[CM] fm and transposition

[Oded Ben-Tal]

I'm using clms fm-bell instrument to produce sounds to be used in an 
experiment. Each short sound is presented in 3 transpositions. I'm 
extracting two numbers out of the sounds RMS amplitude and a mean 
frequency.(*) So here is my question: RMS 
amplitude and mean frequency values of the transposed sounds are not 
simple transpositions. in other words if 1a and 1b are two sounds using 
fundamental freq. f0, 2a and 2b are copies of the clm code with f0 shifted 
up. the RMS amplitude of 1a is larger than 1b but the reverse is true of 
2a and 2b. (and similarly for mean frequency). 
I'm trying to understand why is that so. Or if it shouldn't be to track my 
error.

thanks
Oded

(*)For the mean frequency I'm averaging windowed fft of the
sound
weighted by local amplitude (the trail end of the sound is soft such that
the average frequency is that of the noise; the sounds are not single
pitch so I'm not using fundamental frequency).