P12's discussion

[Bernhard Stopper]

There is probably some misunderstanding of the P12 in your post.
What you say about beat rates of 3rds 5ths and 4ths is correct, they serve
us aural tuners as anchor points for spacing the temperament octave (and
more).
A P12 is a octave + fifth and is pure, when the 3rd harmonic of then lower
key has the same frequency of the base frequency of the upper key.
You can check this aurally by checking a M6th below the lower key and a
Double octave + M3rd with the same beat rate.
Spacing this P12 interval evenly, will result in stretched octaves of about
1,2 cent + inharmonicity stretch.

regards,

Bernhard Stopper

----- Original Message ----- 
From: "Joseph Garrett" <joegarrett@earthlink.net>
To: <pianotech@ptg.org>
Sent: Wednesday, June 02, 2004 9:49 PM
Subject: Re: P12's discussion


> I've been following all of the discussion on the use of Perfect 12ths. I'm
a
> bit confused and hope some of you high-end tuner types can enlighten me.
The
> way I perceive it, is that we set the thirds, in the temperament to
certain
> "beat rates". This gives us a "Tempered Octave" that is the foundation for
> the rest of the piano. The example that I tried, for a perfect 12th, was
E5.
> The test note, I used, was C4. The C4 and E4 beat at a certain rate. If I
> tune E5 to yield no beats when testing it against the C4, then the octave
of
> E4 and E5 will be off, (ie E5 will be flat of where I think it should be.)
> Am I going about this wrong? My impression of P12ths is that the octaves
> will be narrowed, thus making the "stretch" flat and beating on the narrow
> side. Please elucidate.
> Best Regards,
> Joe Garrett, RPT, (Oregon)
> Captain, Tool Police
> Squares Are I
>
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