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Given that a composed sound is composed of a fundamental frequency and its harmonics (multiples of the fundamental), we could easily image that a pitch (with a fundamenal frequency f) is played and then another pitch with fundamental frequency 3f is played. Wouldn't the resulting sound be highly agreable to hear ? I tend to think it would be agreable because all the harmonics 3f, 6f, 9f, and so on would "resonate".

What would be the name of such an interval (3:1 or 1:3 would be the ratio, but is there a name?) ?

For example, if I play a C (third fret on the second string of a guitar), what should be the next key I need to play in order to do a 3:1 (or 1:3) interval ?

Thank you in advance.

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  • That C note is 3rd fret, 5th string. They're always numbered thin to thick.
    – Tim
    Commented Feb 27 at 10:39

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Wouldn't the resulting sound be highly agreable to hear ?

Likely yes. It is attributed to Pythagoras to discover that notes which frequency ratios can be expressed with small integers are consonant.

What would be the name of such an interval (3:1 or 1:3 would be the ratio, but is there a name?) ?

Twelfth or an octave + fifth.

For example, if I play a C (third fret on the second string of a guitar), what should be the next key I need to play in order to do a 3:1 (or 1:3) interval ?

I guess you mean C on the third fret of the fifth string? (Counting starts from the treble strings). The note would be G on the third fret of the first string.

See also Wikipedia article on Harmonic series.

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  • As a side note, folks should visualize the fundamental as the entire string moving up and down; the first harmonic as the upper half vibrating opposite to the lower half; the second harmonic as the middle third opposite to teh top and bottom thirds, and so on.
    – Carl Witthoft
    Commented Mar 1 at 15:37

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