In Search of the Missing Fundamental: by Richard K. Jones
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Carter: “Octave Harmonics”

The Application

The octave harmonic was a rather short-lived extended technique and doesn’t appear all that much in modern timpani scoring due to its weak effect. However, since it was used by the eminent American composer Elliot Carter in his Eight Pieces for Four Timpani, it deems investigation.

Not a lot 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 the seminal PAS articles are below.

John J. Papastefan from his article, Contemporary Timpani Techniques (Percussionist V17 N2 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 from 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 half- way 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 program notes) appeared to be misunderstood and proved to be 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.”Initially Carter had some reservations about the musical efficacy of the original pieces in the 1950 set and his intent with the 1966 revisions and additions was to make all of the works more effective in performance 10, however, he had no intention of revising them again even though he was not always pleased with the performances he had experienced post the 1966 revisions.11  Consequently, they remain as they are and timpanists are left to devise the necessary techniques needed to perform them.

In 2006, Stuart Marrs unveiled his educational DVD Stuart Marrs on Elliott Carter Eight Pieces for Four Timpani: Performance and Analysis. This milestone achievement 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 interactive viewing angles so the viewer can watch the performances from different perspectives. Angle 4/4 provides an overhead view of the four timpani so it is very clear to see what Marrs is doing in the Recitative and Adagio with regard to producing the octave harmonic.

In the performance of the Adagio, Marrs for the most part, is eliciting 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 inline with both his finger and thumb (see fig 2b).  He is using Yamaha TP9000 timpani on this DVD and this technique elicits the effect best on the 32 inch drum.  The 29 inch drum does not speak as well as the others and whether it is intentional or not, he changes the striking position and angle somewhat on the 26 and 24 inch drums. Even with the quality of these drums and the high mastery of the performance, the effect is not consistent from drum to drum. This could be due to the difficulty in preparing the harmonic due to the tempo and complexity of the piece as well as less than optimal atmospheric conditions, which affected that particular partial.  When using this technique, the placement of the thumb/finger and the striking point on the head have to be in an exact spot to elicit mode 1,2 or the effect will not project well.

During the performance of Recitative, Marrs consistently uses the same technique as he used on the 32 inch drum for Adagio, however, he strikes close to the rim of the drums; the effect speaks well on both the 26 and 24 inch drum.

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