Re : [tuning] Re: More sweet Mozart

> [John Thaden:]
>>Interesting. If you decide to include like calculations for other
>>12-note fixed tunings, would you please consider Werckmeister III?
(John deLaubenfels:)>
>
> I'll add it to my list of things to do :-) Right now, I generate the
> fixed tunings I use from either COFT or n-tET, but I could add others
> or even allow them to be read in from external files. Lessee: going
> back to a post by Wim Hoogewerf from May 4, Werckmeister III apparently
> has the following deviation from 12-tET, in cents:
>
> C 0
> C# -10
> D -8
> D# -6
> E -10
> F -2
> F# -12
> G -4
> G# -8
> A -12
> Bb -4
> B -8
>
> If this is wrong, would somebody please correct me? Boy, that seems
> like a STRANGE set of numbers! I'm now curious to see how much "pain"
> it causes... Any recommendations for particular pieces to throw at it?

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.

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!) 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.

--Wim Hoogewerf