Huh?? was RE: pRCT got ears again...

[John M. Formsma]

According to Owen Jorgensen's book on Tuning, a 4:2 octave will yield
contiguous 4ths and 5ths that beat the same. E.g., a just 4:2 A3-A4 octave
will yield an A3-D4 that beats the same as D4-A4. This is why we often tune
octaves in that area slightly larger than a 4:2. It makes the 5ths beat
slower, makes the octave-5th less narrow, and generally balances out the
piano better, IMO. 

Obviously, you should make the octave only as large as will suit the piano,
so great care is needed in listening to determine optimum tempering of the
piano. It also depends on what you value more in your tuning. If you like
pure double octaves, you'd begin with a 4:2 octave for A3-A4. But if you
like a purer octave-5th, you'd use a slightly larger octave, which causes
double octaves to beat very slightly, but lessens the beating of the
octave-5th. I like to make the double octaves beat the same as the
octave-5ths, so I begin with an A3-A4 octave that is between a 4:2 and a
6:3. The double octaves and octave-5ths (12ths and 15ths) usually don't beat
more than 1/2 bps, unless it's a poorly-scaled piano. 

John Formsma

-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of Alan Barnard
Sent: Wednesday, May 03, 2006 10:24 PM
To: Pianotech List
Subject: RE: Huh?? was RE: pRCT got ears again...

I took it to mean that the 4ths and 5ths are both slower than 4ths and 5ths
in another temperament. He also said the octaves were "pure" which I take
to mean a pure 4:2 in the center, which would force a slightly narrower 4th
in some pianos if you didn't move the 5th. But I'm a little confused, too.

Could you post the temp sequence and what the suggested widths or beat
rates for each interval are, please?

Alan Barnard
Salem, Missouri


> [Original Message]
> From: John M. Formsma <john at formsmapiano.com>
> To: <ilvey at sbcglobal.net>; Pianotech List <pianotech at ptg.org>
> Date: 05/03/2006 9:55:19 PM
> Subject: Huh?? was RE: pRCT got ears again...
>
> -----Original Message-----
> From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On
Behalf
> Of David Ilvedson
> Sent: Wednesday, May 03, 2006 6:37 PM
> To: tune4u at earthlink.net; pianotech at ptg.org
> Subject: RE: pRCT got ears again! was S.O.S. my pRCT has gone deaf!!!
>
> <<...4ths & 5ths were a bit slower beating than standard equal temperment
> (what ever that is).   Strictly pure octaves, F3-A3 was about 6 to 6.5
beats
> per second...leaning towards 6.   They used an A440 fork to tune A3
> (temperment starting point)  F3 -A3 = F3 - Fork>>
>
> How do you get 4ths and 5ths to both be slower? In equal temperament, a
> slower 5th means a faster 4th.
>
> John Formsma