EBVT Figures correction

[Don]

Hi Bill,

Why not photocopy the letter in question and snail mail it to Jason.

At 12:19 PM 10/4/02 EDT, you wrote:
>In a message dated 10/4/02 9:58:22 AM Central Daylight Time,
>jkanter@rollingball.com writes:
> 
> 
> You're saying basically "I'm not careful with numbers, therefore others
>make mistakes too." I won't issue any new charts with your data until you
>publish scans of Owen's letter. 
> 
> Jason
> 
>
> 
>     So, yes, I mixed up a few numbers.
> 
>     As some of the 3rds and 6ths routinely turned out Equal Beating, I
>eventually specified them that way too.
> 
>   I have very carefully checked to see that they are what Owen wrote.
> 
>     +3.8
>   -0.8
>    +0.9
>   +3.1
>     -2.0
>     +1.8
>   -2.7
>    +3.1
>   +1.2
>       0.0
>    +2.4
>       0.0
> 
>     The rest falls into line as a consequence.
> 
>    Why not try these correction figures first before you go making another
>graph and tell me if what you get matches the description on my website.
> 
> Here is that bearing plan in plain text:
> 
> Aural Instructions for the EBVT:
> 
>  Tune A4 to A-440 pitch source.
> 
>  Tune A3 to A4, stretching the octave to a a 6:3 type.
> 
>  Temper F3 from A3, a wide 3rd, estimating it to beat at 6 per second, 
>    just slightly slower than it would be in Equal Temperament (ET). 
> 
>  Tune C4, a pure 5th from F3.
> 
>  Temper E4 a wide 3rd from C4, making it also beat at 6 per second. (About
>half the speed of the same interval in ET.)
> 
>  Temper G3 from E4, a wide Major 6th so that it beats exactly the same as
>the F3-A3 and C4-E4 3rds. (6 beats per second). This will make the G3-C4
>4th be tempered a little more than in ET.
> 
>  Temper D4 from both G3 and A3 so that both the G3-D4 5th and the A3-D4
>4th beat at exactly the same mild rate. (Each one just slightly more
>tempered than in ET).
> 
>   Now, the F3-D4 6th will also beat rapidly but a little faster than the
>previous series of Rapidly Beating Intervals (RBI). It will probably beat
>at 8 beats per second.
> 
>  Tune F4 a pure 4th from C4. This will make a pure sounding 4:2 octave
>from F3-F4.
> 
> 10. Temper by 1 beat per second, Bb3(A#3) a 5th from F4.
> 
>  Temper C#4 from A3, a wide 3rd, so that the A3-C#4 3rd beats exactly the
>same as the Bb3(A#3)-D43rd. This will probably be about 9 beats per second,
>about the same as in ET.
> 
> 12. Tune F#3 a pure 5th from C#4.
> 
> 13. Tune G#3 a pure 4th from C#4.
> 
>& D#-A#. 
> 
>& 6th beat exactly the same. Example: to tune E3, form a beatless octave
>with E4, then sharpen or flatten until the 6th, E3-C#4 beats exactly the
>same as the 3rd, A3-C#4.
> 
> The octave should be stretched enough so that there is a very slight beat
>in the single octave (approximately 1/2 beat per second) and that the
>tempered 5th will beat slower than the 4th.
> 
> When both the 4th and the 5th were pure in the temperament, the octave
>will naturally be stretched a little less than an octave whose 4th and 5th
>are tempered.
> 
> 16. When expanding the outer octaves, try to reconcile the double octave
>and the octave and 5th (12th) so that the double octave and the 12th beat
>exactly the same. (A very slight beat, almost inaudible). This will
>naturally result in octaves which vary slightly in size up and down the
>keyboard. These will quite effectively be "Tempered Octaves". (See my
>complete article on How to Tune Tempered Octaves).
> 
> ***************************************************
> 
>    Sometimes that 4th ends up quite pure sounding, sometimes it doesn't
>but either way, follows the rules for Well Tempered Tuning.
> 
>   Once I am sure of it, then when I have to make small modifications to
>accommodate scaling and/or Inharmonicity irregularities, I have a
>foundation from which to do that.
> 
>    But I only have so much time to spend on this.
> 
> Bill Bremmer RPT
> Madison, Wisconsin
> www.Billbremmer.com 

Regards,
Don Rose, B.Mus., A.M.U.S., A.MUS., R.M.T., R.P.T.

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