Towards Pure(er) 5ths in ET

[Richard Moody]

----- Original Message -----
From: Jim Coleman, Sr. <pianotoo@imap2.asu.edu>
To: pianolover 88 <pianolover88@hotmail.com>
Cc: <pianotech@ptg.org>
Sent: Monday, April 09, 2001 3:45 PM
Subject: measuring FAC on SAT


| For example, I measured the A4 stretch number of an Acrosonic spinet
to be
| 8.2. Then I tuned the note 1/2 step flat, reset the A4 to that pitch
for
| its A5 reading, then measured the stretch number at A6. It became
9.1.
| That is quite a difference and will give a different tuning. As a
matter
| of fact it will be very close to a pure 5ths Equal Temperament.
|
| Jim Coleman, Sr.
|

Jim, List
    I have been intrigued with the "pure 5ths ET" ever since Jim
proposed it back in 96 (on this list at least), experimenting with it
both in spread sheet calculations and actual tuning.  Then three years
ago I  got to spend a couple of  afternoons with Jim in Phoenix and on
one of those I was chigrinned to have my temperament evalulated as
having 4ths too wide.
This was pointed out as in the old days of learning..."these beats are
a little fast.....". and all of a sudden I heard them.
    However the 5ths to me sounded within the parameters I had always
been trained, I realized if Jim said my 4ths were too wide, that meant
my 5ths were too narrow.
    I had never been trained to use fourths during the tuning
procedure but after visiting Jim, I thought if they are used for
checks perhaps I might try using them to actually tune. I  tried few
pitch raises tuning by 4ths and found it faster and more accurate than
using 5ths.  If they  (4ths) beat they ain't right.  The trick is to
get them on the sharp side without beats.  At any time during this
"4ths tuning" is is permissible to do a quick check of the 3rds.
    The other aspect of making  4ths less wide means the 5ths will be
closer to pure.  To make a long story short,  I seem to get purer 5ths
(by paying extra attention to getting pure 4ths then nudging slightly
sharp) with no noticible change in the variation of 3rds and 10ths.
And I do like this sound.  I don't know if this is due to the
realities of inharmonicity  or higher tension scales of modern
os.     ---ric