Updated and new web pages

I added a few more retunings to the Pavane for a Warped Princess page. The
big surprise is 64-ET. I tried it to see just how bad it would be, but it
turned out to be better than many of the other non-meantones. It turns out
that 64-ET's "wolf" fifth is really a pretty good fifth after all. The
comma is negative, so the wolf fifth ends up sharper than just: only a
little bit sharper than the regular 64-ET fifth is flat. And since 64-ET is
inconsistent, the sharp fifth improves the minor third. It's interesting
that inconsistency can be an advantage in this case.

So I sorted the list of tunings by the size of the wolf fifth. It seems to
be as good an ordering as any, for an initial pass, but there are a few
tunings that sound out of place in the listing.

http://www.io.com/~hmiller/music/pavane.html

And I added a new page on porcupine temperament, with an illustration of a
possible notation system. To avoid confusion with standard notation, I'm
using lowercase letters for the basic 7-note MOS. The 15-note MOS uses Dave
Keenan's "[ ]" symbols for the 33;32 comma "flat" and "sharp".

. g] d]
. e b f]
. c[ g d a e]
. b[ f c
. d[ a[

I also moved the porcupine chord progression example to this page from the
Canon page.

http://www.io.com/~hmiller/music/temp-porcupine.html

--
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

hi Herman,

> From: Herman Miller <hmiller@IO.COM>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, March 02, 2002 7:47 PM
> Subject: [tuning] Updated and new web pages
>
>
> I added a few more retunings to the Pavane for a Warped Princess page. The
> big surprise is 64-ET. I tried it to see just how bad it would be, but it
> turned out to be better than many of the other non-meantones. It turns out
> that 64-ET's "wolf" fifth is really a pretty good fifth after all. The
> comma is negative, so the wolf fifth ends up sharper than just: only a
> little bit sharper than the regular 64-ET fifth is flat. And since 64-ET
is
> inconsistent, the sharp fifth improves the minor third. It's interesting
> that inconsistency can be an advantage in this case.
>
> So I sorted the list of tunings by the size of the wolf fifth. It seems to
> be as good an ordering as any, for an initial pass, but there are a few
> tunings that sound out of place in the listing.
>
> http://www.io.com/~hmiller/music/pavane.html

this is really great! i saw your previous posts on it but
have only now had time to take a peek.

i agree with you that 64edo sounds terrific for this piece!

others of my favorites, in order, are 40 and 28.

all the meantones work, but have a flatness (narrowness)
to some of the intervals that doesn't sound as effective
to me as 64, 40, or 28.

of the lowest-cardinality EDOs, my fave is 14.

-monz

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--- In tuning@y..., Herman Miller <hmiller@I...> wrote:
> I added a few more retunings to the Pavane for a Warped Princess
page. The
> big surprise is 64-ET. I tried it to see just how bad it would be,
but it
> turned out to be better than many of the other non-meantones. It
turns out
> that 64-ET's "wolf" fifth is really a pretty good fifth after all.
The
> comma is negative, so the wolf fifth ends up sharper than just:
only a
> little bit sharper than the regular 64-ET fifth is flat. And since
64-ET is
> inconsistent, the sharp fifth improves the minor third. It's
interesting
> that inconsistency can be an advantage in this case.

64-equal has always been my favorite example of a tuning where the
best triad has neither the best fifth nor the best major third. iirc.

> So I sorted the list of tunings by the size of the wolf fifth. It
seems to
> be as good an ordering as any, for an initial pass, but there are a
few
> tunings that sound out of place in the listing.
>
> http://www.io.com/~hmiller/music/pavane.html

this is truly awesome. thank you for doing this!

am i correct that in the non-meantone tunings, you still only use 12
pitches per octave? you might want to specify on the page whether
this is the case or not.

On Sun, 03 Mar 2002 08:20:05 -0000, "asarkiss" <asarkiss@yahoo.com> wrote:

>am i correct that in the non-meantone tunings, you still only use 12
>pitches per octave? you might want to specify on the page whether
>this is the case or not.

I do make the distinction between G# and Ab, which brings the total to 13
distinct pitches. I still plan on eventually providing adjusted versions of
some of the tunings, with more than 13 pitches, although I'll probably
leave the original unadjusted versions for comparison. But first I need to
figure out which version of the harmony on the 5-limit lattice makes the
most sense, and whether or not it would be appropriate to include a few
7-limit intervals in some cases.

--
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

On 3/2/02 10:47 PM, "Herman Miller" <hmiller@IO.COM> wrote:

> It turns out that 64-ET's "wolf" fifth is really a pretty good fifth after
> all. The comma is negative, so the wolf fifth ends up sharper than just: only
> a little bit sharper than the regular 64-ET fifth is flat.

I occasionally find intervals in higher temperaments and don't realize that
they're multiples of things I've already used. After spending a day or so
messing with the 9/37 minor third, I realized it was 27/111, the Pythagorean
minor third from 111.

The "wolf fifth" in 64, 712.5¢, 38/64... Is also 19/32. It's the usual
fifth from 32-tET which can be, I've heard, very useable.