Changing (IN)Harmonicity

[Robert Scott]

Baoli writes:

> When we check the inharmonicity, any tuning machine
> simply assume that the first partial(fundamental) has
> none inharmonicity. In the real world, any
> partial,including the fundamental, has
> imharmoniucity. In other words, the tuning machine check
> the "relative inharmonicity", not the real one.

That is true.  But you can calculate the "real" inharmonicity from the 
relative ones if you use the model described in "The Calculating 
Technician" by David Roberts:

   Offset(cents) = K * n * n

where n is the partial number and K is the inharmonicity constant.  
Suppose for example that you have the offsets for the fundamental and the 
second partial:

   Offset1 = K * 1 * 1
   Offset2 = K * 2 * 2

 From this we get K = (Offset2-Offset1) / 3.  Knowing K, we can now say 
that the offset of the fundamental due to inharmonicity is K.  And all we 
needed to get this conclusion was (Offset2-Offset1) which is a relative 
measurement of the kind that tuning machines do make.

Robert Scott
Ypsilanti, Michigan