During the late 1950s and early 1960s, many central European composers were exploring new harmonic devices, orchestration techniques, instrumental colors, timbres, and cluster effects. Percussion was central to many of these new sounds, including a new extended technique for timpani commonly called the octave harmonic. The effect appears in works such as Krzysztof Penderecki’s Dimensions of Time and Silence (1959; revised 1961), Kazimierz Serocki’s Segmenti (1961), and Włodzimierz Kotoński’s Musica per fiati e timpani (1963).1
Elliott Carter helped bring the effect into modern American percussion literature after hearing it at a conference in Warsaw, Poland.2 He used it in two movements of his Eight Pieces for Four Timpani: Recitative and Adagio, as found in the 1966 revised edition. Originally composed as six pieces in 1949, the set was later revised and expanded in collaboration with percussionist Jan Williams in 1966.3 The two movements added to the original six were Adagio and Canto. Adagio exploits the use of the octave harmonic most fully, while the earlier composed Recitative uses it briefly as a result of the 1966 revision. The octave harmonic does not appear in the original manuscript4 or in the 1960 published edition of Recitative.5
Carter indicates in Performance Note #6, Special Effects – III, of the 1968 edition (1966 revision), that “Harmonics sounding an octave above the tuned pitch of the drum may be produced by pressing one or two fingers on the head the drum half-way between the rim and the center, and striking near the rim.” In practice, however, many performances using this technique produce an effect that is more of a muted thud than a clearly ringing overtone. As a result, timpanists have developed a variety of practical solutions for producing the sound.
The term octave harmonic is useful as a performance instruction, but it is acoustically misleading. A timpano does not produce true harmonics in the same way a string does because its modes do not form a true harmonic series. What performers call an octave harmonic is better understood as an octave-like upper modal effect: the player suppresses the normal principal tone while exciting a higher response that can approximate the octave above the perceived pitch. When the drum, head, room, and technique cooperate, the result can be striking. When they do not, the effect may sound weak, percussive, or little more than a muted thud.
There are varied opinions on the correct method for achieving the octave harmonic on timpani. Is there a reason for the discrepancy in interpretations? Is there one definitive technique that works on all timpani? The main objective is to excite an upper modal response that sounds close to one octave above the principal tone of the drum while also damping enough of the principal tone to allow that upper response to be heard. A large part of achieving the effect is determined by air density, atmospheric conditions, the mechanical integrity of the instrument, the quality and condition of the head, and how well the head is tempered. The second part of the equation is understanding the acoustical limitations of the instrument itself.
The Science
Can timpani produce true harmonics like many other musical instruments? No. Timpani do not produce true harmonics in the same sense as a string, where lightly touching a nodal point isolates an exact integer partial of a harmonic series. Since timpani heads do not vibrate with a natural harmonic series, the so-called octave harmonic is not a true harmonic above a fundamental. One must always keep in mind that the spectrum of a timpano’s sound is a lingering quasi-harmonic series without a true fundamental, surrounded by an initial core of noise.
The sound we hear as the pitch of the instrument, the principal tone, is not the lowest physical mode of the vibrating head. The principal tone is associated most closely with mode 1,1, the first strongly pitch-bearing diametric mode. In practical musical terms, this is the pitch the listener accepts as the “note” of the drum, even though it is not the lowest vibration of the membrane.
The overtone structure we hear as the pitch of a timpano starts on this principal tone and continues through a limited group of near-harmonic preferred modes. It is a quasi-harmonic series, not a true harmonic series. This missing fundamental and the lack of a true harmonic overtone series prevent timpani from producing true harmonics in the ordinary sense. By trying to excite a harmonic partial above the principal tone mode 1,1, the player is not isolating a true harmonic. Instead, the player is encouraging an upper modal response that can sound close enough to the octave to function musically.
Timpani have several types of modes of vibration occurring within the membrane: concentric modes, diametric modes, and composite modes that combine aspects of both. For a good timpani sound—one rich with near-harmonic pitch content—the goal is to encourage the lower diametric modes and reduce the less pitch-useful concentric and composite activity as much as practical. The modes that give timpani their strong sense of pitch are the lower diametric modes, often referred to as the preferred modes.
In practical terms, good timpani tone depends on encouraging the preferred diametric modes while minimizing the less pitch-useful concentric and composite activity. The octave harmonic technique deliberately changes that balance. Instead of producing the normal principal-tone response, the player suppresses part of the usual pitch structure and encourages an upper modal response that can sound octave-like.
Within the diametric preferred modes of an air-loaded vibrating membrane, there is a partial with a frequency very close to the octave above the principal tone mode 1,1. This is preferred mode 3,1, often described as the fifth partial of the vibrating membrane. However, the techniques timpanists use to produce the octave harmonic do not simply isolate and emphasize mode 3,1. They also involve the composite mode 1,2, which can lie very close in frequency to that octave-like region.
Mode 1,2
Mode 1,2 is a composite mode that combines a diametric division of the head with an internal circular nodal line. More precisely, it contains one nodal diameter and one internal circular nodal line, in addition to the fixed boundary at the rim. Rossing et al., Fleischer and Fastl, and others have documented that the ratio of mode 1,2 and mode 1,1 of an air-loaded/baffled membrane—that is, a modern timpano in this case—is very close to 2:1, the octave.25 This sixth mode of vibration is also very close in frequency to preferred mode 3,1, which is also near a 2:1 ratio with the principal tone mode 1,1.
When a timpano is struck in the normal playing area, mode 3,1 and the other lower preferred modes usually dominate the perceived pitch structure. Mode 1,2 is not normally heard as the main pitch-bearing response. However, when the drum is struck very close to the lip and the head is lightly touched or stopped at useful nodal areas, the normal balance changes. The principal tone is partially suppressed, and mode 1,2, reinforced by nearby upper modal activity, can become audible as an octave-like effect.
Mode 1,2
Figure 1
Mode 1,2 combines one nodal diameter with an internal circular nodal line.
This mixed modal shape is why it behaves differently from the lower preferred diametric modes.
Mode 1,2 in motion
Animation courtesy of Dr. Dan Russell, Grad. Prog. Acoustics, Penn State
Animation by Clayton Shonkwiler
In order to hear this sound, the player must strike the drum very close to the rim while lightly touching the head at an effective nodal area for mode 1,2. The exact touching point may vary from drum to drum, but the response is usually clearest when the strike is aligned with the hand position used to suppress the normal pitch-bearing response. See figure 2b.
Figure 2b
This stroke does not excite the normal diametric preferred modes in the same way a standard timpani stroke does. Instead, it changes the modal balance by reducing the dominance of the principal tone and encouraging a higher composite response, especially mode 1,2, along with some contribution from mode 3,1. A small amount of mode 1,1 will usually remain present, because when a timpano head is tempered properly, the principal tone will almost always be present to some degree no matter where the drum is struck.
Due to the air loading of the head, composite mode 1,2 is often very close in frequency to preferred diametric mode 3,1. Mode 3,1 is near the octave above preferred diametric mode 1,1, the principal tone. When striking the drum in this manner, the player emulates the sound of an octave harmonic by combining the percussive attack of composite mode 1,2 with upper modal reinforcement from mode 3,1 and the remaining presence of mode 1,1.
When the drum is struck in the normal manner, mode 1,2 is usually not perceived as dominant because the lower preferred modes are more strongly excited and more clearly define the pitch. When the drum is struck near the lip and the head is touched in the right place, the normal principal-tone response is suppressed, allowing the upper octave-like response to project more clearly. In other words, the player is not producing a true octave harmonic above a fundamental; the player is manipulating the balance of the drum’s modal response.
This effect is therefore not a true octave harmonic partial above a fundamental. It significantly mutes the preferred modes that we normally associate with the pitch of the instrument while exciting the composite mode 1,2 and related upper modal activity that produce the effect. When the conditions are right and the technique is executed successfully, the result can be musically effective and quite striking. When conditions are not favorable, the effect may be weak, inconsistent, or nearly impossible to produce.
It has been documented by a reputable performer that “most of them were extremely difficult, if not impossible, to produce.”6 Inadequate response or inconsistent execution occurs because all timpani do not respond in the same way. There is no universal technique that works equally well on every drum. What the player can hear will depend on the weather, the integrity of the instrument, the kind of membrane used, the condition of the head, how well the membrane has been tuned, and careful experimentation with the specific instruments at hand.
Factors Influencing the Effect
- Air volume and air loading: The volume of air inside the bowl and the prevailing air density—temperature, barometric pressure, and humidity—affect the upper partials, including the composite and symmetrical modes. You can choose the size of the bowl, but you cannot control the weather. One day the upper response may speak clearly; the next day it may not.
- Mechanical integrity: If the drum has technical issues, such as an out-of-round bowl, a counterhoop that does not sit flush, uneven tensioning, or linkage problems, the instrument may not be able to produce suitable upper partials consistently.
- Head material and condition: Natural skin heads often emphasize a warmer, stronger principal tone and may make the upper octave-like effect harder to isolate. Synthetic heads may make upper modal activity more apparent, but their success still depends on head condition, seating, tension history, and the drum itself.
- Tempering and clearing: A head that has not been properly cleared or tempered will not allow the upper partials to align closely enough to produce a convincing octave-like effect.
- Stroke placement: The striking point must usually be very close to the rim, but not directly on the rim or bowl. Small changes in placement can make the difference between a clear upper response and a dull thud.
- Finger placement and release timing: The hand must suppress the normal pitch-bearing response without killing the upper modal response. In some approaches, quickly releasing the fingers after the attack helps the sound speak more clearly.
- Mallet choice and dynamic level: A mallet that is too soft may not excite the upper response clearly, while one that is too hard may produce a brittle attack without enough resonance. The dynamic level must be strong enough to excite the desired mode without overwhelming the effect.
The Application
The octave harmonic was a relatively short-lived extended technique and does not appear frequently in modern timpani scoring, probably because the effect can be weak and unreliable. However, since it was used by the eminent American composer Elliott Carter in his Eight Pieces for Four Timpani, it deserves investigation.
Not much has been written about how to produce harmonics on timpani, but a few references can be found in older PAS articles. Two descriptions of how to execute the octave harmonic technique from important PAS articles are given below.
Carter’s Published Instruction and Papastefan’s Description
John J. Papastefan, in his article Contemporary Timpani Techniques (Percussionist, Vol. 17, No. 2, Winter 1980), writes:
Harmonics sounding an octave above the tuned pitch of the drum may also be produced by pressing one or two fingers on the head of the drum halfway between the rim and the center, and striking near the rim. The harmonic is usually notated as a diamond.7
The Papastefan description is essentially the same as Performance Note #6 found in the 1968 published edition.
Jan Williams’s Clarification
Jan Williams, in his article Elliott Carter’s “Eight Pieces for Timpani” —The 1966 Revisions (Percussive Notes, December 2000), writes:
The description of the technique that emerged from our (Carter & Williams) experimentation is as follows:
1. Straddle the center (node) of the drumhead, with the thumb and middle finger of either hand-held about 4 to 6 inches apart, lightly touching the head.
2. Strike the drum at the very edge, but not directly on the rim of the bowl.
3. A split second after striking the drum, quickly lift the fingers from the head. The harmonic will sound one octave higher than the pitch to which the drum is tuned.
The reason for lightly touching the head, as described above, is to remove all the fundamental pitch from the resulting harmonic. Striking the drum very close to the rim without touching the head will produce the harmonic, but there will be a vestige of the fundamental still present in the sound. This quick removal of the fingers from the head cannot be overemphasized. If the fingers remain on the head too long, the resonance of the harmonic will be greatly reduced.
In Munich, many of the performers executed the harmonics improperly. Most simply touched the head about halfway between the center and the rim and left their fingers on the drum.8
It is apparent from the Williams Munich reference above that the technique described by Papastefan, essentially Carter’s description from the performance notes, was easily misunderstood and often inadequate for eliciting the effect. Carter himself acknowledged that this effect depends “terribly on the drum and type of head used” and that “the vibrating harmonics need not last as long as indicated.”9 Carter’s intent with the 1966 revisions and additions was to make all of the works more effective in performance,10 but he had no intention of revising them again, even though he was not always pleased with the performances he heard after the 1966 revisions.11 Consequently, the pieces remain as they are, and timpanists are left to develop the practical techniques necessary to perform them.
Stuart Marrs’s Practical Demonstration
In 2006, Stuart Marrs unveiled his educational DVD Stuart Marrs on Elliott Carter Eight Pieces for Four Timpani: Performance and Analysis. This DVD is an excellent reference for studying the Carter pieces, but there is no written documentation on how to elicit the octave harmonics in the errata and performance notes included with the DVD. The interactive DVD, however, provides multiple viewing angles. Angle 4/4 provides an overhead view of the four timpani, making it possible to observe what Marrs does in Recitative and Adagio to produce the octave harmonic.
In the performance of Adagio, Marrs appears to elicit the effect by touching the center of the drum with his middle finger and the second symmetrical nodal point with his thumb while striking the drum closer to the normal striking position than to the rim of the drum. His striking point is generally in line with both his finger and thumb. See figure 2b. He uses Yamaha TP9000 timpani on this DVD, and this technique seems to elicit the effect best on the 32-inch drum. The 29-inch drum does not speak as well as the others. The visual evidence suggests that he adjusts the striking position and hand angle from drum to drum, reinforcing the point that the effect often requires practical adaptation.
Even with high-quality drums and a highly accomplished performer, the effect is not consistent from drum to drum. This may be due to the difficulty of preparing the harmonic within the tempo and complexity of the piece, as well as atmospheric conditions that affected that particular partial. When using this technique, the placement of the thumb, finger, and striking point must be extremely precise in order to elicit mode 1,2 clearly enough for the effect to project.
During the performance of Recitative, Marrs consistently uses the same general technique as he uses on the 32-inch drum in Adagio, but he strikes close to the rim of the drums. In that context, the effect speaks well on both the 26-inch and 24-inch drums.
Discussion
The description given by Williams—“straddle the center (node) of the drumhead”12 is ambiguous.
Does it mean:
1) Spread the thumb and fingers and lightly touch the nodal area at the second symmetrical/concentric mode of vibration halfway between the rim and the center, similar to what Papastefan13 describes? See figure 2a.
Figure 2a
Or does it mean the technique demonstrated by Marrs on his DVD:
2) Lightly touch the center of the drum with the middle finger and the nodal area at the second symmetrical/concentric mode of vibration with the thumb? See figure 2b.
Figure 2b
It is possible to elicit a response from mode 1,2 by exciting it in either manner. Is one better than the other? The only way to determine the best response is to experiment with the various techniques on the drums and in the environment in which the performance will occur. It is useful to learn multiple approaches so the player can adapt to variations in instrument design, head type, drum size, and environmental conditions.
The most important thing to remember is that timpani are incapable of producing true harmonics above a true fundamental. The sound produced by this technique is an upper modal response of the vibrating membrane, not a true harmonic in the string-instrument sense. It will never be perfectly harmonic, but it may sound close enough to the octave when the technical approach, instrument, head, and environmental conditions cooperate.
Practical Takeaway
The octave harmonic is best understood as an octave-like extended technique rather than a literal harmonic. To produce it reliably, the timpanist must suppress enough of the normal principal tone while encouraging an upper modal response near the octave. This requires careful experimentation with finger placement, release timing, stroke placement, mallet choice, drum size, head material, tuning, and room conditions.
No single method will work equally well on every timpano. The player’s task is not to apply one universal rule, but to understand the modal behavior well enough to find the best practical solution on the instruments at hand.
Footnotes:
1), 7), 13) John J. Papastefan. “Contemporary Timpani Techniques.” Percussionist V17 N2, Winter 1980.
2), 6), 9), 11) “Elliott Carter: Eight Pieces for Four Timpani.” Interviewed by Patrick Wilson. Percussive Notes, October 1984.
3), 8), 12) Jan Williams. “Elliott Carter’s ‘Eight Pieces for Timpani’ — The 1966 Revisions.” Percussive Notes, December 2000.
4) Morris “Arnie” Lang. “Elliott Carter’s ‘Eight Pieces for Four Timpani’: A Comparison of the Original Manuscript and the Published Version.” Percussive Notes, November 2012.
5) Stuart Marrs. Stuart Marrs on Elliott Carter: Eight Pieces for Four Timpani: Performance and Analysis. DVD. GUDMUSE, 2006.
10) David Schiff. The Music of Elliott Carter. 2nd ed. Cornell University Press, 1998.