Two 12-ets and a comma

Two 12-et scales, separated by a comma of 23.4 cents, would allow a
considerable improvement of the 12-et thirds and an even more
striking improvement of the 7. Has this idea been suggested before?
It came up in the course of a systematic survey of 7-limit linear
temperaments.

I believe Margo covered quite a bit of this territory!

genewardsmith@juno.com wrote:

> Two 12-et scales, separated by a comma of 23.4 cents, would allow a
> considerable improvement of the 12-et thirds and an even more
> striking improvement of the 7. Has this idea been suggested before?
> It came up in the course of a systematic survey of 7-limit linear
> temperaments.
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., genewardsmith@j... wrote:

> Two 12-et scales, separated by a comma of 23.4 cents, would allow a
> considerable improvement of the 12-et thirds and an even more
> striking improvement of the 7. Has this idea been suggested before?
> It came up in the course of a systematic survey of 7-limit linear
> temperaments.

I did this many years ago on my Casio. I simply couldn't get used to
the major thirds being 10 cents flat of JI. I guess a lifetime of
hearing them 14 cents sharp ruins you for the flat ones forever.

Much better, but only 5-limit, is my frequent suggestion of two 12-
tET scales separated by 15 cents. I just brought this up again on
tuning-math@yahoogroups.com.

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> I believe Margo covered quite a bit of this territory!

Not that I recall(!) . . . Margo?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

> I did this many years ago on my Casio. I simply couldn't get used
to
> the major thirds being 10 cents flat of JI. I guess a lifetime of
> hearing them 14 cents sharp ruins you for the flat ones forever.

You are a big fan of the 22-et. Where do you draw the line?

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > I did this many years ago on my Casio. I simply couldn't get used
> to
> > the major thirds being 10 cents flat of JI. I guess a lifetime of
> > hearing them 14 cents sharp ruins you for the flat ones forever.
>
> You are a big fan of the 22-et. Where do you draw the line?

The major thirds are only 3 or 4 cents flat in 22-tET -- they sound
just in most registers.

The major third is much flatter still in 26-tET; somehow the good
minor third makes the 26-tET triads OK, once I spend some time
getting used to the sound. The fact that it's meantone also helps in
the familiarity department.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_30479.html#30484

> --- In tuning@y..., genewardsmith@j... wrote:
>
> > Two 12-et scales, separated by a comma of 23.4 cents, would allow
a
> > considerable improvement of the 12-et thirds and an even more
> > striking improvement of the 7. Has this idea been suggested
before?
> > It came up in the course of a systematic survey of 7-limit linear
> > temperaments.
>
> I did this many years ago on my Casio. I simply couldn't get used
to
> the major thirds being 10 cents flat of JI. I guess a lifetime of
> hearing them 14 cents sharp ruins you for the flat ones forever.
>
> Much better, but only 5-limit, is my frequent suggestion of two 12-
> tET scales separated by 15 cents. I just brought this up again on
> tuning-math@y...

This concept of the parallel 12-tET scales is included in 72-tET,
correct? Do we get the 23 cent separation, though? I know we get a
16 cent and a 33 cent...

Thanks!

JP

--- In tuning@y..., jpehrson@r... wrote:

> This concept of the parallel 12-tET scales is included in 72-tET,
> correct? Do we get the 23 cent separation, though? I know we get
a
> 16 cent and a 33 cent...

The 48-et gives you 25 cents, and is the one to use if you want to
complete this system to an equal temperament.

--- In tuning@y..., genewardsmith@j... wrote:

/tuning/topicId_30479.html#30665

> --- In tuning@y..., jpehrson@r... wrote:
>
> > This concept of the parallel 12-tET scales is included in 72-tET,
> > correct? Do we get the 23 cent separation, though? I know we
get
> a
> > 16 cent and a 33 cent...
>
> The 48-et gives you 25 cents, and is the one to use if you want to
> complete this system to an equal temperament.

Thanks, Gene!

JP