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I would like to know a bit more about how the valves of trumpets (and other brass instruments) work than is here: Trumpet at Wikipedia.

I am ignoring issues such as it being a transposing instrument. I only interested in the relative pitches of the notes and not the absolute pitches.

The fundamental is not usually used so the first few harmonics are: C4, G4, C5, E5, G5, *, and C6. (I have skipped the 7th harmonic, its use might become another question).

There are valves to drop the pitch by 2, 1, or 3 semitones. So, I can use these to fill in the gaps between the harmonics. The biggest gap is between C4 and G4. Filling this gaps requires 7 of the 8 conceivable fingerings. Only valve 3 by itself seems to be unused.

Now, let's do some maths. The full length is 1.480m. So, to drop it by a well tempered semitone, this needs to be extended to 1.568m. So, you might expect valve 2 to add 88mm of tube. To drop by 2 semitones, the length needs to become 1.661m so an extra 181mm (note more twice that needed for the semitone). Now comes the problem: to drop by 3 semitones requires the length to be 1.760m so an extra 280mm which is more than the sum of the lengths added by the previous valves. My calculation is that adding 88mm and 181mm only drops the pitch by 2.89 semitones.

So:

  1. Is the valve mechanism more complex than I am assuming and using 1 and 2 adds more length than the sum of 1 alone and 2 alone?

  2. The player corrects the difference somehow (e.g. embouchure)?

  3. It is just a little bit out of tune?

  4. Something else?

There is the further problem that the gap between the 2nd and 3rd harmonics will be a just tempered 5th rather than a well tempered one. I'll ignore that as well for the moment.

Note: I have played a variety of woodwind instruments but no brass. My knowledge of the trumpet is primarily theoretical through reading.

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    The difference between a just fifth and an equally tempered fifth is so small as to be effectively absent. (On top of that I suspect that, the trumpet not being an ideal instrument, the overtones are probably not precisely aligned with the theoretical overtone series.) The theoretical equally tempered F at A=440 Hz is 349.228 Hz, and the one that is precisely 1.5 times the B flat at 233.082 is 349.623 Hz. The bigger problem will be the just major third, which is rather lower than in equal temperament.
    – phoog
    Commented Aug 12, 2023 at 17:24
  • Thanks. The difference in fifths was not my main interest. It is notes in between which require valves that interest me.
    – badjohn
    Commented Aug 12, 2023 at 17:42

5 Answers 5

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Yes, the additional length required for each semitone drop is proportional to the original length. If adding valve 2 to an 'open' note is sufficient to drop a semitone, it will not be enough to drop a note that is already using valves 1 and 3. Or even just valve 1.

This is addressed in several ways. Valves 1 & 2 theoretically add the same length of tubing as valve 3 alone. In practice, valve 3 is adjusted to add more than that. This helps correct many multi-valve notes.

The next level of correction is that all but the cheapest trumpets have finger-operated slides on valve 3 and often valve 1. In this picture we see the ring that is directly connected to the 3rd valve slide, the trigger mechanism on the 1st. The player adjusts these while playing, as required for a note that would otherwise be out of tune.

enter image description here

On the larger brass instruments, Euphonium, Tuba etc. where the additional tubing lengths required are substantial, there are complex systems of 'compensating valves' which do indeed contrive that 1 and 2 combined add more length than 1 and 2 separately. Look at the diagrams in this page:

http://www.dwerden.com/eu-articles-comp.cfm

You will also sometimes see tuba players 'playing the slides' - manually adjusting a tuning slide for a particularly problematic note.

A 'Full double and compensating' French Horn is something to behold! Here's a TRIPLE horn! (Actually, it appears to be a double plus an extension. There are two sets of tuning slides, not three.)

enter image description here

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  • Thanks. I had noticed these correction slides but I did not know how they are used. Do you need to adjust them to optimize the instrument for a specific passage? Do you need to adjust them while playing? Does the horn that you show achieve the compensation without effort by the player?
    – badjohn
    Commented Apr 24, 2019 at 11:59
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    @badjohn You adjust them while playing, generally, as the third valve is used for three different fingerings that all have different requirements (2+3, 1+3, 1+2+3).
    – David Rice
    Commented Apr 24, 2019 at 14:57
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A good brass player can use any combination of valves. Mind - what I always tell them: the pitch is in your ear!

You may certainly know that trumpets (not all of them) have a tuning slide:

The pitch of the trumpet can be raised or lowered by the use of the tuning slide. Pulling the slide out lowers the pitch; pushing the slide in raises it. To overcome the problems of intonation and reduce the use of the slide, Renold Schilke designed the tuning-bell trumpet. Removing the usual brace between the bell and a valve body allows the use of a sliding bell; the player may then tune the horn with the bell while leaving the slide pushed in, or nearly so, thereby improving intonation and overall response.

Edit: As Laurence Pawne mentioned this quotation above is concerning the general tuning slide that all brass instruments possess. What I am thinking of is the trigger for compensation the length to play a well tuned D and Db (the tones of the valves 1+3 and 123 in Bb tuning)

For more information:

https://en.wikipedia.org/wiki/Trumpet

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    Indeed and when I saw that valve 3 was for 1.5 semitones, I had expected that it would be normal for E4 (for example) but oddly it isn't (according to the chart in Wikipedia). I can see that for the higher notes, you will often have choices but between C4 and G4, the choices seem very limited. How can a player get these pitches accurate?
    – badjohn
    Commented Apr 24, 2019 at 11:27
  • I had to edit my answer. Commented Apr 24, 2019 at 14:46
  • I don't think you'll find any practical trumpet without a tuning slide! It can indeed be situated in several positions - at the mouthpipe, at the first bow of tubing, in the bell section...
    – Laurence
    Commented Apr 24, 2019 at 16:47
  • I mean the tuning slide for the third valves, of course. The main tuning slide will have every brass instrument. Commented Apr 24, 2019 at 17:04
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    I mean the tuning slide for the third valves, of course, that we call the trigger. The main tuning slide will have every brass instrument. But you are right, the sentence I have quoted is concerning the latter one. Commented Apr 24, 2019 at 17:17
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Many trumpets have a mechanism (a spring-loaded lever or a simple ring) attached to the third valve slide.

When using all three valves at the same time the mechanism makes it possible to manually lengthen the third valve slide. As you noted, the third slide isn't long enough on its own, so unless the this mechanism used, the pitch will be too sharp.

Some trumpets have a similar mechanism on the first valve slide too. The middle valve is too short to need a mechanism like this.

Many larger instruments like tubas feature compensated valves, where the valves have extra ports, which means the tubing is automatically lengthened when using the third valve. Of course uncompensated tubas exist too, but to play one in tune you have to manually extend tuning slides as you play.

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There are some good answers already, but I don't see any mention of embouchure being used to correct tuning.

When I played in brass bands 40 years ago, cornets, flugels, horns and baritones did not have compensation systems. Euphonium and lower instruments did have compensation. Trombones did not, as it was not required.

The small instrument players were expected to correct their tuning using their embouchure. This was a difficult technique to master, and tonal quality tended to suffer. Modern instruments with tuning slides are a great improvement, but short notes tend to still require "lipping" into tune as there is no time to move a slide.

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  • Thanks; the tuning was my primary question. That matches my guesses. I play the clarinet and saxophone and we can bend a note with the embouchure (think of Rhapsody in Blue) but, of course, it is a very different embouchure. So, I did not assume that it would apply to brass instruments, hence the question. Trills and other rapid passages might use easier but less accurate fingerings.
    – badjohn
    Commented Aug 12, 2023 at 7:55
  • Modern cornets often have 1st and 3rd valve triggers (which is something quite different to a 'compensating' valve system, though the result may be similar). It's perhaps unfortunate that 3rd Cornet players, probably the least experienced and playing less advanced models, spend so much of their time in the region that uses 2/3. 1/3 and 1/2/3 fingerings. Yes, we can maybe get away with iffy tuning in rapid passages, but if there's time to 'lip' a note into tune, there's time to operate a finger slide!
    – Laurence
    Commented Aug 12, 2023 at 19:39
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I've been using a lot of alternate fingerings, that is, 3 instead of the more common 1&2, 4 instead of the more common 1&3 (tuba). My logic is: any time you push a valve down, you are essentially changing your BBb "bugle" to a bugle of some other pitch, therefore making any of the other slides too short to lower the horn the desired 1/2 tone, full tone, etc. So, at least in theory, any two or three valves used in combination will have to be sharp. By tuning 3 to a more-perfect 1-1/2 tone lowering, and 4 to a more-perfect 2-1/2, those fingerings have at least a fighting chance to being in tune. Granted, 2&4 for a low B, or 2&3 for Db, Gb, are somewhat compromised, but I can't help that. I can't really reach any suitable slide for tromboning it.

I've had some difficulty convincing anyone of the beauty of this logic, including my older, PHD-in-Music-Ed, tuba-playing brother, but it helps me sleep better to know I've done what I could to tune.

I'll have to admit, there's not a person in a thousand that would ever hear the difference in a Dixieland tune, but...

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