Carter: “Octave Harmonics”
The description given by Williams, “straddle the center (node) of the drumhead”12 is ambiguous at best.
Does it mean:
1) Spread the thumb and fingers and lightly touch the node at the second symmetrical/concentric mode of vibration halfway between the rim and the dead center, similar to what Papastefan13 describes (fig. 2a).
Or does it mean the technique as demonstrated by Marrs on his DVD:
2) Lightly touch the center of the drum with the middle finger and the node at the second symmetrical/concentric mode of vibration with the thumb (fig 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 in the environment which you will be performing. Perhaps learn multiple ways to elicit the response from the drums you will be using to accommodate for variations in instrument design and environmental conditions.
The most important thing to remember is that since timpani are incapable of producing true harmonics above a fundamental, the sound you elicit can only be one of the inharmonic upper modes of the vibrating membrane (a partial). This sound will never be harmonic, but it may sound close enough to harmonic with the right technical approach and cooperating environmental conditions.
1), 7), 13) Contemporary Timpani Techniques. John J. Papastefan. 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) Elliott Carter’s “Eight Pieces for Timpani” —The 1966 Revisions. Jan Williams. Percussive Notes December 2000
4) Elliott Carter’s ‘Eight Pieces for Four Timpani’ A comparison of the original manuscript and the published version. Morris “Arnie” Lang. Percussive Notes, November 2012
5) Stuart Marrs on Elliott Carter Eight Pieces for Four Timpani: Performance and Analysis DVD. GUDMUSE 2006
10) The Music of Elliott Carter. David Schiff. Cornell University Press; 2 edition (November 12, 1998)