Hendrik Broekman wrote:
 > (...)
 > For my own ears, I find 1/5 MT and its ordinaire extensions to be the
 > most useful over a large swath of the 17th & 18th c. literature &
 > instruments.  The good diatonic chords have a warm texture, even more
 > quiet and stable than 1/4 MT thanks to the slower 5th and its equally
 > slow +3rd.  Depending on the extensions one has applied (or not) to
 > the chromatics, the effect of playing away from the center of the
 > temperament can be almost as excruciating as 1/4 MT or quite
 > acceptable.  As Owen so correctly observes, this can be highly
 > dependent on the individual instrument. (...)

Amen to all that.  The playing of misspelled notes (wrong enharmonics) 
is its own problem.

If something is going to be regular (whether 1/4, 1/5, 1/6, somewhere in 
between, whatever), at least on the naturals: for me and my own 
"musician's point of view", the correctly-spelled major 3rds are not the 
main issue.  They'll take care of themselves, and the ear quickly 
adjusts to enjoy whatever size the major 3rd happens to be, as long as 
the other major 3rds in related keys sound somewhat similar.  I like 5:4 
pure 3rds as much as anybody (in 1/4 comma); I also like slightly wider 
3rds, for the *different* reason that they make better contrapuntal 
forward motion.  If I'm just going to be plowing through a bunch of 16th 
century repertoire, or early-17th such as that terrific A-R book of 
"English Pastime Music", based more on full and common triads than on 
contrapuntal interplay...then I'll most often pick 1/4 comma.  Let's 
wallow in those static major 3rds within full triads.  Play it and sit 
there until the next harmony comes along, to be wallowed in.  Yum.

No.  Most of the 17th century music I play is either in _style brise_, 
or contrapuntally complex, or both at once.  Regular 1/5 and 1/6 make me 
feel more comfortable *melodically* than 1/4 does.  Huge diatonic 
semitones (as in 1/4) distract me...and they seem more static than 
forward-going.

But furthermore, and this is my main point: the main problem (for me) 
with regular 1/4 comma is the rough 5ths and 4ths.  When the 
counterpoint is chuckling along nicely, I really don't like to have my 
ear drawn suddenly to ugly 5ths or 4ths, especially in suspensions, that 
are yakketing vigorously with 1/4 comma errors in them.  These sounds do 
occur, and there's no major or minor 3rd of any size to distract us away 
from them.  The 4ths and 5ths get played directly, sometimes with 
another tempered 4th suspended into them.  They'd better sound decent. 
[And 1/4 comma naturals, played that way, sound nasty...at least on my 
main Flemish hpsi here.]

Here is a concrete example.  It's the first two pages from one of the 
stanzas in Böhm's "Christe, der du bist Tag und Licht".  Print these out 
and play through all the circled spots, with regular 1/4 comma on all 
your naturals.  (It might be necessary, at least with Internet Explorer, 
to reduce both these pages to 40% or so, before printing.)
http://www-personal.umich.edu/~bpl/bohm_du_bist_p1.gif
http://www-personal.umich.edu/~bpl/bohm_du_bist_p2.gif

Playing straight through both pages, don't your ears get drawn to those 
suddenly-rough spots of heavily tempered 4ths/5ths?  Mine certainly do. 
  Those rapidly-beating harmonic moments disturb my concentration on the 
melodic flow of the music.

On the separate question of playing correctly-spelled accidentals, this 
piece shows off the common problem of using both G# and Ab in the same 
composition.  Here they're only 7 bars apart: G# within an E major triad 
in bar 27, and Ab as the bass of an Ab major triad (with C on top!) in 
bar 34.  There is also the blatant playing of an Ab to C 10th in bar 45, 
with no other voices to soften this.  I've put rectangular boxes around 
these various spots.  Have a play at it.  Tune the G#/Ab, and the other 
accidentals, however you want to....

I gravitate toward 1/5 and 1/6 comma in this repertoire for the reasons 
stated above...*and* for the musicianly reason that it makes it easier 
to find workable spots to put the compromised accidentals.  If we're in 
something as tight as 1/4 comma, there's just no maneuvering room left. 
  Make your C-E pure, and you're stuck: both of E-G# and Ab-C are 
constrained to be nearly Pythagorean.  Same way for G-B.  If it's pure, 
there's no place left over to put D#/Eb without having either B-D# or 
Eb-G (or both!) quite nasty.

I used 1/4 comma based temperaments for years.  I was seduced by those 
lovely pure 3rds.  But, these other two huge problems (the yakkety 
5ths/4ths, and the D#/Eb/G#/Ab placements) eventually compelled me to 
change my mind.  1/4 comma made my instruments too frequently sound 
distractingly ugly, through spots of music that look normal and 
unproblematic on the page.

When Tilman S was here last year to have a go at my instruments, I had 
them all set up differently from one another, for contrast.  I had the 
Bach on the good Flemish and on the clavichord.  The junker had regular 
1/6.  And (if I recall correctly) the Italian virginal had either 1/5 or 
1/4...because I'd been bashing through the "English Pastime Music" and 
the Fitzwilliam VB on that one.


Brad Lehman