Consonance and Coincidental Harmonics
Consonance, as it pertains to musical pitch, is often experienced as relative smoothness, stability, or agreement between pitches. One important contributor is the amount of beating or roughness produced when nearby partials interact. Beats are the alternate rise and fall of sound intensity that occur when two frequencies are close enough to reinforce and interfere with one another. The human ear is especially sensitive to beating between upper partials when two or more tones sound simultaneously.
Beating is not the only factor in consonance. The ear also responds to harmonicity, shared partials, musical context, temperament, style, and learned expectation. Still, when one or more coinciding upper partials, sometimes called coincidental harmonics, come close enough in frequency to create detectable beats, the interval may be perceived as rough, unstable, or out of tune.
What does it mean to be in tune? The simplest definition is to be in concord or in agreement. How does the ear judge that agreement? When it parses multiple frequencies sounded together, the ear is often drawn to points of relative smoothness in the combined overtone structure. In harmonic instruments, coinciding upper partials can help the ear judge interval purity. The more partials contrasting pitches have in common, and the more exactly those shared partials align, the more concordant the interval will usually sound.
This is most noticeable when pitches are stacked vertically, as in a chord. When pitches move horizontally, as in a melody, the ear may tolerate or even prefer different tuning tendencies. Herein lies the old problem of temperament: how does one combine chords and melody in a fixed-pitch system when some intervals sound better harmonically but not melodically, and vice versa? The answer is compromise.
Humans have devised many temperaments over the centuries, and none is a panacea. The most frequently discussed in modern Western music are equal temperament, Pythagorean tuning, and just intonation. Equal temperament is a useful compromise, but it is not acoustically pure. Just intonation agrees beautifully with simple frequency ratios, but it is not always practical in modulation or in fixed-pitch systems. Pythagorean tuning can sound persuasive melodically, but its vertical sonorities can become problematic. In practice, good ensemble musicians constantly adjust among equal-tempered reference points, justly tuned vertical sonorities, and melodic tendencies often associated with Pythagorean or expressive intonation.
Do any of these systems really work for timpani?
Not completely. Equal temperament is a useful reference. Just intonation can help with vertical sonorities. Melodic tuning tendencies can help lines make sense. But timpani require an additional layer: the drums must also agree with themselves. Good timpani intonation is not the search for one perfect mathematical answer. It is a managed compromise between the available preferred modes, the musical context, the room, the ensemble, and the listener’s ear.
Why Timpani Are Different
Musicians naturally formulate pitch perception through the sound of the instruments they play. This perception is shaped by the inherent acoustic properties of each instrument. In Western classical music, pitch perception in solo playing is often treated differently from ensemble playing, especially because melodic and harmonic structures create different kinds of tension and resolution.
Timpanists listen to the pitch of their instruments intimately and intently over long periods of time. As a result, they develop an intense personal awareness of the many subtleties in the timpani spectrum. Many of those sounds may be categorized as noise by non-percussionist musicians, but to the timpanist they are part of the instrument’s identity.
Most pitched orchestral strings, winds, and brass instruments produce spectra dominated by harmonic or near-harmonic partials. Timpani pitch is different. The perceived pitch of a timpano depends on a limited set of near-harmonic preferred modes and the ear’s ability to organize those modes into a convincing pitch center. This is why timpani intonation cannot be reduced entirely to equal temperament, just intonation, Pythagorean tuning, gauges, or an electronic tuner. Those are references. The real work is learning how each drum’s principal tone, preferred modes, decay, and overtones blend with the other drums and with the ensemble.
A drum can appear close at the gauges or at individual lug points and still fail as a whole membrane. Good intonation begins with a stable principal tone on each drum. If the head is not clear, the pitch center may shift during the decay, and the listener may hear a pitch that the player did not intend.
Spectral and Holistic Listening
The young timpanist must also develop both spectral and holistic listening. A spectral listener tends to hear the partial structure inside the sound. A holistic listener tends to hear the composite pitch center. Most players lean more heavily on one approach or the other, especially under stress, but a mature timpanist develops both.
Under stress, especially when using unfamiliar instruments at an audition or when sudden environmental changes take effect, the player may default to their dominant listening habit. A predominantly spectral listener can become distracted by the limited near-harmonic structure and the many non-harmonic components of timpani sound. The actual principal tone may become obscured in the player’s mind by upper partials, especially if the instruments have not been cleared properly.
On the other hand, a predominantly holistic listener under stress may ignore the useful near-harmonic preferred modes that do exist in timpani pitch. That player may place the pitch where the composite sound seems comfortable, but where it does not blend well with the overtones of other instruments or even with the other drums in the setup.
A well-seasoned, competent, and confident timpanist has a working balance of both listening approaches and knows when to use each. Developing this skill is just as important to the timpanist as technical mastery of the instrument.
Auditions and Unaccompanied Timpani Pitch
In a timpani audition, the non-timpanists on the committee, and even some percussionists, may assess timpani pitch according to how they normally hear pitch on other instruments. Since timpani do not vibrate with a true harmonic series, timpani pitch is not perceived in the same way as the pitch of most other orchestral instruments.
The timpanist must remember that the committee may not hear unaccompanied timpani pitch the way a specialist does. A seasoned timpanist knows what to listen for in timpani sound, while the committee may be less familiar with the sound of unaccompanied timpani. They may hear non-harmonic partials that the timpanist has learned to place in context or ignore. They may not know the acoustical reason for a problem, but they will hear when the drums do not blend with themselves.
In an audition situation with unknown instruments and acoustics, mallet choice can make a large difference in the strength and number of partials the drums produce. Instead of reaching automatically for the pair normally used for a given excerpt, the player should be flexible with stick choices in order to control the partial structure of the spectra.
The Overbearing Fifth and Pitch Blend
Compared with the way we hear pitch from instruments whose spectra are dominated by harmonic partials, the perception of timpani pitch is based on the ear’s ability to organize a limited, near-harmonic structure into a usable pitch center. This may be thought of as a harmonic pitch illusion, or a harmonic pitch allusion. The drum suggests harmonic pitch without actually producing a full harmonic series.
Timpani have only a limited set of near-harmonic preferred modes in their spectrum. This structure changes from note to note, drum to drum, head to head, room to room, and mallet to mallet. One of the most persistent preferred modes is mode (2,1), heard roughly as a fifth above the principal tone. The fifth is not the enemy; it is part of a good timpani sound. It becomes a problem only when it outlives or overpowers the principal tone.
Unfortunately, this fifth can often overpower the principal tone and imply intonation problems if the head is not tempered, balanced, or cleared well. If mode (2,1) dominates after the initial attack, the listener may perceive pitch creep or a false pitch center. A well-tempered head does not eliminate mode (2,1); it keeps it in proper relationship to mode (1,1), the principal tone.
If the timpanist tempers intervals so that the various drums make use of the few near-harmonic relationships available, such as the fifth or the tenth, the perceived pitch may sound in tune because the partials in the various intervals blend more convincingly. The result may not conform perfectly to any predefined temperament system, but it may still be pleasing to the ear.
The human ear can be forgiving with respect to the exact frequencies of a sequence of pitches as long as their partials blend together well and the pitch centers remain convincing. This is one reason equal temperament is a viable compromise and why stretch-tuned octaves, melodic Pythagorean tendencies, and justly adjusted vertical intervals can all be useful in different contexts.
Using Temperament Systems as References
With timpani, every sequence of pitches can create different inharmonicity problems, so no predefined temperament system is sufficient by itself. Setting tuning indicators or gauges to equal temperament is always a good benchmark, but the player should adjust the various intervals in the sequence, whether harmonic or melodic, so they blend well together using whatever near-harmonic preferred modes are available on the drums at that particular time.
This is why seasoned timpanists often say, “just use your ears.” Pitch is a fluid commodity, and the pitch center can change continuously in an ensemble situation. In auditions and performances, unfamiliar rooms, foreign instruments, and environmental changes can shift the apparent pitch center. The player must listen for the drum’s current behavior, not only for where the gauge says the pitch should be.
At an audition, the player only has to blend well with themselves, 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 listening carefully to the blend of the pitches produced. If the pitches do not blend together well, adjust accordingly.
Exact pitch precision based on an arbitrary standard is not always as important as pitch blend based on what is musically convincing to the ear. A pitch that is a few cents away from a predetermined standard may matter less than whether the drums agree with each other and produce a convincing pitch center. Committees may not know the acoustical reason for the problem, but they will hear when the drums are not in tune with themselves. Needless to say, well-tempered heads are essential for good intonation.
Final Practical Takeaway
Timpani intonation is not solved by choosing one temperament system and applying it mechanically. Equal temperament, just intonation, Pythagorean tuning, gauges, tuning forks, and electronic tuners are all useful references, but they are not final answers. The timpanist must learn how each drum’s principal tone, preferred modes, decay, and overtones interact with the other drums and with the ensemble.
Standards of timpani intonation are also historically conditioned. What sounds centered, dry, resonant, or blended in one era, room, school, or ensemble may not be identical to another. The goal is not mathematical purity. The goal is a stable principal tone, a convincing pitch center, and a musical blend that serves the context.
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?