Scala analysis: breed14_tuning_58799_58809
a 49/48 and 81/80 Fokker block in breed plane
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: 49/45 147.428097 BP minor semitone 3: 7/6 266.870906 septimal minor third 4: 49/40 351.338099 larger approximation to neutral third 5: 9/7 435.084095 septimal major third, BP third 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: 14/9 764.915905 septimal minor sixth 10: 49/30 849.383098 larger approximation to neutral sixth 11: 12/7 933.129094 septimal major sixth 12: 147/80 1053.293100 13: 343/180 1116.254004 14: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 360/343 83.7460 1: 21/20 84.4672 minor semitone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 15/14 119.4428 major diatonic semitone 4: 21/20 84.4672 minor semitone 5: 360/343 83.7460 6: 28/27 62.9609 Archytas' 1/3-tone 7: 21/20 84.4672 minor semitone 8: 15/14 119.4428 major diatonic semitone 9: 28/27 62.9609 Archytas' 1/3-tone 10: 21/20 84.4672 minor semitone 11: 360/343 83.7460 12: 343/320 120.1640 13: 28/27 62.9609 Archytas' 1/3-tone 14: 360/343 83.7460
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 28/27 62.961 cents Archytas' 1/3-tone 1: 3 360/343 83.746 cents 1: 4 21/20 84.467 cents minor semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 343/320 120.164 cents 2: 2 160/147 146.707 cents 2: 3 49/45 147.428 cents BP minor semitone 2: 3 54/49 168.213 cents Zalzal's mujannab 2: 2 10/9 182.404 cents minor whole tone 2: 1 2401/2160 183.125 cents 2: 3 9/8 203.910 cents major whole tone 3: 5 8/7 231.174 cents septimal whole tone 3: 7 7/6 266.871 cents septimal minor third 3: 1 405/343 287.656 cents 3: 1 189/160 288.377 cents 4: 1 32/27 294.135 cents Pythagorean minor third 4: 1 6/5 315.641 cents minor third 4: 1 98/81 329.832 cents 4: 6 60/49 350.617 cents smaller approximation to neutral third 4: 5 49/40 351.338 cents larger approximation to neutral third 5: 3 80/63 413.578 cents wide major third 5: 3 343/270 414.299 cents 5: 7 9/7 435.084 cents septimal major third, BP third 5: 1 21/16 470.781 cents narrow fourth 6: 8 4/3 498.045 cents perfect fourth 6: 1 3240/2401 518.830 cents 6: 1 27/20 519.551 cents acute fourth 6: 2 49/36 533.742 cents Arabic lute acute fourth 6: 1 135/98 554.527 cents 6: 1 441/320 555.248 cents 7: 3 480/343 581.791 cents 7: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 4 10/7 617.488 cents Euler's tritone 7: 3 343/240 618.209 cents 8: 1 640/441 644.752 cents 8: 1 196/135 645.473 cents 8: 2 72/49 666.258 cents Arabic lute grave fifth 8: 1 40/27 680.449 cents grave fifth 8: 1 2401/1620 681.170 cents 8: 8 3/2 701.955 cents perfect fifth 9: 1 32/21 729.219 cents wide fifth 9: 7 14/9 764.916 cents septimal minor sixth 9: 3 540/343 785.701 cents 9: 3 63/40 786.422 cents narrow minor sixth 10: 5 80/49 848.662 cents smaller approximation to neutral sixth 10: 6 49/30 849.383 cents larger approximation to neutral sixth 10: 1 81/49 870.168 cents two (septimal major third, BP third) 10: 1 5/3 884.359 cents major sixth, BP sixth 10: 1 27/16 905.865 cents Pythagorean major sixth 11: 1 320/189 911.623 cents 11: 1 686/405 912.344 cents 11: 7 12/7 933.129 cents septimal major sixth 11: 5 7/4 968.826 cents harmonic seventh 12: 3 16/9 996.090 cents Pythagorean minor seventh 12: 1 4320/2401 1016.875 cents 12: 2 9/5 1017.596 cents just minor seventh, BP seventh 12: 3 49/27 1031.787 cents 12: 3 90/49 1052.572 cents 12: 2 147/80 1053.293 cents 13: 1 640/343 1079.836 cents 13: 2 28/15 1080.557 cents grave major seventh 13: 4 40/21 1115.533 cents acute major seventh 13: 3 343/180 1116.254 cents 13: 4 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.92308 = 64/13
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 84.5 147.4 266.9 351.3 435.1 498.0 582.5 702.0 764.9 849.4 933.1 1053.3 1116.3 1200.0 84.5 : 63.0 182.4 266.9 350.6 413.6 498.0 617.5 680.4 764.9 848.7 968.8 1031.8 1115.5 1200.0 147.4 : 119.4 203.9 287.7 350.6 435.1 554.5 617.5 702.0 785.7 905.9 968.8 1052.6 1137.0 1200.0 266.9 : 84.5 168.2 231.2 315.6 435.1 498.0 582.5 666.3 786.4 849.4 933.1 1017.6 1080.6 1200.0 351.3 : 83.7 146.7 231.2 350.6 413.6 498.0 581.8 702.0 764.9 848.7 933.1 996.1 1115.5 1200.0 435.1 : 63.0 147.4 266.9 329.8 414.3 498.0 618.2 681.2 764.9 849.4 912.3 1031.8 1116.3 1200.0 498.0 : 84.5 203.9 266.9 351.3 435.1 555.2 618.2 702.0 786.4 849.4 968.8 1053.3 1137.0 1200.0 582.5 : 119.4 182.4 266.9 350.6 470.8 533.7 617.5 702.0 764.9 884.4 968.8 1052.6 1115.5 1200.0 702.0 : 63.0 147.4 231.2 351.3 414.3 498.0 582.5 645.5 764.9 849.4 933.1 996.1 1080.6 1200.0 764.9 : 84.5 168.2 288.4 351.3 435.1 519.6 582.5 702.0 786.4 870.2 933.1 1017.6 1137.0 1200.0 849.4 : 83.7 203.9 266.9 350.6 435.1 498.0 617.5 702.0 785.7 848.7 933.1 1052.6 1115.5 1200.0 933.1 : 120.2 183.1 266.9 351.3 414.3 533.7 618.2 702.0 764.9 849.4 968.8 1031.8 1116.3 1200.0 1053.3: 63.0 146.7 231.2 294.1 413.6 498.0 581.8 644.8 729.2 848.7 911.6 996.1 1079.8 1200.0 1116.3: 83.7 168.2 231.2 350.6 435.1 518.8 581.8 666.3 785.7 848.7 933.1 1016.9 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 120.1640 cents 1323/1280, 57.2031 cents 28/27, 62.9609 cents 2: 146.7069 .. 203.9100 cents 1323/1280, 57.2031 cents 51200/50421, 26.5429 cents 3: 231.1741 .. 288.3772 cents 1323/1280, 57.2031 cents 64/63, 27.2641 cents 4: 294.1350 .. 351.3381 cents 1323/1280, 57.2031 cents 5120/5103, 5.7578 cents 5: 413.5778 .. 470.7809 cents 1323/1280, 57.2031 cents 3200/3087, 62.2397 cents 6: 498.0450 .. 555.2481 cents 1323/1280, 57.2031 cents 64/63, 27.2641 cents 7: 581.7910 .. 618.2090 cents 117649/115200, 36.4180 cents 51200/50421, 26.5429 cents 8: 644.7519 .. 701.9550 cents 1323/1280, 57.2031 cents 51200/50421, 26.5429 cents 9: 729.2191 .. 786.4222 cents 1323/1280, 57.2031 cents 64/63, 27.2641 cents 10: 848.6619 .. 905.8650 cents 1323/1280, 57.2031 cents 3200/3087, 62.2397 cents 11: 911.6228 .. 968.8259 cents 1323/1280, 57.2031 cents 5120/5103, 5.7578 cents 12: 996.0900 .. 1053.2931 cents 1323/1280, 57.2031 cents 64/63, 27.2641 cents 13: 1079.8360 .. 1137.0391 cents 1323/1280, 57.2031 cents 51200/50421, 26.5429 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 85.7143 cents Largest one step interval : 343/320, 120.1640 cents Average / Smallest step : 1.361389 Largest / Average step : 1.401913 Largest / Smallest step : 1.908550 Median interval of one step : 84.10659 cents, amount: 0 Least squares average step : 85.74928 cents, oct.: 1200.48990 cents Scale is strictly proper Step pattern alph. order: ABCADBACBADEBD Step pattern size order : CADCBACDACBEAB Scale is a Constant Structure, by a margin of 5.75780 cents Scale diversity : 1.364025 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.397621 Number of different interval sizes : 64 = 4.92308 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 4.92308 = 64/13 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 8 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 8, average 701.9550 cents Scale contains a complete diamond : 3 7 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 50.0000% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 2401 (O: 2401 U: 2401) Highest odd numerator or denominator: 343 Scale harmonicity : 0.015574 Average absolute harmonicity : 0.143259 Specific harmonicity : 0.091455 Fundamental : 1/5040, -12.2992 octaves, 0.0519 Hz. Guide tone : 12348, 13.5920 octaves, 3230552.480 Hz. Exponens Consonantiae : 6.223392E+07, 25.89120 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 575.5, average 41.10714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 16.49344, average 1.17810 Sum of Tenney's harmonic distance : 32.43688, average 2.31692 Vogel's harmonic complexity : 24.78571 Wille's k value : 4630 Wilson's harmonic complexity : 45 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 343.64535, average 3.27281 Lattice compactness (without 2's) : 244.52169, average 2.32878 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.57143 20 1 3: -2 .. 2 -0.21429 15 2 5: -1 .. 0 -0.50000 7 7: -1 .. 3 0.92857 17 11 Average exponent except 2's : 3 / 14 = 0.21429 Average absolute exponent except 2's: 39 / 14 = 2.78571 Scale is weakly epimorphic with val: <14 20 31 38| Scale is weakly epimorphic with val: <14 20 33 38| Scale is weakly epimorphic with val: <14 20 35 38| Scale is JI-epimorphic with val: <14 22 32 39| Scale is weakly epimorphic with val: <14 24 31 40| Scale is weakly epimorphic with val: <14 24 33 40| Scale is weakly epimorphic with val: <14 24 35 40|
FIT/MODE
14: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 13.1806 c. M: 24.7217 c. 17: 1 1 2 1 1 1 1 2 1 1 1 2 1 1 P M ME SD: 10.4803 c. M: 17.8063 c. 24: 2 1 2 2 2 1 2 2 1 2 2 2 1 2 P B ME I SD: 11.5040 c. M:-17.4878 c. 27: 2 1 3 2 2 1 2 3 1 2 2 3 1 2 N D3 SD: 7.7048 c. M: 14.0948 c. 31: 2 2 3 2 2 2 2 3 2 2 2 3 2 2 SP M ME SD: 5.8998 c. M: 9.2776 c. 41: 3 2 4 3 3 2 3 4 2 3 3 4 2 3 P D3 SD: 2.5755 c. M: 4.0589 c. 58: 4 3 6 4 4 3 4 6 3 4 4 6 3 4 P SD: 1.6855 c. M: 3.2018 c. 72: 5 4 7 5 5 4 5 7 4 5 5 7 4 5 SP SD: 1.5950 c. M: 3.2931 c. 99: 7 5 10 7 7 5 7 10 5 7 7 10 5 7 P SD: 0.9934 c. M: 1.9736 c. 113: 8 6 11 8 8 6 8 11 6 8 8 11 6 8 SP SD: 1.0920 c. M: 1.9657 c. 130: 9 7 13 9 9 7 9 13 7 9 9 13 7 9 SP SD: 0.8228 c. M: 1.3903 c. 171: 12 9 17 12 12 9 12 17 9 12 12 17 9 12 SP SD: 0.2891 c. M: 0.6615 c. 400: 28 21 40 28 28 21 28 40 21 28 28 40 21 28 SP SD: 0.2837 c. M: 0.5122 c. 571: 40 30 57 40 40 30 40 57 30 40 40 57 30 40 SP SD: 0.2590 c. M: 0.4041 c. 742: 52 39 74 52 52 39 52 74 39 52 52 74 39 52 SP SD: 0.2548 c. M: 0.4629 c. 877: 62 46 87 62 61 46 62 87 46 62 61 88 46 61 SP SD: 0.2375 c. M:-0.3840 c. 935: 66 49 93 66 65 49 66 93 49 66 65 94 49 65 SP SD: 0.1997 c. M:-0.3967 c. 1007: 71 53 100 71 70 53 71 100 53 71 70 101 53 70 SP SD: 0.1826 c. M:-0.3375 c. 1048: 74 55 104 74 73 55 74 104 55 74 73 105 55 73 SP SD: 0.1694 c. M:-0.3122 c. 1106: 78 58 110 78 77 58 78 110 58 78 77 111 58 77 SP SD: 0.1272 c. M:-0.2331 c. 1236: 87 65 123 87 86 65 87 123 65 87 86 124 65 86 SP SD: 0.1166 c. M:-0.2509 c. 1277: 90 67 127 90 89 67 90 127 67 90 89 128 67 89 SP SD: 0.0767 c. M:-0.1133 c. 1448: 102 76 144 102 101 76 102 144 76 102 101 145 76 101 SP SD: 0.0452 c. M:-0.0857 c. 1619: 114 85 161 114 113 85 114 161 85 114 113 162 85 113 SP SD: 0.0384 c. M:-0.0704 c. 1677: 118 88 167 118 117 88 118 167 88 118 117 168 88 117 SP SD: 0.0238 c. M: 0.0435 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: 11.6585 cents 4 x x x 5 x x x 6 x x 7 x x 8 S SD: 12.4939 cents 5 x x x 6 x x 7 x x 8 x 9 x 10 S SD: 12.3657 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 5.8660 cents 7 x x 8 x 9 x 10 x 11 x 12:13 x 14 S SD: 8.0119 cents 8 x 9 x 10 x x 11:12 x 13:14 x 15:16 S SD: 10.8415 cents 9 x 10 x 11 x 12:13 x 14:15 x x 17:18 SD: 9.3714 cents 10 x 11 x 12:13 x 14:15 x 16:17:18:19:20 S SD: 6.8797 cents 11 x 12:13 x 14:15 x x 17:18:19:20:21:22 SD: 5.4637 cents 12 x 13:14:15 x 16:17:18:19:20:21:22:23:24 S SD: 6.0523 cents 13 x 14:15:16:17 x 18 x 20:21:22:24:25:26 S SD: 5.4342 cents 14 x 15:16:17:18:19:20:21:22:23:24:26:27:28 S SD: 5.7729 cents 15:16 x x 18:19:20:21 x 23:25:26:28:29:30 SD: 7.1963 cents 16:17 x 19:20 x 21:22:24:25:26:27:29:30:32 SD: 6.7316 cents 17:18:19:20:21:22:23:24 x 26:28:29:31:32:34 SD: 5.6579 cents 18:19:20:21:22:23:24:25:27:28:29:31:33:34:36 SD: 3.5718 cents 22:23:24:26:27:28:29:31:33:34:36:38:40:42:44 SD: 3.2382 cents 24:25:26:28:29:31:32:34:36:37:39:41:44:46:48 SD: 3.0198 cents 32:34:35:37:39:41:43:45:48:50:52:55:59:61:64 SD: 2.5446 cents 35:37:38:41:43:45:47:49:53:54:57:60:64:67:70 SD: 2.2815 cents 36:38:39:42:44:46:48:50:54:56:59:62:66:69:72 SD: 1.8868 cents 42:44:46:49:51:54:56:59:63:65:69:72:77:80:84 SD: 1.7177 cents 54:57:59:63:66:69:72:76:81:84:88:93:99:103:108 SD: 1.4803 cents 60:63:65:70:74:77:80:84:90:93:98:103:110:114:120 SD: 1.2609 cents 66:69:72:77:81:85:88:92:99:103:108:113:121:126:132 SD: 1.0454 cents 78:82:85:91:96:100:104:109:117:121:127:134:143:149:156 SD: 1.0266 cents 80:84:87:93:98:103:107:112:120:124:131:137:147:152:160 SD: 0.9170 cents 98:103:107:114:120:126:131:137:147:152:160:168:180:187:196 SD: 0.7452 cents 102:107:111:119:125:131:136:143:153:159:167:175:187:194:204 SD: 0.6068 cents 120:126:131:140:147:154:160:168:180:187:196:206:221:229:240 SD: 0.5838 cents 137:144:149:160:168:176:183:192:206:213:224:235:252:261:274 SD: 0.5322 cents 155:163:169:181:190:199:207:217:233:241:253:266:285:295:310 SD: 0.5300 cents 156:164:170:182:191:201:208:218:234:243:255:267:287:297:312 SD: 0.5197 cents 158:166:172:184:194:203:211:221:237:246:258:271:290:301:316 SD: 0.4852 cents 160:168:174:187:196:206:213:224:240:249:261:274:294:305:320 SD: 0.4325 cents 168:176:183:196:206:216:224:235:252:261:274:288:309:320:336 SD: 0.4253 cents 178:187:194:208:218:229:237:249:267:277:291:305:327:339:356 SD: 0.3572 cents 200:210:218:233:245:257:267:280:300:311:327:343:368:381:400 SD: 0.3547 cents 204:214:222:238:250:262:272:286:306:317:333:350:375:389:408 SD: 0.3342 cents 234:246:255:273:287:301:312:328:351:364:382:401:430:446:468 SD: 0.2968 cents 245:257:267:286:300:315:327:343:368:381:400:420:450:467:490 SD: 0.2916 cents 258:271:281:301:316:332:344:361:387:401:421:442:474:492:516 SD: 0.2428 cents 294:309:320:343:360:378:392:412:441:457:480:504:540:560:588 SD: 0.2242 cents 336:353:366:392:412:432:448:470:504:523:549:576:617:640:672 SD: 0.2231 cents 360:378:392:420:441:463:480:504:540:560:588:617:662:686:720 SD: 0.1049 cents