Every string manufacturer provides the mechanical characteristics of the wires he produces enabling comparison with other brands.
Stephen Paulello's Type M (as "Modern") corresponds to the standard wire universally used in contemporary piano making. However, traction tests in laboratories do not take into account the quality of the raw material or the specificities of the drawing methods employed. Even if mechanical characteristics are similar, sound characteristics may be slightly different. Consequently, choosing Stephen Paulello's type M rather than another brand's wire is a question of taste.
The other types (XM, 0, 1 and 2) have no equivalent today.
The mechanical characteristics of the strings are also one of the elements required in order to carry ou to your own scaling calculations.
Click on the following link to reach the Table of characteristics of the 5 types of Stephen Paulello wire.
Manufactured in the city of Firminy in the center of France, "Firminy" wires were used by most French piano makers at the end of the XIXth century. The characteristics of Stephen Paulello's Type 0 strings are very close to the Firminy steel of that period. However, the gauge used by Firminy is not current anymore today. If you wish to respect the gauges indicated on the instrument, it is necessary to make a conversion before ordering the strings in contemporary gauge.
Click on the following link to reach the Firminy - Paulello conversion table.
- According to the make, date and place of manufacture of the piano? These data are of documentary interest but far from sufficient as a guide for optimal string replacement.
According to the density of the metal? This criterion is not of major importance.
This indication seems relevant because it enters into the calculation formula of a string's tensile strength. The density is expressed in grams / cm3 and varies, according to the alloy, between the minimum values of 7,65 g/cm3 for iron and maximum of 7,95 g/cm3 for some steels. However, considering that between these extremes we obtain a discrepancy of tensile strength of only 4%, this information can be considered irrelevant.
- According to the modulus of elasticity (or Young's modulus "E")? This is an interesting parameter.
- The modulus of elasticity plays a very small part in the calculation of tensile strength. On the other hand, it is a major element of the calculation of the rate of inharmonicity of a vibrating string. Numerous measurements of inharmonicity made on antique stringings in excellent condition showed that the elastic properties of the various different wires examined were very similar.
Thanks to the stress rate? This is THE determining criterion.
This criterion concerns the tone and the mechanical behavior of the string.
The tone : it is unanimously accepted that, in order to vibrate to its full potential (that is to say with a minimum of internal amortization as well as a good spectral balance), a string should be stressed at around 50 to 75 % of its practical breaking load (PBL), depending on the register (this notion is explained below). An under-stress (less than 45%) as well as an over-stress (more than 85%) gives bad sound results.
The mechanical behaviour : It is necessary to understand the following three notions:
- The nominal breaking load (NBL): This value corresponds to the maximal tensile strength to which a steel wire can be subjected before it breaks. The results, obtained in laboratory conditions, extends from 1000 to 3000 Newton by mm², according to the diameter and the type of steel used.
- The practical breaking load (PBL): The phenomenon of fatigue as well as the various bends, loops and twists applied to the wire weaken the performances of the strings once set in a piano. It makes it necessary to underestimate the results of nominal breaking load (NBL) by 15 % safety margin for Type 2, and 25 % for the other types. These values are given for every type and every diameter in a following table.
The elastic limit: apart from the ultimate phase called "break", a string put under tension goes through two phases:
- The elastic phase during which a stress of small intensity produces a stretch which disappears as soon as the tension is released.
- The plastic phase during which a stress of strong intensity produces a stretch which partially remains when the tension stops. We then have to deal with an irreversible deformation, the string does not hold tuning, becomes very inharmonic and ultimately breaks.
In order to respect the ideal stress rate of the metal, the frontier between the elastic phase and the plastic phase should never be exceeded. This border is named the elastic limit. It is situated at approximately 85% of the practical breaking load depending on the type of wire
The stress rate of a string thus depends not only on the resistance of the steel used but also on the length and diameter of the string and on the frequency at which it is tuned. To determine the ideal stress rate for every string you should know the characteristics of the steel used, the vibrating length of every string, its diameter and the pitch at which the instrument will be stabilized.
- You will find the characteristics of the 5 types of wires in the following table : Characteristics of the 5 types of Stephen Paulello wire
- Speaking length and diameters should be measured directly in the piano
- You choose the pitch : A=440?
- As for the tedious calculations, the Typogram will make them for you.