Equal Beating Victorian-Aural Tuning Sequence

[Douglas Hershberger]

Bill,
   Thanks so much for going to the trouble of writing this sequence up.
I wasn't able to make the convention so this will be fun to try.
Doug Hershberger

Billbrpt@aol.com wrote:
> 
> Dear List,
> 
> Here is a newly revised version of the Aural Tuning Sequence for the Equal
> Beating Victorian Temperament which I used on the Walter Grand in Providence.
> This should replace any previous post or document that you may have from me on
> this, including the Convention handout.
> 
> As you can see, this requires highly refined aural tuning skills.  It is not
> recommended for a novice tuner.  It should be considered as an innovative way
> to tuned the piano so if the person has any reservations about using it, ET
> will always be the safe alternative.  Tuning in this style can only become
> commonplace if many people learn it, advocate it and use it as I do and I have
> no real expectation of that happening.  It will probably remain a little known
> alternative practiced by a very few.
> 
> Bill Bremmer RPT
> Madison, Wisconsin
> 
>                       Equal Beating Victorian Temperament
> 
>       (Equal Beating Victorianized Modified Meantone Temperament)
> 
>                       Instructions for Aural Tuning
>                          (With Tempered Octaves)
> 
> 1.  Tune A4 to A-440 pitch source.
> 2.  Tune A3 to A4, stretching the octave to a a 6:3 type.
> 3.  Temper E4 from A3, a narrow 5th, a little more than an Equal
>     Temperament (ET) 5th but still slightly less than 1 beat per second.
>     This is an estimate and may be checked or adjusted later, if
>     necessary.
> 4.  Listen to the 4th, E4-A4.  It should beat faster than the 5th, A3-E4
>     but should not be faster than 2 beats per second.
> 5.  Temper C4 from E4, a wide Major 3rd to beat approximately 6 beats per
>     second. (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 C4-E4 3rd. (Approximately 6 beats per second).
> 7.  Temper B3 from G3, a wide Major 3rd so that it beats exactly the same
>     as both the C4-E4 3rd and the G3-E4 6th. (Approximately 6 beats per
>     second).
> 8.  Temporarily tune D4 a pure 4th from A4 then notice the strong beat
>     in the 5th G3-D4 and sharpen D4 until the beat is exactly the same
>     in both the G3-D4 5th and the A3-D4 4th. (Faster than the same
>     interval in ET.)
> 9.  Tune F3 a pure 5th from C4.  To check this interval, use G#2 as the
>     test note and prove that the Ab2-F3 6th beats exactly the same as
>     the Ab2-C4 10th.
> 10.  Tune F4 a pure 4th from C4.  To check this interval, use G#3 as the
>     test note and prove that the 3rd Ab3-C4 beats exactly the same as the
>     Ab3-F4 6th.
> 11. Verify the F3-F4 octave.  Using the test for a pure 5th which chooses
>     the lowest coincident partial of F3 & C4 and the test for the pure 4th
>     C4-F4 will yield a properly stretched octave, usually a compromise
>     between a 4:2 & 6:3 type.
> 12. Check the speed of the 3rd, F3-A3.  It should beat exactly the same
>     or very similarly to the 3rds G3-B3 and C4-E4.  If it is too slow,
>     adjust the note, E4 slightly flatter and begin the sequence again.
>     If too fast, adjust E4 slightly sharper and restart the sequence.
> 13. Tune Bb3 a pure 5th from F4.  Use the test note C#3 to prove that the
>     Db3-Bb3 6th beats exactly the same as the Db3-F4 10th.
> 14. Listen to the resultant 3rd, Bb3-D4.  Temper C#4 so that the A3-C#4
>     3rd beats exactly the same as the Bb3-D4 3rd.
> 15. Tune F#3 a pure 5th from C#4.  Use the test note A2 to prove that the
>     A2-F#3 6th beats exactly the same as the A2-C#4 10th.
> 16. Tune G#3 a pure 4th from C#4.  Use the test note E3 to prove that the
>     E3-G#3 3rd beats exactly the same as the E3-C#4 6th.  The Ab3-C4 3rd
>     will beat exactly the same as the F#3-A#3 3rd.
> 17. Temporarily tune D#4 a pure 5th from G#3 then notice the slight beat
>     between D#4 & A#3 and flatten D#4 until the G#3-D#4 5th beats exactly
>     the same as the A#3-D#4 4th. It will be a very slight beat, less than
>     the same interval in ET. The B3-D#4 3rd will beat very rapidly, at
>     least as fast as the F#3-A#3 & Ab3-C4 3rds below and similar to but
>     perhaps not quite as fast as the D#4-F4 3rd above.
> 18. 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.
> 19. 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".
> 
> Bill Bremmer RPT
> Madison, Wisconsin
> July 21, 1998
> (Post Providence Convention revision)