Last in this discussion of the theoretical implications of the various parts of the pan, we have to take a look at the sticks. While the sticks are not a physical part of the instrument, they still play a very important role in the tone generation.
To get a sound out of a musical instrument you have to get it to vibrate in some way - to put energy into it. This is called the exitation of the note, and the properties of the exiting body are of vital importance for the tone. The properties of the stick that may have importance for the tone are: weight, length and hardness.
Weight and length
The importance of the weight of the stick is easy to understand. The heavier the stick, the more energy can be transferred to a note when it is hit. This means that a heavier stick gives the pan a stronger tone, but on the other hand you risk getting a sound that "breaks". It is also easier to hit the notes out of tune. The same thing goes for the length - a longer stick makes louder playing possible. The acoustical implications of the weight and the length as such can almost be disregarded, as they can be seen as a part of the stroke, the force of which the player can vary within a wide range.
To get a good sound out of a pan it is important to have sticks with the right hardness. If the sticks are too hard, the sound will be harsh with a weak fundamental and many non-harmonic overtones. If they are too soft the tone will be weak and muffled. Small notes need a hard stick and big notes need a soft stick to sound good. This means that ideally you should use sticks with varying hardness for the different sized notes in one pan. This is not possible, of course, so you have to compromise.
Measurements of the striking indicate that the optimal hardness of the stick seems to be when the contact time equals the period time of the fundamental, see fig. 27.1. This results in the fundamental being the only vibrant mode of the note that is exited by the stroke. The higher modes, that vibrate faster than the fundamental, will tend to move up and down several times during the time of contact, which causes them to be damped by the soft stick.
Fig. 27.1 Contact time of the stick in relation to the first milliseconds of a steel pan tone.
The smoothness of the beginning of the curve in fig. 27.1 also shows that it is only the fundamental that vibrates in the beginning of the tone. The ruggedness occurring later shows that the higher partials are beginning to occur, see fig. 19.1.
The findings on the exitation of the note are well in line with my hypothesis concerning the sound generation. According to this, the exitation that would lead to the most harmonic tone would be a stroke that only excites the fundamental mode of vibration, and lets the non-linear mechanism do the work of converting the energy to the higher, harmonic partials.