The overtone series is an acoustic principle that is sometimes cursorily discussed in music theory and other music courses, but is often poorly understood even by musicians. The “short, short version” is that the pitch sounding when, say, an open string is plucked or bowed is actually a complex sound containing a number of tones, sometimes called “partials” or “harmonics.” Readers of this blog will be more interested in how this applies to brass instruments. Consider here the “pedal B-flat” on tenor or bass trombone. Here is that note along with the twenty-three notes above it in first position.
That pedal B-flat is the fundamental pitch of an air column vibrating in a tube approximately nine feet in length (i.e. a trombone in first position with no valves engaged). It is a complex tone, containing all of the notes here listed above it (and more). Ascending to pitches higher than the fundamental on brass instruments is achieved by “overblowing” to higher partials in the overtone series by increasing the air speed and the speed of the vibrations of the lips. This makes an exponentially larger number of notes available to the player, and as one ascends to higher harmonics multiple fingering possibilities with differing timbres and tuning tendencies become available for each note. You’ll notice that while the fundamental and its octaves tend to be more or less in tune, the other harmonics deviate to various degrees from a perfectly tuned version of that note as registered by a tuner.
At this point I have nearly exhausted my rudimentary technical knowledge of the physics behind the overtone series, but the practical ramifications of this for brass players and teachers are both familiar to me and vitally important. Here are a few thoughts on the benefits of understanding the overtone series for every brass player and teacher.
1. Every brass instrument is built on this same principle. This might seem obvious at first, but if you’ve never thought about how brass instruments work in this way perhaps it isn’t obvious at all. While different instruments have different fundamental pitches, from there the overtone works in exactly the same way on every brass instrument. The second partial is always an octave above the fundamental, the third partial a perfect fifth above that, the fourth partial a perfect fourth above that (or two octaves above the fundamental), etc. Combine this with the fact that the second valve (or second position on the trombone) always lowers the open pitch by one half-step, the first valve (or third position) by one whole-step, etc. and you will see that understanding the overtone series provides a tool by which you can quickly and easily find multiple available fingerings for any note on any brass instrument. And the similarities don’t end there.
2. The tuning tendencies of each partial are the same on every brass instrument. While individual instruments will have a few notes that deviate from the rule, in most cases on any given brass instrument the third partial will be slightly sharp, the seventh partial quite a bit flat, and so on. Moreover, doubles of each partial (or octaves) will always have the same tendency. Thus, partials 1, 2, 4, and 8 are normally true; partials 3, 6, and 12 are sharp; partials 5 and 10 are flat, and so forth. Understanding how this works—and how simple it really is—enables the player or band director to anticipate the likely tuning tendencies of any note using all of the available fingerings for that note. When armed with a solid understanding of the overtone series choosing the best fingering for a note in a given set of circumstances becomes a rather simple matter.
3. Benefits of understanding the overtone series for doublers. As I have repeatedly opined here and in my book on the subject, doubling is a professional necessity for the working low brass player. The player with an understanding of the overtone series and how it works can quickly gain a working knowledge of a new instrument. Rather than slowly and laboriously memorizing notes, fingerings, and tuning tendencies one at a time, the player who understands the overtone series can quickly apply that knowledge to the new instrument, thus anticipating particular tuning difficulties and even associating known fingering patterns from other brass instruments with their applications on the new instrument. Those who find themselves teaching related instruments that they seldom play, such as when I teach F or CC tubas, can use that understanding to help correct students’ fingering errors and even find solutions for their tuning or timbre difficulties. This teaching-related benefit is even greater for band directors.
4. Benefits of understanding the overtone series for band directors. As I just mentioned, I use my knowledge of the overtone series as a means of effectively teaching every member of the tuba family, despite my rarely playing some of those instruments. How much more, then, can the band director, who works with trumpets, horns, trombones, euphoniums, and tubas on a daily basis—and these sometimes in multiple configurations—use such an understanding to effectively identify incorrect fingerings, correct tuning problems, and suggest alternative fingerings for particular situations? Memorizing just the first 8-12 open (or first position) notes on each instrument along with the tuning tendencies of each partial (which, remember, are the same for every brass instrument) will provide a basis from which you can extrapolate as needed to the overtone series for each finger combination or slide position. This will enable you to find multiple fingerings for any note on every brass instrument and prescribe those fingerings which best address specific tuning or execution difficulties.
Despite my best efforts, verbally describing how understanding the overtone series improves both teaching and performance always makes the process sound more cumbersome than it really is. In practice, the process is very fast, efficient, and intuitive, far superior to trying to memorize chromatic fingering charts for every instrument and learning every fingering and tuning tendency none note at a time. Overtone series charts for every brass instrument can be found easily through various search engines; I have several available on my website, as well.