Let's play: What's your favorite number? (14, 15, 16, 17, 18, 26, 27-tone Fokker periodicity blocks)

14-tone Fokker periodicity blocks:

Unison vectors:
-1 -2 4
4 -1 0
-1 0 2
Scale:
0 1 1
84.467 21 20
146.71 160 147
266.87 7 6
351.34 49 40
435.08 9 7
498.04 4 3
618.21 343 240
701.96 3 2
764.92 14 9
848.66 80 49
933.13 12 7
1053.3 147 80
1115.5 40 21
Lattice:

40/21
14/9-------7/6
* `. | ,' @ `.
4/3-------1/1-------3/2
`.49/40----147/80
12/7`.-|-,'9/7
21/20
* 160/147 goes here
@ 343/240 and 80/49 go here

(I can't show all the connections)

Unison vectors:
-1 -2 4
4 -1 0
0 2 -2
Scale:
0 1 1
84.467 21 20
147.43 49 45
266.87 7 6
350.62 60 49
435.08 9 7
498.04 4 3
582.51 7 5
701.96 3 2
764.92 14 9
849.38 49 30
933.13 12 7
1052.6 90 49
1115.5 40 21
Lattice:
40/21
14/9-------7/6
`. | ,' *-`.----90/49
4/3---|---1/1-------3/2
49/30 `. | ,' | `.
\`. 12/7---|---9/7
\ 7/5------21/20
\ |
\|
49/25
* 60/49 goes here

15-tone Fokker periodicity blocks:

Unison vectors:
2 -3 1
-3 3 1
0 -3 0
Scale:
cents numerator denominator
0 1 1
70.672 25 24
182.4 10 9
244.97 144 125
315.64 6 5
386.31 5 4
498.04 4 3
568.72 25 18
631.28 36 25
701.96 3 2
813.69 8 5
884.36 5 3
955.03 125 72
1017.6 9 5
1129.3 48 25
Lattice:
125/72
/ \
/ \
/ \
/ \
25/18-----25/24
/ \ / \
/ \ / \
/ \ / \
/ \ / \
10/9-------5/3-------5/4
\ / \ / \
\ / \ / \
\ / \ / \
\ / \ / \
4/3-------1/1-------3/2
\ / \ / \
\ / \ / \
\ / \ / \
\ / \ / \
8/5-------6/5-------9/5
\ / \ /
\ / \ /
\ / \ /
\ / \ /
48/25-----36/25
\ /
\ /
\ /
\ /
144/125

Unison vectors:
1 0 3
-3 3 1
-2 0 -1
Scale:
cents numerator denominator
0 1 1
76.034 256 245
155.14 35 32
231.17 8 7
315.64 6 5
413.58 80 63
470.78 21 16
546.82 48 35
653.18 35 24
729.22 32 21
786.42 63 40
884.36 5 3
968.83 7 4
1044.9 64 35
1124 245 128
Lattice:
245/128
,'
35/24-----35/32
,' \ / \
5/3 \ / \
\ \ / \
80/63 \ \ / \
\ \ 7/4------21/16
\ \ ,' \
\ 1/1 \
\ ,' \ \
32/21------8/7 \ \
\ / \ \ 63/40
\ / \ \
\ / \ 6/5
\ / \ ,'
64/35-----48/35
,'
256/245

Unison vectors:
1 0 3
2 -3 1
0 -3 0
Scale:
cents numerator denominator
0 1 1
84.467 21 20
155.14 35 32
231.17 8 7
301.85 25 21
386.31 5 4
470.78 21 16
541.45 175 128
658.55 256 175
729.22 32 21
813.69 8 5
898.15 42 25
968.83 7 4
1044.9 64 35
1115.5 40 21
Lattice:
175/128
/
/
/
25/21 /
/ 35/32
/ ,'/ \
/ 5/4 / \
/ /| / \
40/21 / |/ \
/ \ / 7/4------21/16
/ \ /,' \ /
/ \ 1/1 \ /
/ \ ,'/ \ /
32/21------8/7 / \ /
\ /| / 21/20
\ / |/ /
\ / 8/5 /
\ /,' /
64/35 /
/ 42/25
/
/
/
256/175

Unison vectors:
1 0 3
2 -3 1
-1 0 2
Scale:
cents numerator denominator
0 1 1
84.467 21 20
146.71 160 147
231.17 8 7
315.64 6 5
386.31 5 4
462.35 64 49
546.82 48 35
653.18 35 24
737.65 49 32
813.69 8 5
884.36 5 3
968.83 7 4
1053.3 147 80
1115.5 40 21
Lattice:
35/24
,' `.
5/3-------5/4
,' \ /| 49/32
40/21 \ / | ,' \
,' \ \ / 7/4 \
160/147 \ \ /,' \ \
\ \ 1/1 \ \
\ \ ,'/ \ \ 147/80
\ 8/7 / \ \ ,'
\ ,' | / \ 21/20
64/49 |/ \ ,'
8/5-------6/5
`. ,'
48/35

Unison vectors:
1 0 3
2 -3 1
-2 0 -1
Scale:
cents numerator denominator
0 1 1
84.467 21 20
155.14 35 32
231.17 8 7
315.64 6 5
386.31 5 4
470.78 21 16
555.25 441 320
644.75 640 441
729.22 32 21
813.69 8 5
884.36 5 3
968.83 7 4
1044.9 64 35
1115.5 40 21
Lattice:

35/32
,'/ \
5/3-------5/4 / \
,' \ /| / \
40/21 \ / |/ \
/ \ \ / 7/4------21/16
/ \ \ /,' \ /
/ \ 1/1 \ /
/ \ ,'/ \ \ /
32/21------8/7 / \ \ /
\ /| / \ 21/20
\ / |/ \ ,'
\ / 8/5-------6/5
\ /,'
64/35

16-tone Fokker periodicity block:

Unison vectors:
1 0 3
2 -3 1
0 2 -2
Scale:
0 1 1
84.467 21 20
155.14 35 32
231.17 8 7
315.64 6 5
386.31 5 4
470.78 21 16
533.02 200 147
617.49 10 7
666.98 147 100
737.65 49 32
813.69 8 5
898.15 42 25
968.83 7 4
1053.3 147 80
1115.5 40 21
Lattice:
35/32
200/147 ,'/|\
| 5/4 / | \
| ,'/| /49/32\
40/21-----10/7 / |/,' `.\
\ /| / 7/4------21/16
\ / |/,' \ /|
\ / 1/1 \ / |
\ /,'/ \ \ 147/100
8/7 / \ \ /,'/
| / \ 21/20/
|/ \ ,'/| /
8/5-------6/5 / |/
| 147/80
|/,'
42/25

17-tone Fokker periodicity blocks:

Unison vectors:
-5 1 2
-2 0 -1
1 2 1
Scale:
cents numerator denominator
0 1 1
48.77 36 35
155.14 35 32
203.91 9 8
266.87 7 6
342.91 128 105
435.08 9 7
498.04 4 3
546.82 48 35
653.18 35 24
701.96 3 2
764.92 14 9
857.09 105 64
933.13 12 7
996.09 16 9
1044.9 64 35
1151.2 35 18
Lattice:

35/18-----35/24-----35/32----105/64
/ \ /
/ \ /
/ \ /
/ \ /
14/9-------7/6
,' `. ,' `.
16/9-------4/3-------1/1-------3/2-------9/8
`. ,' `. ,'
12/7-------9/7
/ \ /
/ \ /
/ \ /
/ \ /
128/105----64/35-----48/35-----36/35

Unison vectors:
3 -1 -3
-5 1 2
1 2 1
Scale:
cents numerator denominator
0 1 1
62.961 28 27
155.14 35 32
218.1 245 216
266.87 7 6
342.91 128 105
435.08 9 7
498.04 4 3
546.82 48 35
653.18 35 24
701.96 3 2
764.92 14 9
857.09 105 64
933.13 12 7
981.9 432 245
1044.9 64 35
1137 27 14
Lattice:

245/216

35/24-----35/32----105/64
/
/
/
/
28/27-----14/9-------7/6
`. ,' `.
4/3-------1/1-------3/2
`. ,' `.
12/7-------9/7------27/14
/
/
/
/
128/105----64/35-----48/35

432/234

18-tone periodicity blocks:

Unison vectors:
-3 3 1
-3 -2 3
0 -3 0
Scale:
cents numerator denominator
0 1 1
70.672 25 24
119.44 15 14
218.1 245 216
266.87 7 6
337.54 175 144
386.31 5 4
456.99 125 96
505.76 75 56
645.47 196 135
694.24 112 75
764.92 14 9
813.69 8 5
884.36 5 3
933.13 12 7
1031.8 49 27
1080.6 28 15
1151.2 35 18
Lattice:

125/96
/
/
175/144 /
/ `. /
/ 25/24
245/216 / / \
/ `. / / \ 75/56
/ 35/18 / \ /
/ / \`. / \ /
/ / \ 5/3-------5/4 /
49/27 / \ |\ / `. /
/ `. / \| \ / 15/14
/ 14/9-------7/6 \ / /
/ \ / `.\ / /
/ \ / 1/1 /
196/135 \ / / `. /
\ / / 12/7
28/15 /
/ `. /
/ 8/5
/
/
112/75

Unison vectors:
-3 3 1
-3 -2 3
0 2 -2
Scale:
cents numerator denominator
0 1 1
48.77 36 35
119.44 15 14
196.2 28 25
266.87 7 6
315.64 6 5
386.31 5 4
463.07 98 75
533.74 49 36
582.51 7 5
666.26 72 49
736.93 75 49
813.69 8 5
884.36 5 3
933.13 12 7
1003.8 25 14
1080.6 28 15
1151.2 35 18
Lattice:

25/14
35/18 |\`.
|\`. | \75/49
| \ 5/3-------5/4 \ |
49/36\ |\ / `. \|
`.\| \ / 15/14
7/6 \ / /
/ `.\ / /
/ 1/1 /
/ /|\`. /
/ / | \12/7
28/15 / 7/5 \ |\`.
|\`. /,' `.\| \72/49
| \ 8/5-------6/5 \ |
98/75\ | `.\|
`.\| 36/35
28/25

Unison vectors:
3 -1 -3
-3 3 1
-3 -2 3
Scale:
cents numerator denominator
0 1 1
70.672 25 24
119.44 15 14
218.1 245 216
266.87 7 6
337.54 175 144
386.31 5 4
484.97 1715 1296
533.74 49 36
617.49 10 7
666.26 72 49
736.93 75 49
813.69 8 5
884.36 5 3
933.13 12 7
1003.8 25 14
1080.6 28 15
1151.2 35 18
Lattice:

175/144
1715/1296 / `.
`. / 25/24
245/216 / / \`.
`. / / \25/14
35/18 / \/|\`.
|\`. / /\| \75/49
| \ 5/3-------5/4 \ |
49/36\ |\`. /,'/ `. \|
`.\| \10/7-/----15/14
7/6 \ | / /
/ `.\|/ /
/ 1/1 /
/ / `. /
/ / 12/7
28/15 / `.
`. / 72/49
8/5

(No 20-, 21-, 23-, 24-, or 25-toners found)

26-tone Fokker periodicity block:

Unison vectors:
1 0 3
3 -1 -3
0 2 -2
Scale:
cents numerator denominator
0 1 1
35.697 49 48
84.467 21 20
155.14 35 32
195.48 384 343
231.17 8 7
266.87 7 6
315.64 6 5
386.31 5 4
422.01 245 192
462.35 64 49
498.04 4 3
546.82 48 35
582.51 7 5
653.18 35 24
701.96 3 2
737.65 49 32
777.99 384 245
813.69 8 5
884.36 5 3
933.13 12 7
968.83 7 4
1004.5 343 192
1044.9 64 35
1115.5 40 21
1164.3 96 49
Lattice:
245/192
,' | `.
35/24--|--35/32
,' | 343/192 |
5/3---|-,'5/4`. |
,'/|\ 49/48-----49/32
40/21/ | ,' `.| ,'
|\/ 7/6-------7/4 \
|/,' \`.\ /,'/ \`.\
4/3-----\-1/1-/---\-3/2
\`.\ ,\/|\/. ,\/|
\ 8/7-/\|/\12/7 /\|
,\ | /.7/5,\ | /21/20
64/49-\|/,96/49.\|/,'
| `.8/5-------6/5
| ,' * `. | ,'
64/35-----48/35
`. | ,'
384/245
* 384/343 goes here

(I can't show all the connections)

27-tone Fokker periodicity blocks:

Unison vectors:
3 -1 -3
2 -3 1
-2 0 -1
Scale:
cents numerator denominator
0 1 1
48.77 36 35
84.467 21 20
119.44 15 14
182.4 10 9
231.17 8 7
266.87 7 6
315.64 6 5
351.34 49 40
386.31 5 4
435.08 9 7
498.04 4 3
546.82 48 35
582.51 7 5
617.49 10 7
653.18 35 24
701.96 3 2
764.92 14 9
813.69 8 5
848.66 80 49
884.36 5 3
933.13 12 7
968.83 7 4
1017.6 9 5
1080.6 28 15
1115.5 40 21
1151.2 35 18
Lattice:
35/18-----35/24
,'/ \`. ,'/ \`.
10/9-/---\-5/3-/---\-5/4
|\/. ,\/|\/. ,\/|\`.
|/\40/21/\|/\10/7-/\|-\15/14
14/9-------7/6-------7/4 \/|
`.\|/,'/@\`.\ /,'/|\`.\|
4/3-/---\-1/1-/-|-\-3/2
|\/.\|/,\/|\/49/40\/|\`.
|/\ 8/7-/\|/,'-*-`.\| \-9/7
28/15\-|-/ 7/5------21/20\/|
`.\|/,' `.\|/,' `.\|
8/5-------6/5-------9/5
`.\ /,' `.\ /,'
48/35-----36/35
* 12/7 goes here
@ 80/49 goes here

(I can't show all the connections)

Unison vectors:
-1 -2 4
2 -3 1
0 -3 0
Scale:
cents numerator denominator
0 1 1
34.976 50 49
70.672 25 24
119.44 15 14
196.2 28 25
231.17 8 7
266.87 7 6
315.64 6 5
351.34 49 40
386.31 5 4
421.29 125 98
498.04 4 3
546.82 48 35
582.51 7 5
617.49 10 7
653.18 35 24
701.96 3 2
778.71 196 125
813.69 8 5
848.66 80 49
884.36 5 3
933.13 12 7
968.83 7 4
1003.8 25 14
1080.6 28 15
1129.3 48 25
1165 49 25
Lattice:

125/98
25/24 /|
/|\`. |
/ | \25/14
/35/24'/|\
/ /$\ /\| \
5/3-/---\-5/4 \
/|\/. |/,\/|\`.\
/ |/\10/7-/\|-\15/14
/ 7/6-------7/4 \/|
/,'/@\ /\|/,'/| `.\|
4/3-/---\-1/1-/-|---3/2
|\/. |/,\/|\/49/40'/
|/\ 8/7-/\|/,'/* /
28/15------7/5 / | /
\`.\|/.'/| /.\|/
\ 8/5-/-|/--6/5
\ |\/49/25 /
\|/,'/& /
28/25/ | /
| /.\|/
|/ 48/25
196/125

* 12/7 goes here
@ 80/49 goes here
$ 50/49 goes here
& 48/35 goes here

(I can't show all the connections)

Unison vectors:
-1 -2 4
2 -3 1
-3 -2 3
Scale:
cents numerator denominator
0 1 1
34.976 50 49
84.467 21 20
119.44 15 14
182.4 10 9
231.17 8 7
266.87 7 6
315.64 6 5
350.62 60 49
386.31 5 4
435.08 9 7
498.04 4 3
533.74 49 36
582.51 7 5
617.49 10 7
666.26 72 49
701.96 3 2
764.92 14 9
813.69 8 5
849.38 49 30
884.36 5 3
933.13 12 7
968.83 7 4
1017.6 9 5
1080.6 28 15
1115.5 40 21
1165 49 25
Lattice:

50/49
10/9-------5/3-------5/4
|\`49/36'/|\`. | ,'/|\`.
| \ @\`. | \10/7-/-|-\15/14
14/9 \ | \ 7/6-------7/4 \/|\
\`.\|/,\ \ /\|/,'/& `.\| \
\ 4/3--\--\-1/1-/-----3/2 \
\ |\`49/30\/|\/. /,'/|\`.\
\| \ %\-/\|/\12/7-/-|-\-9/7
28/15----\-7/5-----/21/20\ |
`.\|/.\ | `.\|/,' * `.\|
8/5--\|---6/5-------9/5
49/25

% 8/7 goes here
* 72/49 goes here
$ 50/49 goes here
@ 40/21 goes here
& 60/49 goes here

(I can't show all the connections)

Unison vectors:
-1 -2 4
2 -3 1
-2 0 -1
Scale:
cents numerator denominator
0 1 1
34.976 50 49
84.467 21 20
119.44 15 14
182.4 10 9
231.17 8 7
266.87 7 6
315.64 6 5
351.34 49 40
386.31 5 4
435.08 9 7
498.04 4 3
533.02 200 147
582.51 7 5
617.49 10 7
666.98 147 100
701.96 3 2
764.92 14 9
813.69 8 5
848.66 80 49
884.36 5 3
933.13 12 7
968.83 7 4
1017.6 9 5
1080.6 28 15
1115.5 40 21
1165 49 25
Lattice:

200/147----50/49
10/9-------5/3-------5/4
|\`. | ,'/|\`. | ,'/|\`.
| \40/21/-| \10/7-/-|-\15/14
14/9 \ |\/.7/6-------7/4 \/|\
\`.\|/,' %\ /\|/,'/|\`.\| \
\ 4/3-----\-1/1-/-|-\-3/2 \
\ |\`.\ /,\/|\/49/40\/|\`.\
\| \ 8/7-/\|/,'/*\`.\|-\-9/7
28/15------7/5-/---\21/20\ |
`.\|/.' | /.\|/,\ | \|
8/5---|/--6/5--\|---9/5
49/25----147/100
* 12/7 goes here
$ 50/49 goes here
% 80/49 goes here

Unison vectors:
-1 -2 4
2 -3 1
-5 1 2
Scale:
cents numerator denominator
0 1 1
48.77 36 35
84.467 21 20
133.24 27 25
182.4 10 9
231.17 8 7
266.87 7 6
315.64 6 5
350.62 60 49
400.11 63 50
435.08 9 7
498.04 4 3
533.74 49 36
582.51 7 5
617.49 10 7
666.26 72 49
701.96 3 2
764.92 14 9
799.89 100 63
849.38 49 30
884.36 5 3
933.13 12 7
968.83 7 4
1017.6 9 5
1066.8 50 27
1115.5 40 21
1151.2 35 18
Lattice:
LEFT AS EXERCISE FOR READER

Unison vectors:
-1 -2 4
3 -1 -3
0 -3 0
Scale:
cents numerator denominator
0 1 1
35.697 49 48
70.672 25 24
119.44 15 14
196.2 28 25
231.17 8 7
266.87 7 6
315.64 6 5
350.62 60 49
386.31 5 4
422.01 245 192
498.04 4 3
546.82 48 35
582.51 7 5
617.49 10 7
653.18 35 24
701.96 3 2
777.99 384 245
813.69 8 5
849.38 49 30
884.36 5 3
933.13 12 7
968.83 7 4
1003.8 25 14
1080.6 28 15
1129.3 48 25
1164.3 96 49
Lattice:
LEFT AS EXERCISE FOR READER

Unison vectors:
-1 -2 4
3 -1 -3
-3 -2 3
Scale:
cents numerator denominator
0 1 1
35.697 49 48
83.746 360 343
119.44 15 14
183.12 2401 2160
231.17 8 7
266.87 7 6
315.64 6 5
350.62 60 49
386.31 5 4
435.08 9 7
498.04 4 3
533.74 49 36
582.51 7 5
617.49 10 7
666.26 72 49
701.96 3 2
764.92 14 9
813.69 8 5
849.38 49 30
884.36 5 3
933.13 12 7
968.83 7 4
1016.9 4320 2401
1080.6 28 15
1116.3 343 180
1164.3 96 49
Lattice:
LEFT AS EXERCISE FOR READER

Unison vectors:
-1 -2 4
3 -1 -3
-2 0 -1
Scale:
cents numerator denominator
0 1 1
35.697 49 48
84.467 21 20
119.44 15 14
182.4 10 9
231.17 8 7
266.87 7 6
315.64 6 5
351.34 49 40
386.31 5 4
435.08 9 7
498.04 4 3
533.74 49 36
582.51 7 5
617.49 10 7
666.26 72 49
701.96 3 2
764.92 14 9
813.69 8 5
848.66 80 49
884.36 5 3
933.13 12 7
968.83 7 4
1017.6 9 5
1080.6 28 15
1115.5 40 21
1164.3 96 49
Lattice:
LEFT AS EXERCISE FOR READER

Unison vectors:
-1 -2 4
3 -1 -3
-5 1 2
Scale:
cents numerator denominator
0 1 1
48.77 36 35
84.467 21 20
132.52 2592 2401
182.4 10 9
231.17 8 7
266.87 7 6
315.64 6 5
351.34 49 40
399.39 432 343
435.08 9 7
498.04 4 3
533.74 49 36
582.51 7 5
617.49 10 7
666.26 72 49
701.96 3 2
764.92 14 9
800.61 343 216
848.66 80 49
884.36 5 3
933.13 12 7
968.83 7 4
1017.6 9 5
1067.5 2401 1296
1115.5 40 21
1151.2 35 18
Lattice:
LEFT AS EXERCISE FOR READER