I have been wondering for quite some time whether I should normalize all the historical temperaments for TuneLab so that their average offset is zero. This question has been touched on briefly here on pianotech, but I thought I might poll the users of historical temperaments to see if there is any consensus. Basically, the question is how to normalize a temperament that is defined by 12 offsets from equal temperament. It seems to me that a very important goal is to be able to switch between an historical temperament and equal temperament without changing the overall pitch of the piano and thus not incurring any pitch-raise problems. I have seen some historical temperaments that are defined by offsets that are all positive. This means that every note is either at the same pitch or a higher pitch when the piano is tuned to the historical temperament. The average pitch change can be as much as 5 cents. Given the choice between tuning a piano that is already at pitch and a piano that needs a 5 cent pitch raise, what would you choose? On the other hand, if the 12 offsets for an historical temperament are all uniformly raised or lowered so that their average becomes zero, then this minimizes the pitch-change difficulties when applying the temperament. The musical properties of the temperament would be unaffected by such a shift since the properties of a temperament are dependent on the differences between the 12 offsets and not their absolute value. The other common way to normalize a temperament is to ensure that the offset for A is zero. This goal ensures that if someone were to check the tuning of the piano using an A-440 fork, they would be satisfied. While checking A-440 in ET may be valid way to check the overall pitch setting of a piano, I don't think it has as much meaning when tuning an HT. But then if A-440 is used as a pitch reference for tuning an orchestra, perhaps the absolute pitch of this one note does matter, even in HT. So my question is, which is more important to you when you tune an historical temperament - the average pitch of the whole piano or the absolute pitch of A? -Robert Scott Real-Time Specialties
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