How the Tailpiece Dances with the Violin: Insights into Tailpiece Tuning

1. How the Tailpiece Dances with the Violin: Insights into Tailpiece Tuning T.B (Ted) White VSA Meeting - Baltimore November 2013

2. What Is The Ideal Tonal Adjustor? • No modification of instrument required • Inexpensive • Does not require adding parts • Adds flexibility to the setup process • Does not require string take-down

3. Desirable Possible Effects • Tonal “quality” improvement • Playability improvement • Wolf note management

4. Sinks and Sources • Think of energy flowing around in the instrument from various sources into sinks • Bow into string into bridge into instrument body • But what about the other way around? • And what about the tailpiece and nut?

5. Helmholtz Motion of a String Bridge Reflection Nut Reflection Tailpiece Instrument Body

6. Tailpieces • Tailpieces are easy to work with • They are attached directly to the strings • Likely to affect bridge mobility • Likely to act as part of a mass damper • Certain modes of the afterlength/tailpiece/tailgut system may be close to the wolf

7. Tonal Changes Are Known To Occur With: • Afterlength adjustment • Tailgut adjustment or change • Changing tailpieces • Weighting tailpieces • Carving or lightening tailpieces

8. Possible Theoretical Basis • Mass resonator as a rigid mass and sprung suspension • Damping via flexure of the tailpiece • Sympathetic vibration of after-lengths (Tuning to 1/6th rule etc.) • Radiation damping

9. Rigid Body Mass Resonator Factors • Tailpiece mass • Tailpiece mass distribution • Elasticity and tension of string after-lengths and tailgut • Lengths of afterlengths and tailgut • Other mechanical properties of strings and tailgut

10. Simple Mass and Spring Systems

11. Flexural Damping Factors • Wood properties of the tailpiece • Sectional properties of the tailpiece shape • Mass distribution • Boundary conditions at supports

12. Identified Tailpiece Modes • Stough, 1996, CASJ 3, Series II showed for violins: • 3 “swing” modes below open G (roll) • 2 rotational modes • About a vertical axis (yaw) • About a horizontal axis (pitch) • E. Fouilhe, et. al. 2011, measured 9 modes for cello both rigid and flexural

13. Afterlength Tuning Factors • Presumed interval or length ratio • Length of tailpiece vs. length of tailgut • Effect of silking • Effect of fine tuners • Effect of end type – loop or ball • Mute or wolf eliminator mass

14. Frequency Response Functions of Nine Cello Tailpieces

15. Tailgut vs. Afterlength

16. Tailpiece Survey Conclusions • Pitch and Yaw modes dominate rigid body modes • Pitch mode closest to wolf note • Tailgut length more important than afterlength in rigid mode resonances • Higher modes highly variable

17. Finite Element Analysis (FEA) • Computer analysis • Accurate material and structural models • Possible to predict stress and strain • Possible to predict structural acoustics • Very useful in design

18. Cello Tailpiece Pitch Modes

19. Cello Tailpiece Yaw Modes

20. Cello Tailpiece Roll and Translate Modes

21. Cello Tailpiece Flex Mode

22. C String After-length Modes

23. G String After-length Modes

24. D and A String After-length Modes

25. What does it all mean? • Remember that it is the energy flow between the sinks and sources that matters • A light part can move a lot with out much energy • A heavier part will contain more energy for the same movement

26. Cello Tailpiece and After-length Modes

27. How can we use this knowledge? • Try various tailpieces, tailguts, etc. and see what works • Or, invent a tailpiece which can permit some adjustment of one or more of the important factors

28. New Tailpiece Design Goals • Must be able to adjust pitch and yaw modes • Must be able to adjust flexural modes • Adjustment must simple • No requirement for re-tuning or other instrument changes • No increase in tailpiece weight

29. New Cello Tailpiece Underside Adjustable Mass

30. Adjustable Weight System

31. Adjustable Weight System

32. Violin with Adjustable Weight Forward Tailpiece – light green Bridge Admittance – green Pitch Mode B1+ B1-

33. Violin with Adjustable Weight Midway Tailpiece – blue Bridge Admittance - Red Pitch Mode (split by B1+) B1- B1+

34. Violin with Adjustable Weight Aft Tailpiece Horizontal Axis – green Bridge admittance - blue Pitch B1- B1+ (split by Pitch)

35. Violin Bridge Admittance Weight Forward - blue Weight Midway - red Weight Aft - green Higher Modes

36. User Feedback • Many makers are now using the new tailpiece • Found to be effective at adjusting tone and reducing the wolf note • Users like the ease of adjustment • Has been compared to soundpost adjustment

37. Conclusions • Any tailpiece affects tone and may also mitigate wolves • Adjusting tailgut length changes tone • Changing tailpieces or adding or removing mass will affect tone • An adjustable tailpiece can be a significant tool in tonal adjustment

38. Practical Applications • Learn to “play” the tailpiece • Pluck or use a Fuhr tube to vibrate the tailpiece modes • Listen to the pitch • Matching pitch with a wolf note may reduce it

39. The End (for now!) Arbutus Fittings 3938 Gilbert Drive, Victoria, BC, Canada, V9C 4B2 info@arbutusfittings.com This work was supported by a grant from the National Research Council of Canada and the University of Victoria