Claudio wrote:

 > (...) My main objection to your Bach temperament is a small, simple
 > thing, but with far-reaching implications: your system makes E major
 > the worst tonality, even if Bach wrote quite a few important works 
for > it (as detailed in my book). Conversely, you make more consonant 
other > tonalities (F# major, C#/Db major) for which Bach hardly wrote 
at all.
 > (...)

Thanks for the cordial and complimentary reply!

The E-G# in my system is wide-ish, yes; but as you know, Vallotti's has 
THREE major 3rds larger than that, and Barnes's has two.  So, anyone 
favoring either Barnes or Vallotti can't really object to the mere size 
of E-G#, but only to its placement.  It breaks the *expectation* that 
the widest should be on F#-A#, B-D#, Ab-C, or Db-F (Lindley 
perpetually!).  Those four are classically the wolves, coming down from 
meantone.  Well, as you also know, there are also some of Neidhardt's 
and Sorge's published systems that do have E-G# as their widest major 
3rd.  If one accepts E-G# as slightly wider than all four of F#-A#, 
B-D#, Ab-C, and Db-F, all the old meantone-inherited problems are wiped 
out.  It looked ridiculous to me, too, until I actually tried it.

One might also think of it this way: the note G#/Ab is closer to C (the 
home key of tonality) by moving four 5ths flatward than by moving eight 
5ths sharpward; so, why *shouldn't* E-G# be at least as wide as Ab-C?

It's not merely a matter of looking at what Bach used as tonic triads. 
It's a look at where he went inside compositions.  To me, playing in 
Barnes, I can't stand the way it makes the music sound: whenever F minor 
or C minor music modulates to the related major keys, or whenever the 
hideous dominant F# major comes up within music in B minor and E minor.

For that matter, in the Bach E major harpsichord music (WTC, Invention, 
Sinfonia, early Capriccio, French suite, concerto...)...why "should" we 
expect things to go farther and farther out of tune whenever the music 
does ordinary things with dominants, secondary dominants, or into the 
relative minor (C# minor)?  Why "should" there be a lousy B# and E# when 
it gets near C# minor, or a hotly high A# anywhere, since these are 
perfectly normal notes (for Bach) within E major?

We can't just point in isolation at a tonic triad such as E and assert 
that things are "worst" there, as if that's all that matters.  The 
primary reason why meantone-inherited temperaments such as Barnes's 
don't work -- at least for me -- is that all these extreme sharps or 
flats aren't treated smoothly enough.  They sound more exotic than they 
necessarily would need to.

Apropos of my temperament getting a good workout and use: this week I'm 
enjoying Julia Brown's new Naxos disc of WF Bach fantasias and fugues. 
Those things go to some of the wildest spots, and apparently for shock 
value sometimes.  That's on a Kingston harpsichord.  There are at least 
three complete sets of WTC 1 out now (Watchorn, Egarr, Beausejour), plus 
the excerpts disc by me, giving good opportunity to hear how it 
interacts with players of different personal temperament in the music. 
I get complaints from some people that the tuning sounds too moderate 
for their tastes, and complaints that it's too spicy for others, or 
peaks in the "wrong" place.  There are also plenty who don't even know 
it's in there, like on Beausejour's and Brown's, because the program 
notes say nothing; where the reviewers simply say things like "that 
instrument sounds especially good", I recognize that the temperament is 
drawing no undue attention to itself, but rather highlighting the music 
and the instrument's tone appropriately.


Brad Lehman