[pianotech] Steinway A Bass Rescaling

[Ron Nossaman]

Bruce Dornfeld wrote:

> I find it fascinating how the ideas and formulae for inharmonicity have 
> developed.  I don’t believe that the concept of inharmonicity is 
> mentioned in tuning texts until sometime after the development of 
> electronic tuning devices.  Stretching octaves maybe, but not 
> inharmonicity.  Wasn’t the use of early ETDs what lead to the 
> measurement and discovery of inharmonicity?

Yes, I think that's right. Looking at existing scales, it 
appears to me that they were primarily concerned with break%, 
which seems to be favored over tension. A Z calculation 
doesn't seem to have been available for consideration either.


> On a more practical line, we know that longer unwound portions on a bass 
> string create more inharmonicity.  I find that most German grands have 
> the windings come real close to the bridges and agraffes.  It has always 
> struck me as something that was done to show a certain virtuosity on the 
> string maker’s part.  It also creates lower inharmonicity in the bass of 
> these pianos which is usually a very good thing.  There are some 
> however, where the transition to the plain wire strings is too abrupt 
> and perhaps the last wound strings should have had longer unwound 
> portions.  I observed this quality of bass strings in a Hamburg Steinway 
> O that I serviced last week.

If you'll play with the inharmonicity calculation some, you'll 
find that a little difference in the bare end and step length 
makes very little difference in Inh. It's saner and safer to 
keep a standard length and design a bridge layout and scale 
that works with that.
Ron N