Basically, everything that has been written about pitch for the performance of early music needs to be reconsidered in light of what we know about the performers and their instruments. Although a great deal of interesting work has been done, it is done using a fixed pitch system. We know, however, that for most of the middle ages, renaissance and baroque, musicians used a movable hexachord system. In a strange way, this is like mistaking fixed Do for movable Do, or forgetting to transpose the trumpet, horn & clarinet parts in a concert of orchestral music.

Basically, a ny staement, article or book that staes anything in the following form

a=xHz

where "a" is the note a, and x is the frequency of the note in Hertz (the speed of the vibrations)

Must Be Wrong.

So a=415 Hz, a=465Hz, a=392Hz, a+whatever are not really descriptive of performance practice.

In geberal, the people of the renaissance left very clear and vivid information on how to tune and play their instruments.

The classic example is the instruction on how to tune the lute.

Take the lute, and tune up the top string until just before it breaks.

It doesn't say what the note of the top string is; that note could (and would) be F, G, A or any other note.

Or, as John Ward brilliantly points out in his article on lute modes, these pitch frames may be relative constructs.

The directions do not dictate the size of the lute and the length of the string to 60.5cm or any other silly number. That's because the lutes came came in different sizes, like shoes. And, like shoes, there were variations in size even among similar patterns.

We live mostly in a single pitch world (unless you play a transposing instrument); they lived in a multipitch world. Unless we look at it their way, and not our way, we will keep messing up the pitch.

Aha, you say, but on the piano a is a and b is b!

But they did not look at it that way.

The famous Bermudo diagram of a keyboard instrument (not a piano, sorry) labels the note we call "C" an "F." And so it goes.

The moral of the story: Don't mistake cat for piggy.

Another way to look at it: read Flatland. Fie, Fie! How frantickly I square my talk!