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

In order to hear this sound, you have to strike the drum very close to the rim and lightly touch the head along the nodal point of mode 1,2. The touching of the head can be anywhere along the circumference of the node, however, it is best to strike the head in-line with where you are touching the node. (See figure 2b)

Figure 2bFigure 2b

This does not excite the asymmetrical preferred modes to any significant degree, but instead, it excites mostly the inharmonic symmetrical modes especially composite (mode 1,2), plus a small amount of the asymmetrical (mode 1,1) and some of (mode 3,1), which helps sustain and reinforce the sound. ( N.B. When a timpano head is tempered properly, the principal tone (mode 1,1) will always be present to some degree, no matter where you strike the drum.) Due to the different influence the air loading of the membrane has on the frequencies of the upper partials, it just so happens that the symmetrical mode 1,2 ( the sixth mode of vibration) is often very close in frequency to the preferred asymmetrical mode 3,1 (the fifth mode of vibration), which is the octave above preferred asymmetrical mode 1,1 (the principal tone). When striking the drum in this manner, it emulates the sound of an octave harmonic by combining the percussive attack of symmetrical mode 1,2 with the sustain of asymmetrical mode 3,1 and mode 1,1 .

When the drum is struck in the normal manner, composite mode 1,2 is not really as prominent because it radiates it energy more efficiently and decays faster than the preferred modes, which dominate the spectrum. When striking the drum at the lip to create the octave harmonic you excite less of the preferred modes and more of the inharmonic symmetrical modes; you are in fact using both the inharmonic and the harmonic modes to create this sound.

Indubitably, this effect is not really producing a true octave harmonic partial above a fundamental.  It instead significantly mutes the preferred modes that we normally associate with the pitch of the instrument while exciting the composite mode 1,2 that produce the effect.  Either way, when the conditions are right and it is executed successfully, it produces interesting sounds. It has been documented by a reputable performer that “most of them were extremely difficult – if not impossible – to produce.”6 Inadequate response or the inability for consistent execution of the effect lies in the fact that since all timpani are not the same, all timpani will respond differently. Consequently, there is no standard technique for achieving this effect.  It must be stressed that much of what you are going to be able to hear will depend on the weather, the integrity of the instrument, the kind of membrane used, how well the membrane has been tuned and foremost, experimentation with how to achieve the technique on the instruments at hand.

Factors influencing the effect:

1) The volume of air inside of the bowl along with the prevailing air density (temperature, barometric pressure and humidity) greatly affect the upper partials (including the symmetrical modes.)  You can control the size of the bowl (volume) but you can’t control the weather.  One day you might be able to get some great sounding partials, the next day…not so good.

2) If the drum has technical issues e.g., not in-round, counterhoop not flush, uneven tensioning, the instrument will never be able to produce suitable upper partials.

3) Natural skin heads will yield less higher overtones than synthetic heads and it is much easier to hear mode 1,1 and consequently more difficult to suppress.  Use plastic heads if you want to hear more of the upper inharmonic partials.

4) A head that has not been cleared (tuned) will never yield upper partials that are in alignment and close to being harmonic.

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