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
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