[CAUT] Stretch

[RicB]

Hi Richard, see comments interspersed :

    Numbers, numbers, numbers.  Yes, they can be helpful, but do they  
    adequately represent a piano tuning.  Look at it this way. (If you  
    don't want to wade through the first part, jump to "Conclusion" below)

In the final analysis... no they do not represent adequately a tuning... 
but thats just my opinion.  That said....

    F#4 aural tests = 2 beats to C#4, nearly pure to B3, 1 beat faster  
    than D3F#3, this makes a stretched octave.  If you had to do the  
    equivalent test by the numbers it would take several measurements,  
    and the resulting numbers would probably not end up exactly the same  
    figure.

Look at it this way then... you have a 4:3 fourth and a 3:2 fifth that 
you have specific desired beat rates for. If you have f.exp. Tunelab set 
just to C#4 you have only to adjust its offset  2 hz higher for the 
forth and say 0.25 hz higher for the fifth, tuning to the display in 
each case.  Actually, this is very quickly done with pocket Tunelab and 
is essentially (for not to say exactly) what the ear does.



    Now look at B4.  Since F#4 was stretched a little bit, F#4/B4 can be  
    2 beats and the E4/B4 could be nearly pure.  The octave could have 1  
    beat without doing any harm and the 10th (G3/B4) could be one beat  
    faster than the third (G3/B3).  If you tried to figure all that out  
    by the numbers, I think you'd get different figures, and those  
    numbers would vary from piano to piano.  But aurally, those checks  
    lock in a note.  Go too far with any interval and it will show up in  
    the others.

Yes, using numbers as solid anchours for tunings doesnt work as well as 
it should.  Jason Kantor's article even showed something I've been 
suspicious about in the treble area relative to the dependability of 
numbers.  But that doesnt mean that they are not useful as a means to 
communicate tuning talk.  We are still talking about beat 
rates/characteristics at specific coincident partials.  F#4 / C#4 has at 
least two very easy to hear... 4:3 and 8:6  which pair did you mean ?  I 
know and you know in this example... but students get easily confused... 
and  this is a very simple example anyways. We dont always refer to the 
lowest common denominator. Saying that C1 and E1 should have any 
specific beat rate for example is quite meaningless in my book. Saying 
that C1(5) and E1(4), i.e. the 5:4 pair have a specific (or near 
specific)  beat rate is immediately clear.


    Now look at the B5.  Since the B4 was stretched, it would seem that  
    the B5 will also be able to be pushed high.  But wait.  What about  
    the double octave.  Since the B3 is below A4, the B3 is actually  
    stretched a little low.  Therefore if you push the B5 too high, it  
    won't fit with the B3.  But the 10th/17th can be a little wide, with  
    the 17th a beat faster than the tenth, which is already a beat faster  
    than the G3/B3 third.


Again... I agree that tuning strictly by the numbers can be iffy.  But 
how ETD users combine tuning by the numbers and tuning with their ears 
is another discussion me thinks... and one again where discussion based 
on descriptors using coincidents would facilitate understanding.

    Now look at the B6.  It can be stretched higher than the other  
    octaves because the double octave B4/B6 uses the B4 which was an  
    upwardly stretched note.  The triple octave can be nearly pure  
    because the B3 is stretched slightly low.  The only octave to really  
    suffer is the single octave B5/B6.  But that octave is also a limiter  
    because no matter how you might want to stretch, there is a limit to  
    stretching that single octave and there's a limit to how fast the  
    17th (G4/B6) can really be.

    Conclusion:
    All of these aural tests would be possible to calculate, but  
    difficult and time consuming to do, especially for every note of the  
    piano.  Numbers and measuring don't, IMHO, capture the essence of  
    tuning.  ETD's can crunch some numbers, average them out, and give an  
    excellent calculated result, but whether or not those calculations  
    actually fit the piano depends on what you hear.

I do to, when it comes down to it.  But I use the ETD in very much the 
fashion I describe above to help me get there.  I dont think too many 
ETD users are using their apparatus's this way, i.e. direct referencing 
in the same way the ear references coincidents. But they do have 
conscious ways of combining theory/numbers with what their ears 
esthetically are pleased with.  Much in the same fashion that strictly 
aural tuners know on some level the basic coincident relationships and 
fudge as necessary on their way through the tuning.  Describing those 
fudges tho in terms that are equally vague and seemingly arbitrary as we 
actually tune gets quickly into water so mucky that no one can be sure 
of what the other is saying without having a piano (and each other) 
right there to demonstrate on.


      Years ago I chose to stick with the aural methods because there was  
    more satisfaction in it.  The pattern I described above is what I  
    strive for because it seems to be what the piano "wants" and I think  
    it's safe to say that I'm not the only technician to aim for the same  
    pattern.  In fact that's the core of my contention that there really  
    is only one way to tune a concert grand.

    If you can agree that most technicians tune the middle 75 to 80 notes  
    the same, then why haven't we described that pattern? To me, that's  
    the standard that any technician should know about and strive for.   
    Going by the numbers can lead to confusion, because the numbers can  
    create a construct that doesn't really fit a piano.

I dont think most piano tuners do tune the middle 75-80 notes the same. 
Actually I think you find quite a significant divergence from piano 
tuner to piano tuner.  Significant in the sense of what a very fine 
tuning is in any case. An overall stretch to accomodate 8:1 coincidents 
being clean is a very different puppy then one that requires a very 
pureish 4:2:1 set.  Temperaments vary much more then I think we take for 
granted.

I agree that going strictly by the numbers is not a good idea... but as 
a base for teaching, communicating and even as tool for getting very 
close to where the highly accomplished ear wants to go with an 
instrument... they are a fine tool IMB. They also often enough reveal 
just how conscious a tuner really is about what he/she is doing.  And 
also IMB, as a general rule with very few exceptions.. the more aware 
you are of the theory behind any endeavour one is... the better equipped 
one is to develop skill in that endeavour.


    Also, see comment in text below

    Richard West

Cheers
RicB