'dominant 7th' tuning

[Dave Keenan, TD 178.7]
> One such possibility for the dominant 7th is
> C E G Bb Errors in 12-tET
> ------------------------------
> 4:5:6 +13.6c, -15.6c, -2.0c
> 5:6 -15.6c
> 5 : 7 +17.5c
> 5 : 9 -17.6c

Your point was clearer to me with lattice diagrams,
so I'll share them:

Monzo lattice

()
/ '-._
/ Bb
/ /
G /
/ '-._ /
E / ()
'-._ /
C --..___
'-- Bb

Paul/Paul lattice

E
/|\
/ | \
/ Bb \
/,' `.\
C---------G
\
\
\
\
Bb

Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

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Joe Monzo wrote:

>[Dave Keenan, TD 178.7]
>> One such [contradictory consonance] possibility for the dominant 7th is
>> C E G Bb Errors in 12-tET
>> ------------------------------
>> 4:5:6 +13.6c, -15.6c, -2.0c
>> 5:6 -15.6c
>> 5 : 7 +17.5c
>> 5 : 9 -17.6c
>
>
>Your point was clearer to me with lattice diagrams,
>so I'll share them:
...
>Paul/Paul lattice
>
> E
> /|\
> / | \
> / Bb \
> /,' `.\
>C---------G
> \
> \
> \
> \
> Bb

Thanks Monz. Almost correct. Try

E
/|\
/ | \
/ Bb \
/ \
C---------G
`. \
`. \
`. \
`. \
Bb

But E could also be chosen as the one that appears in two places. e.g.

E
/ \
/ \
/ \
/ \
C---------G
`. \
`. \ E
`. \ |
`. \|
Bb

And possibly others. All such lattices are treated equally by the
appropriate temperament.

Regards,
-- Dave Keenan
http://dkeenan.com