Henrius wrote:Thanks for the info. I will try the Lehman temperament, which I'd read snippets about before. He makes a good case for this being Bach's preferred temperament. But from what I have read, unlike harpsichords, organs of Bach's day were tuned in quarter-comma meantone and were not easily changed.
Right. I accept that the Lehmann temperament is an acceptable member of the class of Temperaments used on Harpsichords in Bach's day. Functionally, as good as any and makes more sense than many. For Organs, it allows playing in keys that would be very stressed in 1/4-comma Meantone. It functions as what they called a "circulating temperament", and could be called "Well-Tempered". Certainly no Organ (until the present era) was ever actually tuned exactly like this, but it is the sort of thing Organ Builders were looking for in going beyond the limitations of Meantone. Again, functionally as good as any and makes more sense than many.
Henrius wrote:I wish there were an explanation somewhere of the goals of all the temperaments. In other words, what does each really seek to accomplish? I assume some seek purer fifths at the expense of thirds, and some seek the opposite.
That's exactly right. The Medieval aesthetic called for pure fifths at any cost. In the Renaissance, there was a revolution in favour of pure thirds. Since then we have had a slow but steady progression back to pure fifths again. The Mean-Tone Tunings were gradually rendered less extreme (sacrificing the Thirds a little bit to partially restore the Fifths), going from 1/4 Comma to 1/5 to 1/6 and so forth. By the time they reached 1/12 Comma Meantone, that's the same as Equal Temperament! Thirds are compromised quite a bit (but sound good on a Grand Piano because the sharp Thirds help add brilliance to the tone, which otherwise cannot compare with a good Harpsichord.
On modern Grand Pianos, the Octave itself is stretched, to compensate for the inharmonicity of the Strings, which are very thick and heavy compared to the Harpsichord. This has the side benefit of correcting the (still-slightly-flat) Fifths to the point that they can be absolutely Pure!
For one of my Sampled Pianos, I tune Pure Fifths all the way from top to bottom (letting the Octaves stretch accordingly to fit) and it does sound delightful!
Henrius wrote:So the dividing line between early and late Baroque is when for you? Bach's clavecin music was written in more diverse keys than his organ music. Maybe this is the clue that Bach's music for harpsichord demanded more tempering than his organ music.
Exactly! The usual Mean-Tone today allows for C# but not Db, Eb but not D#, F# but not Gb, G# but not Ab, and Bb but not A#. In Bach's Day, a string or two would be re-tuned just before playing any piece that required a different accidental. Otherwise, maybe one bad accidental can be tolerated but probably not two. For music that uses more than that, ie Flats beyond Eb or Sharps beyond G#, some compromise of the Tuning is required... such as a modified Mean Tone, or the Lehmann Tuning.
Ideally, playable in all keys but all keys with a distinct flavour. This was still the Standard on PianoFortes in the day of both Mozart and Beethoven. Only slowly through the 19th Century did the idea of Equal Temperament take hold for the Piano. And other than the Piano, perhaps it never really did.