Scala analysis: bree3
Third breed ball around 49/40-7/4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 49/48 35.696812 slendro diesis, septimal 1/6-tone 2: 21/20 84.467193 minor semitone 3: 15/14 119.442808 major diatonic semitone 4: 49/40 351.338099 larger approximation to neutral third 5: 5/4 386.313714 major third 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 10/7 617.487807 Euler's tritone 8: 3/2 701.955001 perfect fifth 9: 49/32 737.651813 10: 12/7 933.129094 septimal major sixth 11: 7/4 968.825906 harmonic seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 4: 343/300 231.8953 5: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 6: 28/25 196.1985 middle second 7: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 8: 21/20 84.4672 minor semitone 9: 49/48 35.6968 slendro diesis, septimal 1/6-tone 10: 384/343 195.4773 11: 49/48 35.6968 slendro diesis, septimal 1/6-tone 12: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 3 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 21/20 84.467 cents minor semitone 1: 1 384/343 195.477 cents 1: 1 28/25 196.198 cents middle second 1: 1 8/7 231.174 cents septimal whole tone 1: 1 343/300 231.895 cents 2: 1 360/343 83.746 cents 2: 1 21/20 84.467 cents minor semitone 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 343/320 120.164 cents 2: 4 8/7 231.174 cents septimal whole tone 2: 4 7/6 266.871 cents septimal minor third 3: 1 15/14 119.443 cents major diatonic semitone 3: 1 35/32 155.140 cents septimal neutral second 3: 1 400/343 266.150 cents 3: 1 7/6 266.871 cents septimal minor third 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 1 343/288 302.568 cents 3: 4 6/5 315.641 cents minor third 3: 1 64/49 462.348 cents 2 septatones or septatonic major third 3: 1 98/75 463.069 cents 4: 4 60/49 350.617 cents smaller approximation to neutral third 4: 4 49/40 351.338 cents larger approximation to neutral third 4: 4 4/3 498.045 cents perfect fourth 5: 4 5/4 386.314 cents major third 5: 1 200/147 533.021 cents 5: 1 49/36 533.742 cents Arabic lute acute fourth 5: 3 48/35 546.815 cents septimal semi-augmented fourth 5: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 3 480/343 581.791 cents 6: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 3 10/7 617.488 cents Euler's tritone 6: 3 343/240 618.209 cents 7: 3 10/7 617.488 cents Euler's tritone 7: 3 35/24 653.185 cents septimal semi-diminished fifth 7: 1 72/49 666.258 cents Arabic lute grave fifth 7: 1 147/100 666.979 cents 7: 4 8/5 813.686 cents minor sixth 8: 4 3/2 701.955 cents perfect fifth 8: 4 80/49 848.662 cents smaller approximation to neutral sixth 8: 4 49/30 849.383 cents larger approximation to neutral sixth 9: 1 75/49 736.931 cents BP fifth 9: 1 49/32 737.652 cents 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 576/343 897.432 cents 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 1 12/7 933.129 cents septimal major sixth 9: 1 343/200 933.850 cents 9: 1 64/35 1044.860 cents septimal neutral seventh 9: 1 28/15 1080.557 cents grave major seventh 10: 4 12/7 933.129 cents septimal major sixth 10: 4 7/4 968.826 cents harmonic seventh 10: 1 640/343 1079.836 cents 10: 1 28/15 1080.557 cents grave major seventh 10: 1 40/21 1115.533 cents acute major seventh 10: 1 343/180 1116.254 cents 11: 1 600/343 968.105 cents 11: 1 7/4 968.826 cents harmonic seventh 11: 1 25/14 1003.802 cents middle minor seventh 11: 1 343/192 1004.523 cents 11: 1 40/21 1115.533 cents acute major seventh 11: 1 35/18 1151.230 cents septimal semi-diminished octave 11: 3 96/49 1164.303 cents 11: 3 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 35.7 84.5 119.4 351.3 386.3 582.5 617.5 702.0 737.7 933.1 968.8 1200.0 35.7 : 48.8 83.7 315.6 350.6 546.8 581.8 666.3 702.0 897.4 933.1 1164.3 1200.0 84.5 : 35.0 266.9 301.8 498.0 533.0 617.5 653.2 848.7 884.4 1115.5 1151.2 1200.0 119.4 : 231.9 266.9 463.1 498.0 582.5 618.2 813.7 849.4 1080.6 1116.3 1165.0 1200.0 351.3 : 35.0 231.2 266.1 350.6 386.3 581.8 617.5 848.7 884.4 933.1 968.1 1200.0 386.3 : 196.2 231.2 315.6 351.3 546.8 582.5 813.7 849.4 898.2 933.1 1165.0 1200.0 582.5 : 35.0 119.4 155.1 350.6 386.3 617.5 653.2 702.0 736.9 968.8 1003.8 1200.0 617.5 : 84.5 120.2 315.6 351.3 582.5 618.2 667.0 702.0 933.9 968.8 1165.0 1200.0 702.0 : 35.7 231.2 266.9 498.0 533.7 582.5 617.5 849.4 884.4 1080.6 1115.5 1200.0 737.7 : 195.5 231.2 462.3 498.0 546.8 581.8 813.7 848.7 1044.9 1079.8 1164.3 1200.0 933.1 : 35.7 266.9 302.6 351.3 386.3 618.2 653.2 849.4 884.4 968.8 1004.5 1200.0 968.8 : 231.2 266.9 315.6 350.6 582.5 617.5 813.7 848.7 933.1 968.8 1164.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 231.8953 cents 16807/15000, 196.9197 cents 50/49, 34.9756 cents 2: 83.7460 .. 266.8709 cents 2401/2160, 183.1249 cents 108000/117649,-148.1493 cents 3: 119.4428 .. 463.0694 cents 1372/1125, 343.6266 cents 45/49,-147.4281 cents 4: 350.6169 .. 498.0450 cents 49/45, 147.4281 cents 2250/2401,-112.4525 cents 5: 386.3137 .. 582.5122 cents 28/25, 196.1985 cents 15/16,-111.7313 cents 6: 581.7910 .. 618.2090 cents 117649/115200, 36.4180 cents 2400/2401,-0.7212 cents 7: 617.4878 .. 813.6863 cents 28/25, 196.1985 cents 2400/2401,-0.7212 cents 8: 701.9550 .. 849.3831 cents 49/45, 147.4281 cents 15/16,-111.7313 cents 9: 736.9306 .. 1080.5572 cents 1372/1125, 343.6266 cents 2250/2401,-112.4525 cents 10: 933.1291 .. 1116.2540 cents 2401/2160, 183.1249 cents 45/49,-147.4281 cents 11: 968.1047 .. 1165.0244 cents 16807/15000, 196.9197 cents 108000/117649,-148.1493 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 343/300, 231.8953 cents Average / Smallest step : 2.859135 Largest / Average step : 2.318953 Largest / Smallest step : 6.630199 Median interval of one step : 42.23360 cents, amount: 0 Least squares average step : 89.78500 cents, oct.: 1077.42001 cents Scale is not proper Step pattern alph. order: ABCDCECFAGAH Step pattern size order : BCAHAFADBEBG Scale is not a Constant Structure Scale diversity : 1.382939 Lumma stability : 0.058293 Lumma impropriety factor : 0.552124 Rothenberg efficiency : 0.281409 redundancy: 0.718591 Efficiency x scale size : 3.376912 Number of different interval sizes : 56 = 5.09091 / class Number of one step interval sizes : 8 Highest interval variety : 9 Mean interval variety : 6.00000 = 6 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 6 Most common triad is 0.0 582.512 617.488 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 5 7 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 25.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Limited inverse transpositions with margin 343.6266 cents: 3 -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.017860 Average absolute harmonicity : 0.155139 Specific harmonicity : 0.096618 Fundamental : 1/3360, -11.7142 octaves, 0.0779 Hz. Guide tone : 2940, 11.5216 octaves, 769179.162 Hz. Exponens Consonantiae : 9.878400E+06, 23.23585 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 206.5, average 17.20833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.12538, average 1.01045 Sum of Tenney's harmonic distance : 23.94532, average 1.99544 Vogel's harmonic complexity : 22.91667 Wille's k value : 2572 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 251.09930, average 3.21922 Lattice compactness (without 2's) : 147.79869, average 1.89485 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.33333 24 1 3: -1 .. 1 0.25000 5 1 5: -1 .. 1 0.00000 6 1 7: -1 .. 2 0.50000 12 9 Average exponent except 2's : 9 / 12 = 0.75000 Average absolute exponent except 2's: 23 / 12 = 1.91667 Scale is weakly epimorphic with val: <12 20 26 33| Scale is weakly epimorphic with val: <12 20 28 31| Scale is weakly epimorphic with val: <12 20 28 33| Scale is weakly epimorphic with val: <12 20 28 35| Scale is weakly epimorphic with val: <12 20 28 37| Scale is weakly epimorphic with val: <12 20 30 35|
FIT/MODE
12: 0 1 0 2 1 2 0 1 0 2 1 2 N B D3 SD: 27.1093 c. M: 51.3381 c. 14: 0 1 0 3 0 3 0 1 0 3 0 3 N B SD: 26.9502 c. M: 51.9375 c. 15: 0 1 0 3 1 2 1 1 0 3 0 3 N SD: 23.2201 c. M: 39.4428 c. 16: 0 1 1 3 0 3 0 1 1 2 1 3 N SD: 21.6254 c. M: 35.6968 c. 17: 0 1 1 3 0 3 1 1 0 3 1 3 N SD: 21.0769 c. M: 35.6968 c. 19: 1 0 1 4 0 3 1 1 1 3 0 4 N SD: 17.3064 c. M:-27.6093 c. 21: 1 0 1 4 1 3 1 1 1 3 1 4 N G SD: 14.1150 c. M: 27.3243 c. 24: 1 1 0 5 1 4 0 2 1 4 0 5 N SD: 14.2008 c. M: 19.4428 c. 25: 1 1 0 5 1 4 1 2 0 4 1 5 N SD: 13.9072 c. M: 23.4428 c. 26: 1 1 1 5 0 5 0 2 1 4 1 5 N SD: 12.7511 c. M:-19.0187 c. 27: 1 1 1 5 1 4 1 2 1 4 1 5 N SD: 9.2354 c. M:-17.9037 c. 28: 1 1 1 5 1 5 0 2 1 5 1 5 N SD: 11.3511 c. M:-17.4878 c. 31: 1 1 1 6 1 5 1 2 1 5 1 6 N SD: 3.3606 c. M: 7.0478 c. 41: 1 2 1 8 1 7 1 3 1 7 1 8 N SD: 3.7044 c. M: 6.4285 c. 68: 2 3 2 13 2 11 2 5 2 11 2 13 N SD: 2.4667 c. M:-4.0866 c. 72: 2 3 2 14 2 12 2 5 2 12 2 14 N SD: 2.1169 c. M: 4.3185 c. 99: 3 4 3 19 3 16 3 7 3 16 3 19 N SD: 1.0065 c. M:-1.7693 c. 130: 4 5 4 25 4 21 4 9 4 21 4 25 N SD: 0.8914 c. M: 1.3903 c. 140: 4 6 4 27 4 23 4 10 4 23 4 27 N SD: 0.7604 c. M: 1.4111 c. 171: 5 7 5 33 5 28 5 12 5 28 5 33 N SD: 0.3763 c. M: 0.8097 c. 270: 8 11 8 52 8 44 8 19 8 44 8 52 N SD: 0.2595 c. M:-0.5572 c. 441: 13 18 13 85 13 72 13 31 13 72 13 85 N SD: 0.2050 c. M: 0.3227 c. 935: 28 38 27 181 27 153 27 66 28 152 28 180 N SD: 0.1855 c. M:-0.3197 c. 966: 29 39 28 187 28 158 28 68 29 157 29 186 N SD: 0.1660 c. M:-0.3280 c. 1007: 30 41 29 195 29 165 29 71 30 164 30 194 N SD: 0.1534 c. M: 0.2770 c. 1038: 31 42 30 201 30 170 30 73 31 169 31 200 N SD: 0.1682 c. M: 0.3677 c. 1106: 33 45 32 214 32 181 32 78 33 180 33 213 N SD: 0.1118 c. M:-0.1990 c. 1137: 34 46 33 220 33 186 33 80 34 185 34 219 N SD: 0.1061 c. M:-0.1871 c. 1277: 38 52 37 247 37 209 37 90 38 208 38 246 N SD: 0.0734 c. M:-0.1106 c. 1308: 39 53 38 253 38 214 38 92 39 213 39 252 N SD: 0.0827 c. M: 0.1768 c. 1376: 41 56 40 266 40 225 40 97 41 224 41 265 N SD: 0.0759 c. M:-0.1389 c. 1407: 42 57 41 272 41 230 41 99 42 229 42 271 N SD: 0.0573 c. M:-0.1241 c. 1547: 46 63 45 299 45 253 45 109 46 252 46 298 N SD: 0.0383 c. M:-0.0835 c. 1578: 47 64 46 305 46 258 46 111 47 257 47 304 N SD: 0.0333 c. M: 0.0565 c. 1848: 55 75 54 357 54 302 54 130 55 301 55 356 N SD: 0.0326 c. M: 0.0516 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 x 3 x x x 4 S SD: 0.0000 cents 3 x x x x x 4 x x x 5 x 6 S SD: 32.5120 cents 4 x x x x 5 x x 6 x x 7:8 S SD: 0.0000 cents 5 x x x 6 x 7 x x 8 x 9:10 S SD: 19.4258 cents 6 x x x 7 x 8 x 9 x 10:11:12 S SD: 25.3499 cents 7 x x 8 x 9 x 10 x 11:12 x 14 S SD: 21.6494 cents 8 x x 9 x 10:11 x 12 x x 14:16 S SD: 15.0072 cents 9 x x 10:11 x x 13 x 14:15:16:18 SD: 12.9447 cents 10 x x 11:12:13:14 x 15 x 17:18:20 SD: 12.8385 cents 11 x x 12:13:14:15:16 x 17:19 x 22 SD: 12.0424 cents 12 x x 13 x 15 x 17:18 x x 21:24 SD: 3.9994 cents 13 x x 14:16 x 18:19 x 20:22:23:26 SD: 6.8394 cents 14 x x 15:17:18 x 20:21 x 24:25:28 SD: 7.7390 cents 15 x x 16:18:19:21 x x 23 x 26:30 SD: 6.6079 cents 16 x x 17 x 20:22:23:24:25:27:28:32 SD: 6.3498 cents 17 x 18 x 21 x 24 x x 26:29:30:34 SD: 4.3242 cents 18 x 19 x 22:23:25:26:27:28:31:32:36 SD: 6.0445 cents 19 x 20 x 23:24 x 27 x 29 x 33:38 SD: 4.6428 cents 20 x 21 x x 25:28:29:30:31:34:35:40 SD: 4.0341 cents 21 x 22:23 x 26:29:30 x 32:36:37:42 SD: 5.5656 cents 22 x 23:24:27:28:31 x 33:34:38:39:44 SD: 5.5351 cents 23 x 24:25:28:29:32:33 x 35:39:40:46 SD: 4.2911 cents 24 x 25:26:29:30 x 34:36:37:41:42:48 SD: 3.8763 cents 25 x 26:27 x 31:35:36 x 38:43:44:50 SD: 3.7547 cents 26 x 27:28:32:33:36:37:39:40:45:46:52 SD: 4.3771 cents 27 x 28:29:33:34:38:39 x 41:46:47:54 SD: 3.8949 cents 28 x 29:30:34:35:39:40:42:43:48:49:56 SD: 2.7236 cents 29:30 x 31 x 36:41 x x 44:50:51:58 SD: 4.6774 cents 30:31 x 32:37:38:42:43:45:46:51:53:60 SD: 3.7316 cents 31:32 x 33:38:39:43:44 x 47:53:54:62 SD: 3.7221 cents 32:33 x 34:39:40:45:46:48:49:55:56:64 SD: 2.5605 cents 33:34:35 x 40:41:46:47:50:51:57:58:66 SD: 3.9341 cents 34:35:36 x 42:43:48:49:51:52:58:60:68 SD: 3.8219 cents 35:36:37:38:43:44:49:50:53:54:60:61:70 SD: 3.1706 cents 36:37:38:39:44:45:50:51:54:55:62:63:72 SD: 2.7414 cents 39:40:41:42:48:49:55:56:59:60:67:68:78 SD: 2.4566 cents 40:41:42:43:49:50:56:57:60:61:69:70:80 SD: 1.3647 cents 56:57:59:60:69:70:78:80:84:86:96:98:112 SD: 1.3572 cents 80:82:84:86:98:100:112:114:120:123:137:140:160 SD: 1.0364 cents 84:86:88:90:103:105:118:120:126:129:144:147:168 SD: 0.8483 cents 96:98:101:103:118:120:134:137:144:147:165:168:192 SD: 0.8427 cents 98:100:103:105:120:123:137:140:147:150:168:172:196 SD: 0.7723 cents 100:102:105:107:123:125:140:143:150:153:171:175:200 SD: 0.7492 cents 124:127:130:133:152:155:174:177:186:190:213:217:248 SD: 0.7241 cents 128:131:134:137:157:160:179:183:192:196:219:224:256 SD: 0.7033 cents 136:139:143:146:167:170:190:194:204:208:233:238:272 SD: 0.6673 cents 137:140:144:147:168:171:192:196:206:210:235:240:274 SD: 0.6319 cents 140:143:147:150:172:175:196:200:210:214:240:245:280 SD: 0.4973 cents 156:159:164:167:191:195:218:223:234:239:267:273:312 SD: 0.4909 cents 182:186:191:195:223:228:255:260:273:279:312:319:364 SD: 0.4726 cents 192:196:202:206:235:240:269:274:288:294:329:336:384 SD: 0.4183 cents 196:200:206:210:240:245:274:280:294:300:336:343:392 SD: 0.2734 cents 240:245:252:257:294:300:336:343:360:368:411:420:480 SD: 0.2667 cents 280:286:294:300:343:350:392:400:420:429:480:490:560 SD: 0.1189 cents 476:486:500:510:583:595:666:680:714:729:816:833:952 SD: 0.1126 cents 480:490:504:514:588:600:672:686:720:735:823:840:960 SD: 0.1033 cents