A Waveguide Model for Slapbass Synthesis

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A Waveguide Model for Slapbass Synthesis

• paper by Erhard Rank and Gernot Kubin
• presented by Elliot Sinyor for MUMT 614
• April 4, 2005

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Contents

• What is slap bass?
• How does an electric bass guitar work?
• pickups vs. body
• Related Work
• Waveguide Model for Slapbass Synthesis
• initial conditions
• modifications to traditional string algorithms
• Rank Kubins results
• Conclusion
• my project

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What is slap bass?

• Slapping - act of hitting the strings with
  knuckle of thumb such that it bounces off the
  frets
• Popping - plucking the string with a high initial
  displacement such that it bounces off the frets

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Fretboard meets body
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Who started it?

• Larry Graham (Sly and the Family Stone) is the
  first person to record the technique in 1970.
• Very common in funk, up until 1980s.

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How does an electric bass work?

• Upright bass strings - bridge - body
• Electric bass strings - pickups - amplifier -
  speakers
• Pickups
• permanent magnet surrounded by coil of wire
• string plucked, vibrates near pickup, varies
  magnetic flux through coil, induces current
  (Faradays law)
• output signal proportional to velocity of
  vibrating string

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Pickups in Action

• http//wildcat.phys.nwu.edu/classes/2002Fall/Phyx1
  35-2/Projects/Guitar_pickup/electric_guitar_pickup
  s/ferromagfields.html

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Related Work

• Karplus Strong (1983)
• Delay line low-pass filter noise excitation
• Jaffe Smith - Extensions (1983)
• Describe methods of augmenting the model to
  control
• Decay of Harmonics
• Quantization of pitch at high f
• Decay time alteration
• Dynamics of plucking
• Glissandi and Slurs

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Related Work

• Jaffe Smith - Extensions (contd)
• Describe methods of augmenting the model to
  control
• Sympathetic String Vibration
• Simulation of Moving Pick
• Varying Character and Number of attacks
• Stimulation of Stiff Strings

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Related Work

• Karjalainen, Valimaki, Janosy (1993)
• Discusses implementations of ideas presented by
  Jaffe Smith
• use of FIR filter for body modeling
• Design of FIR/IIR loop filters for terminations
• Control of model

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A Waveguide Model for Slapbass Synthesis -
Overview

• Two main modifications to model
• Extend string waveguide model to account for the
  fretboard underneath
• Different initial conditions
• high velocity - zero displacement (slap)
• zero velocity - high displacement (pop)

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A Waveguide Model for Slapbass Synthesis

• Physics of the slapbass
• String hits fret during first fundamental periods
  of tone
• Strongly pulled (popped) string - modeled by
  rounded triangular initial displacement
• Slapping string - similar to striking piano
  string with a hammer

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A Waveguide Model for Slapbass Synthesis

• When the string hits the frets
• nonlinear limitation of string amplitude to space
  above the fretboard.
• Must test for limitation at several points
• Straightforward if displacement is used as
  state-variable of the waveguide
• If the string hits the fret - samples between
  nearest two delay elements reflected in the
  opposite direction

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Amplitude Limitation - Implementation
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Initial Conditions
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Initial Conditions - Implementation

• Using displacement as state variable
• Plucking - intitialize delay lines with
  triangular function of half the total amplitude
  (see textbook page 129)
• Slapping - sum of displacements must be zero,
  difference proportional to cumulative sum
  (integral) of velocity pulse.
• To avoid over-idealized initial conditions, both
  are rounded

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Amplitude-limiting two-ports

• Can be added between every delay element
  (expensive) at wider spacing
• yfret(x) - linear function, determined by
  distance between strings and fingerboard at the
  bridge and at the nut.
• to achieve typical timbre, the wave must be
  limited by the first fret where the neck meets
  the body
• also must be limited near the nut, but not zero -
  decays too quickly.

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String terminations

• RL(z) - ideal reflection
• RR(z) - single pole lowpass filter
• varying pole (or frequency characteristics in
  general) controls decay, and varies the timbre
• yfret(x) has a larger effect on the sound

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Signal at pickup

• Since real pickup signal is proportional to
  velocity, delay line samples must be
  differentiated by FIR filter H(z) 1 - z-1
• Also, pickup is not a single point in space
• Lowpass output
• Gaussian-weighted tapping of delay lines centered
  at pickup position to model magentic field of
  pickup. (damps high frequencies)

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Putting it all together
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Simulation Results - Slap

• 1 - delay between last fret and bridge
• 2,3 - recoil of string due to knuckle
• similar to piano hammer, since it does not bounce
  back immediately and thus acts as reflection
  point
• not modeled

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Simulation Results - Pop

• Broad-band noise pulse generated due limiting of
  other frets along the fingerboard.
• Roughly periodic after 2 periods, with decay due
  to reflection filter.

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Simulation Results - Slap

• Simulation shows more regular structure, possibly
  due to missing knuckle reflections, or by
  non-linear effects in string itself.

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Conclusion

• The high quality of the synthesized sounds is
  confirmed by informal listening experiments
• Unlike most models - displacent used as state
  variable
• My project implement in MatLAB, possibly with
  knuckle reflections.

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References

• E. Rank and G. Kubin, A waveguide model for
  slapbass synthesis, Proc. Intl. Conf. Acoust.
  Speech Sign. Process. (ICASSP)., (Munich,
  Germany), pp. 443-446, 1997.
• D. Jaffe and J. Smith, Extensions of the
  Karplus-Strong plucked-string algorithm,
  Computer Music J., vol 7, no. 2, pp. 56-69, 1983
• M. Karjalainen, V. Valimaki, and Z. Janosy,
  Towards high-quality sound synthesis of the
  guitar and string instruments, Proc.
  International Computer Music Conference, (Tokyo,
  Japan), pp. 56-63, 1993.
• K. Karplus and A. Strong, Digital synthesis of
  plucked string and drum timbres, Computer Music
  J., vol 7, no. 2, pp. 43-55, 1983.
• J. O. Smith III, Physical Audio Signal
  Processing (August 2004 draft)