Reply to Wim Hoogewerf

[Wim wrote:]
>John, it's not so strange if you know how the Werckmeister III is
>constructed. It's the result of an circular chain of 8 perfect fithts
>and 4 fifths which are each tempered by a quarter of a Pythagorean
>comma. The tempered fifths are C-G, G-D, D-A and B-F#. The deviations
>in cents may perhaps be calculated in a more precise way. Right now
>the pure fifth is considered to be 702 cents and the Puthagorean
>comma 24 cents.

Yes, I see better now the serviceability of Werckmeister III than when
I shot off that "strange" comment.

>Werckmeister III is not an attempt to obtain the ideal tuning for a
>singular piece, as you did marvellously well with Mozart's KV 606. (I
>listened to it many times!).

Glad you like it!

>As all Well-temperaments, Werckmeister III offers a solution to play
>reasonably in tune in all of the twelve keys, both minor and major. It
>becomes specially interesting when you listen to a set of pieces in
>many different keys, like Bach's two-part Inventions, the three-part
>Sinfonias or the Well-tempered clavier. Each key has it's own tuning
>characteristics. You can hear for example, without being absolute, if a
>piece is in D major or in Eb major.

>Intuitively I think you will find about as much 'pain' as in
>meantone-tuning.

I hear what you're saying, and it would be interesting to experience
some of the works you cite in Werckmeister III tuning. My guess
(without yet having heard it) is that I'd long for "better" tuning in
the keys for which this fixed tuning is not so well suited, but in this
respect my ears may be different from others'.

Do you happen to know of any MIDI sequences tuned in this fashion? I'm
sure listening to them would improve my education!

JdL