Re: [tuning] Re: Werckmeister on the move

In a message dated 2/22/02 6:06:46 PM Eastern Standard Time,
paul@stretch-music.com writes:

> *literally*. they do have a few very slightly *sharpened* fifths but
> this was common for example in french temperament ordinaire. please
>

If there is no evidence for sharpened fifths in Germany, it wouldn't matter
that it happened in France. It is possible, and maybe even likely, that
Werckmeister IV-VI are real Werckmeister inventions. The lack of enthusiasm
for these 3, even by the author, may reflect that people felt Werckmeister
might have left well enough alone with his explanations and demonstrations of
I-III.

First question: do IV-VI consist of 39 intervals as well? (Manual, don't
laugh!)

Best, Johnny

--- In tuning@y..., Afmmjr@a... wrote:

> First question: do IV-VI consist of 39 intervals as well?
(Manual, don't
> laugh!)

werck iv has 47 different intervals, with a minimum difference of 8
cents.

werck v has 42 different intervals, with a minimum difference of 6
cents.

werck vi has 69 different intervals, with a minimum difference of 3+
cents.

manuel, is this correct?

Paul wrote:
>werck iv has 47 different intervals, with a minimum difference of 8
>cents.

Yes, including the octave.

>werck v has 42 different intervals, with a minimum difference of 6
>cents.

Idem.

>werck vi has 69 different intervals, with a minimum difference of 3+
>cents.

No, it's a rational scale with 106 (or 107 with octave) intervals
with minimum difference of 0.1 cent.

Manuel

Paul and all,

There is nothing further in the book about the variants of iv, v, and vi.
They are contained in the monochord illustrations that come with the book,
however. Werckmeister's mention that no. iv (based on 1/3 comma) is in his
book Orgel-Probe is only for its first edition. In the second edition, which
is the one that received wide distribution, all issues on tuning are referred
to "Musical Temperament" and this is the case for every single book to
follow. It is even included in the posthumous publication of his "Musical
Paradox."

What is increasingly amazing to me now is that Johann Cristoph Bach (the
uncle living kitty-corner to J.S. in Eisenach) never criticized Werckmeister
(though others surely did). They were clearly on the same page.

Best, Johnny Reinhard