I have been working for many years on a checklist of surviving renaissance recorders. The idea is to try to document each instrument, giving as much information as possible about it, and then establishing a data base from which many different conclusions can be drawn. In getting familiar with a great number of original instruments, I slowly became aware that none of the recorder treatises of the sixteenth century, gives fingering charts that worked with the instruments we know. In particular the fingering for the fourteenth note, (a'' on a tenor) was always given as Ø12 - - - - - instead of the more usual Ø12 - - - 67 or variant. This suggested to me that perhaps some the instruments were more cylindrical than the surviving specimens I knew and that 'the renaissance recorder' was maybe not such a fixed design as I had previously thought. This question led to my making some very different small consorts based on the woodcut illustrations in the treatises of Virdung and Agricola.
My first point of departure was the Rafi/Grece instruments in Bologna. I had heard of these instruments while still at college and tried to make a few prototype instruments then. I had however, dismissed their long slender ramps and almost square windows as something rather too exotic, and used instead a more conventional shape. Now some years later, having seen this type of voicing in many paintings and woodcuts of the period, in addition to those of Virdung and Agricola, I decided to try to use some of the details of these instruments to make a new design. The first attempts were based heavily on the Bologna instruments. Their narrow, almost cylindrical bores gave excellent results in the high register, but I found the low notes far too soft to use as consort instruments. I then came across another highly unusual recorder in the Leipzig collection, which had a very similar internal shape to the Rafi/Grece instruments, but it's bore was huge in comparison to the length of the instrument. I tried a different ratio between these two parameters and found that by increasing the bore size, I got a better balance between the low and high registers and, depending on the shape of the foot, could get two octaves with Ganassi's fingerings.
My next concern was the question of pitch, I knew that any bass instrument had to be a fifth below the tenor, but I felt that using this construction, I wouldn't be able to make such a huge instrument. The fingerholes of the tenor were already enormous and I couldn't see how I could get over this  problem without using additional keys. In the end I resolved this problem by moving the pitch up a whole tone. The Rafi instruments were already much higher than a=466hz and instead of going down in pitch, I moved them up to the next convenient semitone. This solution gave me a bass instrument in modern g# , a tenor/alto in d#  and a discant in a#. Their nominal pitch then works out at three semitones higher than modern a=440hz, at an uncompromising a=520hz. I have seen several sets of original instruments, including the high HIER.S consort in Vienna at something approaching this pitch, and of course if you are playing consort music, the pitch is not really a problem, so long as all the recorders are tuned together. I have even seen original cases for recorders whose probable pitch judging from their lengths, must have been even higher than a=520hz.
I used the wood cut illustrations from Virdung to model the outside form of the instruments, and have used both a cap blown and a direct blown design for the bass. After some trials with Pythagorean tuning, I settled on a more meantone temperament, which seems to work better for most consort music.