Im trying to see how well different instruments can do these tones - and of course Im wondering how well it can be done on a ukulele?
Hi MyLele
An overtone frequency can be produced on ukulele and is usually called harmonics. The terminology can be messed up and confusing.
If you pluck an open string (nothing fretted), you will prodce a certain frequency (fundamental frequency). You can produce the twice of fundamental if you put your index finger ona string over the 12th fret. You do *not* fret. YOu just put your fingertip right above the 12th fretwire. Then you pluck the string. Yu will hear a clear high-pitched sound. That's harmonics, and the frequency is twice of the fundamental (first overtone)
You can do the same if you touch 7th fret. The harmonics is one octave and 5th above, that is, three times the fundamental frequency (2nd overtone). This is a bit difficult.
If you do this on the 5th fret, the sound is four times the fundamental (3rd overtone).
YOu can do higher and higher but most ukuleles do not have the range to produce these frequencies.
Try
http://www.youtube.com/watch?v=6UOypfd00Hw (it's not me but he did a nice job)
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To be exact, the 12th fret harmonics contains all 2x, 4x, 6x, 8x etc of the fundamental. The 7th fret harmonics is 3x 6x 9x the fundamental.
Also, 7th fret harmonics is not exactly equal to one octave and 5th since it's usually in well-tempered scale, and harmonics are integer multiples.
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By the way, 12th fret is "exactly" one half length of the string; 7th fret is 2/3 (or 1/3) of scale length; 5th fret is 3/4 length. "Exactly" but for the compensation......
Cheers
Chief