The Chord of Nature (harmonic series) (3)

The earliest reference is probably 1636, however:

Joseph Sauveur (in 1701) is usually cited as the discoverer of the 'chord of nature' (see, for example, Weiss and Taruskin, Music in the Western World, NY, 1984, p. 220).

Sauveur's observations were in fact preceded (as some biographical reference books note) by Wallis, in 1677 (See 'On the Trembling of Consonant Strings, a New Musical Discovery', Philosophical Transactions, 12, 839 - 842), and Roberts, in 1692 ('A discovery concerning the musical notes of the trumpet and the trumpet marine, and of defects of the same', PT, 17, 559 - 563). 

It has been relatively less acknowledged that all these instances were preceded in 1636 by a clear (though not entirely accurate) account of the phenomenon by none other than Mersenne, who spoke of it in relation to bowed viol strings and the lyre (Harmonie Universelle, Paris, 1636-7, Tr Roger E Chapman, 1957, pp. 254-5; 263 ff.).

NB ! These are known documented accounts. They do not prove that the Chord of Nature was first discovered only as late as the 17th century.

Consonance

The particular Chord of Nature illustrated on the previous page was:

This shows only the first 10 harmonics, inherent in a note C an octave below middle C. In theory, there are an infinite number of harmonics. Above the 10th are the 'higher' harmonics (or partials), separated by ever decreasing intervals. In effect, they become a continuous musical 'cluster'. Up to the about 25th partial they are roughly a semitone apart. From the about the 26th to about the 50th, they are roughly a 'quarter tone' apart. And so on.

Suppose we put one Chord of Nature together with another. If both Chords have the same lowest harmonic, the Chords will be the same. If one Chord's lowest note (in acoustics called the fundamental) is an octave above the other chord's, then of the first eight harmonics, which ones from the two Chords would coincide at the same pitch?

find out here