… and I don’t mean anything to do with the psychological state of the performer, or, in my case, the owner of a Stuart piano.
All tunings of any keyboard instrument are approximations. This is very well explained by the American composer Kyle Gann on his website (http://www.kylegann.com/histune.html). As an example, the size of a major third is 386.3 cents, a cent being one 1200th of an octave. Since three consecutive major thirds on a keyboard equal one octave (for example C->E, E->G#, Ab->C) it is clear we have a problem, since 3 x 386.3 = 1158.9, i.e. we are out by 41.1 cents. The whole problem with tunings where there are 12 semitones to an octave is how do we approximate the tunings to compensate for this discrepancy?
By and large there have been four historical steps in this process:
1) Pythagorean tuning, where (to quote from the above web site)
“Before the advent of meantone tuning, the French academy at Notre Dame (13th and 14th centuries) followed a medieval tradition since Boethius (4th century) in decreeing that only a series of perfect fifths could make up a scale; their ratio was 3/2, and 3, after all, was the perfect number, connoting the Trinity among other things. Thus the Pythagorean scale is a just-intonation scale on a series of perfect fifths, all the ratio numbers powers of either 3 or 2”. Pythagorean tuning thus focuses on perfect fifths. Thirds are somewhat dissonant, which helps to explain some of the compositional traits of the period.
2) During the 16th century, composers began to include major and minor thirds in their harmonies, thus introducing major and minor triads, amongst other things. Given that in Pythagorean tuning the major thirds are 400 cents (urk!) rather than 386.3, clearly some adjustments needed to be made. This gave rise to meantone tuning, where the thirds are more consonant but the fifths less so. The major disadvantage, however, was that some triads (Db, F#, Ab, and B) were horribly dissonant. This disconcerted a certain J.S.Bach, who (not alone, of course) wished to be able to play and compose in all keys.
3) This led to the concept of a well-tempered scale, where the dissonances, if you like, are spread out between the intervals more (but not totally) equally. Bach had his own tuning standard, but two of the major tunings were Werckmeister III (mainly used for harpsichords) and Young 1799 (mainly used for pianos).
4) Equal temperament, namely where all semitones are equally spaced over the octave, is really a 20th century standard, although it was known but not by all accounts accepted, during the 19th century. It can be argued that equal temperament removes the subtle characteristics of various keys which, to a sensitive ear, are clearly identifiable in a well-tempered tuning.
Before I acquired the Stuart, I had my little upright piano tuned to Young 1799. There was a noticeable difference in the sounds I produced from the piano. My colleague who tuned it for me was initially put off by the changes (he has a very good musical ear), but admitted to me later that after a while he had adjusted to the tuning and in fact had tuned his own piano in the same way. Whether it was better or not is a matter of individual taste since there are no right or wrongs here, but it was not difficult to understand why some keys are better than others for a particular style of music.
Wayne tunes my piano to equal temperament. He does this totally by ear, focusing on beats and tones rather than quantitatively measuring the frequency, and has a very precise method for so doing. The clarity of each note (even the very low and high ones) makes this job much easier than with a standard piano.
The question now arises as to how would the Stuart piano sound in a well-tempered tuning. It could be argued that whilst this may be more suitable for pre-20th century music, this may make modern music less viable on the piano, since most of that style of music relies much less on the 19th century concept of keys, but this has really yet to be tested in practice.
Using Wayne’s tuning specifications as a basis, I have developed a methodology for tuning a well-tempered (or any other temperament for that matter) piano, using a fully aural method, i.e. no quantitative frequency measurement, similar to way he tunes equal temperament.
The results should be interesting, to say the least.