F3/A4 as pitch test

[Ric Brekne]

Ed and others.

First let me say how much I appreciate everyone bringing this back into 
a topical discussion. The disspasionant relating of simple facts is 
quite a bit more enlightening to student level readers then what we 
started off with.

Ok. to the heart(s) of the matter,  one of which you describe quite well 
just below in your opening paragraph. Its true that the F2/A4 test 
relate directly to 440 Hz. The 5:1 coincident to be exact. Tuning A3 
then to a perfect 2:1 octave type will result in A3's 2nd partial at 
440hz which is the PTG standard.  No arguement from me that this is the 
most direct path.

My arguement simply went to the idea that doing things otherwise was 
synonymous with somebody not knowing what they were doing.

Using F3/A4 simply requires you to take into consideration that you are 
dealing with a 5:2 coincident and, as several of you have pointed out, 
because the pitch fork yields 880.00 Hz at this coincident  the 
resulting fundemental for A4 will be just under 440Hz because of the 
inharmonicity of pianostrings. This is however quite an easy matter to 
compensate for... I would argue every bit as easy from a practical 
standpoint as executing the routine above. In both cases you are simply 
required to controll beat rates for the relevant comparisons appropriatly.

Remember... the end desired 440 Hz is to be achieved at A3's 2nd 
partial.  If one has A4's fundemental at 440hz then you simply tune a 
perfect octave. If you've got A4's fundemental at 439.7 or so because of 
useing A3, then you simply squezze the octave a hair.   Whats easier or 
more dependable for the individual tuner is IMHO up to the individual 
tuner. 

Now.. to another heart.... All of this is based on the absolute need to 
get A3's 2nd partial within a quarter beat or less of 440.000 Hz... 
which in itself is another discussion entirely.  Certainly one needs to 
do this for the PTG test.

btw.. I just checked Carl Forss's latest book on tuning. He is one of 
the biggies over here in Europe.  He advocates the F3/A4 test for 
setting temperament.

I think its clear that there are many views on how to set pitch. Which 
partial of which A to use, and how important it is to be just how close 
to exactly A440Hz in all cases.  My own experience tells me that a 1 
cent window is what is evident out there in the world.  If you are in 
one of those situations where there is a director with 0.000 tolerance 
then you should be IMHO using an ETD to set pitch to begin with. No 
sense leaving anything to chance at all in such cases.

Ed. You do bring up something at the end of your post that is alarming 
if true.  You seem to hint at high degrees of inharmonicity in pitch 
forks... para inharmonicity at that.  If it is indeed true that the 
second partial of pitch forks is as wildly irratic as you state.... then 
its an unreliable pitch source to begin with.  If so... well we are in a 
whole new ballpark.... I'll be the first to agree on the need for a 
reliable pitch source.

Cheers, and thanks for the well thought and put replies.

RicB


-----------------------------
Ric and List:

The problem I have with this is that if we use F3/A4 as a test, we are 
listening to the pitch at A5, not at A4.
Tuning forks have a weak partial at A5, so it is possible to hear a 
rather weak beat there.  When we play F3/A4 on the piano, we seem to 
hear a beat at A4, but with careful listening, we realize the beat 
occurs at A5.  We are setting pitch to the second partial of the fork at 
A5.  If we test F3/A3, we are setting A3 to the fork at A5.

Using Cybertuner on Pianalyzer mode, I tested 7 tuning forks 6 times 
each, reading the pitch readouts at A4 and A5.  The forks range from 2 
19th century forks to two contemporary Walker forks and a new Nippon fork.

At A4, the forks were very stable, showing a small drop in pitch over 
the six tests, averaging about 0.3 cents, with a maximum drop of 0.9 
cents.  This was probably due to temperature change from being held in 
my hand at the handle.

At A5, the measured variance is so wild and erratic that I wonder if it 
is correct, or an artifact of the measuring system.
Dropping the most extreme reading of each fork, and dropping the 19th 
century forks, which were extremely wild, the remaining forks show 
variences of 2.1, 9.9, 5.4, 12, and 11.5 cents at A5.  There is no 
pattern relating to time the fork was held, or how hard it was struck.  
The variances are erratic and unpredictable.

Perhaps someone else could test a fork against a spectrum analyzer and 
report the results.

Ed Sutton