What's the tuning and temperament for Estampie, Estampie Retrove and 4 Pieces from Lochamer Liederbuch for which I prepared practice scores recently?
Music of the Middle ages (Estampie) might have been performed on the Pythagorian temperament while pieces from the Renaissance - on some kind of Meantone temperament (most common - Quarter-Comma Meantone).
The Pythagorian temperament is very easy to set up - tune 11 fifths pure (Eb-Bb-F-C-G-D-A-E-B-F#-C#-G#). Each of those fifths will be 702 cents wide. Almost as in Equal temperament (700 cents). By the way, 100 cents is a semitone in Equal temperament (such as C-C#).
By pure perfect fifth I mean without any beats or vibrations.
The result will be that an interval G#-Eb, although enharmonically would look like a perfect fifth (G#-D# or Ab-Eb) but in reality it's a diminished 6th - an ugly sounding "Woolf" interval.
Also all the remaining fifths will sound beautiful but the thirds will be too wide (408 cents).
The temperament for the Lochamer Liederbuch is another story. The Quarter-Comma Meantone temperament is a tuning system of 8 pure without vibrations major thirds.
A pure major third will have a calming effect. It will be narrower (about 386 cents) than in our modern Equal temperament we have on the piano most of the time (400 cents).
Here are those pure major thirds: C-E, D-F#, Eb-G, E-G#, F-A, G-B, A-C#, and Bb-D.
How do we know this?
In Estampie, we can hear a lot of fifths while in the Lochamer Liederbuch - major thirds are more prevalent.
If you want to play those pieces, check out my practice scores of Estampie, Estampie Retrove and 4 Pieces from Lochamer Liederbuch with fingering and registration suggestions. (50 % discount is valid until January 11).
[Thanks to Andrew fot this excellent question]