Learning Aural Tuning

[David Love]

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You don't really need to decide on a beat rate for the F3-A3 third.  =
Tune A4 and then tune A3 and A2 to get octaves and double octave that =
you want.  How wide you can set these octaves will vary from piano to =
piano.  As Bill says, aim for a compromise between a 4:2 and 6:3 octave =
checking the double octave to be sure that it isn't so wide as to be =
objectionable.  This is a bit of an artistic judgment call and the width =
of these octaves will vary from piano to piano.  In general they will be =
narrower on a smaller piano and wider on a larger piano.  On some =
spinets you may need to set the octaves a pure 4:2 or even narrower.  =
Then set a sequence of contiguous thirds from A2 to A4 so that their =
beat rates have a relationship of 4:5.  The narrower you set up your =
initial double octave spread, the slower the F3-A3 third will beat.  Let =
the piano rather than a preconceived notion about what the F3-A3 third =
should sound like guide you.  Once you have laid in the sequence of =
thirds it is relatively easy to fill in the rest.

David Love =20
  ----- Original Message -----=20
  From: SidewaysWell1713@aol.com=20
  To: pianotech@ptg.org=20
  Sent: September 22, 2002 9:45 PM
  Subject: Re: Learning Aural Tuning


  In a message dated 9/22/02 7:14:41 PM Central Daylight Time, =
mathstar@salemnet.com writes:=20



    HERE THE QUESTION (Looks like several questions, but really asking =
the same thing each time ...)=20

    How do you really know that your A-A is ideal? That it isn't a =
smidge two narrow or wide for the inharmonicity of that particular =
instrument? That you have even started the temperament "correctly" for =
that piano? How do you KNOW that your F33-A37 is ideal for that =
particular instrument?=20

    This talk about Franz Mohr, etc., highlights the point: A lot of you =
folks can--in your sleep--set a really sweet temperament on any decent =
piano you face, Yet the starting intervals seem arbitrarily set, to me! =
"About 7 bps ..."=20

    So what the heck does "about" mean?  Do you have to set the whole T. =
before you "know"?=20

    (Is this making sense?) I'm not talking about getting just a useful =
temperament, as I believe the "about" thing will do that every time. I =
am talking about getting a really good temperament for each piano.=20

    'Preciate some comments.=20

    Alan Barnard=20
    Listening in Salem=20




  I'd be glad to answer your question because I do know the answer.  But =
I usually get some smart remark from some creep when I do.  I hope I =
don't because if I don't, you won't see words this list does not want me =
to write.=20

  The initial A3-A4 octave is best set as a compromise between a 4:2 and =
6:3 octave.=20
  This has been determined by the PTG Exam Committees and Dr. Sanderson. =
 What you try to establish is an octave in which neither test is exactly =
right.  On pianos with low Inharmonicity, there might not be much =
audible difference and so, if both tests seem to produce Equal Beating, =
then the octave is good.=20

  On high Inharmonicity pianos such as the Steinway, a clearly audible =
distinction can be heard between the two tests.  Tune A3 from A4 so that =
the results are slightly too fast for the 4:2 octave but slightly too =
slow for the 6:3 octave but placing the discrepancy right in the middle. =
 The kind of distinction I am talking about is very small but at the =
highest level of aural tuning.=20

  As for the initial F3-A3  3rd, yes, you must first *estimate* its =
speed and it will vary from piano to piano.  If your initial A3-A4 =
octave indicates low Inharmonicity, then you would estimate a little =
slower than if the indication was high Inharmonicity.  A good way to =
make this estimate is to have a pocket sized electronic metronome =
(Schaff sells them).  Set it at 120.  At 6 beats per second, you will =
hear 3 beats per tick.  Find that point, then flatten F3 ever so =
slightly to hear the beat rate increase.  Listen now to hear 7 beats =
against 2 ticks.  This is still just in the estimate stage.  There is =
also a device made by Dr. Sanderson which plays the basic beat rates for =
the contiguous 3rds, F3-A3-C#4-F4.=20

  Now, construct an octave from F3 to F4 and use the same 4:2 and 6:3 =
octave tests you did for the initial A3-A4 octave.  Now, fill in the C#4 =
from A3.  Your F3-A3 third was 7 beats per second, your A3-C#4 will be =
just a little faster.  This is that hotly disputed 4:5 ratio of =
contiguous 3rds.  Forget about whether that is exactly the ratio or not. =
 What you are looking for is just a slight increase in beat speed which =
will work with all the other intervals created thus far.=20

  If, at this point, you cannot get this slightly faster relationship of =
contiguous 3rds, F3-A3-C#4-F4-A4, then your initial F3-A3 3rd needs =
adjustment.  The irony of finding this essential preliminary grid is =
that it is much easier to identify when the relationship is not correct =
than to really be sure of when it is.  So, really, it will always end up =
being that it could possibly have been more perfect but having it seem =
to work out will yield results which will be within the PTG's Exam =
tolerance of plus or minus 1 cent.=20

  Good aural tuning requires making good estimates.  Once you have the =
F3-A4 contiguous 3rds the best you can get them balanced, you can make =
small errors on everything else and not create unintended effects.  It =
is the good old 4ths & 5ths through the cycle of 5ths temperament =
sequence which is prone to undesirable effects as the result of =
cumulative errors.=20

  No one can count beats which are irrational numbers (such as 7.2, 9.4, =
12.7).  All you can do is compare one pulse with another and try to =
establish the proper relationship.  Nothing is exactly on in ET.  You =
cannot have entirely pure 5ths but the amount of tempering can be =
manipulated if desired.  Each decision to favor has an opposite and =
theoretically equal consequence but Inharmonicity can be used to a =
limited degree to absorb some of the Comma, the reason why tempering is =
necessary.=20

  The fact that you have this question tells me you are doing quite =
well, so take comfort in that.=20

  Bill Bremmer RPT=20
  Madison, Wisconsin=20
  Click here: -=3Dw w w . b i l l b r e m m e r . c o m =3D-=20




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