Jim, baroque music for flute was played on a variety of one-key conical flutes. In the late 17th century and into the 18th, they were very low pitch (around A392 or so) three piece flutes. In the new century, they went up in pitch a bit (maxing at 415 or so, later made an arbitrary baroque standard pitch by modern players), and around 1720 broke into the 4 piece one key. So Bach and Handel would have been played on a 3 or 4 piece flute (mostly the latter), in pitches roughly 392 to 415, Mozart, later in the century, a 4 piece one-key at around 430.
All these flutes were/are chromatic with cross fingering (and the use of the one-key for venting and the D#/Eb itself.), but in just intonation, whereby tuning was relative to itself (it became “equal” later by squashing fifths and thirds, etc., into equal segments that work out mathmatically, if not sonically, most accomplished on the piano, the modern tuning standard – everyone must tune to a piano). As I mentioned on another thread, sharps and flats were once considered separate entities, not the same tones with different names, whereby Bb was sharper than A#, Ab sharper than G#, etc. The only note this wasn’t true on was the Eb/D# keyed note, and a player back then needed to lip up and down to differentiate the two. Quantz went as far as adding an extra key for D#, as opposed to an Eb, but it never caught on.
In answer to your question, why keys, the short answer; tastes had changed. Keys made “weak” notes stronger, and by the time they came about, the differentiation between sharps and flats had left the music, and tuning was now ruled by the piano – equal temperament was king. Keys eliminated the variety of colors the weak notes produced within the music – now considered a bad thing – and they eliminated alternate fingerings that shaded just tuning. As tastes changed, flutes were made with less and less tone colors, boasted a uniformity of tone throughout the flute range, rather than boasting a non-uniformity.
Modern ears are often bothered by these shadings, where once though they once were not only assumed, but desired and appreciated.
Generally speaking, these flutes sound best in the lower pitches, more mellow, sonorous – modern pitch baroques usually sounds a bit weak and thin in comparison, and a bit too “quick” in response. They are very flexible and fun instruments to play, come in a variety of styles and models some of which, I think, handle either a wider or a more limited range of music (some of the earliest, lowest pitch instruments, for eg, really can’t play Bach, and certainly not Mozart, very well). To play, they all take a bit of getting used to after a big-embouchured, big holed 19th century conical, but ultimately are great, rewarding instruments to play, either seriously or just for fun.
Finally, in perspective, keep in mind that the baroque one key, in its overall form, survived happily from between the mid-to-late 17th century through the early 19th, and they could be found in a watered-down version even in the early 20th. The 19th century classical wooden flutes most of us covet, on the other hand, came and went in a much shorter time span, replacing the baroque slowly, a key at a time and then with a variety of wildly different specimens, only to be overthrown by the Boehm system in the late part of the same century. In short, the baroque one-key is one of the longest lived “modern” flutes in western music – almost anything can be played on one.
Gordon