Deciding how to string a fortepiano in an historically appropriate manner is a less challenging task than designing stringing schemes for harpsichords, because a large number of instruments have survived with gauge markings. Unfortunately, interpreting these markings is not easy. Until now, most who have tackled this problem have followed two approaches:
Both approaches have serious drawbacks, and not surprisingly, no convincing solutions to the puzzle have yet been found.
The main problem may well be our mindset. We assume that numbers found on instruments represent codes of a particular gauge "system", just like on the modern piano, and that each code indicates a certain diameter within a fairly small tolerance range. These systems are supposed to have been determined by regional manufacturing guilds or groups. However, there is more than adequate historical documentation to tell us that this approach is fundamentally flawed:
In light of all this documentary evidence to the contrary, one cannot but wonder at the valiant efforts of organologists to determine the "system" for a given group of instruments; though well intended, their quest has about as much chance of success as that for the Holy Grail.
Nonetheless, instrument makers wrote gauge numbers on their instruments. How did these makers deal with the anarchical situation described above, and what was the purpose of these markings?
The answer is given to us by Bleyer, Thon, and Blüthner: the chordometer. Each instrument maker probably had his own measuring device with which he sorted the available wire so as to best approximate his or her own "system". Individual sorting systems may have originally been based on wire from a specific source, or perhaps on tradition, and may well have closely resembled one another within a regional or temporal grouping of makers, though there is no guarantee of this.
Bleyer also tells us that the whole point is "to give the thickness of the strings the proper proportions" [my italics] so that the tone of the instrument has an "even sound". Thus the gauge marks written upon the instruments were probably not so much indications for precise diameter placement, but more so the delineation of broad diameter zones or regions, mile posts used as guides in a sorting process intended to distribute the available string mass in a roughly-even proportional manner.
Both Bleyer and Blüthner refer to a specific kind of "chordometer": the slip gauge. Such a device is incredibly easy to make and mark-out with whatever sort of scale one may desire, and, if carefully made, can be surprisingly accurate. Luckily, Bleyer even goes so far as to tell us precisely what sort of proportions he marked on his own slip gauge, comparing his system to that of the "locally available" strings, which are "like the Nürnberg strings". Though one could argue that Bleyer's description of Viennese/Nürnberg strings is open to interpretation, if we take his words literally, there is only one possibility: the system was defined by a logarithmic progression based on the 7th root of 2, that is, halving on the 8th gauge number. He specifically states that one can interpolate half sizes, in which case the proportion would become the 14th root of 2, halving on the 15th size. The only information left unspecified by Bleyer is a reference diameter: we know the proportions, but not the absolutes. (Click here for Bleyer's text and an in-depth analysis.)
In order to discover if Bleyer's description is credible, and to determine the absolute "ideal" diameters for a particular builder or group of builders, we must return to the evidence of surviving string sets and examine them through the "filter" of a slip gauge. Based on the above comments, it is logical to assume that the range of diameters with which instrument makers had to work varied infinitely. Due to the rapid wear of the draw plates, even a single spool of wire probably had a thicker diameter at the end than at the beginning (or vice versa, depending on how many times the wire had been wound onto smaller spools after drawing). If a slip gauge were used to constantly check and sort the wire, we can assume that any diameter which fit within a tolerance of +/- one half gauge would have been assigned that particular gauge number. If half sizes were used on the instrument, the tolerance is reduced to +/- one quarter gauge. Such a sorting process can produce stringings with a rough overall proportional distribution of diameters, but with absolute diameters which vary considerably. Therefore, it is logical to assume that the diameters found among surviving string sets would provide us with a "scatter shot" data set, providing broad ranges or clusters of diameters. It thus becomes obvious how ludicrous it is to attempt to establish the absolute diameters which define any given "system", even that of a particular builder, by taking the diameters of a single set of surviving strings, even a set which could be proven to be undoubtedly original.
String sets which agree amazingly well with such a scheme have indeed been found on the pianos of many 18th and 19th century Viennese builders, when the tolerance level of a slip gauge is taken into consideration. Many makers who began building before the turn of the century and some of their followers seem to fit a general grouping, while others making later/larger instruments apparently used Bleyer's Nürnberg proportions but with heavier absolute diameters. Based upon such an analysis, I feel confident in recommending the following general interpretation for the instruments of Walter, Streicher, and Brodmann. Considering the similarity between the early pianos of Streicher and those of her father, one could assume these diameters could also be used for the pianos of Stein. Hofmann's gauge seems to have been calibrated slightly heavier: take the next larger half gauge diameter for the markings on his pianos. It is probably safe to assume the same diameters are applicable for other pre-1800 Viennese makers as well. In the near future, I will add my recommendations for the instruments of Graf, Fritz, J. B. Streicher, and other later makers.
Bear in mind that these are ideal "target" diameters based on the logic described by Bleyer (14th root of 2). After examining many "original" string sets, I have chosen .55mm as the reference diameter for gauge 1/0, from which all larger and smaller diameters are calculated. The Malcolm Rose diameters given are "best fit" to the ideal diameters. Many sizes are non-standard, which Rose provides for a 20% surcharge. Of course, one could duplicate the original methodology and use standard Rose diameters sorted for a best fit agreement. However, the steps are often too coarse, and the resulting stringing schedules would always have clumsy jumps and inequalities.
c.1800 ideal diameters for "Nürnberg" gauge markings in mm
Disclaimer: I make no guarantees whatsoever that specific instruments, either modern copies or originals, will be able to withstand the resultant tension levels when strung according to these suggestions. The design of any stringing schedule should always take into account the pitch level, the structure of the instrument (type of joinery and/or case design), the type of glue used, the quality of construction, and the overall health of the structure. Use of this information is absolutely and without exception AT YOUR OWN RISK.
For more information, I recommend the following works:
Alphons Huber, "Saitendrahtsysteme in Wiener Klavierbau zwischen 1780 und 1880", Das Musikinstrument, Vol. 37 #9, pp. 84-94. This article is an excellent introduction to the topic, as well as a source of good basic information. Huber argues the case for general systems, but his data base is extremely limited.
Michael Latcham, The Stringing, Scaling and Pitch of Hammerflügel built in the Southern German and Viennese Traditions 1780-1820, München 2000. This new work contains a wealth of material on original string gauge markings as well as a complete examination of the organological literature on the topic to date. The section on gauge interpretation argues against the idea of general systems. The Thon and von Kees passages referred to above can be found here. However, although Latcham quotes Bleyer's description of Nürnberg strings, he curiously neglects to include this information in his various attempts to determine which diameters this "system" may have described (though he does discuss Bleyer's own system in depth). Furthermore, most of the original stringing sets he cites as evidence for the "limited application" of one or another of various "systems" also fit well with a Bleyer "Nürnberg" proportional scheme.
Paul Poletti, "The interpretation of Early Wire Gauge Systems - Fixed Diameters or Proportional Relationships", Matière et Musique. The Cluny Encounter. (collected lectures of the 1999 Facture Instrumentale en Bourgogne conference in Cluny, France), Alamire, Belgium 2000. To my knowledge, this is the first time that the evidence of surviving strings has been examined in light of the methods and concepts described by actual 19th century piano makers - in short, the methods by which the evidence was most likely created in the first place.
Malcolm Rose/David Law, A Handbook of Historical Stringing Practice for Keyboard Instruments, Lewes 1991. A good basic collection of raw data. A second expanded edition is in preparation.