Yes, an intonation issue. Causes and fixes:
1. Strings too high in nut, as per earlier comment. Deepen nut slots, but make sure that buzzes from poor string fit in the slot or interference with fret 1 do not result.
2. Poor strings, as per earlier comment - change strings.
3. Frets too high - may need level/dressing.
4. Saddle too high - similar effect to strings high in nut. Lower saddle, if possible.
5. Scale length too short - check the distance from nut to fret 12 and fret 12 to the string bearing point on the saddle. The distance from fret 12 to the saddle should be 2-3 mm longer than the distance from the nut to fret 12. It is sometimes possible to crib a mm or two by angling the saddle top so that the bearing point is as far from the nut as possible (these comments assume that the strings are going sharp up the neck....which is almost always the case).
6. Frets are in the wrong place. I recently worked on an old uke for a friend. It seemed to have never been played. No wonder - the intonation was way off. After checking on the wonderful
Stewmac fret position calculator I found that the first fret was placed 4 mm too far up the neck. I was able to put in a nut extension that gave a good scale length with the frets and hey presto - the uke played in tune.
With the Stewmac calculator, I like to measure the distance from the nut to fret 12 and double it to give the scale length input. The calculator then gives you the "real" scale length required to get good intonation and also the fret position measurements.
I understand that Vincenzo Galilei, father of Galileo, developed the 17:18 rule behind fret positions...he played the lute, but only because ukes had not been invented yet.....
