Overview

When we studied vibrating bodies in Chapter 2, we observed that they can produce either harmonics (strings and tubes) or partials (bells, membranes, percussions). Man may have been more sensitive to the former than the latter, it would seem, when constructing his musical scales. We can suggest the following explanation: strings (the hunter's bow) and tubes (the first known flutes, crafted from bones, date back to 60,000 BC) produce sounds that last longer than with percussions, and it is easier to perceive the harmonics of the former, depending on the degree of their consonance (see section 2.1.2), than the partials of the latter. It is therefore likely that the strong consonance of the fifth ^[1], which corresponds to a frequency ratio of 3/2, became predominant very early on in musical history.

We saw earlier that dividing a string into successive portions with lengths L/1, L/2, L/3, L/4, L/5 produced a sequence of harmonics with frequencies equal to 1, 2, 3, 4, 5 times the fundamental f. The first of these two sequences is said to be harmonic, the second arithmetic. Note that they would have turned up in the reverse order if, instead of shortening the length of the string, we had multiplied its length by 1, 2, 3, 4, 5 to obtain frequencies equal to f /1, f/2, f /3, f /4, f/5. The first thirteen harmonics are roughly equivalent to the notes given in...