Natural harmonics

Natural harmonics are created at the points of a string where it can be divided in integers. If you dampen the strings at these points so that the exact sound that lies on this fret can not be heard, but the rest of the string can still swing freely, only the overtones are audible. This results in a bell-like, bright sound. Harmonics

are really just a dalliance; but have their own charm, and make, brightly and definitely produced, good effect …1)
FretRatioIntervalHarmonics–IntervalOvertones (C6)Overtones (D6)
73:2fifthOctave + FifthDGBEEAC♯F♯
54:3fourth2 OctavesCGEAADF♯B
35:4third2 Octaves + ThirdDGBEEAC♯F♯
Harmonics on the Ukulele

In an ukulele, third, fourth and fifth harmonics are hard to play and sound very quiet. The following sound examples are all amplified by 10 dB.

Each string is played open. The index finger of the strumming hand lies loosely – without exerting pressure on the string – at the position of the specified fret (not before) on the string. Behind it, the thumb strokes across the string at the height of the indicated fret.

Artificial Harmonics

In order to be able to play other notes in addition to the six possible natural harmonics of a ukulele, artificial harmonics are used. For this purpose, the output tone is picked as usual with the fret hand on the fretboard; at the same time, as with the natural octave flageolet, the index finger of the strumming hand 12 strings lower the string while the thumb strokes 3–4 frets higher across the string. The result is a tone that is one octave higher than the tone picked up.

Johann Ernst Häuser: Guitarre-Schule. Basse 1835, p. 7