＜Pitch deviation caused by pistons in brass instruments＞
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 recorders, the lowest note is produced when all the holes are covered and the instrument is played.
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 stretch the tube by a certain percentage.
To make it easier to understand, let's say that stretching the length of the tube by 10% lowers the note by a semitone.
For example, to produce a pitch that is a semitone lower than the pitch produced by a 1m tube, you can add 10cm of tube to make it 1m10cm, but to produce a pitch that is another semitone lower, you need to add 10% of that, or 11cm of tube, to the 1m10cm tube.
If you extend a 1m tube by 10% at a time, it will look like the picture below.
| Total length of tube (and extension) required to lower the pitch by a semitone | Fingering | Actual length of tube | Error |
|---|
| 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 tubes attached to each piston of a brass instrument are always the same length, even if the design allows the pitch to be accurately lowered (1 for one tone, 2 for a semitone, 3 for a half tone) when only one piston is pressed, if other pistons are already pressed and the original tube length is longer, it will not be possible to extend the required length.
This error 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 score 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 notes such as "D" when playing the first and third notes are also high for the same reason, so you need to be careful when playing these notes. On the euphonium, it is a C.
On instruments such as the cornet, you can adjust the pitch by removing the tuning tube while playing using the hooks or rings on the first and third tubes to hang your fingers on, but on instruments with a low range, the pitch error becomes larger in proportion to the length of the tube, and such adjustments are no longer sufficient.
Because the length of the tubes is twice as long for instruments that are an octave lower, the pitch that can be adjusted by removing 1 cm on a cornet must be removed 2 cm on a euphonium and 4 cm on a tuba.
For this reason, some euphoniums and tubas have a fourth tube (piston) that is a little longer than the combined length of the first and third 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.
