using beats to tune

[Billbrpt@AOL.COM]

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In a message dated 11/16/01 7:40:55 AM Central Standard Time, Tvak@AOL.COM
 writes:


> Did I misinterpret something that was posted recently in the discussion 
> regarding temperaments?  I was surprised to learn that ET did not really 
> exist prior to 1917.  Now, the part I'm unclear on: I believe that it was 
> stated that this treatise, published in 1917, was the first to utilize the 
> concept of listening to beats in order to tune a temperament.  
> 
> First of all, is the above information correct?  And if it's true that 
> tuners 
> didn't use beats to tune a piano prior to 1917,  what did they listen to?  
> I 
> can't imagine.  (I must have misunderstood the information posted.)  
> Certainly, tuning unisons could not be done without eliminating beats.   
> Perhaps tuners didn't use coincidental partials to tune prior to 1917?
> 
> Straighten me out!

I find it very ironic that 1917 was also the year of the Communist Revolution 
in Russia and that it took about the same amount of time to liberate those 
people as it did for people to begin to understand that there really can be 
more than one way to tune a piano.

I concur with both Richard B. and Ed Foote.  People have always used beats to 
tune even if they have not recognized them for what they are or "counted" 
them as such.  Until at least the middle of the 19th Century it was thought 
that no one could discern a beat rate of more than a few beats per second.  
Now, highly skilled technicians can discern rates up to 15 beats per second 
or maybe even more.

Maybe this will ease the mind a little. "Counting" beats as such is not 
really the goal as much as *comparing* them is.  When I tune a temperament 
other than ET (which is *always*), I don't even try to follow any schemes 
where the only information provided is in irrational numbers (3.6, 9.7, 10.1, 
etc.) which are never correct anyway because they are only theoretical.  When 
tuning aurally, I only use methods which employ the *Equal Beating* 
principals because the ear can really discern very accurately when two 
intervals, especially the rapidly beating ones beat *exactly the same*, 
whatever that rate is.

Unfortunately and ironically as well, *Equal Temperament* has no Equal 
Beating intervals to tune!  Yes, when completed, all 4ths & 5ths need to have 
that very slightly tempered sound which should all be alike but each of the 
Rapidly Beating Intervals, the 3rds and 6ths should be different from each 
other.  Any two 3rds which beat exactly the same indicates an error.

What is important in learning to tune ET aurally is the ability to make an 
*estimate* and to compare.  Really, the only beat rate to learn is that first 
7 beats per second that F3-A3 should have.  After establishing the first 
note, A4 by comparing it with the fork as a dead unison and verifying it with 
the F2-A4 test and ascertaining that the F2-A4 of the piano and F2-Fork beat 
*exaclty the same* (whatever that rate happens to be), the first octave A3-A4 
is tuned.

That is found by first finding an apparently beatless sound, then flattening 
the A3 just slightly until just the beginning of a beat can be heard.  Then, 
the best placement for A3 is found by making 2 comparisons which reveal the 
4:2 and 6:3 type octaves.  For ET, a compromise between these two is usually 
best.

Play F3-A3, then F3-A4.  If both intervals beat exactly the same, you have a 
4:2 octave.  Play A3-C4 then C4-A4.  If both intervals beat exactly the same, 
you have a 6:3 octave.  The trick is to get something that falls between the 
two, neither one nor the other.  The beats are very rapid so don't think in 
terms of *counting* them but comparing very fine gradations of rapid beats.  
If the piano has low inharmonicity, there won't be much distinction but if it 
has high inharmonicity, the distinction can be easily heard.

After getting this first octave tuned, *estimate* the 7 beats per second of 
the F3-A3 interval.  Then tune F4 from F3 and try to find that same kind of 
compromise that was done between A3 and A4.  Now, fill in C#4.  If your 7 
beat per second estimate for F3 was correct, you should be able to hear the 
all important 4:5 Ratio of Contiguous 3rds.

Again, don't *count* but *compare*.  for every 4 beats in F3-A3, there should 
be 5 beats in A3-C#4.  For every 4 beats in A3-C#4, there should be 5 in 
C#4-F4.  For every 4 beats in C#4-F4, there should be 5 in F4-A4.  After 
practice with this concept, it will be discovered that it is easier to hear 
when the relationship is *incorrect* than when it is correct.

If two contiguous 3rds beats exactly the same, there is an error.  If the 
lower one beats faster than the upper one, there is a significant error.  If 
the upper one beats much faster than a 4:5 ratio would be, there is an error. 
 The trick is to get these 4 beginning notes to have the proper relationship 
to each other.  After that, the rest of the notes of the temperament will 
fill in with comparative ease.

Practicing just this 4 note beginning sequence is the best thing an aural 
tuner can do to achieve the kind of standards which are expected today.  If 
this relationship is not correct and cannot be established, the temperament 
can never really be what is known today as a true Equal Temperament.

Incidentally, if you are at all interested in a very mild alternative to ET, 
you can easily learn to tune the Quasi Equal Temperament known as "Marpurg" 
because it starts with this very same relationship.

I hope this answers more questions than it generates but if it does generate 
new questions, don't be afraid to ask.

Bill Bremmer RPT
Madison, Wisconsin

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