<HTML>In a message dated 9/22/02 7:14:41 PM Central Daylight Time, mathstar@salemnet.com writes: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">HERE THE QUESTION (Looks like several questions, but really asking the same thing each time ...) 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? 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 ..." So what the heck does "about" mean?  Do you have to set the whole T. before you "know"? (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. 'Preciate some comments. Alan Barnard Listening in Salem </BLOCKQUOTE> 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. The initial A3-A4 octave is best set as a compromise between a 4:2 and 6:3 octave. 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. 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. 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. 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. 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. 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. 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. The fact that you have this question tells me you are doing quite well, so take comfort in that. Bill Bremmer RPT Madison, Wisconsin <A HREF="http://www.billbremmer.com/">Click here: -=w w w . b i l l b r e m m e r . c o m =-</A> </HTML>