ramblin' (tuning by pure 5ths) (fwd)

[Jim]

With Frank's permission I am forwarding this answer which was sent to him
yesterday.  Jim Coleman, Sr.

---------- Forwarded message ----------
Date: Wed, 25 Jun 1997 00:36:20 -0700 (MST) 
From: Jim <pianotoo@imap2.asu.edu>
To: Frank Weston <waco@ari.net>
Subject: Re: ramblin' (tuning by pure 5ths) 


Hi Frank:

I tho't I would try to respond to some of the good points you make.

On Tue, 24 Jun 1997, Frank Weston wrote:

> Jim,
> 
> 
> A few points about preference polls:
> 
> 1. When a majority votes for X over Y, the conclusion must be that the
> majority prefers X over Y, NOT that X is necessarily superior to Y.

You are right about this.
> 
> 2. Unless comparisons are made with identical instruments, positioned
> identically, played identically, and with no prior knowledge of which is
> which by the voters, the results will most likely be a popularity poll
> rather than an honest indication of musical preference.  Jim - it may be
> that you're just a popular guy.
> 
In the Austin, TX comparison, I had tuned both pianos so it ruled out
the popularity portion. Also we made no effort to try to conceal which
piano had been tuned which way, so it was not a blind test. In previous
tests I have conducted, we did make part of it a blind test.

We haven't been able to have a setup where we could place each piano in
the same location. In the AZ State Conference, we had 3 pianos which I
had tuned differently, and they were switched around for the second class.
In this instance the piano in the corner received the highest vote each
time, so even though pianos were switched and no one knew in advance which
piano was tuned which way, the corner piano always won. The Well tempered
piano was always second. It was not moved.      In Orlando we
will have 4 pianos to judge and we will try to switch them around to 
eliminate any position preference. Also in this case, no one will know
which piano was tuned by whom.

> Aurally, I find it very difficult to make perfect fifths fit into
> acceptably stretched octaves. 

You are probably right about the acceptable octaves. I didn't like the
stretch either at first, but after playing the piano awhile, the 
stretched octaves didn't bother me any more than the normal beating
4ths. And the benefits of the overall matching of octaves outweighed
that little problem.

I suppose that in the end this little thread or discussion may lead us
to a slightly wider stretch of the octaves and not necessarily to
totally pure 5ths.

 In any temperament, something (one
> interval or intervals) always has to give, and to my ear I would rather
> it not be octaves.  On the purely numerical side of things saying that
> stretching octaves has very little affect on other intervals is like
> saying that making a year 380 days will have very little affect on
> months, weeks, and the hourly wage.  NOT SO!  Government workers would
> gain another two weeks paid vacation, and my houly wage would go from
> $1.98 to $1.90.

When one considers that to have a pure 5th temperament, the octave needs
to beat no more than 1 bps more than we commonly stretch octaves in 
pianos, and that there are 3 M3rds that complete an octave, this means
that the individual M3rds are increased by a third of a beat each, 
actually less due to inharmonicity. And at the same time, the minor 3rds
are decreased about 1/4 bps each, so, the main changes are in the 4ths 
and octaves. The 6ths behave about like the M3rds.

 > 
> As you are well aware, every piano sounds best with just a little bit
> different stretch.  If fifths are actually tuned pure, then the total
> stretch in the piano is defined by the tuning of fifths, and not by the
> piano.  How do you resolve this issue?

Letting the 5ths define the tuning of the piano seems to produce a 
better tempering of all of the octaves, giving a better match for the
overall piano. Up to now we have had every interval except the octave 
and the unison tempered. Will unisons be next in the continuum? I hope 
not.

  Are your fifths actually a
> little less than pure?
> 
After tuning a number of pianos this way using the SAT, I discovered that
there was a little variance in the 5ths. This is due primarily to the
fact that wire size changes occur at different places on different pianos.
When I tuned aurally, I primarily controlled the pure fifths, and let the
very slight variances occur in other intervals which were more noticeable
in the 4ths, octaves, but not in the 3rds and 6ths.

> Hoping to raise the level of discussion,

Me too.

> 
> Frank Weston
> 


Jim Coleman, Sr

PS I posted this privately since your post to me was private. If you think
others might benefit from this interchange, you have my permission to
forward it to the list along with any additional comments you may wish to
make   JWC