<HTML>In a message dated 12/28/02 1:55:10 AM Central Standard Time, bigda@gte.net writes: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">>19.  Flatten E4 until the A3-E4 4th and the B3-E4 4th beat exactly the same. Bill----do you mean "....until the A3-E4 5th...."  instead of what's written above? David A. _______________________________________________ </BLOCKQUOTE> Yes, thanks for the correction.  Whenever I write up instructions like these, my eyes start to glaze over.  It's much easier to just do it than it is to write it down.  I have a WordPad Document with this on file.  I'll make the correction immediately.  My apprentice is coming over this morning to practice it.  When I am sure about the whole thing, I'll place it on my website. As Jim Coleman and others who teach tuning have suggested, I taught unisons first.  He practiced for months just cleaning up unisons.  Then, he learned how to tune what sound like "pure" octaves.  He is now at the point where he can tune "pure" 4ths and 5ths. This scheme I have developed is taken from an idea which I understand to be the highest refinement in temperament construction although in my opinion, it seems to be the very most elementary, the most foolproof.  Almost any other verbal instructions provide you with  figures, beat speeds which are compound numbers.  It is virtually impossible to know whether or not what you have is correct and even if you could determine it to be so, an adjustment for inharmonicity has not been made. The Equal Beating (EB) method is quite different.  Pure 4ths & 5ths are very easy to hear when they sound perfectly still.  There remains an Equal Beating test for each of these to further prove their correctness.  I have not put these tests in my instructions because I did not want to clutter up what are otherwise very clear and easy to understand instructions.  The other EB instructions use the actual inharmonicity properties which the piano has to determine the final results.  This minimizes the subjectivity a tuner may put into it. Even the  EB test for a 6:3 octave is superfluous.  A 4:2 or a compromise between a 4:2 and a 6:3 could be used, as is recommended for ET but I recommend a 6:3 in this case for the best results.  One writer said that the C4 must be tuned exactly where it will end up being for the test to work.  This is not quite true.  It must be in a *convenient* place.  A minor 3rd is a narrowed interval (and a Major 6th, a widened one).  When fine tuning an octave's width using a note either within it or outside of it, the interval must be tempered properly but need not and may is best not tuned exactly as it will end up.  One may actually (and should) adjust the interval's speed so that a clear distinction between the two test intervals may be heard.  If the beat speed is too slow, the distinction may not be heard, likewise if it is too fast. I'm still looking for an answer to my two questions, one of which I think I already know.  1.  If F3-A3 beats at 4 beats per second and C4 is tuned pure to F3, what is the beat speed of the minor 3rd, A3-C4?  2.  According to my scheme, what will be the speed of the final resultant 3rd, C4-E4? In Jorgensen's book, Tuning, the Thomas Young has F3-A3 at 3.8 and G3-B3 at 4.3 (theoretically).  Both may be expected to be slightly faster when adjusted for inharmonicity but I have pegged both at exactly 4.0 beats per second.  I think this may result in the C4-E4 3rd being slightly slower than the 4.1 which Jorgensen lists.  Each time I have tuned it, that interval has ended up a little slower than the F3-A3 and the G3-B3, not the same or nearly the same. This would be acceptable, of course and still leaves the temperament matching the description of a "representative" 18th Century style Well Tempered Tuning, perhaps as close to the Thomas Young as one might be able to produce aurally using any other method. David, if you are interested in what a basic WT sounds like, I suggest you try this, you should be able to do it easily.  Now, as for the octaves, you won't be able to use the method you use for ET and although I may be challenged on this, I suggest you use the method found in my website called "Tempered Octaves".  It is also an EB method and so easy as to be "mindless".  When I tuned the Thomas Young temperament for Owen Jorgensen at the Convention in Dearborn, he specified the octaves have "optimum stretch".  I took that to mean what I do because that is what I consider it to be, *optimum*.  When I asked him how they sounded after his performance, he proclaimed they "sounded *perfect*." 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>