24. The note
The note properties that most affect the tone are the size, the shape, the tension and the arching of the note.
The size of the note is the property that most obviously affects the tone. The size of the vibrating dent is crucial for the pitch - the larger the dent, the lower the tone. This is analogous to the situation in a guitar string or a horn, where a longer string or a longer horn results in a lower tone. But it is not as simple as in a string, because in a steel pan, notes of equal size can have different pitches, due to varying height and shape of the dent.
Another complicating ingredient in the pan is the fact that the size of the vibrating dent is not the same as the size of the note. The acoustic "size" of the note is not set by the boundaries defined by the groove, but rather by the ending of the dent arch. The size of the sounding dent is always less than the area restricted by the groove, see fig. 24.1. This is proved by the tuning, where a hit from above near the side of the note decreases the note-size and thus raises the pitch.
Fig. 24.1 Note dent shape in relation to groove border.
The optimal note design seems to be when the dent has the same size as the area inside the groove. In this way no space is lost. But this is a critical situation; if the note area is made too small it will be impossible get the pitch low enough. If the note is a little too big, you can always make the dent a bit smaller inside the groove. This safety-measure is the reason why the notes usually are a bit larger than they need to be. There seems to be a trend towards making the notes smaller and smaller. This is primarily done to be able to put more notes in each drum, but it may also have acoustical implications, such as minimizing the loss of acoustic energy.
I have measured the note sizes of various pans as a part of my research. It would be plausible to think that notes with the same pitch on different pan models could have the same size. Therefore, I have compiled the data in a graph on the average length and width for each note on the musical scale, see fig. 24.2. By looking at this graph, a tuner can get a hint as to which notes of his design that can be made smaller. Please note that the lengths and widths in fig. 24.2 are measured from the groove, not on the actual note dent.
Fig. 24.2 Average note sizes.
According to tuner Denzil Fernandez it is the area of a note that determines its pitch. He has calculated the ratio between the areas of successive notes to approximately 0.94. This means that the area of a note always is 94% of the next larger one. Converted to a ratio between lengths this will be 0.97. As a comparison, lines following this theoretical ratio have been drawn in fig. 24.2.
It would seem like an easy and straightforward project to study the relation between the note size and the pitch. But the diffuse ending of the note dent arch and the other variables affecting the pitch have made it difficult to establish a simple relationship between size and pitch. A way to progress with these studies could be to make a number of dents that exactly fill some notes with pre-defined sizes, and then try to tune them as low as possible. Such an experiment would give a practical measure of the minimum note sizes.
The first thing to say about the note shape is that the shape of the area delimited by the groove has little to do with the shape of the actual vibrating dent. The groove area can be of any shape, as long as the groove surrounds the dent, again see fig. 24.1. It is the shape of the dent that is important for the acoustic properties. Theoretically, the relation between the length and the width of the note should determine the frequency relationship between the fundamental, the octave and the third mode of vibration. It is still to be revealed if this is the case in practical tuning.
In old steel pans, the inner notes were often round, but nowadays they are elliptical. The upper line in fig. 24.2 represents the length of the notes and the lower line represents the width. The relationship between the width and the length is about 2 to 3 (0.65) for notes in the outer ring and about 6 to 7 (0.85) for the notes in the inner ring. This means that the smaller notes are more round in their shape, while the outer are more elliptical. Tuner Denzil Fernandez says that he is working with an average ratio that is 5 to 6 (0.83). The optimal ratio between length and width is still to be revealed.
The arch shape of the note dent is the most difficult property to measure, describe and relate to the tone. To a tuner, its effect on the tone is obvious, because the note needs a very special arch to generate a good steel pan tone. But how do you measure and describe an arch technically?
I started with the intention to measure the heights of various notes to see how they were related to their sizes and pitches. My first measurements revealed that the notes had one height when they were measured lengthwise and another when they were measured across. The reason for this was the lack of a well-defined plane to relate the heights to. I had related my measurements to the groove, which followed the spherical shape of the basin.
Then I started to use a shape-mould and realised that the note dents are fairly flat in their length direction, and more curved across, see fig. 24.3. I found that the quota between height and length is most often less than 1%, whereas the quota between height and width is about 2.5%, which means that a note that is 10 cm across is 2.5 mm high. The length axis seems always to be flat, regardless if the length axis of the note is oriented radially or tangentially in the pan.
Fig. 24.3 The arch shape of a note.
The cylindrical arch is likely to be due to the cross-section between the spherical concave shape of the pan and the elliptical shape of the note. To get a better view of the arch shape, I did an experiment: I made a spherical ball of clay and then I pressed objects of various shapes against it to make indentions in it. To get a shape like an elliptical steel pan note, I had to use a cylindrical rod, see fig. 24.4.
Fig. 24.4 Reproducing the cylindrical arch of a note by pressing a rod against a sphere.
The cylindrical arch of the dents seems to agree with the acoustical behaviour of the note. Presumably, the non-linear tone generation mechanism works best when the note is almost flat in the lengthwise direction. According to my hypothesis, the note behaves like a non-linear string in its length direction, and these vibrations generate all the high partials. If you listen to the vibrational modes across the note, you will find an acoustical behaviour that is much more like a shell (or a bell) with a hard and metal-like sound.
Thus, the optimal arching of a steel pan note seems to be very close to the cylindrical, raising less than one percent lengthwise. The more flat the note is lengthwise, the more partials it will generate. But a flat note will also be less stable and it will be very sensitive to strokes that tend to change its shape. Therefore, the tuning result will have to be a compromise between an ample overtone generation and considerations to keep the tone stable.
There are two different tuning philosophies related to the shape and the corresponding generation of partials in the note. The first, that can be called the "steelband" philosophy, is to shape the note with a rather high arch. Notes of this type will demand a relatively strong stroke to produce harmonic partials - to get right timbre. On the other hand, the note will be able to produce a strong sound without "breaking", i.e., producing a harsh, distorted sound. Due to the relative stiffness it will also stay in tune longer.
The other school of tuners, which can be called the "jazz" or the "soloist", makes the notes more flat, which will make them produce a brilliant sound with many partials at relatively modest playing levels. This is good for solo or electrically amplified playing, but the flat note will produce a weaker tone and is easier played out of tune.
The best way to go further with the discussion about the shape of the arch would be to refine the measurements by using holographic methods to study the shape and the wave-patterns in the vibrating dents.
As mentioned earlier, two notes with the same area can have quite different pitches. This is due to the arching of the note - a higher dent yields a higher pitch. This pitch change can be caused by changes in the geometric relations of the dent but also by variations of the tension in the metal.
When a note is tuned, it is first stretched. This may result in a plastic deformation by the hammering from underneath. This stretching of the metal raises the pitch.
It is likely that the lowering during the tuning removes the stretching tension and it is substituted by a compressive tension that lowers the pitch further. This occurs because the plastic de-formation can't be compensated by a plastic "re-formation". This means that the stretched metal is not moulded together, but forced into the arch. The suppressive tension will give the note a lower pitch with the same arch height as before.
One thing that indicates the existence of suppressive tensions in steel pan notes is the notion that they tend to raise when they are played out of tune. If the only effect of playing would be that the dent was lowered by the hitting, the result would be the opposite - lowered pitches. My hypothesis here is that the playing successively releases the suppressive tension from the note, which will result in raised pitches.
It has not yet been possible to do any measurements to verify that there are any tensions in the notes of the steel pan.
The measurements showing that the notes are cylindrical in shape and the hypothesis for non-linear partial generation give us some new clues to the secrets of steel pan tuning. There are three properties of the note that the tuner can modify while he is tuning: the size, the arch and the tension.
Variations in the area have most effect on the fundamental mode of vibration. Changes in the length affect the octave mode, whereas changing the width affects the third mode that is responsible for the timbre.
The shape of the arch is responsible for the generation of higher overtones and has to be adjusted to be sufficiently flat. The tension, last, seems to affect mainly the pitch of the fundamental.
The non-linear mechanism for tone generation shows the importance of tuning the fundamental and the octave to a perfect 1:2 frequency relationship. The secret of good tuning is to change the frequency of the fundamental and the octave separately so that they will meet at the right pitch. If the above mentioned hypothesis holds true and the area and the tension are mainly responsible for the frequency of the fundamental, this gives us a simplified model for the tuning: The fundamental can be changed without affecting the octave by hitting the note along the sides. This will affect the third mode, but the pitch of the third mode is not as critical as the octave.
The best place to use for changes of the fundamental, with a minimum of impact on the octave and the third mode, would be the "corners" of the elliptical note, see fig 24.5. Lowering the note here will affect the area with a minimum of change in length and width.
Fig. 24.5 Places to tune the fundamental with minimum effect on other modes.
The best way to adjust the octave is to re-shape the dent lengthwise - by hitting it at the ends, along the vibrational axis in fig. 24.5. These adjustments will also affect the fundamental, but to a lesser extent than the octave.
The tuning will have to be a balancing act, adjusting the area, the length, the width, the arch and the tension at the same time. The area and the tension should be adjusted so that the fundamental is right, while the length is right for the octave. At the same time, the arch shape has to be the very special one that generates harmonical overtones. The last consideration is that the width of the dent should place the third mode at a frequency that has a harmonic relationship to the fundamental.