The Mathematics of Drums

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The Mathematics of Drums

• Methods and History of Hand Drums

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The History of Drums

• First Known Drum 6000 BCE
• Found in Mesopotamia 3000 BCE
• Perhaps as far back as 5000BCE

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Anatomy of a Drum

• The Parts
• Body
• Membrane
• Tuning Pegs/Strings
• Striking Object/Stick

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Early Drums

• The first drums were used for communication
  across great distances.
• So-called Talking Drums can still be found in
  many cultures (ex.Africa)

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Talking drum from Ghana
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Message Drums

• Another Style, called Message Drums or slit
  gongs, evolved in Africa also.

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Message Drums/Slit Gongs(W.Africa)
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History of Bongos

• The history of bongo drumming can be traced to
  the Cuban music styles known as Changüi and Son.
• These styles first developed in eastern Cuba
  (Oriente province) in the late 1800's around the
  time that slavery was abolished.

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Abakua
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More History

• Initially, the bongo had heads which were tacked
  and tuned with a heat source.
• By the 1940s metal tuning lugs were developed to
  facilitate easier tuning.

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Typical Bongo
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Types Drums by Shape

• Bongo
• Often confused w/Conga
• Can be Cylindrical or Waisted
• Conga
• Tapers to soft point at bottom
• Can be free-standing or attached.
• Cylindrical
• Most Common
• Used by Native Americans and in Antiquity

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Shapes/Types

• Goblet
• Can be made from
• Gourds
• Carved Wood
• Waisted
• Like name suggest, nips in at center

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Darabuka
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Shapes/Types

• Bowl
• Also used in Antiquity
• Simplest Form

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Other Distinctions

• May be double or single-headed
• May be handheld or in a stand
• Wide variety of styles and methods

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Pitches and Tuning

• Tuning
• Strings
• Tightness of membrane

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Mathematics and Drums

• Article Can you hear the shape of a Drum?
• Rebuttal You cant hear the shape of a Drum!
• Formulas/Proofs

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Mathematics Involved in Drum Design

• The drums that we have discussed are all three
  dimensional, enclosed spaces. Mathematically
  modeling the flow of sound in a space such as
  that is very tricky. It requires the mastering
  of some very advanced techniques
• partial differential equations
• numeric approximations for numeric solutions

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Mathematics Involved in Drum Design

• When trying to calculate things like the
  wavelengths and frequencies, and thus, the sound
  produced by certain drums, it is much easier to
  think of a one dimensional drum i.e. a
  guitar string.
• -With a string there are definite boundaries for
  wavelength per cycle. Think of a guitar a wave
  of sound is stretched out along the string,
  starting with zero amplitude at one end at the
  neck, and the wave rises and falls in amplitude
  until it reaches the other end, which is also
  zero. This allows for only a certain number of
  definite possibilities for sounds produced. As
  does the frequency of the sound produced because
  it too has those common boundaries. The only
  real variables involved are the strings tension
  and their lengths.

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Mathematics Involved in Drum Design

• A three dimensional drum, like the ones we have
  discussed, do not have such definite boundaries.
  Sound is produced by striking a plane, or the
  drum head, and then it is resonated through the
  cylinder on which it is stretched.
• There are many different sounds produced by
  hitting the same drum, with the same head at the
  exact same tension, in different regions of the
  plane. Every time you hit a drum on a different
  spot, it theoretically has different boundaries.
• Also, the sound produced relies on the length and
  diameters of the cylinder as well as the type of
  material it is made of

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Mathematics Involved and Drum Design

• There are many more variables and components
  involved when the shape changes from 1 to 3
  dimensions. It gets much more complicated and
  requires much more abstract and advanced
  techniques than I know, for sure.
• The sound advice I have gathered is trial and
  error. Drums have been made for years and years.
  There are certain shapes and dimensions that
  produce the desired sound and some that do not.
  You just have to study up on what drums make what
  sounds and then construct and design using them
  as models.

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Links and Bibliography

• http//www.wikepedia.org
• http//www.percussiveartssociety.org
• http//www.wisegeek.com
• http//www.googleimages.com

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Conclusion

• Which came first
• The Drums or The Math?