Aural Pure 5ths Equal Temperament

[Horace Greeley]

Jim,

I have looked for years to find ways to describe how I tune.  I should have
known to ask you.

Without too much jumping the gun on the balance of this series,  the method
(s) you describe for tuning (in roughly the second half of the article)
pretty concisely cover what I do.  I would go so far as to state that I
will instantly sacrifice a "perfect" octave, if it makes musical sense to
do so.  Also, I do think that managing the 5ths is a crucial key to
understanding how the 3rds and 6ths are "supposed" to sound under differing
circumstances.

Do I correctly remember that Broadwood was the first maker to "standardize"
on "equal temperament"  (in 1853)?  (Yes, yes, yes - at 435, or
thereabouts.)  If so, then it would seem altogether likely that varying
methods of establishing the temperament would have sorted themselves out by
the time Braide White was first writing (roughly 50 years later).  That
kind of time line is not unusual in transitions from theory to practice,
especially in the 19th Cent.

A few comments are interspersed:

>Eventually a scientific system was developed where one could tune
>the circle by 4ths and 5ths and check with 3rds and 6ths.

It was hard to decide where to "snip" what was here, each of the
writers/teachers you mention have made significant contributions to  the
instruction and practice of tuning.  My more modest contribution is that in
each of these cases, the scope of the area in which the temperament is set
is expanded.  That is, Braide White wanted everything to be "doable" within
the major 7th (yes, with checks outside, but that was his basic range for
temperament tuning).  By the time we get to Ric and Al, we are using two
octaves.  An observation that comes to mind, is that we are, in actuality,
tempering the entire instrument.

>Many have held tenaciously to the idea that octaves should be
>pure.
>
>Can we talk about this? Is there a law of nature that says that
>octaves must be pure? What about double octaves, must they also be
>pure? What about triple octaves, or quadruple octaves? Must they
>also be pure? Who is to say?

This is where I seem to be constantly getting myself into trouble.  I think
the clue is, as you suggest, the "judicious" stretching of the octaves,
using the the (essentially) pure 5th as the delimiting factor.  From an
application standpoint, this means that I will (virtually) never
(knowingly) turn the 5ths inside out.  I will, however, work to make them
squeaky-clean, as I feel the musical situation warrants.  It is good to
know that, while our descriptive vocabulary may differ, there are others
who will carrying the octave to the "very edge of the limit".

>The next logical question becomes: "What is the limit to the
>stretch of an octave?"  Can single octaves be stretched to the
>point where triple octaves will sound good?
>Can octaves be stretched as much as 3 beats in 5 seconds?
>What is the practical limit of beats which we can tolerate in the
>sound of the single octaves and the 4ths? Could they be balanced
>out equally? Should they be balanced out equally?
>
>I believe the answer to that question can be found in the 5ths.

I completely concur that the answer is in the 5ths.  Most of the other
questions in this paragraph depend, for me, on many other variables - most
of them subjective.  What is the literature?  What is the piano?  Who is
playing?  Where is it played?  etc.

>The overall sound of the piano is quite exciting.

The combination of ingredients can have very exciting results indeed -
rather like a good snare drum, in which the tension of the heads is so well
balanced with the tension of the snares that the slightest movement creates
an explosion of sound.

Jim, this is great - Thank you very much!

Best.

Horace




Horace Greeley			hgreeley@leland.stanford.edu

LiNCS				voice: 415/725-4627
Stanford University		fax: 415/725-9942