Scala analysis: bluesji
7-limit JI version of Graham Breed's Blues scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 10/9 182.403712 minor whole tone 3: 5/4 386.313714 major third 4: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 5: 4/3 498.044999 perfect fourth 6: 35/24 653.184619 septimal semi-diminished fifth 7: 40/27 680.448711 grave fifth 8: 81/50 835.192576 acute minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 140/81 947.319617 11: 35/18 1151.229619 septimal semi-diminished octave 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 250/243 49.1661 maximal diesis, Porcupine comma 3: 9/8 203.9100 major whole tone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 35/32 155.1396 septimal neutral second 7: 64/63 27.2641 septimal comma, Archytas' comma 8: 2187/2000 154.7439 Gorgo limma 9: 250/243 49.1661 maximal diesis, Porcupine comma 10: 28/27 62.9609 Archytas' 1/3-tone 11: 9/8 203.9100 major whole tone 12: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 250/243 49.166 cents maximal diesis, Porcupine comma 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 2187/2000 154.744 cents Gorgo limma 1: 1 35/32 155.140 cents septimal neutral second 1: 2 9/8 203.910 cents major whole tone 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 7000/6561 112.127 cents 2: 2 972/875 182.008 cents 2: 2 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 125/108 253.076 cents semi-augmented whole tone 2: 2 7/6 266.871 cents septimal minor third 3: 3 8/7 231.174 cents septimal whole tone 3: 2 7/6 266.871 cents septimal minor third 3: 2 6/5 315.641 cents minor third 3: 2 875/729 316.037 cents 3: 1 243/200 337.148 cents acute minor third 3: 1 2187/1750 385.918 cents 3: 1 5/4 386.314 cents major third 4: 2 32/27 294.135 cents Pythagorean minor third 4: 2 100/81 364.807 cents grave major third 4: 1 2187/1750 385.918 cents 4: 1 5/4 386.314 cents major third 4: 2 9/7 435.084 cents septimal major third, BP third 4: 1 162/125 448.879 cents 4: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 4: 2 21/16 470.781 cents narrow fourth 5: 1 9/7 435.084 cents septimal major third, BP third 5: 1 162/125 448.879 cents 5: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 5: 6 4/3 498.045 cents perfect fourth 5: 1 27/20 519.551 cents acute fourth 5: 1 875/648 519.947 cents 5: 1 81/56 638.994 cents 6: 2 4/3 498.045 cents perfect fourth 6: 2 48/35 546.815 cents septimal semi-augmented fourth 6: 2 1000/729 547.211 cents 6: 2 729/500 652.789 cents 6: 2 35/24 653.185 cents septimal semi-diminished fifth 6: 2 3/2 701.955 cents perfect fifth 7: 1 112/81 561.006 cents 7: 1 1296/875 680.053 cents 7: 1 40/27 680.449 cents grave fifth 7: 6 3/2 701.955 cents perfect fifth 7: 1 54/35 750.725 cents septimal semi-augmented fifth 7: 1 125/81 751.121 cents 7: 1 14/9 764.916 cents septimal minor sixth 8: 2 32/21 729.219 cents wide fifth 8: 1 54/35 750.725 cents septimal semi-augmented fifth 8: 1 125/81 751.121 cents 8: 2 14/9 764.916 cents septimal minor sixth 8: 1 8/5 813.686 cents minor sixth 8: 1 3500/2187 814.082 cents 8: 2 81/50 835.193 cents acute minor sixth 8: 2 27/16 905.865 cents Pythagorean major sixth 9: 1 8/5 813.686 cents minor sixth 9: 1 3500/2187 814.082 cents 9: 1 400/243 862.852 cents grave major sixth 9: 2 1458/875 883.963 cents 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 2 12/7 933.129 cents septimal major sixth 9: 3 7/4 968.826 cents harmonic seventh 10: 2 12/7 933.129 cents septimal major sixth 10: 1 216/125 946.924 cents semi-augmented sixth 10: 1 140/81 947.320 cents 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 875/486 1017.992 cents 10: 1 6561/3500 1087.873 cents 10: 1 15/8 1088.269 cents classic major seventh 11: 2 16/9 996.090 cents Pythagorean minor seventh 11: 1 64/35 1044.860 cents septimal neutral seventh 11: 1 4000/2187 1045.256 cents 11: 1 50/27 1066.762 cents grave major seventh 11: 2 27/14 1137.039 cents septimal major seventh 11: 2 243/125 1150.834 cents octave - maximal diesis 11: 2 35/18 1151.230 cents septimal semi-diminished octave 11: 1 63/32 1172.736 cents octave - septimal comma Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 7.45455 = 82/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 133.2 182.4 386.3 449.3 498.0 653.2 680.4 835.2 884.4 947.3 1151.2 1200.0 133.2 : 49.2 253.1 316.0 364.8 519.9 547.2 702.0 751.1 814.1 1018.0 1066.8 1200.0 182.4 : 203.9 266.9 315.6 470.8 498.0 652.8 702.0 764.9 968.8 1017.6 1150.8 1200.0 386.3 : 63.0 111.7 266.9 294.1 448.9 498.0 561.0 764.9 813.7 946.9 996.1 1200.0 449.3 : 48.8 203.9 231.2 385.9 435.1 498.0 702.0 750.7 884.0 933.1 1137.0 1200.0 498.0 : 155.1 182.4 337.1 386.3 449.3 653.2 702.0 835.2 884.4 1088.3 1151.2 1200.0 653.2 : 27.3 182.0 231.2 294.1 498.0 546.8 680.1 729.2 933.1 996.1 1044.9 1200.0 680.4 : 154.7 203.9 266.9 470.8 519.6 652.8 702.0 905.9 968.8 1017.6 1172.7 1200.0 835.2 : 49.2 112.1 316.0 364.8 498.0 547.2 751.1 814.1 862.9 1018.0 1045.3 1200.0 884.4 : 63.0 266.9 315.6 448.9 498.0 702.0 764.9 813.7 968.8 996.1 1150.8 1200.0 947.3 : 203.9 252.7 385.9 435.1 639.0 702.0 750.7 905.9 933.1 1087.9 1137.0 1200.0 1151.2: 48.8 182.0 231.2 435.1 498.0 546.8 702.0 729.2 884.0 933.1 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 203.9100 cents 567/512, 176.6459 cents 64/63, 27.2641 cents 2: 111.7313 .. 266.8709 cents 35/32, 155.1396 cents 128/135,-92.1787 cents 3: 231.1741 .. 386.3137 cents 35/32, 155.1396 cents 48/49,-35.6968 cents 4: 294.1350 .. 470.7809 cents 567/512, 176.6459 cents 128/135,-92.1787 cents 5: 435.0841 .. 638.9941 cents 9/8, 203.9100 cents 48/49,-35.6968 cents 6: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 224/243,-140.9491 cents 7: 561.0059 .. 764.9159 cents 9/8, 203.9100 cents 224/243,-140.9491 cents 8: 729.2191 .. 905.8650 cents 567/512, 176.6459 cents 48/49,-35.6968 cents 9: 813.6863 .. 968.8259 cents 35/32, 155.1396 cents 128/135,-92.1787 cents 10: 933.1291 .. 1088.2687 cents 35/32, 155.1396 cents 48/49,-35.6968 cents 11: 996.0900 .. 1172.7359 cents 567/512, 176.6459 cents 128/135,-92.1787 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 3.667828 Largest / Average step : 2.039100 Largest / Smallest step : 7.479068 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 101.23700 cents, oct.: 1214.84399 cents Scale is not proper Step pattern alph. order: ABCDEFGHBDCE Step pattern size order : ECHDBGAFCDHB Scale is not a Constant Structure Scale diversity : 1.477472 Lumma stability : 0.045440 Lumma impropriety factor : 0.596177 Rothenberg efficiency : 0.319865 redundancy: 0.680135 Efficiency x scale size : 3.838384 Number of different interval sizes : 66 = 6.00000 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 7.45455 = 82/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 4375/4374, 0.3958 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 8 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 8, average 701.9550 cents Formal octave complements present : 1 = 8.3333% Limited inverse transpositions with margin 155.1396 cents: 1 Inversional symmetry on intervals : 0-1 6-7 -- Rational properties -- Prime limit : 7 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.017600 Average absolute harmonicity : 0.152611 Specific harmonicity : 0.106074 Fundamental : 1/16200, -13.9837 octaves, 0.0161 Hz. Guide tone : 22680, 14.4691 octaves, 5933667.821 Hz. Exponens Consonantiae : 3.674160E+08, 28.45284 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 345.5, average 28.79167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.14121, average 1.17843 Sum of Tenney's harmonic distance : 28.03542, average 2.33629 Vogel's harmonic complexity : 26.66667 Wille's k value : 11812 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 12 Triangular lattice diameter : 8 Lattice compactness : 305.23660, average 3.91329 Lattice compactness (without 2's) : 235.37068, average 3.01757 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.16667 16 1 3: -4 .. 4 -0.83333 24 1 5: -2 .. 1 0.33333 12 6 7: 0 .. 1 0.33333 4 4 Average exponent except 2's :-2 / 12 =-0.16667 Average absolute exponent except 2's: 40 / 12 = 3.33333
FIT/MODE
12: 1 1 2 0 1 1 1 1 1 0 2 1 N T3 SD: 33.6540 c. M: 53.1846 c. 13: 1 1 2 1 0 2 0 2 0 1 2 1 N SD: 28.9472 c. M: 53.5895 c. 16: 2 0 3 1 1 2 0 2 1 1 2 1 N SD: 19.3529 c. M: 32.4037 c. 18: 2 1 3 1 0 3 0 3 0 1 3 1 N SD: 18.2009 c. M:-31.4741 c. 19: 2 1 3 1 1 2 1 2 1 1 3 1 N SD: 10.5419 c. M: 21.6057 c. 24: 3 1 4 1 1 3 1 3 1 1 4 1 N SD: 11.7163 c. M:-19.5513 c. 26: 3 1 4 2 1 3 1 3 1 2 4 1 N SD: 10.4855 c. M:-21.9112 c. 27: 3 1 5 1 1 4 0 4 1 1 5 1 N SD: 9.1654 c. M: 13.9863 c. 33: 4 1 6 1 2 4 1 4 1 2 6 1 N SD: 9.2689 c. M:-13.6863 c. 34: 4 1 6 2 1 5 0 5 1 2 6 1 N SD: 8.9754 c. M:-17.4036 c. 37: 4 2 6 2 1 5 1 5 1 2 6 2 N SD: 8.1230 c. M: 16.0945 c. 39: 4 2 7 2 1 5 1 5 2 2 6 2 N SD: 8.3116 c. M:-13.6863 c. 41: 4 2 7 2 2 5 1 5 2 2 7 2 N SD: 9.4961 c. M: 16.1644 c. 42: 5 1 8 2 1 6 1 5 2 2 7 2 N SD: 8.1309 c. M:-13.6863 c. 43: 5 2 7 2 2 5 1 6 2 2 7 2 N SD: 7.2214 c. M:-12.9451 c. 44: 5 2 7 2 2 6 1 6 1 3 7 2 N SD: 7.3588 c. M: 12.9110 c. 46: 5 2 8 2 2 6 1 6 2 2 8 2 N SD: 3.6912 c. M: 8.1892 c. 53: 6 2 9 3 2 7 1 7 2 3 9 2 N SD: 2.4111 c. M:-3.6238 c. 72: 8 3 12 4 3 9 2 9 3 4 12 3 N SD: 1.9530 c. M: 3.1846 c. 99: 11 4 17 5 4 13 2 13 4 5 17 4 N SD: 1.0940 c. M: 1.8651 c. 152: 17 6 26 8 6 20 3 20 6 8 26 6 N SD: 1.0869 c. M:-2.0785 c. 171: 19 7 29 9 7 22 4 22 7 9 29 7 N SD: 0.2460 c. M: 0.5530 c. 395: 44 16 67 21 16 51 9 51 16 21 67 16 N SD: 0.2978 c. M:-0.5285 c. 441: 49 18 75 23 18 57 10 57 18 23 75 18 N SD: 0.1795 c. M: 0.3808 c. 612: 68 25 104 32 25 79 14 79 25 32 104 25 N SD: 0.1536 c. M: 0.2608 c. 665: 74 27 113 35 27 86 15 86 27 35 113 27 N SD: 0.1507 c. M:-0.2963 c. 836: 93 34 142 44 34 108 19 108 34 44 142 34 N SD: 0.1276 c. M:-0.2552 c. 1007: 112 41 171 53 41 130 23 130 41 53 171 41 N SD: 0.1266 c. M:-0.2282 c. 1106: 123 45 188 58 45 143 25 143 45 58 188 45 N SD: 0.1257 c. M:-0.2505 c. 1277: 142 52 217 67 52 165 29 165 52 67 217 52 N SD: 0.1147 c. M:-0.2029 c. 1448: 161 59 246 76 59 187 33 187 59 76 246 59 N SD: 0.1138 c. M:-0.1878 c. 1677: 186 69 285 88 68 217 38 216 69 88 285 68 N SD: 0.0931 c. M: 0.1428 c. 1848: 205 76 314 97 75 239 42 238 76 97 314 75 N SD: 0.0747 c. M: 0.1276 c. 1947: 216 80 331 102 79 252 44 251 80 102 331 79 N SD: 0.0741 c. M:-0.1282 c. 2019: 224 83 343 106 82 261 46 260 83 106 343 82 N SD: 0.0651 c. M: 0.1257 c. 2118: 235 87 360 111 86 274 48 273 87 111 360 86 N SD: 0.0533 c. M: 0.0931 c. 2289: 254 94 389 120 93 296 52 295 94 120 389 93 N SD: 0.0396 c. M: 0.0790 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 10.7531 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.0000 cents 4 x x 5 x x x 6 x x 7 x 8 S SD: 7.6036 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 24.8117 cents 6 x 7 x x 8 x 9 x 10 x x 12 S SD: 17.4324 cents 7 x 8 x 9 x 10 x 11 x 12 x 14 S SD: 13.7769 cents 8 x 9:10 x 11 x 12:13 x 14 x 16 S SD: 9.3176 cents 9 x 10:11 x 12:13 x x 15:16 x 18 SD: 9.2214 cents 10 x 11 x 13 x x 15:16 x 17:19:20 SD: 8.6626 cents 11:12 x 14 x 15:16 x 18 x 19:21:22 SD: 8.0262 cents 12:13 x 15 x 16 x 18:19:20:21:23:24 SD: 6.2311 cents 13:14 x 16:17 x 19 x 21:22 x 25:26 SD: 5.6980 cents 14:15:16 x 18:19:20:21:23 x 24:27:28 SD: 8.0231 cents 15:16:17:19 x 20:22 x 24:25:26:29:30 SD: 5.3351 cents 16:17:18:20:21 x 23:24:26:27:28:31:32 SD: 5.6039 cents 17:18:19:21:22:23 x 25 x 28:29:33:34 SD: 5.8755 cents 18:19:20 x 23:24:26:27:29:30:31:35:36 SD: 5.0268 cents 19 x 21:24 x 25 x 28:31:32:33:37:38 SD: 4.4166 cents 20 x 22:25:26:27:29:30:32:33:35:39:40 SD: 4.6380 cents 21:23 x 26:27:28 x 31:34:35:36:41:42 SD: 3.6806 cents 22:24 x 28 x 29:32:33:36:37:38:43:44 SD: 5.2726 cents 23:25:26:29:30:31 x 34:37:38:40:45:46 SD: 4.3826 cents 24:26:27:30:31:32:35:36:39:40:41:47:48 SD: 3.3132 cents 27:29:30:34:35:36:39:40:44:45:47:53:54 SD: 2.7065 cents 28:30:31:35:36:37:41 x 45:47:48:54:56 SD: 3.4804 cents 29:31:32:36:38:39:42:43:47:48:50:56:58 SD: 3.3581 cents 30:32:33:38:39:40:44 x 49:50:52:58:60 SD: 3.7888 cents 31:33:34:39:40:41:45:46:50:52:54:60:62 SD: 3.7406 cents 32:35:36:40:41:43:47 x 52:53:55:62:64 SD: 4.0274 cents 33:36:37:41:43:44:48:49:53:55:57:64:66 SD: 2.6621 cents 34:37:38:43:44:45 x 50:55:57:59:66:68 SD: 3.1314 cents 35:38:39:44:45:47:51:52:57:58:60:68:70 SD: 2.5954 cents 36:39:40:45:47:48 x 53:58:60:62:70:72 SD: 1.8790 cents 37:40:41:46:48:49:54:55:60:62:64:72:74 SD: 1.6290 cents 48:52:53:60:62:64:70:71:78:80:83:93:96 SD: 1.3422 cents 63:68:70:79:82:84:92:93:102:105:109:123:126 SD: 1.1139 cents 72:78:80:90:93:96:105:107:117:120:124:140:144 SD: 1.0634 cents 81:87:90:101:105:108:118:120:131:135:140:158:162 SD: 1.0239 cents 87:94:97:109:113:116:127:129:141:145:150:169:174 SD: 0.7918 cents 100:108:111:125:130:133:146:148:162:167:173:194:200 SD: 0.7607 cents 108:117:120:135:140:144:158:160:175:180:187:210:216 SD: 0.6885 cents 111:120:123:139:144:148:162:164:180:185:192:216:222 SD: 0.6809 cents 124:134:138:155:161:165:181:184:201:207:214:241:248 SD: 0.6202 cents 129:139:143:161:167:172:188:191:209:215:223:251:258 SD: 0.5796 cents 135:146:150:169:175:180:197:200:219:225:233:263:270 SD: 0.5001 cents 162:175:180:203:210:216:236:240:262:270:280:315:324 SD: 0.4578 cents 179:193:199:224:232:239:261:265:290:298:309:348:358 SD: 0.4471 cents 189:204:210:236:245:252:276:280:306:315:327:368:378 SD: 0.3692 cents 199:215:221:249:258:265:290:295:322:332:344:387:398 SD: 0.3636 cents 216:233:240:270:280:288:315:320:350:360:373:420:432 SD: 0.2184 cents 324:350:360:405:420:432:473:480:525:540:560:630:648 SD: 0.1596 cents 432:467:480:540:560:576:630:640:700:720:747:840:864 SD: 0.1540 cents 476:514:529:595:617:635:694:705:771:793:823:926:952 SD: 0.1460 cents 486:525:540:608:630:648:709:720:787:810:840:945:972 SD: 0.1456 cents 513:554:570:641:665:684:748:760:831:855:887:998:1026 SD: 0.1101 cents 600:648:667:750:778:800:875:889:972:1000:1037:1167:1200 SD: 0.0946 cents