The longer the tube of a wind instrument, the lower the pitch.
With woodwind instruments, the tube is lengthened by covering the holes with your fingers. With a recorder, the lowest note will be produced when all the holes are covered.
With brass instruments, the pistons are pushed to divert the vibrating air column to each tube, changing its length and changing the pitch.
However, in order to change the pitch accurately, it is necessary to extend the tube by a certain rate.
To make it easier to understand, let's say that extending the length of the tube by 10% lowers the note by a semitone(Actually, it's about 6%, the 12th power root of 2).
For example, to produce a note that is a semitone lower than the pitch produced by a 1m tube, you simply add a 10cm tube to make the length 1.1m, but to produce another one semitone lower, you need to add 10 percent of 1.1m, in other words 11 cm, to the 1.1 meter tube.
If you extend a 1m tube by 10% at a time, it will look like the table below.
| Total length of tube (and extension) required to lower the pitch by a semitone | Fingering | Actual length of tube | Deviation |
|---|---|---|---|
| 100cm | 0 | ||
| 110(10)cm | 2 | 10cm | 0 |
| 121(11)cm | 1 | 21cm | 0 |
| 133(12)cm | 1+2(3) | 31cm | 2cm |
| 146(13)cm | 2+3 | 41cm | 5cm |
| 161(15)cm | 1+3 | 52cm | 9cm |
| 177(16)cm | 1+2+3 | 62cm | 15cm |
This table was created assuming that a 10% increase in tube length would lower the pitch by a semitone, but the length of the tube required to lower the pitch by a semitone gradually increases as shown here.
However, since the tube attached to each piston of a brass instrument is always the same length, even though it is designed to be able to lower each pitch (1 is one note, 2 is a half note, 3 is one and a half note) exactly when only one piston is held down, when the original tube length is already longer by holding down another piston, it will not be possible to extend enough length for the pitch.
This deviation increases as the tube becomes longer, and is greatest when pistons 1 and 3 are pressed and piston 2 is added. Due to overtone issues, the low C#
on the music for the cornet and alto horn becomes quite high. On the euphonium, it is a low B
, and on the tuba, it is a B
an octave lower. The note such as "D"
when playing the first and third pistons are also high for the same reason, so students need to be careful when playing these notes. On the euphonium, it is a C 
For instruments such as cornets, there are hooks or rings on the first and third tubes that you can hang your fingers on, to pull out the tuning slides while playing and adjust the pitch, but on instruments with a low range, the pitch deviation becomes larger in proportion to the length of the tube, and such adjustments are no longer sufficient.
Since instruments that are an octave lower have tubes that are twice as long, so the pitch can be adjusted by extending the tuning tube by 1 cm on a cornet, it needs to be extended by 2 cm on a euphonium and 4 cm on a tuba.
For this reason, some euphoniums and tubas have a 4th tube(piston) that is a little longer than the combined length of the 1st and 3rd tubes (52 cm in the table above), and is the original length needed to lower the pitch by two and a half tones (61 cm in the table above), and some tubas used by skilled players have a fifth and sixth valve and tuning tube (not only for adjusting the pitch but also to expand the range).
Since the trombone can freely control the pitch with the slide, this problem does not occur, but if you pay attention to the pitch, the distance between each position should be wider the further away the position is.