Yahoo Tuning Groups Ultimate Backup tuning Repost: For Joseph: Eight 22-tone 7-limit Fokker periodicity blocks

Joseph wrote,

>I have to repeat again, and I WILL NOT USE CAPS this time that this
>post is really one of the most incredible things I have ever seen on
>the Tuning List, and there have been some pretty amazing things over
>the last year.

Actually I'm embarassed about the fact that these all use the
parallelopiped
method, while, as I've indicated, the hexagonal prism and the rhombic
dodecadron can sometimes be preferable as the boundaries for a 3-d
periodicity block . . .

Anyway, on to 22-tone (again, restricted to parallelopipeds):

Unison vectors:
-5 1 2
-4 -2 0
-2 0 -1
Scale:
cents numerator denominator
0 1 1
62.961 28 27
111.73 16 15
155.14 35 32
203.91 9 8
266.87 7 6
342.91 128 105
386.31 5 4
435.08 9 7
498.04 4 3
546.82 48 35
590.22 45 32
653.18 35 24
701.96 3 2
764.92 14 9
813.69 8 5
857.09 105 64
933.13 12 7
996.09 16 9
1044.9 64 35
1088.3 15 8
1137 27 14
Lattice:

35/24-----35/32----105/64
/ `. ,' `. ,' `.
/ 5/4------15/8------45/32
/ / \ / \ /
/ / \ / \ /
28/27-------14/9-------7/6 / \ / \ /
`. ,' `. ,' `. / \ / \ /
16/9-------4/3-------1/1-------3/2-------9/8
\ / \ / `. ,' `. ,' `.
\ / \ / 12/7-------9/7-------27/14
\ / \ / /
\ / \ / /
16/15------8/5 /
,' `. ,' `. /
128/105----64/35-----48/35

Unison vectors:
3 -1 -3
-2 0 -1
0 2 -2
Scale:
cents numerator denominator
0 1 1
35.697 49 48
84.467 21 20
182.4 10 9
231.17 8 7
266.87 7 6
315.64 6 5
386.31 5 4
435.08 9 7
498.04 4 3
546.82 48 35
582.51 7 5
653.18 35 24
701.96 3 2
764.92 14 9
813.69 8 5
884.36 5 3
933.13 12 7
968.83 7 4
1017.6 9 5
1115.5 40 21
1164.3 96 49
Lattice:

35/24
,'/|\`.
10/9-------5/3-/-|-\-5/4
|\`. ,'/|\/49/48\/|\
| \40/21/ |/,' `.\| \
14/9-------7/6-------7/4 \
`.\|/,' \`.\ /,'/ \`.\
4/3-----\-1/1-/---\-3/2
\`.\ ,\/|\/. ,\/|\`.
\ 8/7-/\|/\12/7--\|---9/7
\ |\/.7/5------21/20\ |
\|/,96/49.\|/,' `.\|
8/5-------6/5-------9/5
`.\|/ ,'
48/35

Unison vectors:
3 -1 -3
-3 3 1
-2 0 -1
Scale:
cents numerator denominator
0 1 1
48.77 36 35
84.467 21 20
182.4 10 9
231.17 8 7
266.87 7 6
315.64 6 5
386.31 5 4
422.01 245 192
498.04 4 3
546.82 48 35
582.51 7 5
653.18 35 24
701.96 3 2
777.99 384 245
813.69 8 5
884.36 5 3
933.13 12 7
968.83 7 4
1017.6 9 5
1115.5 40 21
1151.2 35 18
Lattice:
245/192
,'
35/18-----35/24
,' \`. ,'/ \`.
10/9-----\-5/3-/---\-5/4
\`. ,\/|\/ \/|\
\40/21/\|/\ /\| \
\ | / 7/6-------7/4 \
\|/,' \`.\ /,'/ \`.\
4/3-----\-1/1-/---\-3/2
\`.\ ,\/|\/. ,\/|\
\ 8/7-/\|/\12/7 /\| \
\ |\/.7/5------21/20\
\|/,' `.\|/,' `.\
8/5-------6/5-------9/5
`.\ /,' `.\ ,'
48/35-----36/35
,'
384/245

Unison vectors:
3 -1 -3
-5 1 2
0 2 -2
Scale:
cents numerator denominator
0 1 1
48.77 36 35
84.467 21 20
182.4 10 9
231.17 8 7
266.87 7 6
315.64 6 5
386.31 5 4
435.08 9 7
498.04 4 3
533.74 49 36
582.51 7 5
666.26 72 49
701.96 3 2
764.92 14 9
813.69 8 5
884.36 5 3
933.13 12 7
968.83 7 4
1017.6 9 5
1115.5 40 21
1151.2 35 18
Lattice:
35/18
,'/|\`.
10/9-/-|-\-5/3-------5/4
|\/49/36\/|\ /|\
|,'40/21`.| \ / | \
14/9-------7/6-------7/4 \
`.\|/,' \`.\ /,'/ \`.\
4/3-----\-1/1-/---\-3/2
\`.\ ,\/|\/. ,\/|\`.
\ 8/7-/\|/\12/7-/\|-\-9/7
\ | /.7/5------21/20\/|
\|/,' `.\|/,' * `.\|
8/5-------6/5-------9/5
`.\|/ ,'
36/35
* 72/49 goes here

Unison vectors:
3 -1 -3
-5 1 2
-3 3 1
Scale:
cents numerator denominator
0 1 1
48.77 36 35
97.541 1296 1225
182.4 10 9
218.1 245 216
266.87 7 6
315.64 6 5
386.31 5 4
435.08 9 7
498.04 4 3
546.82 48 35
582.51 7 5
653.18 35 24
701.96 3 2
764.92 14 9
813.69 8 5
884.36 5 3
933.13 12 7
981.9 432 245
1017.6 9 5
1102.5 1225 648
1151.2 35 18
Lattice:
1225/648
\
\
\
\
245/216
`.
35/18-----35/24
,' \`. ,'/ `.
10/9-----\-5/3-/-----5/4
\ \/|\/ / \
\ /\|/\ / \
\ / 7/6 \ / \
\ /,' \`.\ / \
4/3-----\-1/1-------3/2
\ \/|\`. ,'/ \
\ /\| \12/7 / \
\ / 7/5 \/|\/ \
\ /,' `.\|/\ \
8/5-------6/5-------9/5
`. /,' `.\ ,'
48/35-----36/35
`.
432/245
\
\
\
\
1296/1225

Unison vectors:
2 2 -1
3 -1 -3
-2 0 -1
Scale:
cents numerator denominator
0 1 1
35.697 49 48
111.73 16 15
155.14 35 32
231.17 8 7
266.87 7 6
315.64 6 5
386.31 5 4
435.08 9 7
498.04 4 3
546.82 48 35
582.51 7 5
653.18 35 24
701.96 3 2
764.92 14 9
813.69 8 5
884.36 5 3
933.13 12 7
968.83 7 4
1044.9 64 35
1088.3 15 8
1164.3 96 49
Lattice:
35/24-----35/32
,'/|\`. ,'/ `.
5/3-/-|-\-5/4-/-----15/8
/|\/49/48\/|\/ /
/ |/,' `.\|/\ /
14/9-------7/6-------7/4 \ /
`. /,' \`.\ /,'/ `.\ /
4/3-----\-1/1-/-----3/2
/ \`. ,\/|\/. ,'/ `.
/ \ 8/7-/\|/\12/7-------9/7
/ \/|\/.7/5 \ | /
/ /\|/,96/49.\|/
16/15------8/5-------6/5
`. / `.\|/ ,'
64/35-----48/35

Unison vectors:
2 2 -1
3 -1 -3
-3 3 1
Scale:
cents numerator denominator
0 1 1
48.77 36 35
119.44 15 14
160.5 192 175
218.1 245 216
266.87 7 6
315.64 6 5
386.31 5 4
435.08 9 7
498.04 4 3
546.82 48 35
582.51 7 5
653.18 35 24
701.96 3 2
764.92 14 9
813.69 8 5
884.36 5 3
933.13 12 7
981.9 432 245
1039.5 175 96
1080.6 28 15
1151.2 35 18
Lattice:
175/96
/
/
245/216 /
`. /
35/18-----35/24
/ \`. ,'/ `.
/ \ 5/3-/-----5/4
/ \/|\/ / \`.
/ /\|/\ / \15/14
14/9-------7/6 \ / \/|\
\`. /,'/ \`.\ / /\| \
\ 4/3-/---\-1/1-------3/2 \
\ |\/ \/|\`. /,'/ `.\
\|/\ /\| \12/7-/-----9/7
28/15------7/5 \/|\/ /
`.\ /,' `.\|/\ /
8/5-------6/5 \ /
`. /,' `.\ /
48/35-----36/35
/ `.
/ 432/245
/
/
192/175

Unison vectors:
2 2 -1
3 -1 -3
-5 1 2
Scale:
cents numerator denominator
0 1 1
48.77 36 35
111.73 16 15
168.21 54 49
218.1 245 216
266.87 7 6
315.64 6 5
386.31 5 4
435.08 9 7
498.04 4 3
546.82 48 35
582.51 7 5
653.18 35 24
701.96 3 2
764.92 14 9
813.69 8 5
884.36 5 3
933.13 12 7
981.9 432 245
1031.8 49 27
1088.3 15 8
1151.2 35 18
Lattice:
245/216
/ `.
/ 35/18-----35/24
/ / \`. ,'/ `.
/ / \ 5/3-/-----5/4------15/8
49/27 / \/|\/ / \ /
`. / /\|/\ / \ /
14/9-------7/6 \ / \ /
`. /,' \`.\ / \ /
4/3-----\-1/1-------3/2
/ \ \/|\`. ,'/ `.
/ \ /\| \12/7-/-----9/7
/ \ / 7/5 \/|\/ / `.
/ \ /,' `.\|/\ / 54/49
16/15------8/5-------6/5 \ / /
`. /,' `.\ / /
48/35-----36/35 /
`. /
432/245

Cheers!
--- End forwarded message ---

Repost: For Joseph: Eight 22-tone 7-limit Fokker periodicity blocks

🔗paul@stretch-music.com

🔗jpehrson@rcn.com