Sesquialtera is a member of the family of proportions identified by Boethius as Genus Superparticularis.
Boethius list includes: Genus multiplex, all proportions which can be expressed as ratios (fractions) with 1 in the denominator: dupla (2/1), tripla (3/1) etc. Genus superparticularis, all proportions which can be expressed as ratios with the numerator being one larger than the denominator. Further genii of proportions included superpartiens (where the numerator is 2, 3 or larger number than the denominator), and superpartiens multiplex, where the previous genus is further affected by multiplications of constants. Needless to say, the terms numerator and denominator wouldn't have occurred to anyone back there, but I have used them because we know them now. Genus Superparticularis, where the first, upper number (numerator) is one larger than the second, lower (donominator) number, starts with 3/2, the simplest case that is not already part of another genus (2/1 is proportio dupla, which is genus multiplex.) This relation was referred to as sesquialtera for short, because "sesqui-" meant "half again as much", and "altera" means "of the other", i.e., 3 is half-again-as-much-as-2. Because of this, all the other genus superparticularis proportions came to be called "sesqui-"..., so we have 3:2 as sesquialtera, 4:3 as sesquitertia, 5:4 as sesquiquarta, and so on. Morley has a graph on page 38 (number 52 in sequence in the PDF facsimile on IMSLP.org at http://216.129.110.22/files/imglnks/usimg/6/6f/IMSLP03933-Morley.pdf which shows all the names of proportions using numbers from 1 to 100.) In each case of superparticularis, the proportion marks a change, after which the larger number of what Apel named Integer Valor, the duration which defines a mensuration, into the time of the smaller, previous value. So when proceeding in minims, sesquialtera causes three minims to be played in the time that two previously occupied. We would probably call this triplets, although it also can be thought of as hemiola or as a new tempo. Under normal circumstances, returning to the original durations uses the 'inverse' proportion: if 3/2 starts it, 2/3 'cancels' and returns to the original condition. Sesquialtera is used as the term for 2/3 as well as 3/2. In white mensural notation, coloration is often used to notate short instances of sesquialtera, and cancellation consists of returning to normal note coloring. And, oddly, "3" alone is used often to notate sesquialtera, even though it should be the indication of proportio tripla. The tactus does not change when the proportion does: if a change in the tactus was desired, a change in mensuration (time signature) would be appropriate. However, the determination of accent within the tactus may be open to interpretation: hence the reason that sesquialtera might be triplets or hemiola, ray brohinsky On Fri, Apr 8, 2011 at 12:40 PM, Bruno Correia <[email protected]> wrote: > Could anybody share any information about the execution of the > sesquialtera? I've been working on a recercare by Spinacino p.40, and > I'm still not sure if the execution is correct. > To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
