Scala analysis: grady_14
Kraig Grady, letter to Lou Harrison, published in 1/1 7 (1) 1991 p5.
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: 9/8 203.910002 major whole tone 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 21/16 470.780907 narrow fourth 6: 4/3 498.044999 perfect fourth 7: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 8: 3/2 701.955001 perfect fifth 9: 63/40 786.422194 narrow minor sixth 10: 27/16 905.865003 Pythagorean major sixth 11: 7/4 968.825906 harmonic seventh 12: 15/8 1088.268715 classic major seventh 13: 63/32 1172.735908 octave - septimal comma 14: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 64/63 27.2641 septimal comma, Archytas' comma 1: 21/20 84.4672 minor semitone 2: 15/14 119.4428 major diatonic semitone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 15/14 119.4428 major diatonic semitone 5: 21/20 84.4672 minor semitone 6: 64/63 27.2641 septimal comma, Archytas' comma 7: 21/20 84.4672 minor semitone 8: 15/14 119.4428 major diatonic semitone 9: 21/20 84.4672 minor semitone 10: 15/14 119.4428 major diatonic semitone 11: 28/27 62.9609 Archytas' 1/3-tone 12: 15/14 119.4428 major diatonic semitone 13: 21/20 84.4672 minor semitone 14: 64/63 27.2641 septimal comma, Archytas' comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 64/63 27.264 cents septimal comma, Archytas' comma 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 5 21/20 84.467 cents minor semitone 1: 5 15/14 119.443 cents major diatonic semitone 2: 4 16/15 111.731 cents minor diatonic semitone 2: 4 10/9 182.404 cents minor whole tone 2: 6 9/8 203.910 cents major whole tone 3: 2 28/25 196.198 cents middle second 3: 4 8/7 231.174 cents septimal whole tone 3: 4 7/6 266.871 cents septimal minor third 3: 1 189/160 288.377 cents 3: 2 25/21 301.847 cents BP second, quasi-equal minor third 3: 1 135/112 323.353 cents septimal wide minor third 4: 3 32/27 294.135 cents Pythagorean minor third 4: 5 6/5 315.641 cents minor third 4: 5 5/4 386.314 cents major third 4: 1 81/64 407.820 cents Pythagorean major third 5: 3 56/45 378.602 cents septimal narrow major third 5: 1 63/50 400.108 cents quasi-equal major third 5: 3 80/63 413.578 cents wide major third 5: 3 9/7 435.084 cents septimal major third, BP third 5: 3 21/16 470.781 cents narrow fourth 5: 1 75/56 505.757 cents marvelous fourth 6: 10 4/3 498.045 cents perfect fourth 6: 2 27/20 519.551 cents acute fourth 6: 2 45/32 590.224 cents diatonic tritone 7: 1 256/189 525.309 cents 7: 1 112/81 561.006 cents 7: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 5 10/7 617.488 cents Euler's tritone 7: 1 81/56 638.994 cents 7: 1 189/128 674.691 cents 8: 2 64/45 609.776 cents 2nd tritone 8: 2 40/27 680.449 cents grave fifth 8: 10 3/2 701.955 cents perfect fifth 9: 1 112/75 694.243 cents marvelous fifth 9: 3 32/21 729.219 cents wide fifth 9: 3 14/9 764.916 cents septimal minor sixth 9: 3 63/40 786.422 cents narrow minor sixth 9: 1 100/63 799.892 cents quasi-equal minor sixth 9: 3 45/28 821.398 cents septimale wide minor sixth 10: 1 128/81 792.180 cents Pythagorean minor sixth 10: 5 8/5 813.686 cents minor sixth 10: 5 5/3 884.359 cents major sixth, BP sixth 10: 3 27/16 905.865 cents Pythagorean major sixth 11: 1 224/135 876.647 cents narrow septimal major sixth 11: 2 42/25 898.153 cents quasi-equal major sixth 11: 1 320/189 911.623 cents 11: 4 12/7 933.129 cents septimal major sixth 11: 4 7/4 968.826 cents harmonic seventh 11: 2 25/14 1003.802 cents middle minor seventh 12: 6 16/9 996.090 cents Pythagorean minor seventh 12: 4 9/5 1017.596 cents just minor seventh, BP seventh 12: 4 15/8 1088.269 cents classic major seventh 13: 5 28/15 1080.557 cents grave major seventh 13: 5 40/21 1115.533 cents acute major seventh 13: 2 27/14 1137.039 cents septimal major seventh 13: 2 63/32 1172.736 cents octave - septimal comma Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.46154 = 58/13
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 84.5 203.9 266.9 386.3 470.8 498.0 582.5 702.0 786.4 905.9 968.8 1088.3 1172.7 1200.0 84.5 : 119.4 182.4 301.8 386.3 413.6 498.0 617.5 702.0 821.4 884.4 1003.8 1088.3 1115.5 1200.0 203.9 : 63.0 182.4 266.9 294.1 378.6 498.0 582.5 702.0 764.9 884.4 968.8 996.1 1080.6 1200.0 266.9 : 119.4 203.9 231.2 315.6 435.1 519.6 639.0 702.0 821.4 905.9 933.1 1017.6 1137.0 1200.0 386.3 : 84.5 111.7 196.2 315.6 400.1 519.6 582.5 702.0 786.4 813.7 898.2 1017.6 1080.6 1200.0 470.8 : 27.3 111.7 231.2 315.6 435.1 498.0 617.5 702.0 729.2 813.7 933.1 996.1 1115.5 1200.0 498.0 : 84.5 203.9 288.4 407.8 470.8 590.2 674.7 702.0 786.4 905.9 968.8 1088.3 1172.7 1200.0 582.5 : 119.4 203.9 323.4 386.3 505.8 590.2 617.5 702.0 821.4 884.4 1003.8 1088.3 1115.5 1200.0 702.0 : 84.5 203.9 266.9 386.3 470.8 498.0 582.5 702.0 764.9 884.4 968.8 996.1 1080.6 1200.0 786.4 : 119.4 182.4 301.8 386.3 413.6 498.0 617.5 680.4 799.9 884.4 911.6 996.1 1115.5 1200.0 905.9 : 63.0 182.4 266.9 294.1 378.6 498.0 561.0 680.4 764.9 792.2 876.6 996.1 1080.6 1200.0 968.8 : 119.4 203.9 231.2 315.6 435.1 498.0 617.5 702.0 729.2 813.7 933.1 1017.6 1137.0 1200.0 1088.3: 84.5 111.7 196.2 315.6 378.6 498.0 582.5 609.8 694.2 813.7 898.2 1017.6 1080.6 1200.0 1172.7: 27.3 111.7 231.2 294.1 413.6 498.0 525.3 609.8 729.2 813.7 933.1 996.1 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 119.4428 cents 135/128, 92.1787 cents 64/63, 27.2641 cents 2: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 224/225,-7.7115 cents 3: 196.1985 .. 323.3528 cents 3375/3136, 127.1543 cents 224/225,-7.7115 cents 4: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 3584/3645,-29.2178 cents 5: 378.6022 .. 505.7565 cents 3375/3136, 127.1543 cents 3584/3645,-29.2178 cents 6: 498.0450 .. 590.2237 cents 135/128, 92.1787 cents 224/225,-7.7115 cents 7: 525.3091 .. 674.6909 cents 35721/32768, 149.3818 cents 8192/8505,-64.9146 cents 8: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 8192/8505,-64.9146 cents 9: 694.2435 .. 821.3978 cents 3375/3136, 127.1543 cents 224/225,-7.7115 cents 10: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 3584/3645,-29.2178 cents 11: 876.6472 .. 1003.8015 cents 3375/3136, 127.1543 cents 3584/3645,-29.2178 cents 12: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 224/225,-7.7115 cents 13: 1080.5572 .. 1172.7359 cents 135/128, 92.1787 cents 224/225,-7.7115 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 85.7143 cents Largest one step interval : 15/14, 119.4428 cents Average / Smallest step : 3.143853 Largest / Average step : 1.393499 Largest / Smallest step : 4.380957 Median interval of one step : 21/20, 84.4672 cents, amount: 5 Least squares average step : 88.44520 cents, oct.: 1238.23284 cents Scale is not proper Step pattern alph. order: ABCBADABABCBAD Step pattern size order : CDBDCACDCDBDCA Scale is a Constant Structure, by a margin of 5.75780 cents Scale diversity : 1.388147 Lumma stability : 0.045440 Lumma impropriety factor : 0.244141 Number of different interval sizes : 58 = 4.46154 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.46154 = 58/13 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 5120/5103, 5.7578 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 10 Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 11, average 701.2540 cents Scale contains two identical disjunct heptachords Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 21.4286% Scale is differentially coherent in interval class 1 Scale is 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 : 189 (O: 189 U: 189) Highest odd numerator or denominator: 63 Scale harmonicity : 0.024538 Average absolute harmonicity : 0.164254 Specific harmonicity : 0.141675 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 3780, 11.8842 octaves, 988944.637 Hz. Exponens Consonantiae : 1.814400E+06, 20.79106 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 209.5, average 14.96429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.99332, average 0.99952 Sum of Tenney's harmonic distance : 26.50134, average 1.89295 Vogel's harmonic complexity : 16.57143 Wille's k value : 472 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 325.78757, average 3.10274 Lattice compactness (without 2's) : 192.77549, average 1.83596 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.92857 33 1 3: -1 .. 3 0.78571 15 4 5: -1 .. 1 -0.07143 5 2 7: 0 .. 1 0.50000 7 7 Average exponent except 2's : 17 / 14 = 1.21429 Average absolute exponent except 2's: 27 / 14 = 1.92857 Scale is weakly epimorphic with val: <14 22 32 37| Scale is JI-epimorphic with val: <14 22 32 39| Scale is weakly epimorphic with val: <14 22 32 41|
FIT/MODE
14: 1 1 1 1 1 0 1 2 1 1 1 1 1 1 N T3 SD: 42.1051 c. M: 69.4736 c. 15: 1 2 0 2 1 0 1 2 1 1 1 2 1 0 N SD: 20.9699 c. M:-36.0900 c. 17: 1 2 1 1 2 0 1 2 1 2 1 1 2 0 N SD: 18.3715 c. M: 33.3725 c. 19: 1 2 1 2 1 1 1 2 1 2 1 2 1 1 P D3 SD: 19.4363 c. M: 35.8938 c. 21: 2 2 1 2 1 1 1 2 2 2 1 2 2 0 N SD: 16.6647 c. M:-29.8185 c. 24: 2 2 1 3 1 1 2 2 2 2 1 3 1 1 N SD: 13.8912 c. M: 22.7359 c. 25: 2 2 2 2 2 0 2 3 1 3 1 3 1 1 N SD: 13.7260 c. M:-21.1291 c. 26: 2 2 2 2 2 1 2 2 2 3 1 3 1 1 N SD: 13.1958 c. M:-19.4236 c. 29: 2 3 1 3 2 1 2 3 2 3 1 3 2 1 N SD: 10.2640 c. M: 18.5950 c. 31: 2 3 2 3 2 1 2 3 2 3 2 3 2 1 N G SD: 7.6227 c. M: 15.5424 c. 33: 2 4 1 4 2 1 2 3 3 3 2 3 2 1 N SD: 9.9368 c. M:-14.2718 c. 36: 3 3 2 4 2 1 3 3 3 3 2 4 2 1 N SD: 9.1503 c. M:-17.4878 c. 37: 3 3 2 4 3 0 3 4 2 4 2 4 2 1 N SD: 9.0713 c. M:-15.7056 c. 40: 3 4 2 4 3 1 2 4 3 4 2 4 3 1 N SD: 7.7822 c. M: 12.5122 c. 41: 3 4 2 4 3 1 3 4 3 4 2 4 3 1 N SD: 3.0574 c. M: 5.8259 c. 72: 5 7 4 7 5 2 5 7 5 7 4 7 5 2 N SD: 3.3863 c. M: 6.0692 c. 84: 6 8 5 8 6 2 6 8 6 8 5 8 6 2 N SD: 2.7542 c. M: 5.8650 c. 87: 6 9 4 9 6 2 6 9 6 9 4 9 6 2 N SD: 2.4785 c. M: 4.8019 c. 89: 6 9 5 9 6 2 6 9 6 9 5 9 6 2 N SD: 2.6722 c. M:-4.6975 c. 99: 7 10 5 10 7 2 7 10 7 10 5 10 7 2 N SD: 1.7573 c. M:-3.2259 c. 130: 9 13 7 13 9 3 9 13 9 13 7 13 9 3 N SD: 0.9485 c. M: 1.8068 c. 171: 12 17 9 17 12 4 12 17 12 17 9 17 12 4 N SD: 0.4249 c. M: 0.8061 c. 270: 19 27 14 27 19 6 19 27 19 27 14 27 19 6 N SD: 0.3997 c. M:-0.8017 c. 395: 28 39 21 39 28 9 28 39 28 39 21 39 28 9 N SD: 0.4352 c. M:-0.7789 c. 400: 28 40 21 40 28 9 28 40 28 40 21 40 28 9 N SD: 0.3645 c. M:-0.7313 c. 441: 31 44 23 44 31 10 31 44 31 44 23 44 31 10 N SD: 0.1357 c. M:-0.2574 c. 612: 43 61 32 61 43 14 43 61 43 61 32 61 43 14 N SD: 0.1273 c. M: 0.2042 c. 966: 68 96 51 96 68 22 68 96 68 96 51 96 68 22 N SD: 0.1228 c. M: 0.2749 c. 1053: 74 105 55 105 74 24 74 105 74 105 55 105 74 24 N SD: 0.1125 c. M: 0.2042 c. 1065: 75 106 56 106 75 24 75 106 75 106 56 106 75 24 N SD: 0.1271 c. M:-0.2218 c. 1106: 78 110 58 110 78 25 78 110 78 110 58 110 78 25 N SD: 0.0997 c. M:-0.1963 c. 1236: 87 123 65 123 87 28 87 123 87 123 65 123 87 28 N SD: 0.0648 c. M:-0.1194 c. 1277: 90 127 67 127 90 29 90 127 90 127 67 127 90 29 N SD: 0.0610 c. M:-0.1087 c. 1407: 99 140 74 140 99 32 99 140 99 140 74 140 99 32 N SD: 0.0507 c. M: 0.1081 c. 1677: 118 167 88 167 118 38 118 167 118 167 88 167 118 38 N SD: 0.0512 c. M:-0.1034 c. 1718: 121 171 90 171 121 39 121 171 121 171 90 171 121 39 N SD: 0.0415 c. M:-0.0737 c. 1848: 130 184 97 184 130 42 130 184 130 184 97 184 130 42 N SD: 0.0309 c. M: 0.0586 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x 3 x x x x x 4 S SD: 0.0000 cents 3 x x x x x 4 x x x 5 x x x 6 S SD: 7.1688 cents 4 x x x 5 x x x 6 x x 7 x x 8 S SD: 0.0000 cents 5 x x 6 x x x 7 x 8 x 9 x x 10 S SD: 14.8330 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 7.4090 cents 7 x 8 x x 9 x 10 x 11:12 x 13 x 14 S SD: 9.3395 cents 8 x 9 x 10 x x 11:12:13 x 14:15 x 16 S SD: 7.8067 cents 9 x 10 x 11 x 12:13 x 14:15:16:17 x 18 S SD: 9.1187 cents 10 x 11:12 x 13 x 14:15:16:17:18:19 x 20 S SD: 8.9317 cents 11 x 12:13:14 x 15 x x 17 x 19:21 x 22 SD: 11.4454 cents 12:13 x 14:15 x 16:17:18:19:20:21:23 x 24 SD: 6.6438 cents 13:14 x 15:16:17 x 18 x 20:22:23:24 x 26 S SD: 7.8536 cents 14:15:16 x x 18:19:20:21:22:24:25:26 x 28 S SD: 7.9563 cents 15:16:17:18:19 x 20:21:23:24:25:26:28 x 30 SD: 6.8711 cents 16:17:18:19:20:21 x 22:24:25:27:28:30 x 32 SD: 4.1850 cents 18:19:20:21:23 x 24:25:27:28:30:32:34:35:36 SD: 5.1477 cents 19:20:21:22:24:25 x 27:29:30:32:33:36:37:38 SD: 4.8266 cents 20:21 x 23:25:26:27:28:30:32:34:35:38:39:40 SD: 4.2582 cents 21:22:24:25:26 x 28:29:32:33:35:37:39:41:42 SD: 5.2519 cents 22:23:25:26:28:29 x 31:33:35:37:39:41:43:44 SD: 4.2943 cents 23:24:26:27:29:30:31:32:35:36:39:40:43:45:46 SD: 3.3297 cents 24:25:27:28:30 x 32:34:36:38:41:42:45:47:48 SD: 2.6968 cents 25:26:28:29:31:33 x 35:38:39:42:44:47:49:50 SD: 3.2279 cents 28:29:32:33:35:37 x 39:42:44:47:49:53:55:56 SD: 3.6206 cents 29:30:33:34:36:38:39:41:44:46:49:51:54:57:58 SD: 3.6139 cents 30:32:34:35:38:39:40:42:45:47:51:53:56:59:60 SD: 3.4156 cents 31:33:35:36:39:41 x 43:47:49:52:54:58:61:62 SD: 3.2555 cents 32:34:36:37:40:42:43:45:48:50:54:56:60:63:64 SD: 2.3605 cents 34:36:38:40:43 x 45:48:51:54:57:60:64:67:68 SD: 3.3784 cents 35:37:39:41:44:46:47:49:53:55:59:61:66:69:70 SD: 2.4304 cents 36:38:41:42:45:47:48:50:54:57:61:63:68:71:72 SD: 2.3861 cents 37:39:42:43:46 x 49:52:56:58:62:65:69:73:74 SD: 2.6685 cents 38:40:43:44:48:50:51:53:57:60:64:67:71:75:76 SD: 2.3303 cents 40:42:45:47:50 x 53:56:60:63:68:70:75:79:80 SD: 1.6552 cents 48:50:54:56:60:63:64:67:72:76:81:84:90:95:96 SD: 1.3994 cents 60:63:68:70:75:79:80:84:90:95:101:105:113:118:120 SD: 1.3504 cents 64:67:72:75:80:84:85:90:96:101:108:112:120:126:128 SD: 1.0183 cents 80:84:90:93:100:105:107:112:120:126:135:140:150:158:160 SD: 0.7059 cents 96:101:108:112:120:126:128:134:144:151:162:168:180:189:192 SD: 0.4719 cents 144:151:162:168:180:189:192:202:216:227:243:252:270:284:288 SD: 0.3824 cents 160:168:180:187:200:210:213:224:240:252:270:280:300:315:320 SD: 0.2934 cents 224:235:252:261:280:294:299:314:336:353:378:392:420:441:448 SD: 0.2911 cents 240:252:270:280:300:315:320:336:360:378:405:420:450:473:480 SD: 0.1308 cents 384:403:432:448:480:504:512:538:576:605:648:672:720:756:768 SD: 0.1179 cents 480:504:540:560:600:630:640:672:720:756:810:840:900:945:960 S SD: 0.0000 cents