HT

[Billbrpt@AOL.COM]

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In a message dated 5/10/01 12:40:25 PM Central Daylight Time, :    
tunenbww@clear.lakes.com (Paul) writes:

> Also, I followed Bill Bremmer's instructions for EBVT. The test piano was a 
> small grand I've just restrung,etc. It sounds better than the ET I had 
> initially tuned it to. There is a chapter meeting at my shop this week end, 
> and we'll scrutinize the tuning. Several of the members are accomplished 
> musicians. I'm anxious to hear their reactions. I must say it takes me 
> awhile to get the temperaments set (aural tuning only).  The EBVT took me 
> about an hour, but the others take me about 15-20 minutes. The practice is 
> helping. All in all, thanks to all who have contributed and encouraged me 
> and others to try. It's very enjoyable!
>  
> Paul Chick

Thanks for you comments, Paul.  I am currently reworking the temperament 
sequence to make it easier to understand and follow.  It only takes me a few 
minutes to run through but I understand that it is foreign to all others.  
Recently, I wrote to Ola of Norway the following remarks.  Maybe they can 
help you understand what I do a little better until I get the whole thing 
rewritten.

(The new version will start with F3-A3 as the first interval to tune at 6 
beats per second and will be the only estimate you have to make.  All other 
intervals are either pure or Equal Beating).

<<The most important steps in the EBVT are the first ones.  F3-A3, 6 beats. 
Now tune F3-C4 pure.  Now copy the 6 beats exactly to make C4-E4 beat at 6 
beats.  Now make the G3-E4 6th beat a 6 beats.  This will make a G3-C4 
tempered 4th.  If this 4th is way too fast, then sharpen G3 until it sounds a 
little better but not as much as you want, then flatten C4 until the G3-C4 is 
tolerable.  This will make the C4-E4 3rd faster.  To even out your 
corrections, flatten E4 just slightly to slow the beat about 1/2 as much as 
you have increased it, then copy that beat to the F3-A3 3rd by flattening F3 
just a little.  Check the F3-C4 5th. It should still sound "pure" to the ear 
even if it ends up slightly wide or narrow.

Doing all of the above will compensate for Inharmonicity.  Now, the G3-B3 3rd 
can be made by copying the rate of beating established in F3-A3, C4-E4 and 
G3-E4.  Now tune D4 by making it beat equally between G3 and A3.  Now tune F4 
a pure 4th from C4.  The F3-F4 octave should sound pure.  Now tune Bb3 a pure 
5th from F4.  The F3-Bb3 4th should sound pure.  Listen to the resultant beat 
of Bb3-D4.  Now tune C#4 from A3 so that it beats exactly the same as the 
Bb-D4 3rd.  If this 3rd sounds too fast, you can compromise by flattening C#4 
slightly.  If the Bb3-D4 3rd has ended up too fast, sharpen the Bb3 just a 
bit, which will temper the F3-Bb3 4th and the Bb3-F4 5th just slightly.  

Now tune F#3 from C#4 a pure 5th.  If the resultant F#3-A#3 3rd seems way too 
fast, sharpen F#3 just slightly which will make the F#3-C#4 be tempered just 
slightly. Now tune G#3 from D#4 a pure 4th.  If the resultant Ab3-C4 3rd 
beats way too fast, then sharpen Ab3 just slightly which will cause the 
Ab3-C4 to be slightly narrow.  This would be OK however, since the 
temperament is modeled after the Modified Meantone type, in which slightly 
wide 5ths and slightly narrow 4ths will occur and are acceptable.

Now, there is only one note left to tune, D#4, which you will make beat 
equally against G#3 and A#3.  This usually ends up being just slightly 
tempered for both intervals.  Sometimes it sounds virtually pure.

Remember that you are trying to make intervals beat within the tolerance your 
own ear has for what sounds too extreme.  This is why I say that when an 
interval beats "way too fast", use your musical judgment to make a compromise 
but be aware of the consequences of that compromise.  This means that you can 
create an even milder form of the EBVT if you wish but the more you 
compromise from the basic formula, the more you risk losing the Equal Beating 
effects and the effects of having 4 pure 5ths within the temperament.

I hope these comments have been helpful.>>


Bill Bremmer RPT
Madison, Wisconsin


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