Standing wave patterns are always characterized by an alternating pattern of nodes and antinodes. There are a variety of patterns which could be produced by vibrations within a string, slinky, or rope. Each pattern corresponds to vibrations which occur at a particular frequency and is known as a harmonic.
http://www.physicsclassroom.com/mmedia/waves/harm3.cfm
The second lowest frequency at which a string could vibrate is known as the second harmonic; the third lowest frequency is known as the third harmonic; and so on. An animation of a string vibrating with the third harmonic is shown below. The frequency associated with each harmonic is dependent upon the speed at which waves move through the medium and the wavelength of the medium.
http://www.physicsclassroom.com/mmedia/waves/harm3.cfm
In acoustics the basic vibration is the 'first harmonic'. The term overtone is used to refer to any resonant frequency above the fundamental frequency. The 'second harmonic' (twice the fundamental frequency) is the first overtone.
http://www.sengpielaudio.com/calculator-harmonics.htm
A harmonic frequency is a multiple of a fundamental frequency, also called harmonic. Especially when it comes to counting, do not say: overtones are harmonics. Musicians prefer the term overtones and physicists prefer the term harmonics. Sound engineers are somewhat uncertain between these two terms.
http://www.sengpielaudio.com/calculator-harmonics.htm
The speed at which waves move through a medium is dependent upon the properties of the medium (tension of the string, thickness of the string, material composition of the string, etc.). The wavelength of the harmonic is dependent upon the length of the string and the harmonic number (first, second, third, etc.). Variations in either the properties of the medium or the length of the medium will result in variations in the frequency at which the string will vibrate.
http://www.physicsclassroom.com/mmedia/waves/harm3.cfm
The harmonics are multiples of the fundamental frequency. So if the fundamental frequency is 100 Hz, the harmonics will be 200 Hz, 300 Hz, 400 Hz, 500 Hz, and so on. If the fundamental frequency were 220 Hz, the harmonics would be 440 Hz, 660 Hz, 880 Hz, and so on.
http://homepage.ntu.edu.tw/~karchung/phonetics%20II%20page%20eight.htm
In terms of intervals on the scale, we hear a base tone, its octave (eight notes up), then a note that is a twelfth up, i.e. a perfect fifth above the octave above the starting pitch, then a note two octaves up from the starting pitch, then one that is a major third above that, and on and on.
http://homepage.ntu.edu.tw/~karchung/phonetics%20II%20page%20eight.htm
These are the overtones of the fundamental frequency of the vibration of your vocal folds. If you'd like to see the overtones in real time and in color, then try downloading the Frequency Analyzer you can get at the link below, from a company called Reliable Software. You can use it on a trial basis for 40 days.
http://homepage.ntu.edu.tw/~karchung/phonetics%20II%20page%20eight.htm
In counting − harmonics are not overtones. There are integer multiples of a certain frequency (fundamental), that are called harmonics, partial tones (partials) or overtones. It is important to note that the term 'overtones' does not include the fundamental frequency. The first overtone is therefore already the second harmonic or the second partial. The term overtone should never be mixed with the other terms, as the counting is unequal. The term harmonic has a precise meaning-that of an integer (whole number) multiple of the fundamental frequency of a vibrating object.
http://www.sengpielaudio.com/calculator-harmonics.htm
G''' (1/5 of length; two octaves and a third up; 410 Hz; 13.2cm; touching the string here suppresses the fourth harmonic so you hear this pitch; in fact a tempered G''' is 415.305 Hz, so the tuner will register this note as sharp if you touch the string right above the fret).
http://homepage.ntu.edu.tw/~karchung/phonetics%20II%20page%20eight.htm
average hertz for third harmonic of string
The average hertz for the third harmonic of the string is 410. The average hertz for a third string of harmonic is 410 hertz.