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There must be a mathematical reason, I've found one that makes sense and is easily proven. I can't find logical reasons to suggest that it doesn't work. I've made a DVD and book about it. www.pianodiy.com.au. I would like to make up some more mathematical models on the subject too.

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-1 and voted to close: I don't see how this relates to math at all; you'd be better off asking some historians... –  Sam Feb 4 '12 at 22:34
    
Possibly related. –  Arturo Magidin Feb 4 '12 at 22:35
    
I know nothing about music, and so I can't categorically claim there isn't a mathematical reason, but it seems far more likely that this is just an accident of the arm span of an average human and the particular musical system used in Europe when the piano was invented. –  Zev Chonoles Feb 4 '12 at 22:38
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Also, please note that self-promotion is frowned upon on StackExchange sites - see here and here. It would be much better if you would at least summarize what the "mathematical reason" you claim to have found is. (Or, were you hoping people would buy your DVDs?) –  Zev Chonoles Feb 4 '12 at 22:43
    
There might exist mathematics involved, and it might have to do with some proportion of (parts of) the human body to the instrument, but I agree this isn't a mathematics question. It seems more like a physiology, or possibly psychology question. –  Doug Spoonwood Feb 4 '12 at 22:44
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closed as off topic by Sam, Asaf Karagila, Qiaochu Yuan Feb 4 '12 at 22:36

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1 Answer

No, it's just tradition. There's some interesting mathematics going into why there are 12 keys in an octave, but there's no intrinsic reason for the upper and lower limits of a standard piano keyboard.

There are piano makers that make models with more than 88 keys, extending the keyboard to the left, and more because the extra strings add resonance to the sound than because playing the extra keys is very useful.

In the other direction, electronic keyboards (those that do not aspire to be "digital pianos") often have only 61 keys.

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