On Tue, 21 Jul 2009, Lorenzo wrote:
It might be useful to think in terms ratios instead of absolute frequency values if you want to generalise your model so instead of 912, 2434, 4575 etc. 1, 2.66..., 5.01 and thus expressing all the frequencies you found experimentally as ratios. This can help when dealing with scales and 'musical' (esp. tonal) intervals because our perception of pitch is not linear (so for example the interval between 110 Hz and 220 Hz is perceived as an octave 'difference', and so is the one between 220 and 440, yet their mathematical difference is respectively 110 and 220).
Maybe you mean: as a product of ratios. This is sort of a way to introduce logararithms without introducing logarithms. I mean, before starting to do math on MIDI notes (or any other log system), conceptually, you'd multiply ratios together, but eventually, whenever multiplications become too cumbersome, you replace them by additions by using logs. Most of the theory of logarithms revolves around "multiplications are annoying, so let's use a trick to turn them into additions".
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