you _can_ modulate freely in meantone!

John A. deLaubenfels wrote,

>Meantone is fine for pieces that don't modulate a whole lot. My problem
>is, when I'm playing I don't want to be confined to a narrow set of
>keys; I want to modulate freely.

In meantone you don't have to be confined to a narrow set of keys unless you
only allow 12 pitches per octave. You can modulate freely in either an open
meantone temperament, where sharps and flats are different and double sharps
and double flats are different from naturals and so on ad infinitum, or you
can use an ET such as 31-tET to modulate infinitely with only a finite
number of pitches. I'm surprised that you of all people would assume 12
fixed pitches per octave!

Dave Keenan's dynamic retuning program allows one to use the 12 keys of the
keyboard to realize the limitless (actually, in his case, a closed cycle of
31) modulation possibilities of meantone.

[I wrote:]
>> Meantone is fine for pieces that don't modulate a whole lot. My
>> problem is, when I'm playing I don't want to be confined to a narrow
>> set of keys; I want to modulate freely.

[Paul Erlich/Brett Barbaro wrote:]
> In meantone you don't have to be confined to a narrow set of keys
> unless you only allow 12 pitches per octave. You can modulate freely
> in either an open meantone temperament, where sharps and flats are
> different and double sharps and double flats are different from
> naturals and so on ad infinitum, or you can use an ET such as 31-tET
> to modulate infinitely with only a finite number of pitches. I'm
> surprised that you of all people would assume 12 fixed pitches per
> octave!

I, of all people, most certainly do NOT assume 12 fixed pitches per
octave. I was responding to a post from Graham Breed in which he (I
think) is advocating a fixed number of pitches per octave, in meantone.

Just a few lines up from the ones you quote, I wrote:

>> Adaptive tuning works best, I agree, when one has the whole pitch
>> spectrum available.

and

>> Why does it matter that you have more than 12 notes per octave,
>> especially if your INPUT is still 12/octave?

Perhaps you missed those lines?

I would never imply that it is not possible to stretch meantone.
Nevertheless, having taken the trouble to equip myself with the means to
tune in real-time, I choose to tune in JI. Why cramp the fifths to get
good thirds when that trade-off is not necessary?

> Dave Keenan's dynamic retuning program allows one to use the 12 keys
> of the keyboard to realize the limitless (actually, in his case, a
> closed cycle of 31) modulation possibilities of meantone.

I will check that out. It's on his web site, I assume?

I just reviewed the math of 31-tET, and see that it is almost PERFECTLY
aligned with 1/4 comma meantone. There is a part of me that takes great
delight in this kind of ET game. By narrowing the fifths, 31-tET
finesses the comma problem of the I-vi-ii-V-I progression, unlike 22-tET
and others: there is no microtonal motion. Still, 5.18 cents error in
the fifth is hard for me to swallow: I love the peaceful pure open fifth
when it's well-tuned (even better than 12-tET's modest 1.96 cents error
if possible - and, of course, it IS possible...).

JdL