Werkemeister III

[Paul N. Bailey]

I think these would be the cents deviation for the Werk. III  in 
Owen Jorgensen's  little book The Equal Beating Temperaments:

Fred Tremper worked this out, a couple years back he offered to
send SASE the cents dev. for all the temperaments in that wonderful
little yellow chapbook. I highly recommend, if he will still honor
requests.

c       0
b       -6.3
a#      -3.9
a       -10.2
g#      -7.8
g       -2.6
f#      -11.7
f       -2
e       -8.2
Eb      -5.9
d       -6.7
c#      -9.8



I hope this comes thru in a readable form-
the left column is Fred's numbers, the middle column is "corrected" to make

A = 440 hz, and the right column is intended to make the overall least
deviation
from the 440 pitch level.




c       0       10.2    6.3
b       -6.3    3.9     -0
a#      -3.9    6.3     2.4
a       -10.2   0       -4
g#      -7.8    2.4     -2
g       -2.6    7.6     3.7
f#      -11.7   -1.5    -5
f       -2      8.2     4.3
e       -8.2    2       -2
Eb      -5.9    4.3     0.4
d       -6.7    3.5     -0
c#      -9.8    0.4     -4

I think the best thing is to go with the right column, as the cents 
deviation are overall smaller, and less of a problem for wind players.
But the middle column will give an orchestra the A 440 they at least
claim to tune at (oh, let's not start a big thread on this just now)
and should save a piano from sounding flat when it joins in after the
intro of a classical concerto.

I like tuning C= 0 and dropping the pitch of the piano a little, but 
of course I seldom do that, due to a practical respect for the 
contemporary pitch level. 

>Dale:

>Here are the offsets from an ET tuning for Werkmeister III.

>dave

>A 0.0
>A# 7.8
>B 3.9
>C 11.7
>C# 2.0
>D 3.9
>D# 5.9
>E 2.0
>F 9.8
>F# 0.0
>G 7.8
>G# 3.9

Isn't the above what appears in the SAT manual?

The Jorgensen-Tremper numbers represent an "equal beating" tempering 
scheme, while the SAT numbers represent a more modern tempering approach, 
where the tempered fifths are all the same size in cents. 

So, if you have enough opportunities, you could tune it both ways for
your artist, (don't tell him 'before' , or do tell him if you think you 
should) and see what he prefers. 

I have found in the majority  that my tuning clients prefer 'equal beating'
temperaments to 'theoretically correct' forms of the same temperaments.

Either way, you will be honoring the request.

                        Paul Bailey RPT
                        Modesto CA