How Much Stretch ?

[Billbrpt@AOL.COM]

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In a message dated 8/9/02 9:21:32 AM Central Daylight Time, 
Richard.Brekne@grieg.uib.no (Richard Brekne) writes:


> On the side of the other threads... I have a question I
> would appreciate some feedback on. Often when using ETDs
> that calculate tuning curves based on inharmonicity samples,
> I find that the resulting tuning curve shows the highest
> notes up in the +40 to +45 cents (sometimes even higher)
> range. 
> 
> This seems reallly high to me, and I wonder if you all
> accept this degree of treble stretch, or you modify things. 
> 
> My fooling around with the 12ths tuning revealed real quick
> that the 3rd partial of F6 almost never gets above +35
> cents.... and this F6's coincident to C8's fundemental.
> Seems like a pretty natural place to stop... or what ?
> 
I have done a lot of measuring and documentation of this for about 10 years 
now.  Tuning double octaves that match all the way to the top will produce 
notes in the +35 cent range in the last part of the 7th octave.  This is 
higher than the 2:1 octaves called for in the PTG exam which will produce 
notes in the +25 cent range.

Tuning triple octaves that match will produce notes in the +45-50 cent range. 
 If you play the note C5 (tuned at standard pitch in ET or a mild WT) but 
have your ETD set on C8, the reading you'll likely see will be about +50 
cents.  To me, this is at least one justification for tuning that note that 
high.

But I have heard over the years many tunings by very respected concert tuner 
types which had notes which were as much as +200 cents and have heard that 
consistently from a few individuals whose work I would encounter regularly.  
So, this, although being obviously way out of bounds, has told me that I 
could seek an even higher plane than the +50 cent range when tuning the last 
part of the 7th octave.

When I have decided upon such a course, which is not what I usually do but 
when I have decided that I really want the most maximum of stretch, I would 
tune the first half of the 7th octave to match quadruple octaves below, that 
is, C3-C7, C#3-C#7, etc., then at F#7, match the quadruple octave and 5th, 
that is B2-F#7, C3-G7, on up to F3-C8.  This produces a C8 which can be as 
high as +80 cents.

Believe it or not, if everything below this is properly and evenly stretched 
out, these last few highest notes will not sound too sharp or dissonant with 
anything below them.  I usually think of this highest limit as only being 
appropriate for a large concert grand in a large hall, such as for a piano 
concerto.  It will certainly allow the piano to project that range, be heard 
and not sound flat with other instruments which may also be pushing the pitch 
when playing in their highest registers.

However, there are exceptions.  I have one customer of many years who has a 
small Chickering grand in his quiet living room.  He was never truly 
satisfied with his piano's upper register until I tuned it as I've just 
described.  When I finally did, he was ever so much delighted that he tipped 
me very generously.  I also tune my own Walter console with PianoDisc system 
with triple matching octaves accross the board.  I love the sound.  But 
certainly, there can and will be people for whom that amount of stretch would 
be outrageous.  

It is these kinds of options and the decision making that goes along with 
them that make our work interesting and challenging.  I never think in terms 
of tuning every piano the same way.  I think of tuning most pianos in ways 
that seem to work best most of the time but also know of ways to manipulate a 
tuning in many other ways to please a customer or provide a more appropriate 
foundation for a special kind of music or event.

Bill Bremmer RPT
Madison, Wisconsin
 <A HREF="http://www.billbremmer.com/">Click here: -=w w w . b i l l b r e m m e r . c o m =-</A> 

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