[CAUT] tuning paradigm (was P12ths)

[Fred Sturm]

On Oct 18, 2008, at 7:19 AM, rwest1 at unl.edu wrote:

> Part of the problem in evaluating any tuning, electronic or aural,  
> is the lack of a concrete tuning paradigm in our profession.  Good  
> tuners all understand the variables and the problems but when I see  
> attempts to describe our tunings, I don't see an adequate unified  
> description of an aural tuning other than in general terms.   
> Whenever I hear people say the thirds are "too wide,"  I always want  
> to know what "too wide" is. There was a time when anything wider  
> than a pure third was "too wide."  Therefore it seems that trying to  
> judge a tuning  without having a paradigm to use as a measuring  
> stick is futile, whether the tuning is a result of electronic  
> "judgements" or aural "judgements."

	Interesting post, Richard. You raise excellent points. I guess I  
don't believe it is possible to arrive at even a rough consensus for a  
paradigm. We might be able to agree on a "range of stretch"  
appropriate for this or that circumstance, but I think that's about as  
far as we would get, and it would need to be a pretty large range. As  
for the width of the M3/M10/M17, it follows naturally from the stretch  
(assuming ET). Or, if you prefer, a decision about the relatively  
minor variance possible in M3 rates will determine the stretch.
	One can focus on alignment of various partials as a paradigm, and  
this will yield different results in different circumstances  
(inharmonicity bulges, overall inharmonicity of scale): any absolute  
choice will create distortions somewhere else.
	Unless we accept some absolute standard, such as the one Stopper  
proposes, we are left making compromises based on our own best  
judgment. Personally, I have no problem with a variety of tuners  
producing a variety of tuning styles. I prefer that, frankly.
	I believe that we should look beyond the piano to get a little better  
perspective. I talk to various professors and students (violin,  
guitar, band, oboe, etc) about the issue of intonation on a frequent  
basis. Our "sea of contradictions" is far narrower than theirs. The  
violinist, for instance, has certain principles of intonation when  
playing solo (the "violin to itself" relative to the open strings), a  
second when playing in ensemble with string quartet or orchestra, and  
a third when playing with piano. Decisions of tuning are all  
"contextual" and have to be made instantaneously on the spot. EG, M3,  
m3 and M6 are "just" (in context) except with piano, where it becomes  
problematic (what notes are sounded on the piano at that instant?).  
Where melodic considerations predominate over harmonic "blending,", a  
different aesthetic of "pitch-bending" is often used.
	Other instruments have similar issues: the guitarist deals with fret  
placement, brass deal with overtone series and breath speed, etc, etc.  
All deal with the idiosyncrasies of their individual instrument. IOW,  
our "problems" in coming up with a standard, and our arguments about  
detail, are miniscule in comparison. We are the sea of tranquility,  
the standard that they conform to or deviate from, depending on  
context. Our differences are far smaller than theirs, and, in fact, I  
find that they are often unable to hear differences on the piano  
(varied temperament for instance, unless it is a big difference on the  
order of Valotti) that are obvious to me.
	I should note that stretch, besides its basis in inharmonicity and  
human psychology, has a practical  basis in at least wind instruments,  
due to the speed of breath in producing high notes (pitches go sharp).  
Strings go sharp on high notes as well, but I think that is "psycho- 
acoustic" (what the ear wants to hear). A violinist seeking that C7  
does so "by instinct" and hits something fairly widely stretched as a  
rule. (I have asked violinists to play high notes, and have checked  
them against my tuning of those notes on a piano). So I think stretch  
is based on far more than the experiences and practices of piano tuners.
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu