EB 18th Cent WT from A Fork F3-F4

[David Andersen]

>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

Thank you, Bill, for your effort.  I'm fascinatd by this, and i will try 
it.  If I have problems---and I may, because I'm a kinesthetic 
learner---it would be 100 times easier for me to watch you do it than to 
read instructions---I'l let you know.
David A.


>In a message dated 12/28/02 1:55:10 AM Central Standard Time, bigda@gte.net 
>writes:
>
>
>> >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.
>> _______________________________________________
>> 
>
>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