wedgie info

I've changed the subject line and migrated this over to
this list ...

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
>
> > I didn't know that the wedgie gave away that info!
>
> <snip>
>
> The 13 doesn't represent the 13-identity. The second 4 means
> that if the period is a 3, then there are 4 generators (3/2
> being a generator) to the 5;

You already lost me here. Is there some reason why
meantone would ever have a period of 3? Can you tabulate
step by step how the 4 generators map the 5 when the
period is 3?

> the 13 then means there are 13 generators to the 7
> (27*7 = 189 is 13 fifths.)

Since i don't understand the simpler mapping to 5,
i'm afraid this doesn't make sense either. Where did
the 27 come from?

> Finally, the period can't be 5, but can be taken to be
> 5^(1/4), in which case the generator can be taken as 1/2,
> or 5^(1/2)/2 if you reduce to [1,5^(1/4)]. Now 12 is the
> number of generators (3) to get to 7, times the number of
> periods in the period-prime of 5 (4.)

Again, i think i need to work out the math here step by step
to see it happen.

-monz
http://tonalsoft.com
Tonescape microtonal music software