Scala analysis: breed14
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: 90/49 1052.571903 13: 40/21 1115.532807 acute major seventh 14: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21/20 84.4672 minor semitone 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: 15/14 119.4428 major diatonic semitone 13: 28/27 62.9609 Archytas' 1/3-tone 14: 21/20 84.4672 minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 28/27 62.961 cents Archytas' 1/3-tone 1: 2 360/343 83.746 cents 1: 5 21/20 84.467 cents minor semitone 1: 3 15/14 119.443 cents major diatonic semitone 2: 1 160/147 146.707 cents 2: 4 49/45 147.428 cents BP minor semitone 2: 2 54/49 168.213 cents Zalzal's mujannab 2: 1 441/400 168.934 cents two (minor semitone) 2: 3 10/9 182.404 cents minor whole tone 2: 1 2700/2401 203.189 cents 2: 2 9/8 203.910 cents major whole tone 3: 3 8/7 231.174 cents septimal whole tone 3: 2 343/300 231.895 cents 3: 1 400/343 266.150 cents 3: 6 7/6 266.871 cents septimal minor third 3: 2 405/343 287.656 cents 4: 1 2401/2025 294.856 cents two (BP minor semitone) 4: 1 6/5 315.641 cents minor third 4: 1 98/81 329.832 cents 4: 7 60/49 350.617 cents smaller approximation to neutral third 4: 4 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: 6 9/7 435.084 cents septimal major third, BP third 5: 1 1029/800 435.805 cents 5: 1 450/343 470.060 cents 6: 7 4/3 498.045 cents perfect fourth 6: 1 2401/1800 498.766 cents 6: 2 27/20 519.551 cents acute fourth 6: 1 200/147 533.021 cents 6: 1 49/36 533.742 cents Arabic lute acute fourth 6: 2 135/98 554.527 cents 7: 1 480/343 581.791 cents 7: 6 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 6 10/7 617.488 cents Euler's tritone 7: 1 343/240 618.209 cents 8: 2 196/135 645.473 cents 8: 1 72/49 666.258 cents Arabic lute grave fifth 8: 1 147/100 666.979 cents 8: 2 40/27 680.449 cents grave fifth 8: 1 3600/2401 701.234 cents two (smaller approximation to neutral third) 8: 7 3/2 701.955 cents perfect fifth 9: 1 343/225 729.940 cents 9: 1 1600/1029 764.195 cents 9: 6 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: 4 80/49 848.662 cents smaller approximation to neutral sixth 10: 7 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 4050/2401 905.144 cents 11: 2 686/405 912.344 cents 11: 6 12/7 933.129 cents septimal major sixth 11: 1 343/200 933.850 cents 11: 2 600/343 968.105 cents 11: 3 7/4 968.826 cents harmonic seventh 12: 2 16/9 996.090 cents Pythagorean minor seventh 12: 1 2401/1350 996.811 cents 12: 3 9/5 1017.596 cents just minor seventh, BP seventh 12: 1 800/441 1031.066 cents 12: 2 49/27 1031.787 cents 12: 4 90/49 1052.572 cents 12: 1 147/80 1053.293 cents 13: 3 28/15 1080.557 cents grave major seventh 13: 5 40/21 1115.533 cents acute major seventh 13: 2 343/180 1116.254 cents 13: 4 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.23077 = 68/13
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 1052.6 1115.5 1200.0 84.5 : 63.0 182.4 266.9 350.6 413.6 498.0 617.5 680.4 764.9 848.7 968.1 1031.1 1115.5 1200.0 147.4 : 119.4 203.9 287.7 350.6 435.1 554.5 617.5 702.0 785.7 905.1 968.1 1052.6 1137.0 1200.0 266.9 : 84.5 168.2 231.2 315.6 435.1 498.0 582.5 666.3 785.7 848.7 933.1 1017.6 1080.6 1200.0 351.3 : 83.7 146.7 231.2 350.6 413.6 498.0 581.8 701.2 764.2 848.7 933.1 996.1 1115.5 1200.0 435.1 : 63.0 147.4 266.9 329.8 414.3 498.0 617.5 680.4 764.9 849.4 912.3 1031.8 1116.3 1200.0 498.0 : 84.5 203.9 266.9 351.3 435.1 554.5 617.5 702.0 786.4 849.4 968.8 1053.3 1137.0 1200.0 582.5 : 119.4 182.4 266.9 350.6 470.1 533.0 617.5 702.0 764.9 884.4 968.8 1052.6 1115.5 1200.0 702.0 : 63.0 147.4 231.2 350.6 413.6 498.0 582.5 645.5 764.9 849.4 933.1 996.1 1080.6 1200.0 764.9 : 84.5 168.2 287.7 350.6 435.1 519.6 582.5 702.0 786.4 870.2 933.1 1017.6 1137.0 1200.0 849.4 : 83.7 203.2 266.1 350.6 435.1 498.0 617.5 702.0 785.7 848.7 933.1 1052.6 1115.5 1200.0 933.1 : 119.4 182.4 266.9 351.3 414.3 533.7 618.2 702.0 764.9 849.4 968.8 1031.8 1116.3 1200.0 1052.6: 63.0 147.4 231.9 294.9 414.3 498.8 582.5 645.5 729.9 849.4 912.3 996.8 1080.6 1200.0 1115.5: 84.5 168.9 231.9 351.3 435.8 519.6 582.5 667.0 786.4 849.4 933.9 1017.6 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 119.4428 cents 405/392, 56.4819 cents 28/27, 62.9609 cents 2: 146.7069 .. 203.9100 cents 1323/1280, 57.2031 cents 64/63, 27.2641 cents 3: 231.1741 .. 287.6560 cents 405/392, 56.4819 cents 64/63, 27.2641 cents 4: 294.8562 .. 351.3381 cents 405/392, 56.4819 cents 823543/820125, 7.2002 cents 5: 413.5778 .. 470.0597 cents 405/392, 56.4819 cents 3200/3087, 62.2397 cents 6: 498.0450 .. 554.5269 cents 405/392, 56.4819 cents 686/675, 27.9853 cents 7: 581.7910 .. 618.2090 cents 117649/115200, 36.4180 cents 64/63, 27.2641 cents 8: 645.4731 .. 701.9550 cents 405/392, 56.4819 cents 64/63, 27.2641 cents 9: 729.9403 .. 786.4222 cents 405/392, 56.4819 cents 686/675, 27.9853 cents 10: 848.6619 .. 905.1438 cents 405/392, 56.4819 cents 3200/3087, 62.2397 cents 11: 912.3440 .. 968.8259 cents 405/392, 56.4819 cents 823543/820125, 7.2002 cents 12: 996.0900 .. 1053.2931 cents 1323/1280, 57.2031 cents 64/63, 27.2641 cents 13: 1080.5572 .. 1137.0391 cents 405/392, 56.4819 cents 64/63, 27.2641 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 : 15/14, 119.4428 cents Average / Smallest step : 1.361389 Largest / Average step : 1.393499 Largest / Smallest step : 1.897095 Median interval of one step : 21/20, 84.4672 cents, amount: 5 Most common interval of one step : 21/20, 84.4672 cents, amount: 5 Least squares average step : 85.73152 cents, oct.: 1200.24121 cents Scale is strictly proper Step pattern alph. order: ABCADBACBADCBA Step pattern size order : CADCBACDACBDAC Scale is a Constant Structure, by a margin of 7.20020 cents Scale diversity : 1.366634 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.403631 Number of different interval sizes : 68 = 5.23077 / class Number of one step interval sizes : 4 Highest interval variety : 7 Mean interval variety : 5.23077 = 68/13 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2401/2400, 0.7212 cents Number of recognisable fifths : 8, average 701.8649 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 : 11 = 78.5714% -- Rational properties -- Prime limit : 7 Odd number limit : 2401 (O: 2401 U: 2401) Highest odd numerator or denominator: 49 Scale harmonicity : 0.014162 Average absolute harmonicity : 0.144874 Specific harmonicity : 0.085251 Fundamental : 1/17640, -14.1066 octaves, 0.0148 Hz. Guide tone : 17640, 14.1066 octaves, 4615074.972 Hz. Exponens Consonantiae : 3.111696E+08, 28.21313 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 300.5, average 21.46429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.80324, average 1.05737 Sum of Tenney's harmonic distance : 30.14462, average 2.15319 Vogel's harmonic complexity : 29.35714 Wille's k value : 10804 Wilson's harmonic complexity : 50 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 342.12025, average 3.25829 Lattice compactness (without 2's) : 255.86409, average 2.43680 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.14286 18 1 3: -2 .. 2 -0.07143 15 2 5: -1 .. 1 -0.21429 7 7: -2 .. 2 0.35714 15 11 Average exponent except 2's : 1 / 14 = 0.07143 Average absolute exponent except 2's: 37 / 14 = 2.64286 Scale is weakly epimorphic with val: <14 20 31 38| Scale is JI-epimorphic with val: <14 22 32 39| Scale is weakly epimorphic with val: <14 24 33 40|
FIT/MODE
14: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 13.0787 c. M:-24.0005 c. 17: 1 1 2 1 1 1 1 2 1 1 1 2 1 1 P M ME SD: 10.5753 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: 11.4194 c. M:-17.4878 c. 27: 2 1 3 2 2 1 2 3 1 2 2 3 1 2 N D3 SD: 7.7644 c. M:-14.0948 c. 31: 2 2 3 2 2 2 2 3 2 2 2 3 2 2 SP M ME SD: 5.8903 c. M: 9.2776 c. 41: 3 2 4 3 3 2 3 4 2 3 3 4 2 3 P D3 SD: 2.5153 c. M: 3.9403 c. 58: 4 3 6 4 4 3 4 6 3 4 4 6 3 4 P SD: 1.7918 c. M: 3.2018 c. 72: 5 4 7 5 5 4 5 7 4 5 5 7 4 5 SP SD: 1.5237 c. M:-2.5719 c. 99: 7 5 10 7 7 5 7 10 5 7 7 10 5 7 P SD: 1.0375 c. M:-1.9736 c. 113: 8 6 11 8 8 6 8 11 6 8 8 11 6 8 SP SD: 0.9694 c. M:-1.5586 c. 130: 9 7 13 9 9 7 9 13 7 9 9 13 7 9 SP SD: 0.8478 c. M:-1.3903 c. 171: 12 9 17 12 12 9 12 17 9 12 12 17 9 12 SP SD: 0.2046 c. M: 0.4609 c. 554: 39 29 55 39 39 29 39 55 29 39 39 55 29 39 SP SD: 0.2603 c. M:-0.4449 c. 571: 40 30 57 40 40 30 40 57 30 40 40 57 30 40 SP SD: 0.2591 c. M:-0.4041 c. 612: 43 32 61 43 43 32 43 61 32 43 43 61 32 43 SP SD: 0.2356 c. M:-0.3693 c. 725: 51 38 72 51 51 38 51 72 38 51 51 72 38 51 SP SD: 0.2352 c. M: 0.4415 c. 783: 55 41 78 55 55 41 55 78 41 55 55 78 41 55 SP SD: 0.2178 c. M: 0.3802 c. 822: 58 43 82 58 57 43 58 82 43 58 57 82 43 58 SP SD: 0.2171 c. M:-0.4867 c. 824: 58 43 82 58 58 43 58 82 43 58 58 82 43 58 SP SD: 0.2686 c. M: 0.3672 c. 836: 59 44 83 59 58 44 59 83 44 59 58 83 44 59 SP SD: 0.2468 c. M:-0.4188 c. 863: 61 45 86 61 60 45 61 86 45 61 60 86 45 61 SP SD: 0.2239 c. M:-0.4580 c. 894: 63 47 89 63 62 47 63 89 47 63 62 89 47 63 SP SD: 0.1904 c. M:-0.3398 c. 935: 66 49 93 66 65 49 66 93 49 66 65 93 49 66 SP SD: 0.1649 c. M:-0.3197 c. 993: 70 52 99 70 69 52 70 99 52 70 69 99 52 70 SP SD: 0.1456 c. M:-0.3235 c. 1024: 72 54 102 72 71 54 72 102 54 72 71 102 54 72 SP SD: 0.2128 c. M: 0.3185 c. 1034: 73 54 103 73 72 54 73 103 54 73 72 103 54 73 SP SD: 0.1563 c. M:-0.3060 c. 1065: 75 56 106 75 74 56 75 106 56 75 74 106 56 75 SP SD: 0.1353 c. M:-0.2112 c. 1106: 78 58 110 78 77 58 78 110 58 78 77 110 58 78 SP SD: 0.1118 c. M:-0.1990 c. 1164: 82 61 116 82 81 61 82 116 61 82 81 116 61 82 SP SD: 0.0958 c. M:-0.2083 c. 1205: 85 63 120 85 84 63 85 120 63 85 84 120 63 85 SP SD: 0.1093 c. M:-0.1972 c. 1236: 87 65 123 87 86 65 87 123 65 87 86 123 65 87 SP SD: 0.0990 c. M:-0.1447 c. 1277: 90 67 127 90 89 67 90 127 67 90 89 127 67 90 SP SD: 0.0752 c. M:-0.1106 c. 1335: 94 70 133 94 93 70 94 133 70 94 93 133 70 94 SP SD: 0.0600 c. M:-0.1226 c. 1448: 102 76 144 102 101 76 102 144 76 102 101 144 76 102 SP SD: 0.0518 c. M:-0.0857 c. 1506: 106 79 150 106 105 79 106 150 79 106 105 150 79 106 SP SD: 0.0353 c. M: 0.0614 c. 1677: 118 88 167 118 117 88 118 167 88 118 117 167 88 118 SP SD: 0.0246 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: 12.2830 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 5.8538 cents 7 x x 8 x 9 x 10 x 11 x 12:13 x 14 S SD: 8.0463 cents 8 x 9 x 10 x x 11:12 x 13:14 x 15:16 S SD: 10.8127 cents 9 x 10 x 11 x 12:13 x 14:15 x x 17:18 SD: 9.3536 cents 10 x 11 x 12:13 x 14:15 x 16:17:18:19:20 S SD: 6.8377 cents 11 x 12:13 x 14:15 x x 17:18:19:20:21:22 SD: 5.4447 cents 12 x 13:14:15 x 16:17:18:19:20:21:22:23:24 S SD: 6.0580 cents 13 x 14:15:16:17 x 18 x 20:21:22:24:25:26 S SD: 5.4613 cents 14 x 15:16:17:18:19:20:21:22:23:24:26:27:28 S SD: 5.8023 cents 15:16 x x 18:19:20:21 x 23:25:26:28:29:30 SD: 7.2400 cents 16:17 x 19:20 x 21:22:24:25:26:27:29:30:32 SD: 6.6935 cents 17:18:19:20:21:22:23:24 x 26:28:29:31:32:34 SD: 5.6324 cents 18:19:20:21:22:23:24:25:27:28:29:31:33:34:36 SD: 3.5528 cents 22:23:24:26:27:28:29:31:33:34:36:38:40:42:44 SD: 3.2219 cents 24:25:26:28:29:31:32:34:36:37:39:41:44:46:48 SD: 3.0282 cents 32:34:35:37:39:41:43:45:48:50:52:55:59:61:64 SD: 2.5550 cents 35:37:38:41:43:45:47:49:53:54:57:60:64:67:70 SD: 2.2818 cents 36:38:39:42:44:46:48:50:54:56:59:62:66:69:72 SD: 1.9002 cents 42:44:46:49:51:54:56:59:63:65:69:72:77:80:84 SD: 1.7093 cents 54:57:59:63:66:69:72:76:81:84:88:93:99:103:108 SD: 1.4765 cents 60:63:65:70:74:77:80:84:90:93:98:103:110:114:120 SD: 1.2366 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: 1.0304 cents 80:84:87:93:98:103:107:112:120:124:131:137:147:152:160 SD: 0.8995 cents 90:95:98:105:110:116:120:126:135:140:147:154:165:171:180 SD: 0.8936 cents 98:103:107:114:120:126:131:137:147:152:160:168:180:187:196 SD: 0.7568 cents 102:107:111:119:125:131:136:143:153:159:167:175:187:194:204 SD: 0.5662 cents 137:144:149:160:168:176:183:192:206:213:224:235:252:261:274 SD: 0.5467 cents 144:151:157:168:176:185:192:202:216:224:235:247:264:274:288 SD: 0.5338 cents 155:163:169:181:190:199:207:217:233:241:253:266:285:295:310 SD: 0.5282 cents 158:166:172:184:194:203:211:221:237:246:258:271:290:301:316 SD: 0.4724 cents 160:168:174:187:196:206:213:224:240:249:261:274:294:305:320 SD: 0.4438 cents 168:176:183:196:206:216:224:235:252:261:274:288:309:320:336 SD: 0.4396 cents 178:187:194:208:218:229:237:249:267:277:291:305:327:339:356 SD: 0.3506 cents 200:210:218:233:245:257:267:280:300:311:327:343:367:381:400 SD: 0.3319 cents 234:246:255:273:287:301:312:328:351:364:382:401:430:446:468 SD: 0.3115 cents 240:252:261:280:294:309:320:336:360:373:392:411:441:457:480 SD: 0.2955 cents 258:271:281:301:316:332:344:361:387:401:421:442:474:491:516 SD: 0.2505 cents 294:309:320:343:360:378:392:412:441:457:480:504:540:560:588 SD: 0.2120 cents 336:353:366:392:412:432:448:470:504:523:549:576:617:640:672 SD: 0.2037 cents 360:378:392:420:441:463:480:504:540:560:588:617:661:686:720 SD: 0.0818 cents