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Corrceted improved blackjack lattice in 72-tET notation (save _th is_ one, Joseph!)

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

5/10/2001 10:35:38 AM

[some of the connections were missing or incomplete before]

It's great how much musical sense this lattice makes to someone used to
12-tET notation and knows a little about 7-limit JI!!

72-tET notation will be 12-tET notation with the following new accidentals:

v = 1/4 tone flat
< = 1/6 tone flat
{ = 1/12 tone flat
} = 1/12 tone sharp
> = 1/6 tone sharp
^ = 1/4 tone sharp

So the blackjack scale is

note degree Semitones
C< 70 11&2/3
B{ 65 10&5/6
Bv 63 10&1/2
Bb< 58 9&2/3
A> 56 9&1/3
Av 51 8&1/2
Ab} 49 8&1/6
G> 44 7&1/3
G 42 7
Gb} 37 6&1/6
F#{ 35 5&5/6
F 30 5
F< 28 4&2/3
E{ 23 3&5/6
Ev 21 3&1/2
Eb< 16 2&2/3
D> 14 2&1/3
Dv 9 1&1/2
Db} 7 1&1/6
C> 2 0&1/3
C 0 0

Here's the lattice (which extends infinitely up, down, right, and left):

F---------C--/---\--G / |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E{------
'/ \`.\ /,'/|\/ \/| / F---------C--/---\--G / |/\ /\|/,'/ \`.\ /
/---\-Ab} / |/\ /\|/,'/ \`.\ /,'/|\/ \/| / F---------C--/---\--G
\/| / Gb}-------Db}-/---\-Ab} / |/\ /\|/,'/ \`.\ /,'/|\/ \/|
/\|/ /|\`.\ /,'/|\/ \/| / Gb}-------Db}-/---\-Ab} / |/\ /\|/
------D>--/-|-\-A> / |/\ /\|/,'/|\`.\ /,'/|\/ \/| / Gb}-\---/-Db}
.\ /,'/|\/ C>--------G>--------D>--/-|-\-A> / |/\ /\|/,'/|\`.\ /,'/|\
-Bv / |/,'/ \`.\|/,'/|\`.\ /,'/|\/ C>--------G>--------D>--/-|-\-A> / |/
| / Av--/---\-Ev--/-|-\-Bv / |/,'/ \`.\|/,'/|\`.\ /,'/|\/ C>--------G>-
. |/,'/|\/ \ /,\/| / Dv-------Av--/---\-Ev--/-|---Bv / |/,'/ \`.\|/,'/|
-F<--/-|/\-C< /\|/,'/ \`.\|/,'/|\/.\ /,\/| / Dv--------Av--------Ev--/-|-
\/| / Eb<-------Bb<-/---\-F<--/-|/\-C< /\|/,'/ \`.\|/,'/|\/.\ /,'/| / Dv
/\|/,'/ \`.\|/,'/|\/ \/| / Eb<-------Bb<-------F<--/-|/\-C< /\|/,'/ \
-B{--/---\-F#{ / |/\ /\|/,'/ \`.\|/,'/|\/ \/| / Eb<-------Bb<-/---
'/|\/ \/| / E{--------B{------\-F#{ / |/\ /\|/,'/ \`.\|/,'/|\/
/ |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E{--------B{--/---\-F#{ / |/\
F---------C--/---\--G / |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E{------
'/ \`.\ /,'/|\/ \/| / F---------C--/---\--G / |/\ /\|/,'/ \`.\ /
/---\-Ab} / |/\ /\|/,'/ \`.\ /,'/|\/ \/| / F---------C--/---\--G
\/| / Gb}-------Db}-/---\-Ab} / |/\ /\|/,'/ \`.\ /,'/|\/ \/|
/\|/ /|\`.\ /,'/|\/ \/| / Gb}-------Db}-/---\-Ab} / |/\ /\|/
------D>--/-|-\-A> / |/\ /\|/,'/|\`.\ /,'/|\/ \/| / Gb}-\---/-Db}
.\ /,'/|\/ C>--------G>--------D>--/-|-\-A> / |/\ /\|/,'/|\`.\ /,'/|\
-Bv / |/,'/ \`.\|/,'/|\`.\ /,'/|\/ C>--------G>--------D>--/-|-\-A> / |/
| / Av--/---\-Ev--/-|-\-Bv / |/,'/ \`.\|/,'/|\`.\ /,'/|\/ C>--------G>-
. |/,'/|\/ \ /,\/| / Dv-------Av--/---\-Ev--/-|---Bv / |/,'/ \`.\|/,'/|
-F<--/-|/\-C< /\|/,'/ \`.\|/,'/|\/.\ /,\/| / Dv--------Av--------Ev--/-|-
\/| / Eb<-------Bb<-/---\-F<--/-|/\-C< /\|/,'/ \`.\|/,'/|\/.\ /,'/| / Dv
/\|/,'/ \`.\|/,'/|\/ \/| / Eb<-------Bb<-------F<--/-|/\-C< /\|/,'/ \
-B{--/---\-F#{ / |/\ /\|/,'/ \`.\|/,'/|\/ \/| / Eb<-------Bb<-/---
'/|\/ \/| / E{--------B{------\-F#{ / |/\ /\|/,'/ \`.\|/,'/|\/
/ |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E{--------B{--/---\-F#{ / |/\
F---------C--/---\--G / |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E{------
'/ \`.\ /,'/|\/ \/| / F---------C--/---\--G / |/\ /\|/,'/ \`.\ /
/---\-Ab} / |/\ /\|/,'/ \`.\ /,'/|\/ \/| / F---------C--/---\--G
\/| / Gb}-------Db}-/---\-Ab} / |/\ /\|/,'/ \`.\ /,'/|\/ \/|
/\|/ /|\`.\ /,'/|\/ \/| / Gb}-------Db}-/---\-Ab} / |/\ /\|/
------D>--/-|-\-A> / |/\ /\|/,'/|\`.\ /,'/|\/ \/| / Gb}-\---/-Db}
.\ /,'/|\/ C>--------G>--------D>--/-|-\-A> / |/\ /\|/,'/|\`.\ /,'/|\
-Bv / |/,'/ \`.\|/,'/|\`.\ /,'/|\/ C>--------G>--------D>--/-|-\-A> / |/
| / Av--/---\-Ev--/-|-\-Bv / |/,'/ \`.\|/,'/|\`.\ /,'/|\/ C>--------G>-
. |/,'/|\/ \ /,\/| / Dv-------Av--/---\-Ev--/-|---Bv / |/,'/ \`.\|/,'/|
-F<--/-|/\-C< /\|/,'/ \`.\|/,'/|\/.\ /,\/| / Dv--------Av--------Ev--/-|-
\/| / Eb<-------Bb<-/---\-F<--/-|/\-C< /\|/,'/ \`.\|/,'/|\/.\ /,'/| / Dv
/\|/,'/ \`.\|/,'/|\/ \/| / Eb<-------Bb<-------F<--/-|/\-C< /\|/,'/ \
-B{--/---\-F#{ / |/\ /\|/,'/ \`.\|/,'/|\/ \/| / Eb<-------Bb<-/---
'/|\/ \/| / E{--------B{------\-F#{ / |/\ /\|/,'/ \`.\|/,'/|\/
/ |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E{--------B{--/---\-F#{ / |/\
F---------C--/---\--G / |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E{------
'/ \`.\ /,'/|\/ \/| / F---------C--/---\--G / |/\ /\|/,'/ \`.\ /
/---\-Ab} / |/\ /\|/,'/ \`.\ /,'/|\/ \/| / F---------C--/---\--G

🔗monz <joemonz@yahoo.com>

5/12/2001 8:39:18 AM

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:

/tuning/topicId_22407.html#22407

> [some of the connections were missing or incomplete before]
>

OK, let's see if I can get this to work this time.
Hopefully it won't look like jumbled garbage again.
(If it does... sorry. I'll just put it on a webpage.)

Paul's 7-limit lattice of "Blackjack"
in Monzo ASCII 72-EDO notation

F.........C../...\..G / |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E-
......
'/ \`.\ /,'/|\/ \/| / F.........C../...\..G / |/\ /\|/,'/
\`.\ /
/...\.Ab+ / |/\ /\|/,'/ \`.\ /,'/|\/ \/| /
F.........C../...\..G
\/| / Gb+.......Db+./...\.Ab+ / |/\ /\|/,'/ \`.\ /,'/|\/
\/|
/\|/ /|\`.\ /,'/|\/ \/| / Gb+.......Db+./...\.Ab+ / |/
\ /\|/
......D>../.|.\.A> / |/\ /\|/,'/|\`.\ /,'/|\/ \/| /
Gb+.\.../.Db+
.\ /,'/|\/ C>........G>........D>../.|.\.A> / |/\ /
\|/,'/|\`.\ /,'/|\
.Bv / |/,'/ \`.\|/,'/|\`.\ /,'/|\/
C>........G>........D>../.|.\.A> / |/
| / Av../...\.Ev../.|.\.Bv / |/,'/ \`.\|/,'/|\`.\ /,'/|\/
C>........G>.
. |/,'/|\/ \ /,\/| / Dv.......Av../...\.Ev../.|...Bv / |/,'/
\`.\|/,'/|
.F<../.|/\.C< /\|/,'/ \`.\|/,'/|\/.\ /,\/| /
Dv........Av........Ev../.|.
\/| / Eb<.......Bb<./...\.F<../.|/\.C< /\|/,'/
\`.\|/,'/|\/.\ /,'/| / Dv
/\|/,'/ \`.\|/,'/|\/ \/| / Eb<.......Bb<.......F<../.|/\.C< /
\|/,'/ \
.B-../...\.F#- / |/\ /\|/,'/ \`.\|/,'/|\/ \/| /
Eb<.......Bb<./...
'/|\/ \/| / E-........B-......\.F#- / |/\ /\|/,'/ \`.\|/,'/|\/
/ |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E-........B-../...\.F#- / |/\
F.........C../...\..G / |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E-
......
'/ \`.\ /,'/|\/ \/| / F.........C../...\..G / |/\ /\|/,'/
\`.\ /
/...\.Ab+ / |/\ /\|/,'/ \`.\ /,'/|\/ \/| /
F.........C../...\..G
\/| / Gb+.......Db+./...\.Ab+ / |/\ /\|/,'/ \`.\ /,'/|\/
\/|
/\|/ /|\`.\ /,'/|\/ \/| / Gb+.......Db+./...\.Ab+ / |/
\ /\|/
......D>../.|.\.A> / |/\ /\|/,'/|\`.\ /,'/|\/ \/| /
Gb+.\.../.Db+
.\ /,'/|\/ C>........G>........D>../.|.\.A> / |/\ /
\|/,'/|\`.\ /,'/|\
.Bv / |/,'/ \`.\|/,'/|\`.\ /,'/|\/
C>........G>........D>../.|.\.A> / |/
| / Av../...\.Ev../.|.\.Bv / |/,'/ \`.\|/,'/|\`.\ /,'/|\/
C>........G>.
. |/,'/|\/ \ /,\/| / Dv.......Av../...\.Ev../.|...Bv / |/,'/
\`.\|/,'/|
.F<../.|/\.C< /\|/,'/ \`.\|/,'/|\/.\ /,\/| /
Dv........Av........Ev../.|.
\/| / Eb<.......Bb<./...\.F<../.|/\.C< /\|/,'/
\`.\|/,'/|\/.\ /,'/| / Dv
/\|/,'/ \`.\|/,'/|\/ \/| / Eb<.......Bb<.......F<../.|/\.C< /
\|/,'/ \
.B-../...\.F#- / |/\ /\|/,'/ \`.\|/,'/|\/ \/| /
Eb<.......Bb<./...
'/|\/ \/| / E-........B-......\.F#- / |/\ /\|/,'/ \`.\|/,'/|\/
/ |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E-........B-../...\.F#- / |/\
F.........C../...\..G / |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E-
......
'/ \`.\ /,'/|\/ \/| / F.........C../...\..G / |/\ /\|/,'/
\`.\ /
/...\.Ab+ / |/\ /\|/,'/ \`.\ /,'/|\/ \/| /
F.........C../...\..G
\/| / Gb+.......Db+./...\.Ab+ / |/\ /\|/,'/ \`.\ /,'/|\/
\/|
/\|/ /|\`.\ /,'/|\/ \/| / Gb+.......Db+./...\.Ab+ / |/
\ /\|/
......D>../.|.\.A> / |/\ /\|/,'/|\`.\ /,'/|\/ \/| /
Gb+.\.../.Db+
.\ /,'/|\/ C>........G>........D>../.|.\.A> / |/\ /
\|/,'/|\`.\ /,'/|\
.Bv / |/,'/ \`.\|/,'/|\`.\ /,'/|\/
C>........G>........D>../.|.\.A> / |/
| / Av../...\.Ev../.|.\.Bv / |/,'/ \`.\|/,'/|\`.\ /,'/|\/
C>........G>.
. |/,'/|\/ \ /,\/| / Dv.......Av../...\.Ev../.|...Bv / |/,'/
\`.\|/,'/|
.F<../.|/\.C< /\|/,'/ \`.\|/,'/|\/.\ /,\/| /
Dv........Av........Ev../.|.
\/| / Eb<.......Bb<./...\.F<../.|/\.C< /\|/,'/
\`.\|/,'/|\/.\ /,'/| / Dv
/\|/,'/ \`.\|/,'/|\/ \/| / Eb<.......Bb<.......F<../.|/\.C< /
\|/,'/ \
.B-../...\.F#- / |/\ /\|/,'/ \`.\|/,'/|\/ \/| /
Eb<.......Bb<./...
'/|\/ \/| / E-........B-......\.F#- / |/\ /\|/,'/ \`.\|/,'/|\/
/ |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E-........B-../...\.F#- / |/\
F.........C../...\..G / |/\ /\|/,'/ \`.\ /,'/|\/ \/| / E-
......
'/ \`.\ /,'/|\/ \/| / F.........C../...\..G / |/\ /\|/,'/
\`.\ /
/...\.Ab+ / |/\ /\|/,'/ \`.\ /,'/|\/ \/| /
F.........C../...\..G

🔗monz <joemonz@yahoo.com>

5/12/2001 8:44:29 AM

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22407.html#22544

> OK, let's see if I can get this to work this time.
> Hopefully it won't look like jumbled garbage again.
> (If it does... sorry. I'll just put it on a webpage.)
>
>
> Paul's 7-limit lattice of "Blackjack"
> in Monzo ASCII 72-EDO notation

OK, shoot... I give up. :(

Here it is in a form that's legible:

/tuning/files/monz/bj-lattice.txt

-monz
http://www.monz.org
"All roads lead to n^0"