It moves in a family of fixed shapes, each with its own pitch, and those pitches do not line up.
Where you hit it decides which shapes you hear.
Fig. 2
A head moves in shapes.A head moves in shapes.
A stretched circular head can vibrate in a set of fixed shapes called modes, each at its own frequency.
Some modes move the whole head up and down together. Others split it into halves, quarters or rings that move in opposite directions. The lines between those parts, where the head does not move at all, are nodal lines.
Fig. 2 / Modes of a 14″ headStrike anywhere · slowed
Strike
Between center and edge
From center
57 mm
Round modes
54%
Fundamental
220 Hz
View
An ideal 14″ head tuned to 220 Hz. Each mode is a shape the head can move in, at its own frequency, and the frequencies are not whole-number multiples. That is why a drum reads as a color more than a note. Hit the center and only the round modes move, because every other mode stands still there. Move toward the edge and the rest join in.
The overtones do not line up.The overtones do not line up.
On a guitar string the overtones fall at whole-number multiples of the fundamental: two, three, four times. That is what gives a string a clear pitch.
A drumhead's modes land at 1.59, 2.14, 2.30 and 2.65 times the fundamental. The ear hears a cluster rather than a note, which is why drums get tuned for color and feel more than for pitch.
Ideal membrane modes: 1, 1.59, 2.14, 2.30, 2.65, 2.92 times the fundamental.
Air loading and the second head pull these ratios around on a real drum.
Where you hit decides what you hear.Where you hit decides what you hear.
A mode can only be driven where it moves. Every mode with a nodal line across it stands still at the center, so a center hit drives only the round modes. The sound is fuller, shorter and more focused.
Move toward the edge and the other modes join in. The sound gets thinner, brighter and longer. Try it in Fig. 2.
Tension sets the scale, not the shape.Tension sets the scale, not the shape.
Tightening a head raises every mode by the same ratio. Frequency goes up with the square root of tension, so doubling the pitch takes four times the tension.
Head weight works the other way. Heavier film lowers everything and takes the edge off the highest modes.
Real heads are not ideal membranes.Real heads are not ideal membranes.
A real head is loaded by the air on both sides, stiffened at its collar, and coupled to a second head and a shell. The pattern of modes survives. The exact numbers move.
Which brings us to the shell.
Bibliography
Selected sources.Selected sources.
Primary papers and references used throughout the essay.
