[CAUT] temperament for Schubert

[Fred Sturm]

On Jan 18, 2009, at 3:14 PM, A440A at aol.com wrote:

> After the performance, when I asked for a critique of the tuning, he  
> told me
> that for the first time in his life, "the overtones were perfectly  
> lined up".
> I told him that it was not in ET and he said he didn't care what it  
> was, but
> that he wished all pianos were tuned like that.

Hi Ed,
	I have no doubt you are reporting an experience accurately. As to how  
to interpret it, I am not so sure I agree with your take, that the  
temperament prompted the praise, particularly considering the  
statement "the overtones were perfectly lined up." In a well done ET,  
well matched to the piano (ie, taking into account inharmonicity which  
expands 3:1 and 6:1 and so forth), there will be an excellent lining  
up of partials 1, 2, 3, 4, 6, and 8. What's missing? 5, 7, and 9.  
Essentially the 5th partial is the one that is "at issue."
	Now, if you are actually going to line up a 5th partial, that means a  
just M3. If you tune a just M3, it is at the expense of the fifths  
(partials 3 and 6) and of the other M3s. The Coleman tuning, though,  
would not have a just M3, but simply a variety of sizes of M3, some  
closer to just at the expense of others farther from just. Like most  
relatively mild WTS, the 5ths will not be so far from just that  
partials and 3 and 6 will line up very noticeably worse. But in any  
case, no uneven, circulating temperament will line up overtones  
overall any better than ET. In fact, an excellent argument can be made  
for the idea that ET is the very best temperament from the point of  
view of  alignment of partials, especially with inharmonicity of  
modern pianos in the picture.
	My own interpretation is that the piano in question had a very high  
standard of unison tuning. The highest standard of unison tuning is by  
no means common, and it is quite possible that your tuning would stand  
out in the experience of the violinist in this regard. The slightest  
waver of a few unisons colors an entire tuning (sometimes with the  
unisons sounding like they don't have a waver when played alone. The  
waver sometimes only appears when played with an interval, like an  
octave. So someone who does what seems to be a truly excellent tuning  
can possibly still find room for improvement). When every single  
unison is clear, the blending of sound is amazing in comparison to a  
tuning with minor unison problems. Use of ETDs has made this much more  
common in the US over the past couple decades. I know my own tunings  
have improved dramatically in that regard since I started using ETDs.
	In any case, my own comment about fixed pitch accompanying  
instruments was aimed at the actual blending of tuning, note against  
note, between a fixed pitch (piano or other) and flexible pitch  
instrument. Take Valotti or Young as an example. They have six sizes  
of M3, great from the point of view of variety of "key color." What  
goes along with this is six sizes of half step and six sizes of whole  
step. And six patterns of diatonic scale of each flavor (major, minor  
- melodic or harmonic). And six patterns of chromatic scale. If the  
flexible pitch instrument is really wanting to match precisely in  
unison, passages of thirds or sixths, etc., this is an impossibly  
complex target.
	Now as to how precisely musicians match pitch (particularly to a  
harpsichord), that is another question, and it may be that the level  
of precision is low enough that it doesn't really matter. I suspect  
this is the case. But in any event, one fixed pitch is the same as  
another in being an artificial fixed target from the point of view of  
the flexible pitch instrument. None will match what the flexible pitch  
instrument would do in other contexts. ET has the benefit of being  
very predictable and familiar, whatever its other sins <G>.

Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu