EB 18th Cent WT from A Fork F3-F4

[Jason Kanter]

Bill, I have electronically calculated each step of your EB 18thc Well. I have sent the chart to your billrpt address. You can compare it to the Young, but it is more like the Vallotti-Young. In answer to your questions, 

In step 4, the A3-C4 m3 beats at 6.0 (not 8) per second.
In step 13, the "strong beating" is 6.2/second.
In step 14, the G3 4th and G3 5th both wind up beating at 2.6.
In step 15, the A3 4th and G3 5th both wind up beating at 1.6. (This means, of course, that step 14 is no longer true; G3C4 is 2.6 but G3D4 is 1.6) 
In step 18, the B3E4 fourth beats at 3.8.
In step 19, the A3 5th and B3 4th both wind up at 1.5 bps.
And for your last question, the C4E4 M3 beats at 3.0.

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 jason kanter * piano tuning * piano teaching
 bellevue, wa * 425 562 4127 * cell 425 831 1561
 orcas island * 360 376 2799
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----- Original Message ----- 
From: <SidewaysWell1713@aol.com>
To: <pianotech@ptg.org>
Sent: Saturday, December 28, 2002 8:03 AM
Subject: Re: EB 18th Cent WT from A Fork F3-F4


| 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
| 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>
|