Re[2]: Temperaments: request for references

John Sankey wrote:

>"Bach's keyboard temperament - Internal evidence from the
>Well-Tempered Clavier", John Barnes, Early Music 7:236-49 (1979)
>shows that the distribution of intervals even in the 48 is
>nowhere near ET - it matches Werckmeister III better than any
>other historical temperament.

This statement looks interesting, but ?

If I had ready access to a music library I would look up the reference, but
since I don't. I'll ask you: Could you please clarify. How does one compare a
"distribution of intervals" to a particular temperament? If, for example, they
were all major thirds, then I could guess that maybe a good "match" means that
the most common one has the fewest beats. But in a whole piece or collection of
pieces it gets pretty fuzzy. How do you enumerate the intervals? E.g., does a
triad count as two or three intervals? And which size intervals do you include?
And how do you compare the goodness of the "match" for one width of interval
relative to another? I am not being facetious here. It would seem that the
conclusion reached in this sort of analysis could be quite sensitive to the
ground rules.

--Don Simons (dsimons@logicon.com)

On Thu, 21 Sep 1995, j.s. mangsen wrote:

> In the Early Music article from 1979, John Barnes develops a method
> of counting the number of major thirds...
> [snip]
>
> I can't see anything wrong with trying to make such a count, and to
> correlate it with the character of the thirds in various temperaments.

Rasch addresses this in his paper, which I recommend reading. He finds
quite a few things wrong with it, but I won't attempt to paraphrase
him here.

I think the main thing is that he has cast enough doubt on the issue
that you can, with a clear conscience, please yourself. You prefer
equal temperament? No problem. You like Werckmeister III? Go for it.

--
Tom Parsons | To me, being an intellectual doesn't mean knowing
D.T.L. | about intellectual issues; it means taking
| pleasure in them. --Jacob Bronowski

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