In Search of the Missing Fundamental: by Richard K. Jones
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How Stick Placement Influences Articulation

Semantics aside, the terms legato and staccato are generally used to describe the opposite ends of the articulation spectrum for timpani sound. Every young timpanist is taught the concept of the legato and staccato stroke, and the difference between a legato and staccato stick. They are also taught that placing pitches in the different ranges of the drums will help with articulation/sustain due to the higher/lower tension of the head. The mature player can generate multiple articulations no matter the stick choice, or the amount of tension placed on the head.

legato: in a smooth, flowing manner, without breaks between notes.

staccato: with each sound or note sharply detached or separated from the others.

What do these terms mean to the timpanist? How do they interpret them? Can the timpanist go beyond stick choice, stroke, and head tension to accomplish this sound?

For quick hand-to hand playing on the same drum, the timpanist has multiple methods under her/his control for generating a difference in sound between a fast articulate rhythm, and a smooth sustained roll. The usual approach is via a combination of head tension, stick choice, and manipulation of one’s grip and stroke. An additional option is based on stick separation. The mature player uses all of the above to achieve the desired effects. Many players, however, are unaware how stick placement affects the sound output.

The finer points of mastering articulation via head tension, grip, stroke, roll speed, the amount of time the stick is in contact with the head etc. (i.e. technique) will be left for another discussion (and to the opinion of the timpanist reader 🙂 Only stick placement on the head, and the physics of how that affects the sound will be addressed here.

When a timpano head is well-tempered, the player can strike the drum at multiple spots around the circumference of the head without generating any discernible pitch discrepancy. This provides the player with a wider palette of tonal colors, as well as more articulation options.

When the head is well-tempered, more of the higher preferred “harmonic” modes will be present in the spectrum. When aligned properly, these preferred “harmonic” modes are what give the timpano its sense of pitch.  The preferred “harmonic” modes of an air loaded vibrating membrane (i.e. a timpani head) vibrate in “pie like” sections. Halves, quarters, sixths, eights, tenths, twelfths etc. The video below demonstrates this phenomenon. Beginning with the principal tone mode 1,1 (what we hear as the pitch of the drum) successive preferred modes are added to the spectrum up to mode 6,1.

All preferred “harmonic” modes in motion.

Preferred “Harmonic Modes 1,1 Through 6,1

How these preferred “harmonic” modes are excited depends on where the head is struck. When the head is struck dead center, only the inharmonic concentric modes are set into motion; none of these preferred “harmonic” modes are excited. The energy from the concentric modes modes is radiated very efficiently, which means that the sound from the instrument dies out relatively quickly when struck in the center.

Inharmonic Concentric Modes

In order to excite the preferred “harmonic “modes, one must strike the head more near the edge of the drum. This starts the head in motion sending an energy wave across the head in a straight line perpendicular to the plane of attack.  Once the energy wave reaches a barrier (the other side of the drum), it returns on the same path in the opposite direction. The video below shows the path of a wave, a single strike of the drum at the “normal” playing spot in slow motion. The preferred “harmonic “modes are not efficient at radiating their energy, so they die away slowly. The longer the wave energy is sustained, the more the vibrating diametric modes (preferred “harmonic “modes) will produce a sustained sense of pitch.

Single Strike to a Timpano
at the “normal” playing spot

When iterations of preferred modes excitation happen at the same striking point in quick succession (i.e. fast repeated notes at the exact same playing spot), advancing and returning waves collide creating destructive interference. This interrupts the full envelope of each stroke and shortens the perceived “attack” portion of the envelope creating the staccato sound. Together with modifying the grip (firm hands), and the amount of time the stick is in contact with the head, the timpanist can strike the head in the same striking spot to create this staccato effect.

When the timpanist separates the hands a bit for fast repeated strokes (i.e. a roll) the direct paths of the iterative waves do not collide head on, but rather they meet at oblique angles causing less destructive interference. This lengthens  the perceived “attack” portion of the envelope of each stroke creating the legato sound.  Together with modifying the grip (relaxed hands), and the amount of time the stick is in contact with the head, the timpanist can strike the head in multiple playing spots to create this legato effect. Some players advocate separating the hands the distance of a “dollar bill” e.g. 6 to 7 inches. Others extend the separation of the hands much further. No rules, just personal preferences as both methods can achieve the same results provided the head is well-tempered.

The video below can help explain the path(s) of the energy waves when the hands are separated. When the grid appears, follow the three balls that transverse from the left to the right of the screen. Now, focus on the outer two of the three balls (“dollar bill distance”) philosophy.  This is essentially the paths of the energy waves as they move across a timpano head when you strike the drum with your hands separated a bit.

Ball Video Courteous of brusspup

Play the movie again and focus on the paths of the balls to either side of the two balls in the “dollar bill distance” philosophy.  The further the balls are separated, the less immediate destructive interference wave occurs; in fact, some constructive interference can actually occur enhancing the sound.

When the sticks are diametrically opposed, destructive interference again occurs.