In Search of the Missing Fundamental: by Richard K. Jones
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Timpani Audition Intonation

Consonance and Coincidental Harmonics

Consonance as it pertains to musical pitch is defined as that which is restful or pleasing. The aural perception of consonance relates to what are called beats – the alternate rise and fall of sound intensities as two waves of slightly different frequency reinforce and interfere with each other. The human ear is particularly sensitive to the beating which can occur between the upper partials of two or more frequencies when they are vibrating simultaneously. This beating causes an unpleasant and often, irritating sensation in the inner ear.  The ear is naturally drawn to those intervals, which produce the least irritation. When one or more of these coinciding upper partials (coincidental harmonics) come close enough in frequency to create detectable beats, the interval is said to be out of tune.

What does it mean to be in-tune? The simplest definition is, in-concord or in-agreement. How then does the ear judge what is in-agreement? As it parses multiple frequencies sounded together, the human ear is drawn to the points of least irritation in the combined overtone series. It utilizes the natural acoustical phenomena known as coincidental harmonics to determine whether organized sounds of different frequencies are pleasant and in-tune.  The more harmonics contrasting pitches have in common, the more concordant they will be.  The more exact the frequencies of the coinciding harmonics, the more in-tune the sound is to the ear.  It is most noticeable when contrasting pitches are lined up vertically as in a chord. When pitches are in a horizontal structure, such as moving melody, it is not as noticeable. Herein lies a problem; how do you combine chords and melody in a fixed pitched system when some intervals sound fine harmonically but not melodically and vice-versa? You compromise. Humans have devised thousands of temperaments over the centuries and none of them seem to be a panacea. The most frequently used in modern Western music are Equal Temperament, Pythagorean tuning, and Just intonation. Equal Temperament is a good compromise, but is it good standard?  Just Intonation agrees with the laws of nature, but is it practical? Pythagorean sounds good to the ear for melodic patterns, but what about harmonic structures? In reality, a group of good musicians will use all three simultaneously without much thought.

Do any really work for timpani?

Due to the repetitive nature of the practice/performance routine, musicians naturally formulate pitch perception based on the sound of the instruments they play. This perception is derived by the inherent acoustic properties of the instrument. Furthermore, in Western classical music, pitch perception in solo playing is often treated very differently from ensemble playing based on the psycho-acoustic concept of tension/resolution with respect to melodic v.s. harmonic structures. Timpanists have the experience of listening to the pitch of their instruments intimately and intently over a long period of time. As a result, they tend to develop an intense personal awareness and appreciation of the many subtleties in the spectra of the sound; many of those of sounds are often categorized as noise to the non-percussionist musician.

The young timpanist must also determine if they are primarily a spectral or holistic listener and refine the weaker of the two. Under stress (especially when using foreign instruments at an audition, or when sudden environmental changes take affect), the young player will default to their primary method, which can lead to second guessing their pitch. The spectral listener tends to breakdown a sound and hear it more as group of individual frequencies rather than a single sound while the holistic listener tends to group all of the frequencies into a single sound. In stressful situations, the predominantly spectral listener could easily be confused by the lack of strong harmonic overtones and the myriad of non-harmonic overtones found in timpani pitch. This can lead to second guessing her/his placement of the pitch because the actual principal tone (in the mind of the player) has been obfuscated by the upper partials. This is even more true when the instruments have not been cleared properly. On the other hand, the primarily holistic listener under stress might be more prone to ignore what “harmonic” partials do exist in timpani pitch, and place the pitch where it doesn’t blend well with the harmonic overtones of the other instruments of the ensemble, or even with the other drums in the setup. A well seasoned, competent and confident timpanist has a good balance of both, and knows when and how to use each equally well. Developing and honing this skill is just as important to the timpanist as her/his technical mastery of the instrument.

In a timpani audition, the non-timpanists on the committee (even some percussionists) will asses the timpani pitch based on how they hear pitch. Since timpani do not vibrate with a harmonic series, timpani pitch is not like the pitch of any of the other orchestral instruments. From the outset, the timpanist is at a disadvantage; the members of the committee will not perceive the pitch the same way as does the timpanist.  A seasoned timpanist knows what to listen for in timpani sound, the committee on the other hand may be unfamiliar to unaccompanied timpani sound.  They seldom hear timpani out of context and will be hearing some of the non-harmonic partials in the sound that the timpanist automatically ignores. They might even consider that as an intonation problem.  No matter what process the timpanist uses to tune, the ears on the committee WILL notice when the different intervals/pitches played don’t blend and/or work well together.

In an audition situation with unknown instruments and acoustics, sometimes the mallet choice can make a large difference in the amount of partials the drums produce. Instead of reaching for the pair that you always use for that excerpt, be prepared to be flexible with your stick choices in order to control the partials in the spectra.

Compared to how we hear true harmonic pitch, i.e. the pitch that all other orchestral instruments produce, the perception of timpani pitch is based on harmonic pitch allusion. Timpani have only a few very weak, near-harmonic overtones in their overtone series. It is nothing close to what the members of  an audition committee are used to hearing with their instruments. The structure of this near-harmonic series changes from note to note and drum to drum. The most constant overtone in this series is a predominant quasi-perfect  5th, which is not always pure. Unfortunately this 5th can often overpower the principal tone and imply intonation problems if the heads is not tempered (balanced or cleared) well. Tempered heads can tame the unruly 5th and strengthen the principal tone. If the timpanist tempers intervals so that the various drums make use of the few near-harmonics available, e.g. the fifth or the tenth, the perceived pitch will sound like it is in-tune because the overtones in the various intervals will be more coincidental in nature. It may not conform to any predefined temperament system but it is pleasing to the ear. The human ear can be quite forgiving with respect to the actual frequencies of a sequence of pitches as long as their harmonics blend together well; this is why Equal Temperament is a viable compromise and why the stretch tuning of octaves as well as melodic Pythagorean tuning works.

With timpani, every sequence of pitches will create different inharmonicity problems so any predefined temperament system is not of any real value. Setting the tuning indicators/gauges to Equal Temperament is a always good benchmark, but the player should attempt to adjust the various intervals in the sequence (whether harmonic or melodic) so they blend well together making use of what near-harmonic overtones are available on the drums at that particular time.

It is no wonder why the most seasoned  timpanists say, “just use your ears.” Pitch is a fluid commodity at best and the pitch center often changes continuously in an ensemble situation.  At an audition, the player only has to blend well with his or herself and not with an ensemble. This can be achieved by knowing intervals, both just and equal tempered, using a fork or gauges for a reference pitch, and by listening to the blend of the pitches produced. If the pitches do not blend together well, adjust accordingly. Exact pitch precision based on some arbitrary standard is not as important as pitch blend based on what is aesthetically pleasing to the ear. Due to the limited periodicity of timpani pitch, no member of an audition committee will  be able to ascertain if a pitch is a few cents sharp or flat from some predetermined standard, but they will be able to tell if the drums aren’t in-tune with themselves.  Needless to say, well-tempered heads are essential for good intonation.

For some strategies on how to practice timpani intonation, please visit the website of Jeremy Epp, Principal Timpanist, Detroit Symphony Orchestra, and read his article Why are we so out-of-tune?