From an historical point of view, I can't say that the tactus does not change, but if you have a citation for that I would be interested.
Respectfully, dt At 04:37 PM 4/9/2011, you wrote: >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
