[CAUT] Claudio Di Veroli & Equal Temperament

[Fred Sturm]

On Jan 30, 2009, at 12:20 PM, rwest1 at unl.edu wrote:

>  I've never tuned an unequal temperament without first investigating  
> what it's supposed to sound like aurally.  Going strictly by the  
> numbers does not guarantee that the numbers actually are correct or  
> that the technician has produced a correct temperament.  Only by  
> knowing, for example, that a particular third is supposed to be 3  
> beats, or no beats does a person know that the temperament is  
> properly rendered.  In other words, it may look like a duck and it  
> may walk like a duck, but it may not sound like a duck.

	Well, actually the historical tuner tuning the historical temperament  
didn't have access to Jorgensen's table of beat rates, and didn't tune  
in accordance with beat rates. And Jorgensen based his beat rates on  
the same information used to generate the cents offsets, a calculation  
based on an interpretation of the historical data. Knowing and  
matching the beat rates he calculated is no more authentic than using  
the cents offsets.
	If you really want to do an aural emulation, you need to go back to  
the source. Sometimes the source is a theoretician, in which case the  
information usually has to do with proportions of commas and where  
they are distributed. So the calculated tuning is probably the best  
emulation you can come up with, as there often isn't a practical  
method for achieving the result (no series of steps and proofs for the  
aural tuner. Instead, one was to match pitch with a monochord).
	If the source is one based on practical tuning instructions, the  
cents and beats given by Jorgensen are his own interpretation of what  
is usually a very nebulous set of instructions. Take Prelleur, for  
example. Read literally, he is giving instructions for ET, though  
there aren't adequate tests/proofs to do a creditable job of it.  
Jorgensen comes up with a set of cents offsets and beats based on some  
historical interpretation and his own notions.
	All this said, in my experience a cents offset tables work just fine  
to produce as good a replication as we can of the historical tuning,  
based on the available evidence.
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu