Workshop Hints
Replacing missing or damaged gong rods or tubes.
By Alan Emmerson
Often a single rod or tube is missing from a set of chimes. It is possible to buy complete sets or un-tuned replacement individual rods. Getting the right length for the correct note can be difficult. Alan Emmerson has provided the following information to allow you to cut a rod or tube to the correct length. To use these relative lengths, you need to know the notes that are played in your chiming sequence. You can look this up in the hints area at www.bhi.co.uk/hints/chimes.htm Once you know the note that is missing, you can use the information below. To calculate the length of the missing chime.
I first saw this table in an article by G. Murray in Newnes Practical Mechanics of July 1949 and learned the theory in training as an engineer eleven years later.
The actual length of the gong depends upon what key you wish to play in.. The relative lengths of the tubes is what is important.
Since frequency of a musical note doubles in every octave, and the octave contains twelve "equally spaced" intervals, and the fundamental frequency of vibration varies inversely as the square of the length, you can obtain relative frequency for each note of the scale by inserting 11 geometric means between 1 and 2 - whence relative length is obtained by dividing 1 by the square root of the relative frequency.
Thus:
| Note | Relative Frequency | Relative Length | Note | Relative Frequency | Relative Length |
| G | 1.00 | 1.00 | D | 1.496 | 0.817 |
| G# | 0.974 | D# | 0.795 | ||
| A | 1.122 | 0.945 | E | 1.680 | 0.773 |
| A# | 0.919 | F | 1.782 | 0.750 | |
| B | 1.26 | 0.892 | F# | 0.729 | |
| C | 1.334 | 0.866 | G | 2.000 | 0.707 |
| C# | 0.843 |
For example, if you have a D rod and your C rod is missing, measure the length of the D rod and multiply it by 0.866/ 0.817 to give the length of the C rod.
The method applies to both cantilever and freely suspended gongs and to both rods and tubes. The rod or tube must be of the same and constant cross section as the original, and of the same material, for the method to work. More elaborate calculation can allow for material and cross section changes.
