Musical Instruments - The steeldrums

A SYSTEMATIC TUNING PROCESS
FELIX ROHNER and SABINA SCHÄRER - PANArt AG

1. Introduction
THIS paper presents a tuning process and a terminology, which is the result of an intense collaboration with scientists and engineers, the study of instruments related to the steelpan and the rich experiences we got through the tuning projects. Due to an enormous boom [in the number] of steelbands, we [felt obliged] to give 'the hammer*' and 'the knowledge*' into the hands of the steelbands. In the last two years [cf 2000], 40 steelbandsmen and steelbandswomen from Germany, France and Switzerland were trained in steelpan tuning.

The study of other instruments like the gongs and gamelan, the physics of string instruments and drums, led to a tuning process which could be explained to our students. It is also the result of a dialogue between tuners. It has been proved under the daily tuning work.

Fig.1 - The Areas of a Steelpan Note

2. The Shape of a Pan Note
The concave-convex shaping of a steelpan note may be described comprising 6 areas [which can be defined as follows] (fig.1):
The Heart, the Crown, the Trunk, the Roots, the Foundation and the Sphere.

The heart is situated in the centre of the cross which is defined by the intersection of the nodal-lines of the second (1,0) and third (0,1) partial. In a flat shell, the frequency of the fundamental (tonic) is very sensitive to [mechanical] changes of curvature; because the heart [coincides with being at that point, on the notes flexing surface, that moves to the maximum in] amplitude. At this point, the note has its minimum stiffness.
In a shell, with a high rise dome, the heart is in the middle of a more stable area. Due to the unequal [edge dimensions] of the notes of a steelpan, [particularly the outer notes for example - trapezoid or egg shaped -] the heart is not in the centre of the note.
The crown [the outer edges of the heart] is the area where the dome (in a steelpan usually a low rise dome) graduates into the [top of the] trunk. The crown is the base of the dome. In a steelpan note with a correct architecture, the dome is a double curved structure. The crown is an area in which hammering leads to changes in all the vibrational modes.
The trunk is a springlike structure. Spring manufacturers make membrane springs, with a stiffened centre, that are similar [in structure] to a steelpan note. The trunk [the circular or oval band], around the stiff [dome] centre, has an anticlastic form. The [bottom] of the trunk embeds itself [through the roots] in soft transition to the sphere [the outer limits of the note]. Its anticlastic form allows to spread the partials.
The roots area has a minimum in curvature. [At the base of the trunk,] it is the bridge to the sphere.
The sphere is the bridge to the neighbouring shells; and also to the skirt.
The foundations are the asymptotes of the anticlastic trunk structure (fig.2). They have minimal curvature.

Fig.2 - Anticlastic structure with asymptote

Corresponding to these areas, PANArt pantuners use for their tuning the heart-blows, crown-blows, trunk-blows, roots-blows and foundation-blows.
The liberation-blow, a strong blow into the heart from the under-side, is demanded when the tuner needs [to bring] a basic order [to the character of the note]. It leads to a more symmetric distribution of stiffness.

3. Mode Designation
To describe the following systematic tuning process, we use the designation of the vibrational modes [first described by investigators] of clamped rectangular plates, [later to be applied to clamped and softly supported circular plates and oval shells] (fig.3).

Fig.3 - Mode designation of a Steelpan Note

4. The Systematic Tuning Process
For a better understanding in the process to successfully construct and tune a steelpan note, a complex shell structure, a basic method of systematic tuning is presented. The art of tuning consists in the synthesis of shape and [the control of] stress. We demonstrate the method with the tuning of a steelpan note tuned with an octave, together with a harmonic third partial.
[We note that this process applies to a steelpan notes of specific structure - the middle and upper voiced pans for example. For notes with deep curvature - usually of the bass steelpan range - a slightly different method of approach applies.]

Fig.4 - To the sea

     To the sea!
     Plant the tree!
     Open the heart.
     Move a stone.
     Cathedral.

To the Sea!
The first step requires the complete destiffening of the roots and trunk area. This minimisation process leads to an anticlastic structure. With heart-blows and foundation-blows from the underside, the frequency of all modes will decrease to their minimum. At this point, the shell has its minimal curvature and its softest boundary [conditions], that means its minimal bending and membrane stiffness. If this is done, consequently the future note will have a stable dome structure and the overtones may be decoupled from the fundamental. The tuner controls this important step by listening for the decrease of the lowest frequency.

Fig.5 - Plant the tree

 
 
 
Plant the tree.
The tree is the octave of the note. Upside root-blows stiffens the trunk, the frequency rises. This has to be done symmetrically, starting from the thicker roots, because thicker roots define more the frequency through their higher stiffness. The octave mode (1,0) is the most stable mode of the three lowest partials, because it is not under residual stress. We have observed that it rarely goes out of tune.

Fig.6 - Open the heart

 
 
Open the heart!
In large steelpan notes, the fundamental will stay low during the second step, because its foundation is not manipulated. In small notes, the fundamental will rise because the foundation is involved. Sensitive heart-blows from the underside will introduce stress into the fundamental mode and it will rise to its absolute frequency. The dome structure is established and we already have a harmonically tuned tone. We arrive at the ratio 1:2.
The octave will have little change in frequency, because this manipulation happens on its nodal-line.

Fig.7 - Move a stone

 
Move a stone.
To reinforce the shell structure with input of membrane stiffness and to get another harmonic; roots-blows at the (0,1) mode, near the octave nodal-line, have to be made (we call them also support-blows). This has to be done symmetrically. This manipulation leads to a strong architecture, of optimal durability and good intonation.

Cathedral
To correct the ratios we manipulate the foundations; symmetrically at the crown from the upside, to lower the fundamental. With upside trunk-blows, we lower the octave. If the fundamental is oscillating, the tuner has to control and to correct the four roots of the foundation.

At this point, the tuner will decide; whether he wants an harmonically correct tone structure, or a brilliant or sharp tone.
For a brilliant tone, he manipulates the (2,0) mode to the second octave. In many notes he has to ignore the third partial to tune in the second octave. He will mask the (1,1) mode which is very near in frequency. When he tunes the (0,1) mode to a third, he will easily get the second octave. The player will make his impact directly into that mode and gets the "kick".
The tuning of the higher overtones becomes a question of timbre. For harmonic correctness, it is necessary to get the three lower modes into an harmonic relationship.

5. Residual Stress
Each deformation provokes compressive and tensile stresses in the macrostructure of the shell. These stresses are used for tuning, but it has to be said that external tension leads nearer to the yield point of the material, and the note will go out of tune faster by hard playing, or by changes in temperature.
There are methods to eliminate these tensions and to relax the structure, for example by low tempering.

6. Conclusion
The systematic tuning process presented in this paper is based on the principals of symmetry, minimisation of stiffness, decoupling of the overtones from the fundamental and splitting of modes by anticlastic boundary. This tuning leads to the optimal architecture.
Tuning means a process which fulfills the following demands: Durability of the shell, harmonic tone structure, balanced sound and control of recoupling.

Compiled & Processed by Islands Research for:
The Steelbands (Pan) of Trinidad & Tobago
http://www.seetobago.org/trinidad/pan/archive/r&d/panart/ir_archivecopy_a_systematic_tuning_process.htm

[2nd Ed] © 2003: tobagojo@gmail.com - 20031103 - 1m20071228 - 2m20140615 Historic Update: 11 December 2003; Last Update: 29 June 2014 02:11:00 TT Processed by: JdeB - Islands Research

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