1. PH 105 Dr. Cecilia Vogel Lecture 19

2. OUTLINE  PERCUSSION  Membrane vibrations  Labeling convention  plates  bells  bars  Indefinite pitch

3.  A membrane is like a string, but 2-D  To vibrate it must be stretched.  A membrane clamped around the edge has a node all along edge.  In lowest mode, this is the only node  In higher modes, also have additional nodes  Radial nodes  Circular nodes Membrane Modes

4.  The membrane may have  Radial nodes  go across the membrane  Circular nodes  go around the membrane  Modes are labeled by  # of radial nodes  then # of circular nodes Notation 11 mode 02 mode 32 mode

5. Membrane Frequency  The resonant frequencies of vibration of membrane  Decreases as radius increases,  Increases as tension increases,  Decreases as density increases.

6. Overtones  The overtones of a membrane are not harmonic. (Fig 13.9)  If you strike membrane at center  Excite 01, 02, 03, …, vibrate at center  Not harmonic, dies off quickly.  If you strike membrane in usual way,  Excite 11, 21, 31, …, not vibrate at center  Consonant: (Fig 13.9) 2.14/1.59 ≈ 4/3 (about fourth), 2.65/1.59 = 5/3 (major sixth)  Ring

7. Cymbals  Cymbals are similar to membranes, except  Stiff — higher freq  Not clamped at edges, so  It has modes with zero circular nodes  Modes similar to circular plates in lab.

8. Carillon Bells  Bells are very similar to plates  that have been bent down at the edges.  Modes Fig 13.30  video animation of modes 20“hum” 21primefpfp 31Minor 3 rd 6/5 f p 31*fifth3/2 f p 41octave2 f p 41*Octave + maj 3 rd 5/2 f p 51Octave + fifth 3 f p 612 octaves4 f p

9. Bar Vibrations  Bars are like strings, except  stiff  not clamped at the ends  Fig 2.17 modes of uniform bar  relate to lab observations  note non -harmonic  Gamut bells  overtones die quickly  pure tone quality from ringing fundamental  VIDEO

10. Non-uniform Bars  Uniform bars have inharmonic overtones  Can shape bar, give it an arch  to tune the overtones to be more harmonic  Marimba bars freq’s in Fig 13.1  find ratio f/f 1 Approx interval ratio f1f1 fundamental1 f2f2 3.9 f3f3 9.2 f4f4 16.3 f5f5 24.2 2 octaves 4 octaves 4 octaves + fifth (16)(3/2)

11. Indefinite Pitch  Many percussion instruments  have indefinite pitch.  There is no strong, ringing fundamental.  There is no harmonic structure  because of inharmonic overtones.  Fig 13.7, 13.12.  bass drum, snare drum, triangles

12. Summary  Modes of bars  determined by # nodes, like string.  Modes of plates and membranes  have radial and circular nodes  Resonant freq’s of percussion instruments often not harmonic  sometimes pitch is determined by strong fundamental  sometimes overtones are tuned to consonant intervals  sometimes no definite pitch