Quasi ET

[Bobby R. Sims]

This is a multi-part message in MIME format.

---------------------- multipart/alternative attachment
"If you have not read my essay on Tempered Octaves, please request it, I =
will send it in a separate post."=20


Hello, I'm fairly new to the list and would like to see the above =
mentioned essay if you don't mind submitting it again.

Thank you,

Bobby Sims
----- Original Message -----=20
  From: Paul=20
  To: pianotech@ptg.org=20
  Sent: Friday, October 19, 2001 8:44 AM
  Subject: Fw: Quasi ET



  ----- Original Message -----=20
  From: Billbrpt@aol.com=20
  To: tunenbww@clear.lakes.com=20
  Sent: Saturday, October 13, 2001 10:27 AM
  Subject: Re: Quasi ET


  In a message dated 10/13/01 9:04:55 AM Central Daylight Time, =
tunenbww@clear.lakes.com writes:=20



    Bill=20
    Sometime ago you responded to the list with a temperament as I =
recall you stating being used by Horace Greeley and others as an =
alternative to ET. I should have brought the description with me, but =
anyway, I've been trying it and it does have a nice openness to the =
sound. My difficulty is setting the F3 to a good Major 3rd below the A3. =
I haven't figured out a reliable method. I was wondering if you have a =
technique I could try.=20

    Thanks for your time and considerations.=20

    Paul Chick


  The 3 contiguous 3rds, F3-A3, A3-C#4 and Db4(C#4)-F4 are *exactly* the =
same as in regular ET.  Therefore, set your F3-A3 *exactly the same* as =
you would when tuning ET, whatever your technique may be is.  Aurally, =
you would estimate 7 beats per second, then tune the F3-F4 octave and =
fill in C#4.  Adjust all intervals until you get the proper 4:5 ratio of =
contiguous 3rds and a good sounding stretched octave.=20

  The F3-F4 octave is usually best as a compromise between a 4:2 and 6:3 =
octave. To get that, use the test for 4:2 which is Db3(C#3)-F3 then =
Db3(C#3)-F4.  If they are exactly the same, you have 4:2 octave.  If the =
upper interval is *slightly* faster, the octave is stretched more than a =
4:2.  Now test for 6:3.  Play F3-Ab3(G#3) and Ab3(G#3)-F4.  If both are =
exactly the same, you have a 6:3 octave.  If the upper interval is =
*slightly* slower, you have the octave stretched less than 6:3.  Try to =
find the spot where the 4:2 tests a little wide and the 6:3 a little =
narrow.=20

  This is a very fine distinction.  Electronically, it would probably be =
less than 2 cents.  A piano with low inharmonicity (such as most Kawai, =
M&H, Baldwin Concert Grands) would reveal practically no distinction =
between the two.  A piano with high inharmonicity (such as a Steinway) =
would provide an easily audible distinction.  Yamahas are usually in the =
middle.=20

  If you use and electronic program such as the FAC, simply tune the =
notes F3-A3-C#4-F4 according to the program and use the above aural =
tests to make any adjustment if necessary.=20

  After tuning F3-A3-C#4-F4, simply tune a pure 4th and 5th from each of =
these notes.  Use the test for a pure 4th or 5th to prove.  I use the =
SAT in the Direct Interval mode to prove.  With practice and good =
understanding, it is quickly and easily done.  After that, place the =
note G3 so that it beats exactly the same between C4 and D4.  Place the =
note B3 so that it beats exactly the same between F#3 and E4.  Finally, =
place the note Eb4(D#4) so that it beats exactly the same between =
Ab3(G#3) and Bb3(A#3).=20

  This will produce 3rds and 6ths which will sound identical to those in =
ET.  Most of the 4ths and 5ths will sound really good because they are =
pure.  You will have just a few "wobbly" ones.  (Now ask yourself, who's =
aural attempt at ET doesn't?).  In my opinion based on many years of =
observation, very few aural attempts at ET are clinically perfect.  They =
are almost always a *Quasi* ET.  (Quasi means "almost").=20

  I strongly suggest you use my Tempered Octaves method for tuning the =
octaves. This will give your piano a "crystal clear" sound and will make =
the "wobbly" 4ths and 5ths in the temperament octave range become =
inaudible in the outer octaves.  If you have not read my essay on =
Tempered Octaves, please request it, I will send it in a separate post.=20

  If you feel this answer to you would be useful to the List in general, =
please feel free to forward it.  There are always new subscribers who =
have not read of this idea before.  By the way, it is properly known as =
the "Marpurg-Neidhardt Composite Quasi Equal Temperament".  It is close =
enough to regular ET to fall within the tolerances of the PTG Tuning =
Exam.  In my opinion, it could be freely substituted for ET under any =
tuning circumstances, including high level concert tuning without the =
technicians feeling an ethical need to disclose any techniques =
whatsoever.=20

  Please let me know of your experience using it.=20

  Bill Bremmer RPT=20
  Madison, Wisconsin=20

---------------------- multipart/alternative attachment
An HTML attachment was scrubbed...
URL: https://www.moypiano.com/ptg/pianotech.php/attachments/28/ac/e4/3e/attachment.htm

---------------------- multipart/alternative attachment--