From a mathematical standpoint, what you are doing when you fill in this data set is interpolation. However, from an engineering standpoint, it is a mischaracterization (note that this is the same word I used before). That is, when the word "interpolation" is used in mathematics it means calculating missing data in a set, it's pure mathematics and who is to say that the data is inaccurate. From an engineering standpoint for filling in samples in a set, "interpolation" generally means guessing or estimating with a mathematical formula points which cannot be accurately predicted. The word "interpolation" is not generally used in engineering for calculating data that can be accurately predicted with mathematics.
You don't have to guess missing points in a sound wave. Calculations of those points are not guesses; they are exact figures. Sound waves can only have one shape per frequency. It does not vary. You can use trigonometry to predict all points between the known samples. If sound waves could vary in shape randomly between two known points, the Nyquist frequency would not even begin to be high enough to accurately record them. You would need to sample them much, much faster to even start to accurately represent them. Basically, digital recording as it exists today would simply not work.
This is not to say that there can't be errors in this process, but that is what oversampling is for. Oversampling does a better job of eliminating or compensating for errors than increasing sampling frequency does, with none of the drawbacks that increasing sampling frequency can have.
My point here had nothing to do with 16 bit vs 24 bit files. I only mentioned in passing that before mastering, you really need to use 24 bit files. After that it's debatable (not that I'm not saying you absolutely don't).
From a mathematical standpoint, what you are doing when you fill in this data set is interpolation. However, from an engineering standpoint, it is a mischaracterization (note that this is the same word I used before). That is, when the word "interpolation" is used in mathematics it means calculating missing data in a set, it's pure mathematics and who is to say that the data is inaccurate. From an engineering standpoint for filling in samples in a set, "interpolation" generally means guessing or estimating with a mathematical formula points which cannot be accurately predicted. The word "interpolation" is not generally used in engineering for calculating data that can be accurately predicted with mathematics.
You don't have to guess missing points in a sound wave. Calculations of those points are not guesses; they are exact figures. Sound waves can only have one shape per frequency. It does not vary. You can use trigonometry to predict all points between the known samples. If sound waves could vary in shape randomly between two known points, the Nyquist frequency would not even begin to be high enough to accurately record them. You would need to sample them much, much faster to even start to accurately represent them. Basically, digital recording as it exists today would simply not work.
This is not to say that there can't be errors in this process, but that is what oversampling is for. Oversampling does a better job of eliminating or compensating for errors than increasing sampling frequency does, with none of the drawbacks that increasing sampling frequency can have.