Perfect fifths temperament (was Perfect Tuning)

[Michel Lachance]

Frans Sedee wrote:
>

> We have a collegue in France (if he still lives) that published a book, that I
> unfortunately lost and I can't remember his name right now) in which he
> advocates pianotuning in pure fifths. He gives a method too.
> Of course this can be done perfectly, and the result is still "well-tempered".
> I tried it but didn't get halfway, because it was to out-of-tune for what
> I'm used to.  About half of the book was filled with letters of
> recommandation written by professional musicians. I do remember that
> espacially violinists were enthousiastic when accompanied by a piano he
> tuned.

I have a book written by Lucas Mason called "The Perfect Tuning" where
he describes a method how to lay out a perfect fifths tuning.  The
principal is simple: the extra wideness provided by the perfect fifths
is assimilated into the normal stretching we would give to a piano.
This gives quite elongated octaves in the medium register but not so
wavy.

I tried the tuning by-the-book in translating all the frequencies
figures in cents resolutions and stored it in my SAT.  I then tried it
on my Yamaha M-1 and was not very excited about it.  Yes, it gives
quite sounding fifths but the harshnes of the major thirds spoils the
soup.

But there is a hidden flaw in that system when you try to tune each
fundamental to its theoratical value.  It doesn't take into account
the inharmonicity.  Perfect fifths are stretched fifths which means
over stretched octaves and major thirds that almost beat like minor
thirds.  I think there is no way out for this interesting but
unapplicable system.

Michel Lachance, RPT