Equal Beating Victorian-Aural Tuning Sequence

[Billbrpt@aol.com]

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)