Several factors affect fretted instrument intonation, including depth of the string slots in the nut, bridge saddle position, the position of the frets themselves, the bending stiffness of the string, and the technique of the musician.
If the instrument doesn't compensate for this with a slight increase in the distance from the bridge saddle to the fret, the note sounds sharp.
A luthier or technician adjusts a floating bridge simply by carefully changing its position until the intonation is correct.
[3] Another cause of poor intonation on a fretted instrument is that the maker didn't cut the string slots in the nut deep enough.
Most woodwind instruments comply to a regular harmonic series of pitches and require one register key to change octaves.
Better manufacturers of three-valve instruments such as Sousaphones often make the third valve slide long enough to partially address this deficiency.
Also, many tuba models place the first valve slide in a position where it may be manipulated by the musician with the left hand during playing, which allows tuning for the always-flat 5th partial harmonic at the C below middle C. Another solution for euphonium or tuba is called a compensating system, and these have been made in both three- and four-valve versions.
Compensating systems add weight and "stuffiness" to a horn, so they are not commonly fitted to tubas.
Intonation is less of a problem in French horn, because it usually plays using higher harmonics where use of the 1-3 and 1-2-3 valve combinations is not needed.
This concept looks at intonation as a basis of musical expression, and relates it to the peculiarities of different national or personal styles.
The basis of the intonation doctrine was laid by Russian musicologist Boleslav Yavorsky (1877–1942) and later developed by Asafiev.