08.15.2008

And… A Little Bit More

Posted by AJ Harbison at 12:05 am

My highly trained professional blogging and SEO consultant Mike (also known as my roommate) has instructed me that responding to comments on my blog is a way to increase interest and also increase commenting, and thus I have decided that I will do so. Therefore, if you leave a comment, I will likely reply to it within a day or so, in the comments section; you can go back to the comments section for that post and there discover my response.

But in the meantime, I thought I would dedicate one more post to tuning before we move on to other things, because Ryan Fleming again brought up an interesting question:

Thank you for the reply! I am glad you clarified that issue for me regarding the brass instruments. I was unaware that brass instruments were naturally tuned. Could you expand on that? What is the reason for this type of tuning if it make some notes extremely sharp (as you mentioned some notes can be up to 40 cents sharp from a justly tuned third)? Is it easier to make a brass instrument with that type of tuning? Or is it because of the harmonic nature of a brass instrument (e.g. the same fingering/tuning can produce different pitches by stepping playing in different harmonic registers)? Please enlighten a curious reader of your blog.

This may get a bit technical, so hang in there with me….

Every pitched note, on any instrument, voice or whatever, actually contains an infinite series of notes within itself. For example, if you play middle C on the piano, there are actually notes sounding above it in addition to middle C: the C an octave higher, the G above that, the C above that, the E above that, etc. etc. ad infinitum. These other notes are an acoustic phenomenon we call “harmonics” or “overtones.” The reason we don’t hear these notes is because they are very weak and diminish as they get higher; but they’re always there, and they’re very influential in the sounds that we hear. When you hear a violin and a flute playing, you can tell that the sounds are being made by different instruments (musicians call this different-sound-quality between instruments timbre pronounced “TAM-bur”]). The reason those instruments sound different is that their overtones are different–various overtones are strengthened or diminished because of the construction and playing method of the instrument, and even though you can’t hear the overtones themselves it’s a big enough difference to allow us to hear very different timbres. Trippy, but true.

Brass instruments, like trumpets for example, are built around this principle. If you take a column of air (like in a garden hose, for example), put a proper mouthpiece on it, and cause the column of air to vibrate (like by blowing through it, for example), it will produce a pitch. And believe it or not, by changing the shape of your mouth (called your embouchure) and the way you blow, you can produce different pitches. The reason for this is that by changing those things, you can access the notes of the overtone series, without the use of any valves, buttons or extra tubes. Also trippy, but also true. The next time you’re around a trumpeter friend who happens to have a mouthpiece and a section of tubing handy, ask him to demonstrate. Here is a diagram of the first 16 harmonics, starting on C and then F (image courtesy of www.usd.edu/~greeves/exercises.htm):

All of the valves, tubes and slides on brass instruments exist for the purpose of making available to the player notes other than these, because with only a tube, these are the only notes that are possible. Valves and slides and such alter the length of tubing, thus making available a different harmonic series. For example, the first valve on a trumpet lowers the pitch by a whole step. If you were playing in the key of C, you would have all of the notes of the C harmonic series (the first one in the diagram) available, and no others. If you played a C note, and then depressed the first valve and “played” the same note (with the shape of your mouth and the way you were blowing air), it would be a B-flat, and you could then use the notes of the B-flat harmonic series, some of which occur in the key of C but not in the C harmonic series or at least not in the same range (for example D; D does occur in the C harmonic series [as the 9th harmonic, as you can see in the diagram above], but if you needed to play the D a whole step above middle C you would need a different series).

This is why brass instruments are said to be in certain keys: “Trumpet in B-flat,” or “Horn in F.” The key is the harmonic series of the instrument without any modifications. Without any valves, the French horn would only be able to play the notes of the F harmonic series detailed in the diagram, because that’s the way the instrument is built.

However, valves and buttons and slides can alter the pitch a little more than intended, and certain combinations have certain tendencies to be off. In addition, many other factors including temperature, playing volume and mouthpiece design can make pitches slightly sharp or flat. A quick glance at this page will give you a much greater appreciation for brass players and the problems they face.

All this to say: Because of the way brass instruments work, depending on the key of the instrument, the key of the piece, what note needs to be played, what valve combination is necessary, the temperature and myriad other variables, some notes need to be altered in order to be “in tune.” (Pitch on a brass instrument can be slightly modified–tuned a little up or down–by changing your embouchure.)

And this, in many cases, includes major thirds.

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    ryan fleming on 08.15.2008

    The complexity of the tuning in brass instruments is quite astonishing! Thanks for the wealth of information.

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