Hi Amir,
your english is just fine.
I think that there is an additional factor that your formula needs. Sense of pitch is not determined acoustically by "Q" unless we are talking about pure sine waves. When we add the overtones found on real musical instruments, funny things happen. Depending on the note played, the first harmonic may not even be a perfect octave - as wind instruments for instance change their acoustical length based on frequency. A trumpet consists of a cylindrical and flared portion. The flare determines the acoustical length of the instrument. If you have a friend that plays trumpet, have him blow a few notes on his instrument and then do the same on a piece of garden hose. The garden hose cannot be used for anything "tonal" even although mathematically it represents a "best case" situation
When we hear a well played instrument, the sound is modelled by the player and the result is pleasing. In a speaker, we have "issues" in phase and relative loudness of each of the speaker drivers used. Also the directivity of the driver can cause a shift in how the sound is reproduced. Spatial distribution also separates the overtones from the fundemental, which requires a given listening distance to allow the sound wave to integrate.
I guess, what I am saying is that even if each driver behaved as a perfect piston and was perfectly integrated to another driver, we would still have issues that make the "cook" responsible for the end result - not the absolutely quality of each ingredient. In this respect, I believe that Audio like cooking is an art form rather than a science. Fast food is the science of eating: calories, salt and sugar, repeatability, profitability. Many audio dealers are very much like McDonalds in this respect. For this type of reproduction, I thing the math can become VERY accurate! |
|