From The Archives 2: Trumpets and the Harmonic Series

Oh hai, welcome back to the time capsule! I didn't really spend much time doing sciencey stuff, but I took a class called Physics in the Arts and Music during my first semester, and I learned very little, but as a musician (and former trumpet player), the harmonic series made sense to me, so that's what I wrote about for my final paper.

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November 2015

            Trumpets are one of the first brass instruments that were created, and are used in bands and orchestras to this day. With only three valves, the trumpet appears simplistic, but the set up of the valves and the techniques used in order to change notes contains significant physics concepts, including the structure of the harmonic series.

            Trumpets, along with the other brass instruments, are made up of curved metal tubes that open up into a flared opening of the tube that is known as the bell. The three valves on the trumpet, when pressed down, change which tubes are open, and therefore change the sound. There are seven different fingering positions: holding down no valves (open), holding the second valve down, the first, the first and second, the second and third, the first and third, and holding down all three valves. The sequence of positions actually follows the chromatic scale and can be used multiple times in order to find the next notes available. 

Because there are only seven different fingering positions, there are multiple notes that use the same fingering. To be able to play more than just one of the notes available to a certain fingering, the player can change up the speed of the air they blow into the trumpet. When they blow faster air, the not they reach will be higher than when they use slower air because the frequency is being changed, and higher frequencies result in higher pitches. The player doesn’t simply blow air, however. In order to create the sound, their lips vibrate together with a small hole between them to blow out the air. The lips are placed on the mouthpiece and the vibrations are transferred from the lips to the air vibrating and moving through the tubes. The length of tubing, designated by the valves that are pressed down, creates the note that is being played, and releases it though the bell to be heard.

The order of the fingerings for the sequence is not random, however. The pattern’s relation to the notes follows the series. In the musical scale, the notes are letters A through G. The note C₄is the often the first note learned because it is the open fingering, lower down in the range of the trumpet. For the trumpet, C₃is the fundamental or base frequency, but it cannot be played because it is not within the natural musical range of the instrument. The first overtone, C₄is the first note within the sequence that can be played with the open fingering. From there, the next four notes that can be played with open are G, C₅, E, and C₆. Looking at the intervals, C₄to G is a perfect fifth, G to C₅is a perfect forth, C₅to E is a major third, and E to C₆is a minor third. This follows the intervals in harmonic series, which starts off with an octave between the fundamental frequency and first overtone. 

If one were to play a trumpet with an open fingering, they could only reach the notes in this sequence, even with blowing air at different speeds. No other notes are achievable.  The same happens when fingerings are changed. If the musician plays with the 2^ndvalve held down, the fundamental frequency would again be out of the natural range for the instrument, but the intervals of all the notes that could be played with the 2^ndvalve would follow the same intervals, starting at an octave above the fundamental, which is B₄. For the frequencies, B₄would have a 1:2 ratio to the fundamental, B₃. Fifths have a 2:3 ratio, forths have a 3:4 ratio, and major thirds have a 4:5 ratio. The process of the interval sizes in the harmonic series follows in a way that is much more connected than at first glance, and as a harmonic series, the tones themselves sound good together. Back to the first example with C₄, the major arpeggio of C-E-G sounds pleasant to our ears because the tones themselves are connected by their harmonic series.

Without physics, the way a trumpet works and is played doesn’t necessarily make any logical sense. By knowing that the different sequences of notes for each fingering are decided from how they work in their harmonic series, and how intervals work within that creates a whole new understanding of the instrument. With physics, all the elements come together to explain how trumpets, truly work, and how music and science are more closely tied than could have been thought.

            

References

Gilbert, Pupa. Physics in the Arts. Waltham, MA :Academic Press, 2012. Print.

Purtle, Jeff. "Trumpet and Brass Playing Frequently Asked Questions." Trumpet and Brass Playing Frequently Asked Questions by Jeff Purtle. Purtle.com, 2003. Web.