I am trying to understand the relationship between mass, tension and length in a vibrating string such as would be found on a violin or guitar. If the string has a uniform gauge throughout and is kept at a constant tension, then reducing the length by 1/2, for example, will cause the the pitch to double, or increase by an octave. My question is, Is it incorrect to view this occurence as a reduction of vibrating mass by 1/2 rather than a halving of the length of the string? It seems to me that the real phenomena that is occuring is a reduction in the amount of mass that is vibrating and that (because the gauge of the string is uniform throughout) it is only coincidental that 1/2 length will also determine 1/2 mass. I hope this makes sense.