Dear Mathias, Funny you should produce this chart. I did one of my own earlier today, much simpler, but with the same conclusion. I ignored the 7th to 11th courses, which present less of a problem, because they are usually played open. This was my chart for the first three courses of a baroque lute in D minor:
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | | | | | | | | | | | | f' | gb' | g | ab' | a' | bb' | b' | c'' | db'' | d'' | eb'' | d' | eb' | e | f' | f#' | g' | g#' | a' | bb' | b' | c'' | a | bb | b | c' | c#' | d' | d#' | e' | f' | f#' | g' | This would be repeated for the next three courses, with all notes an octave lower. It has to be said that a baroque lute with open strings of f', d', and a, is theoretically the same as the 2nd, 3rd, and 4th courses of a renaissance lute, but in practice there is a big difference. The critical factor which makes meantone tunings successful, is the consistency of the intervals between the courses. If all the intervals are the same, e.g. three 5ths on a mandoline, the unequal placing of frets for a meantone temperament (should one be crazy enough to want it on a mandoline), would have a consistent effect across the fingerboard. If the intervals between the courses are all different, frets spaced unequally will affect the pitch of the strings in a haphazard way. The 6-course renaissance lute has four 4ths, and one 3rd. That 3rd causes problems, but since all the other intervals are the same (i.e. 4ths), a meantone fretting is almost possible. Music from the first part of the 16th century tended to be modal, and in a limited range of keys, so the approximation to meantone you get with a renaissance lute, is tolerable, and in practice sweeter than equal temperament. Bad enharmonics are insufficient to upset the apple cart. The D minor tuning of the baroque lute has a mix of two minor 3rds, two 4ths, and one major 3rd. Other baroque tunings will also produce a variety of intervals. Unequal fretting with such tunings will produce a surfeit of bad enharmonics. Baroque music tends to explore a wider range of harmony, which would produce a greater number of bad enharmonics, should the instrument be fretted unequally. It is for these reasons - tuning and repertoire - which pushed players of fretted instruments in the direction of equal temperament. Vincenzo Galilei was one of the earliest to advocate equal temperament on the lute. Important theorists, in particular Mersenne and Praetorius, described the use of equal temperament on the lute. The general view in the 17th century, was that lutes and viols were unsatisfactory instruments, because they were fretted in equal temperament. Keyboard instruments were superior, because, with a separate string for each note, they could be tuned consistently in a meantone temperament. I conclude that the baroque lute was generally fretted in, or close to, equal temperament. I wonder if this is why the baroque lute tended to be used only for solo playing: the temperament of other instruments (and singers) would have been different. Archlutes and theorboes, on the other hand, were in the old vieil ton tuning, where a tolerable approximation to meantone was possible, and so they continued to be used for accompanying voices and other instruments well into the 18th century. Forty years ago, everyone fretted their lutes in equal temperament. When unequal temperaments became fashionable from the 1970s onwards, people started trying to impose unequal fretting on every instrument under the sun. Hopefully we will now re-assess the situation, taking into account what we know was done in the past, and what we find works best in practice, which usually works out the same. Best wishes, Stewart McCoy. -----Original Message----- From: "Mathias Rösel" [mailto:[EMAIL PROTECTED] Sent: 17 June 2008 20:44 To: Anthony Hind Cc: Peedu Timo; Rob MacKillop; [email protected] Net Subject: [LUTE] Re: New Baroque lute/Meantone Anthony, I must confess I should be entirely surprised, withdraw anything I said before and claim the opposite, if any of the several MT temperaments worked with the baroque lute in D minor tuning. The simple reason is that naturals lie on the same frets as sharps and flats, respectively. I put up two charts so as to show the problem, the first for sharps, assuming keys around A major (ton de la chevre); the second for the flat, assuming keys like C or F minor (that way justifying D flat). 1. Sharps (3rd, 5th, 6th, 9th frets don't work) 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | | | | | | | | | | | | f' | f#' | g | g#' | a' | a#' | b' | c'' | c#'' | d'' | d#'' | d' | d#' | e | e#' | f#' | g' | g#' | a' | a#' | b' | c'' | a | a# | b | c' | c#' | d' | d#' | e' | e#' | f#' | g' | f | f# | g | g# | a | a# | b | c' | c#' | d' | d#' | d | d# | e | e# | f# | g | g# | a | a# | b | c' | A | A# | B | c | c# | d | d# | e | e# | f# | g | 2. Flats (1st, 3rd, 5th, 6th, 8th frets don't work) 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | | | | | | | | | | | | f' | f#' | g | ab' | a' | bb' | b' | c'' | db'' | d'' | eb'' | d' | eb' | e | f' | f#' | g' | ab' | a' | bb' | b' | c'' | a | bb | b | c' | db' | d' | eb' | e' | f' | f#' | g' | f | f# | g | ab | a | bb | b | c' | db' | d' | eb' | d | eb | e | f | f# | g | ab | a | bb | b | c' | A | Bb | B | c | db | d | eb | e | f | f# | g | Mathias To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
