Werckmeister temperament

Greetings to all,

I use the Werckmeister temperament often, but I have the most
consistent results with Jorgensen's equal-beating method. It can be found
in his 1976 "Tuning the Historical Temperaments by Ear." It is not one of
the temperaments discussed in his 1991 "Tuning," because he used only
English language sources for the later book.

First tune a line of just fifths and fourths from C4 (middle C) to F3,
F3 to Bb3, Bb3 to Eb4, Eb4 to Ab3, Ab3 to Db4, Db4 to Gb4.

Temper the third Bb3-D4 so that it is wide and beats at the same rate as
the third D4-F#4(Gb). Then temper G3 so that it beats equally with both
C4 and D4 (narrow fifth, wide fourth).

Temper A3 so that the third F3-A3 beats equally with the fourth A3-D4
(both intervals are wide). Finally, tune the just fifth A3-E4, and the
just fourth E4-B3.

The differences, in cents, between the Theoretically Correct and
Equal-Beating versions:

Note T. C. E. B.

C 1200.000 1200.000
> B 1092.179 1093.772
Bb 996.091 996.091
> A 888.269 889.812
G# 792.180 792.180
> G 696.089 697.413
F# 588.269 588.269
F 498.045 498.045
> E 390.224 391.767
Eb 294.135 294.135
> D 192.179 193.293
C# 90.225 90.225
C 0.0 0.0

The E.B. version has one more proportionally beating triad than the T.C.
version.
Laurence W. Key

(flute001@peabody.jhu.edu)

1 East Mount Vernon Place
Baltimore, Maryland 21202
Phone: (410) 659-4009


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