Concepts: tension, diameter, PUL and coefficients

A vibrating string

The frequency of a stretched string depends on three things: its vibrating length, its tension and its mass per unit length. That is the Mersenne–Taylor law: for the same length and mass, more tension raises the pitch; for the same tension, a heavier string lowers it. Choosing a string means deciding what linear mass each note needs to sound at the desired tension, and the catalogue turns that mass into a gauge (plain strings) or a reference (wound strings).

The Selector’s units

The Selector does not work in SI units. It uses frequency in hertz, vibrating length in centimetres, tension in kilograms-force and diameter in hundredths of a millimetre (%mm): a gauge “60” is 0.60 mm. None of this is explained anywhere in the workbook; a luthier worked it out from the program in 2014 (“Savarez use two units of length, centimeters for string length and % mm for string diameter”), and these are the units this site reproduces [1].

From physics to coefficients

For plain strings the Selector does not ask for the material’s density: each material has a coefficient c, and the tension is T = (d·f·L)² / (c²·10⁷). Solving the Mersenne–Taylor law for a cylindrical string in these units shows that the coefficient is just a way of writing the density: ρ = g·10⁷ / (π·c²). With g = 9.81 m/s², nylon’s 170 corresponds to 1.08 g/cm³ and gut’s 155 to 1.30, matching the real densities of those materials; steel’s 63 gives 7.87 g/cm³, the density of steel.

Alliance fluorocarbon (KF) is different. The Selector uses three coefficients depending on the computed gauge — 150 below 100 %mm, 156.9767 between 100 and 150, and 162.6506 from 150 upwards — implying densities between 1.18 and 1.39 g/cm³, far below the real density of fluorocarbon (about 1.8 g/cm³). The KF coefficients do not describe the material: they are an empirical calibration by Savarez that makes the program propose, for a given tension, the Alliance gauges the company actually made. It is one of the reasons this site replicates the original as it is rather than “correcting” it.

Wound strings: PUL

A wound string has no useful “diameter” — core and winding weigh differently — so the Selector characterises it by its linear weight, in French poids unitaire linéique, PUL. It is computed as PUL = 24500·T·10⁵ / (f²·L²) and, in the program’s units, equals the linear mass in kilograms per metre multiplied by 100,000 (or, equivalently, hundredths of a gram per metre): a 0.7 g/m string has PUL 70. The 24500 hides g = 9.8 m/s². Every wound reference in the catalogue has a fixed PUL, and the program picks, within each family, the reference whose PUL is the largest one less than or equal to the computed value, in five hypotheses of increasing tension (+0, +15, +30, +45 and +60 PUL units). For plain strings it does the same with the gauge (+0, +2, +3, +4 and +5 %mm).

Glossary of references

The abbreviations of the 1998–2000 catalogue are Savarez’s own, in French:

• KF — Alliance fluorocarbon (Kureha Fluorocarbon, a PVDF developed with Kureha and launched in the late 1980s) [2]. Series KF30–KF210 and, for harp, HPK.
• NN — nylon nu, plain nylon (inferred from the catalogue’s structure). NN40–NN172 and, for harp, HPN.
• BRH / BRV — boyau rectifié huilé and boyau rectifié verni: oiled rectified gut and varnished rectified gut. BRH38–BRH225; for harp, HPBH and HPBV.
• NFA / NFC / NFP — wound nylon (nylon filé) in silver (argenté), copper (cuivre) and, presumably, plastic (NFP is not explained in any Savarez document we have found).
• BFA / BFC — wound gut (boyau filé) in silver and in copper.

Savarez still makes gut strings; the references on this site, however, are those of the historical catalogue and do not necessarily correspond to the current range.

Sources

1. Delcamp Classical Guitar Forum, “Calculating string tension using PUL (Savarez)”, Trevor Gore’s post of 4 March 2014: https://www.classicalguitardelcamp.com/viewtopic.php?t=84911
2. Patent US4833027A, “Fluororesin string for musical instrument” (Kureha, priority 1986, granted 1989): https://patents.google.com/patent/US4833027A; Savarez, Cordes pour Instruments Anciens (catalogue PDF): https://www.savarez.fr/sites/default/files/public/produit/plaquette/catalogue_instruments_anciens.pdf

Recovered formulas