Invariably we will come to the question, “How shall I tune my square piano, and to what pitch?”
We as a community labor under the assumption that the value of A, (the pitch or ‘cammerton’) began at some fairly low value and increased with the decades settling at A=440 Hz sometime in recent history. This assumption is both wrong and right! Wrong, in that pitch was geographically different for different places at the same time, and different for different musical groups, orchestras, and individuals also at the same time. Right in that pitch did indeed tend to move upward with time, generally rising from A= 400 in the late 17th C to the value today of A=440 hz. But for any given time the pitch was at several different values depending on the technician, musician, or local custom.
Bruce Haynes has given us “A History of Performing Pitch – The Story of A” Scarecrow Press, Oxford 2002 which runs to nearly 600 pages (and $100!) on the subject of pitch. It would be inappropriate to quote extensively from this book, you should think about adding it to your library, but in short, he has pulled from measuring standard woodwinds, technician’s notes, and various apocrypha a range of pitches in use at various periods. For the period that is of most interest to us, say, 1770 to 1800, we find in England a distribution of pitches in vogue, the lowest statistically relevant being A 410, and the highest A 447. The majority are between A 430 and A 437, with most at A 433. However, if your piano was shipped to France or Germany you might shift that pitch down a few cents (100 cents make a semitone). If we were to compromise and agree on A 430 we would not be wrong, but your piano may have been at many pitches over the years. If you play with ensemble players and can transpose, A 415 is convenient, but if you want your players to tune down, as close to A 440 as possible will probably make more friends for you, and choosing A=430 to 435 at least has some historical precedence.
What you ultimately choose will also alter the string tension on your instrument. Tension goes as the square of the frequency, so by raising the pitch we increase the tension as the square of the difference.
T= F2L2 p PI D2 /9.81
Where T is tension, L is length, p is density, PI is 3.14159…, and D is diameter of the wire in meters. 9.81 newtons is 1 kg/force. This should be born in mind when raising the pitch; we can increase tension by a significant amount going from A 415 to A 440. For a 1784 Broadwood, the total tension on the instrument at A=415 is 1168 kg, and 1313 kg at A=440, or a 12% increase for one semitone.
Electronic tuners can get you to your chosen pitch, but what of the temperament? This refers to the various schemes for addressing the fact that you cannot have perfect fifths, fourths, and thirds in all keys. A compromise must be arrived at which allows fifths to be somewhat flat, and thirds and fourths a bit sharp. But how much for each? So much has been written and recorded on this subject. For the person with heightened senses, the difference in temperament is the difference between poor to ordinary, and sublime. In the book “Grand Obsession” Perri Knize spends several years and 371 pages to weave the story of getting her Grotrian grand to perform with the right voicing of the hammers and the right temperament, and remained distraught until she discovered one particular temperament.
For me, I have experimented with several of the major temperaments and on the little squares, I am convinced that it makes little difference. For one, the exact pitch does vary with temperature and humidity, so even if you experience no changes following tuning, it will have an effect of a few hours at most with playing through your favorite pieces. Remember these variations are quite small, and squares are all wood. I could also be a complete troglodyte and Philistine, so to all I encourage you to experiment with temperaments. I find the standard equal temperament to be quite alright.
The mechanics of actually tuning a square are reasonably straightforward. It is possible to weave a thinner cloth between the strings to set the temperament, then tune unisons and octaves, or with a rubber wedge, go note by note and do unisons as you go, advancing the wedge through the circle of fifths. I favor the wedge, a small rubber delta on the end of a tooth pick, for more control, and it helps me not to forget whether to be tuning the first string or the second! But to each his own. Tuning is an acquired skill, and speed comes with practice, as does accuracy. An electronic tuner set nearby will keep you honest and some will allow you to set the value of A so that you can tune to the center of the dial. Some elaborate strobe units allow for setting temperaments by the meter. I find though that particularly the little squares have their own idea of what sounds most pleasing, and despite the mathematical accuracy of the meter, it frequently sounds better to set the pitch first, and then tune by ear.
If you start in the middle registers to set the temperament, then move down the bass and finish going up the treble, the need to retune again is diminished, as the amount of change in pitch in the bass is a relatively lesser value than the treble for the same amount of case movement. Unlike a modern piano where essentially all the stress is across an unyielding metal plate, the square piano will in fact bend ever so slightly under increased stress. If you must raise the pitch by as much as a whole semitone, the additional 10 to 12% tension will alter the case length slightly, and by the time you have finished, your first note is several cents below where you first set it. In the case of raising a pitch by more than about 25 to 40 cents, best to rough tune it first, then go back for a fine tune to get it right, after letting it sit for an hour or two between tunings.
Modern piano tuners hammer the notes hard during tuning, to cause the string to settle into place. There is no need at all for this in a square, and banging away is sure to shorten the life of something important. Medium forte is enough to hear the beats and set the tune.