What pitch relationship does the 3rd harmonic establish in relation to the 2nd harmonic?

The 3rd harmonic establishes a pitch relationship of a major 3rd in relation to the 2nd harmonic. To understand this, it's essential to consider the harmonic series, which is a sequence of pitches produced when a vibrating string is divided into segments.

In the harmonic series, the fundamental frequency is the 1st harmonic. The 2nd harmonic is an octave above the fundamental, while the 3rd harmonic is a perfect fifth above the 2nd harmonic. So, if you consider the frequency represented by the 2nd harmonic, the 3rd harmonic relates to this frequency by a major 3rd interval, meaning it establishes a specific, recognizable relationship within the tonal structure.

This relationship is essential in music theory, as it helps musicians understand how harmonics create consonance and support melody and harmony. The major third is also significant in building chords and understanding the nature of tonal music.