Circular Membrane Modes

Details of four lowest modesPreferred modes for timpaniDiscussion
Index

Percussion instruments

Musical instruments

Reference
Berg & Stork
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Circular Membrane Modes

The four lowest vibrational modes for a circular membrane.

Mode 11 is the lowest of the preferred modes for the timpani.

Index

Percussion instruments

Musical instruments

References
Rossing
Science of Sound
Ch 2
Morse & Ingard
 
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Preferred Timpani Modes

Assuming that these selected modes are excited, the relative frequencies and intervals in cents are given compared to the 11-mode. The preferred vibrational modes for a timpani are a subset of the modes of a circular membrane.

The interval values in cents here are calculated from the mode frequencies given by Berg & Stork. They can be compared to equal tempered intervals. The actual sounding frequencies are affected by air damping.

Index

Percussion instruments

Musical instruments

References
Backus
pg 300

Berg & Stork
 
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Circular Membrane

The vibrational modes of a circular membrane are very important musically because of drums, and in particular the timpani. The expression for the fundamental frequency of a circular membrane has some similarity to that for a stretched string, in that it depends on tension and density. The fundamental or 01 mode of an ideal circular membrane is given by:

A timpani head, made of mylar of thickness about 0.2 mm might have the following values for those parameters:

Starting with the values at left as the default values, parameters can be changed below to explore the effects on the membrane resonance.

T = N/m

σ = kg/m2

f01= Hz

D = m

The nature of vibrational modes in membranes is calculated from the wave equation in two dimensions.

Index

Percussion instruments

Musical instruments

References
Hall
Ch 9

Berg & Stork
 
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