Dear Rainer, Thanks for your interesting observation about Mersenne.
I had always assumed that the music on folio 1v of the ML lute book was associated with change-ringing. Bob Spencer cautiously suggests this as a possibility on page xxi of the facsimile: "Forty-six permutations of the scale of C major in bass clef, suggesting changes for bell ringers, or sight-singing exercises." The seventeenth century was when change-ringing evolved in England, so the connection with Folio 1v is not implausible. The first bar consists of a downward scale of 8 notes in C major. It is normal for bell-ringers to begin with a series of these downward scales, called rounds, before branching off onto some method or other. I think it is significant that the notes alter, from one bar to the next, with adjacent notes changing places, just as they do in bell-ringing. For example, after that first bar of CBAGFEDC, there comes CBAFGEDC. In other words, F and G (in 4th and 5th places) have swapped places. In the next bar we have CBAFEGDC, so G and E (in 5th and 6th places) have swapped places. This is what happens in change ringing. As far as I know, the changes on folio 1v do not make up a recognised method, but I could try to find out more. Wild speculation: one of the scribes of the ML Lute Book was into bell ringing. Further speculation: she was called Margaret. :-) All the best, Stewart. -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Rainer Sent: 08 August 2011 18:52 To: Lute net Subject: [LUTE] Mersenne / ML Dear lute netters, as some of you may know Robert Spencer (editor of the facsimile edition of the ML lute book) was puzzled by the f 1v which contains a list of 46 permutations of 8 notes and by the list of factorials on 56r. Yesterday I noticed that Mersenne's HARMONICORVM LIBER PRIMVS published in 1636 (I am afraid I even don't know if this is a Latin version of his famous Harmonie Universelle) contains: * A complete list of all 24 permutations of 4 notes. * A list of factorials from 1 to 64. Note: 64! has 90 digits and this is probably the largest factorial calculated without computers. By the way, a complete list of all permutations of 8 notes would require to write down 8! = 40320 permutations, which is beyond discussion. Anyway, obviously the scribe computed 8! on f. 56r which probably is not a coincidence. Wild speculation: One of the scribes knew Mersenne's book. Rainer adS To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
