I was provided a report where the amplitudes of spectral harmonics have been extracted from several audio files. The amplitudes have been extracted using Audacity's spectrum visualizer, where the spectrum is provided in dB. I want to compute the ratio between the amplitude of the fundamental and the amplitude of each harmonic. Does it make sense to perform a ratio in dB or should I use the difference between amplitudes? Thank you.
Based on your most recent comment, it sounds violins' like you're measuring harmonic levels from various violins. And you want to represent your measurements in the most appropriate way. The question is, "What is the most appropriate way?" To answer that question ask yourself, "What information do I want to convey to my audience?" Francesco, does your audience want to look at various violins' spectral plots, or maybe just look at bar charts of various violins' harmonic levels, or what?
If you can tell us exactly how you want to represent your measured harmonic dB results, I'll bet someone here can help you.
Because you're dealing with dB values, forget about any notion of computing ratios. Jaket is correct. If the measured dB value of the fundamental freq is 'x' dB and the measured dB value of the 1st harmonic freq is 'y' dB, then you can say that the 1st harmonic is x-y dB below the fundamental. That subtraction works fine for both positive and negative values of 'x' or 'y'.
I think what you are referring to is called the Total Harmonic Distortion (THD). THD is the level of the fundamental divided by the level of the harmonics. You can express this as either as a ratio (X/Y), a percentage (X/Y * 100) or in dB (20*log10(X/Y)). A percentage is probably what most people are familiar with.