EBVT (was using beats to tune)

[Billbrpt@AOL.COM]

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In a message dated 11/16/01 1:11:26 PM Central Standard Time, Tvak@AOL.COM
 writes:


> The thing that got me started thinking about this was the temperament known 
> as Equal BEATING Victorian Temperament.  I would assume that the tuners 
> using 
> this temperament would be listening to beats;  hence the name.  And 
> assuming 
> this temperament was actually in use during the Victorian Age, that would 
> pre-date 1917, which contradicted the comments posted earlier about beats 
> not 
> be used to tune prior to 1917. 
> 
Yes, to tune the EBVT aurally, you need to listen to beats but the important 
point is that you do not need to "count" them, as such, except for making an 
estimate with the very first F3-A3 3rd which is tuned.  That interval is 
tuned at an easy to estimate 6 beats per second and can be slightly slower or 
faster and still have the temperament scheme work out.

The EBVT is a scheme that I designed in 1992 but which was based upon what I 
had learned by tuning many other Equal Beating (EB) temperaments published by 
Owen Jorgensen.  Some of the EB temperaments are very old and some are not 
temperaments at all but true *tunings* where only pure (beatless) intervals 
are tuned.  The feature of these is that one does not *count* beats but makes 
comparisons or tunes pure 4ths or 5ths which can be proven by tests which 
reveal identical beats.

The method I outlined in a previous post for tuning F3-A3-C#4-F4-A4 in ET is 
based on the EB principals although when tuning ET, one ends up verifying 
*mismatches* rather than EB intervals.  For example, to prove that a 5th is 
properly tempered in ET, one can use the tests which prove that a 5th is pure 
but the test must certify two intervals which do *not* beat exactly the same 
but are still close.  A pure 4th or 5th cannot exist in ET, they must be 
tempered.  A truly pure 5th indicates an error. (I'm not taking into account 
the so-called "ET with pure 5ths" which I consider to be *pure* folly).

Many Historical Temperaments (HT) have 3rds, 4ths & 5ths which one compares 
to confirm EB.  In ET, *mismatches* are correct while EB intervals indicate 
an error.  The 4:5 ratio of contiguous 3rds is and example of this.  Also 
3rd-6th tests where the 6th is supposed to beat *slightly* faster than the 
3rd is another example.

Below is the basic scheme for tuning the EBVT.

Bill Bremmer RPT
Madison, Wisconsin

             New Temperament Sequence (Bearing Plan) for the 
               Equal Beating Victorian Temperament (EBVT)

1.  Tune A4 to A-440 pitch source.
2.  Tune A3 to A4, stretching the octave to a a 6:3 type.
3.  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).  
4.  Tune C4, a pure 5th from F3.
5.  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.)
6.  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.
7.  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).
8.  Temper B3 from G3, a wide Major 3rd so that it beats exactly the same
     as the F3-A3, C4-E4 and G3-B3 3rds and the G3-E4 6th. (Approximately 
     6 beats per second).  Now, the F3-D4 6th may also beat at 6 per second.
9.  Tune F4 a pure 4th from C4.   This will make a pure sounding 4:2 octave 
      from F3-F4.
10. Tune Bb3 a pure 5th from F4.   
11. Listen to the resultant 3rd, Bb3(A#3)-D4.  Temper C#4 from A3, a wide 
3rd,  
     so that the A3-C#4 3rd beats exactly the same as the Bb3(A#3)-D4 3rd.
12. Tune F#3 a pure 5th from C#4.   
13. Tune G#3 a pure 4th from C#4.   
14. Temper D#4 from both G#3 and A#3 so that both the G#3-D#4 5th
      and the A#3-D#4 4th beat exactly the same as each other (slightly
      less tempered than in ET or nearly pure).  
15. When expanding the octaves do so in a manner which will cause the 
    2nd inversion major triads of C, G, D, A, E, & B to have the 3rd & 6th
    beat exactly the same.  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 a 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".


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