 205 50 117 118 206 167 205 118 N SD: 0.0337 c. M:-0.0686 c. 1848: 411 130 226 55 129 130 227 184 226 130 N SD: 0.0285 c. M:-0.0516 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x 4 x x x 5 x x 6 S SD: 11.6585 cents 4 x 5 x x x 6 x 7 x 8 S SD: 8.7439 cents 5 x 6 x x 7 x 8:9 x 10 S SD: 15.6849 cents 6:7 x 8 x x 9:10 x 11:12 S SD: 12.4741 cents 7:8 x 9 x 10 x 11:12:13:14 S SD: 16.2306 cents 8:9:10 x 11 x 12:13:14:15:16 S SD: 9.9358 cents 9 x 11:12 x 13:14:15:16:17:18 SD: 10.0948 cents 10 x 12:13 x 14:15:16:18:19:20 S SD: 11.2433 cents 11:13 x x 15:16:17:18:19:21:22 SD: 8.5617 cents 12:14:15:16 x 17:18:20:21:23:24 SD: 5.8508 cents 14:16:17 x 19:20:21:23:25:27:28 SD: 6.4005 cents 15 x 18:20 x 21:23:25:26:29:30 SD: 9.7689 cents 16:19:20:21:22:23:24:26:28:30:32 SD: 6.4441 cents 17:20:21 x 23:24:26:28:30:32:34 SD: 6.0019 cents 18:21:22:24:25:26:27:29:32:34:36 SD: 5.5860 cents 19:22:23:25:26:27:29:31:33:36:38 SD: 4.9534 cents 20:23:25 x 27:29:30:33:35:38:40 SD: 6.1235 cents 21:25:26:28:29:30:32:34:37:40:42 SD: 5.7466 cents 22:26:27:29:30:31:33:36:39:42:44 SD: 4.4731 cents 23:27:28 x 31:33:35:38:40:44:46 SD: 4.6661 cents 24:28:29:32:33:34:36:39:42:46:48 SD: 3.5721 cents 26:30:32:35 x 37:39:42:46:50:52 SD: 4.6474 cents 27:32:33:36:37:39:41:44:47:51:54 SD: 4.4982 cents 28:33:34:37:38:40:42:46:49:53:56 SD: 3.2031 cents 29:34:36:39 x 41:44:47:51:55:58 SD: 4.7750 cents 30:35:37:40:41:43:45:49:53:57:60 SD: 2.2555 cents 36:42:44:48:49:51:54:59:63:69:72 SD: 1.9397 cents 44:51:54:59:60:63:66:72:77:84:88 SD: 1.6888 cents 54:63:66:72:74:77:81:88:95:103:108 SD: 1.6376 cents 60:70:74:80:82:86:90:98:105:114:120 SD: 1.5475 cents 66:77:81:88:90:94:99:108:116:126:132 SD: 1.1396 cents 72:84:88:96:98:103:108:118:126:137:144 SD: 0.7683 cents 84:98:103:112:114:120:126:137:147:160:168 SD: 0.5895 cents 138:161:169:184:188:197:207:225:242:263:276 SD: 0.5230 cents 144:168:176:192:196:206:216:235:252:274:288 SD: 0.5162 cents 156:182:191:208:212:223:234:255:273:297:312 SD: 0.3462 cents 210:245:257:280:286:300:315:343:368:400:420 SD: 0.3065 cents 240:280:294:320:327:343:360:392:420:457:480 SD: 0.1983 cents 324:378:397:432:441:463:486:529:567:617:648 SD: 0.1032 cents 600:700:735:800:817:857:900:980:1050:1143:1200 SD: 0.0793 cents