More on the naming convention

The 5-limit temperament with Ampersand's comma, 7-limit miracle, and
11-limit miracle all have identical TOP tunings of the primes they
cover. Should the Ampersand temperament simply be called miracle?

One might extend this convention to closest points among reasonable
temperament choices. For instance, the 225/224-planar temperament has
TOP tuning [1200.493660, 1901.172569, 2785.167472, 3370.211784]. The
nearest reasonable TOP point in val space to this seems to be 11-limit
marvel, with TOP tuning [1200.508704, 1901.148724, 2785.132538,
3370.019002, 4149.558115]. The projection of this point into 7-limit
val space is at a distance of 0.06867 cents from 225/224-planar TOP,
which seems to me to justify my proposal to give the 7 and 11 limit
planar temperaments the same name of "marvel". A little farther out,
at a distance of 0.08519 cents is the {225/224, 14700/14641}-planar
temperament, which is both a worse temperament and farther away.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> The 5-limit temperament with Ampersand's comma, 7-limit miracle, and
> 11-limit miracle all have identical TOP tunings of the primes they
> cover.

Wow. I'm assuming you gave this tuning in your message giving a few 7-
limit linear TOP tunings.

> Should the Ampersand temperament simply be called miracle?

If it's all the same pitches, I suppose that makes some sense . . .

> One might extend this convention to closest points among reasonable
> temperament choices. For instance, the 225/224-planar temperament
has
> TOP tuning [1200.493660, 1901.172569, 2785.167472, 3370.211784]. The
> nearest reasonable TOP point in val space to this seems to be 11-
limit
> marvel, with TOP tuning [1200.508704, 1901.148724, 2785.132538,
> 3370.019002, 4149.558115]. The projection of this point into 7-limit
> val space is at a distance of 0.06867 cents from 225/224-planar TOP,
> which seems to me to justify my proposal to give the 7 and 11 limit
> planar temperaments the same name of "marvel".

But they have different pitches, right?

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:

> > One might extend this convention to closest points among
reasonable
> > temperament choices. For instance, the 225/224-planar temperament
> has
> > TOP tuning [1200.493660, 1901.172569, 2785.167472, 3370.211784].
The
> > nearest reasonable TOP point in val space to this seems to be 11-
> limit
> > marvel, with TOP tuning [1200.508704, 1901.148724, 2785.132538,
> > 3370.019002, 4149.558115]. The projection of this point into 7-
limit
> > val space is at a distance of 0.06867 cents from 225/224-planar
TOP,
> > which seems to me to justify my proposal to give the 7 and 11
limit
> > planar temperaments the same name of "marvel".
>
> But they have different pitches, right?

Yes, but that is a situation which often arises for names already in
use among planar temperaments. I'm suggesting we systematize things a
little better by using TOP and the val space to sort things out for
us.

On Thu, 15 Jan 2004 19:36:05 -0000, "Gene Ward Smith" <gwsmith@svpal.org>
wrote:

>The 5-limit temperament with Ampersand's comma, 7-limit miracle, and
>11-limit miracle all have identical TOP tunings of the primes they
>cover. Should the Ampersand temperament simply be called miracle?

I'd say "5-miracle" for Ampersand, "7-miracle" for 7-limit miracle, and
"11-miracle" for 11-limit miracle.

Not to be confused with "miracle-21", which is a 21-note miracle tuning.
You could have both a prefix and suffix number, such as "7-meantone-19" for
a 19-note scale of 7-limit meantone.

>One might extend this convention to closest points among reasonable
>temperament choices. For instance, the 225/224-planar temperament has
>TOP tuning [1200.493660, 1901.172569, 2785.167472, 3370.211784]. The
>nearest reasonable TOP point in val space to this seems to be 11-limit
>marvel, with TOP tuning [1200.508704, 1901.148724, 2785.132538,
>3370.019002, 4149.558115]. The projection of this point into 7-limit
>val space is at a distance of 0.06867 cents from 225/224-planar TOP,
>which seems to me to justify my proposal to give the 7 and 11 limit
>planar temperaments the same name of "marvel". A little farther out,
>at a distance of 0.08519 cents is the {225/224, 14700/14641}-planar
>temperament, which is both a worse temperament and farther away.

Or "7-marvel" and "11-marvel" to be specific. If the context is clear (in a
list of 7-limit temperaments, for instance), just "miracle" or "marvel"
would suffice. This sounds like a good plan in general.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

>Not to be confused with "miracle-21", which is a 21-note miracle tuning.
>You could have both a prefix and suffix number, such as "7-meantone-19"
>for a 19-note scale of 7-limit meantone.

The convention is square brackets for cards, "miracle[21]", etc.

-Carl