Notes

1 The author is aware that some mini-rings have not been tuned with respect to the Nominal but to another partial, e.g. the Hum. He suspects that the human ear is detecting a strike note which is not dependent on the Nominal frequency.

References

1 On Bell Tones, Nash's Pall Mall Magazine 7:183-194 (1895). A. B. Simpson

2 Group Theory and The Bell, Journal of Sound and Vibration (1973) 31:411-418. R. Perrin, T Charnley.

3 Normal Modes of the Modern English Church Bell, Journal of Sound and Vibration (1983) 90(1),29-49. R. Perrin, T Charnley, J. DePont.

4 Chladni's Law and the Modern English Church Bell, Journal of Sound and Vibration (1985) 102(1),11-19. R. Perrin, T Charnley, H. Banu & T.D. Rossing.

5 A Comparative Study of the Normal Modes of Various Modern Bells, Journal of Sound and Vibration (1987) 117(3),411-420. R. Perrin, T Charnley.

6 Acoustical Measurements on Church Bells and Carillons, The Hague 1949. E. W. Van Heuven.

7 Acoustical Investigation of the influence of the material on the Sound of Bells, Acustica 29:1-14 (1973), C. R. Schad & H. Warlimont.

8 Architectural Acoustics, Bruel & Kjaer, K. B. Ginn

9 Francois and Pieter Hemony,  17th Century Dutch Bell-founders.

10 Bells & BellFounding, A Practical Treatise upon Church Bells by X-Y-Z. Bristol 1879.

11 E. F. F. Chladni, Die Akustik, 1830.

12 A Rudimentary treatise on Clocks, Watches and Bells with a full account of the Westminster Clock and Bells. London 1860. E. B. Denison

13 The Strike Note of Bells, Netherlands Acoustic Society Pub. No. 7, 1965 pages 8-19. J. F. Schouten & J. 't Hart.

14 John William Taylor I, Bellfounder, John Taylor Bellfounders Ltd, Loughborough

15 For information about  Waveanal  please email Bill Hibbert at bill@hibberts.co.uk or look at Bill's web site for more information about tonal analysis of bells. A worthwhile visit for those who would like to know more!