why we have to temper

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Mark asks: 
<<is inharmonicity the reason why we have to temper a piano?>>

Greetings, 
   No,  we temper because no multiple of 3:2 will ever equal any multiple of 
2:1.  This is the problem caused by the "comma of Pythagoras" showing itself 
in a system where the octave is divided into 12 notes.  
Regards, 
Ed Foote 
(inharmonicity is why we "stretch". )