The trouble with Pavane (that syntonic comma again)

I've been trying to make a 22-ET version of Ravel's Pavane, but it just
doesn't want to cooperate. The most troublesome note seems to be the A.
Since it's in G major, this makes a great deal of sense! Clearly, I can't
just pick one version of the A that works for the entire piece: lots of
dissonances result no matter which one I pick.

http://www.io.com/~hmiller/midi/pavane-22-high.mid
http://www.io.com/~hmiller/midi/pavane-22-low.mid

So the only alternative is to use the high A in some contexts and the low A
in others. But that does bad things to the melody!

http://www.io.com/~hmiller/midi/pavane-22-adj.mid

I could keep playing around with this and try to minimize the ugliness. I
could start tweaking a few of the other notes as well. But now I think this
must have been the reason I abandoned the attempt to do the adjusted
retunings. It becomes painfully obvious that Pavane was written for a
meantone temperament, and nothing else quite fits! But if anyone has
suggestions to improve the 22-ET version, I'll try them out.

For comparison, hear how nice the 19-ET version sounds!
http://www.io.com/~hmiller/midi/pavane-19.mid

--
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

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:
> But now I think this
> must have been the reason I abandoned the attempt to do the adjusted
> retunings. It becomes painfully obvious that Pavane was written for
a
> meantone temperament, and nothing else quite fits!

this is exactly what i've said, in general, about translating works
of western common practice music into 22-equal or other blatantly non-
meantone tunings, especially 15-equal, 27-equal, and even 34-equal.

but i wonder: those 40-equal and 64-equal versions monz loved, were
those the meantone implementations of these tunings?

hi Herman,

> From: "Herman Miller" <hmiller@IO.COM>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, October 27, 2002 6:03 PM
> Subject: [tuning] The trouble with Pavane (that syntonic comma again)
>
>
> I've been trying to make a 22-ET version of Ravel's Pavane, but it just
> doesn't want to cooperate. The most troublesome note seems to be the A.
> Since it's in G major, this makes a great deal of sense! Clearly, I can't
> just pick one version of the A that works for the entire piece: lots of
> dissonances result no matter which one I pick.
>
> http://www.io.com/~hmiller/midi/pavane-22-high.mid
> http://www.io.com/~hmiller/midi/pavane-22-low.mid
>
> So the only alternative is to use the high A in some contexts and the low
A
> in others. But that does bad things to the melody!

i had exactly the same problem in retuning the
Beatles's _Glass Onion_ into 22edo!

i think in this case one troublesome note was D.
i chose to use the high one every time.

http://sonic-arts.org/monzo/beatles/glasson2.mid

-monz
"all roads lead to n^0"

hi paul and Herman,

> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, October 27, 2002 7:22 PM
> Subject: [tuning] Re: The trouble with Pavane (that syntonic comma again)
>
>
> but i wonder: those 40-equal and 64-equal versions monz loved, were
> those the meantone implementations of these tunings?

i don't know what the "meantone implementations" of these
two tunings would be, but let's make a deal: i'll provide
the data, you do the analysis.

here are the subsets of 40 and 64edo which Herman used
in his _Pavane_ retunings:

(view in "Expand Messages" mode if viewing on Yahoo website)

40edo
-----

degrees:

0, 3, 6, 10, 13, 17, 19, 23, 27, 30, 33, 36

triangular lattice:

3
/ \
30--13--36--19
/ \ / \ / \ /
17---0--23---6
\ / \ / \ /
27--10--33

64edo
-----

degrees:

0, 5, 10, 16, 21, 27, 31, 37, 43, 48, 53, 58

triangular lattice:

5
/ \
48--21--58--31
/ \ / \ / \ /
27---0--37--10
\ / \ / \ /
43--16--53

i'm *extremely* interested in what you can say
about these two tunings, paul, because in fact i
prefer these two versions of Herman's _Pavane_ to
*any* of the regular meantone versions.

-monz
"all roads lead to n^0"

--- In tuning@y..., "monz" <monz@a...> wrote:
> hi Herman,
>
> > From: "Herman Miller" <hmiller@I...>
> > To: <tuning@y...>
> > Sent: Sunday, October 27, 2002 6:03 PM
> > Subject: [tuning] The trouble with Pavane (that syntonic comma
again)
> >
> >
> > I've been trying to make a 22-ET version of Ravel's Pavane, but
it just
> > doesn't want to cooperate. The most troublesome note seems to be
the A.
> > Since it's in G major, this makes a great deal of sense! Clearly,
I can't
> > just pick one version of the A that works for the entire piece:
lots of
> > dissonances result no matter which one I pick.
> >
> > http://www.io.com/~hmiller/midi/pavane-22-high.mid
> > http://www.io.com/~hmiller/midi/pavane-22-low.mid
> >
> > So the only alternative is to use the high A in some contexts and
the low
> A
> > in others. But that does bad things to the melody!
>
>
>
> i had exactly the same problem in retuning the
> Beatles's _Glass Onion_ into 22edo!

which is *exactly* why i didn't like the result -- and knew i
wouldn't even before i listened to it . . . actually i do like the
way it sounds very much in certain sections, especially those that
feature "augmented sixth" chords . . .

i've been repeating this mantra since joining this list in '96 . . .
meantone tunings like 19 work for common-practice diatonic
music . . . non-meantones like 22 don't . . .

--- In tuning@y..., "monz" <monz@a...> wrote:
> hi paul and Herman,
>
>
>
> > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> > To: <tuning@y...>
> > Sent: Sunday, October 27, 2002 7:22 PM
> > Subject: [tuning] Re: The trouble with Pavane (that syntonic
comma again)
> >
> >
> > but i wonder: those 40-equal and 64-equal versions monz loved,
were
> > those the meantone implementations of these tunings?
>
>
> i don't know what the "meantone implementations" of these
> two tunings would be,

monz -- take a look at xoomer.gif again. 40 appears in three places
on the graph. one of the places it appears is on the meantone line.
so if you use the versions of consonant intervals indicated by *that*
position of 40 on the graph (by eye, it looks like perfect fifth 12
cents narrow, major third 26 cents narrow, minor third 14 narrow
flat), you're using the "meantone implementation" of 40.

the same thing applies to 64, which you can see more clearly in one
of the zooms in the files section. but even on xoomer.gif, you can
see them -- they're really small, and reddish. the hardest-to-see one
is hanging off the right edge of the "9" in "19". that's the meantone
one, of course. it looks like it's using a perfect fifth that's 8
cents narrow, a major third that's 11 cents narrow, and a minor third
that's 3 cents wide.

> but let's make a deal: i'll provide
> the data, you do the analysis.
>
>
> here are the subsets of 40 and 64edo which Herman used
> in his _Pavane_ retunings:
>
> (view in "Expand Messages" mode if viewing on Yahoo website)
>
>
> 40edo
> -----
>
> degrees:
>
> 0, 3, 6, 10, 13, 17, 19, 23, 27, 30, 33, 36
>
>
> triangular lattice:
>
> 3
> / \
> 30--13--36--19
> / \ / \ / \ /
> 17---0--23---6
> \ / \ / \ /
> 27--10--33

13/40 oct. = 390 cents (~4 cents *wide*)

so no, this *isn't* the "meantone implementation" of 40-equal. and in
fact, if you extended the lattice to include herman's alternate
positions, you'd see that they wouldn't agree with the corresponding
notes on this lattice (they only do in a meantone).

so what ends up happening is that you're approximating the same
consonances in *different* ways depending on where you are in the
lattice. had herman drawn this lattice in any of the numerous other
ways possible, the piece would have ended up sounding different,
since the "odd" approximations would appear between different pairs
of pitches.

> 64edo
> -----
>
> degrees:
>
> 0, 5, 10, 16, 21, 27, 31, 37, 43, 48, 53, 58
>
>
> triangular lattice:
>
> 5
> / \
> 48--21--58--31
> / \ / \ / \ /
> 27---0--37--10
> \ / \ / \ /
> 43--16--53

21/64 oct. = 393.75 cents =~ 6 cents *wide* -> not meantone imp.

same deal!

> i'm *extremely* interested in what you can say
> about these two tunings, paul, because in fact i
> prefer these two versions of Herman's _Pavane_ to
> *any* of the regular meantone versions.

by drawing the lattice in different ways, herman could potentially
create *many* different 40-equal and 64-equal versions like these,
but with the "odd" intervals occuring at different locations in the
scale.

On Mon, 28 Oct 2002 03:22:48 -0000, "wallyesterpaulrus"
<wallyesterpaulrus@yahoo.com> wrote:

>but i wonder: those 40-equal and 64-equal versions monz loved, were
>those the meantone implementations of these tunings?

IIRC, they were the diminished temperament versions of those tunings. The
reason they sound so much better than the other non-meantone versions is
that the syntonic comma goes negative, making the "wolf fifths" sharper
than just.

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:
> On Mon, 28 Oct 2002 03:22:48 -0000, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> >but i wonder: those 40-equal and 64-equal versions monz loved,
were
> >those the meantone implementations of these tunings?
>
> IIRC, they were the diminished temperament versions of those
tunings. The
> reason they sound so much better than the other non-meantone
versions is
> that the syntonic comma goes negative, making the "wolf fifths"
sharper
> than just.

thanks herman, i left that fact out of my analysis.