New answers tagged

2

Anything can inspire creation of mathematical systems expressed in music. However, whether the connection is actually less tenuous than any kind of voodoo is a different question. In the manner you pose the question, I don't think that it can be answered positively with an approach reasonably called justifiable. One obvious problem here is that Fourier ...


3

William Sethares, creator of "xenotality" and "exotonality," wrote a book called Tuning, Timbre, Spectrum, Scale. According to Dave Benson in Music: A Mathematical Offering p. 490: The basic thesis of this book is the idea, first put forward by John Pierce, that the harmonic spectrum or timbre of an instrument determines the most appropriate scales ...


6

For human ears, the relation of the overtone to the fundamental is perhaps not as important as the pitch area that the overtone sounds in. Our ears have evolved to pick out resonance peaks and valleys (see the concept of vocal formants) that are pertinent to distinguishing vowels. An "ah" sound, for example, has an "ah" quality regardless of the fundamental ...


5

On a practical/engineering approach, once we have the spectral analysis (i.e. the characterization of the frequency spectrum along time in terms of transients, and harmonic and inharmonic partials, as explained in Todd Wilcox's answer), we need to compare our instrument to a reference database of previously catalogued instruments. This is done by using a ...


14

A simple list of what overtones are present wouldn't tell you much. What you really want is the relative levels/intensity of each overtone. A list of the overtones with relative intensities for an instrument is called the instrument's spectrum. You might try searching for " spectrum" for the ones you are most interested in. Here's an example for a violin: ...



Top 50 recent answers are included