Nice Chord...aural tuning

[Richard Moody]

> Hi folks.. Dinking around the other day I noticed a nice sounding chord
that
> resulted from tuning completely "wrong"...grin. I had started my usual
A3-A4
> temperament and got as far as F# and this was really flat to begin with.
So flat
> that the A-F# 6th was beating at about 2 beats per second. Playing
A-D-F#-A(4)
> yeilded then a "D Major" that was really pretty to listen to indeed.


You didn't say how the D--F# was beating, but what you are hearing is an
aproximate pure 6th.  However it would be a "bastard" 6th as far as tuning
theory goes because A--D  wouldn't be right according to 1/4 tone Meantone
unless you also tuned A--D "completely wrong" according to ET...grin. (4
cents sharp instead of 2 cents sharp)  But if you tune !/4 MT,  the "D
Major" (triad) is really pretty to listen to.
    If you are concerned with the F# and how it ends up in the ET
temperament there is no law against tuning it as a 6th (to A) according to
the prescribed beat rate alone wo any other reference other than the A--C#
third, the 6th being a little faster than the 3rd from the same root. Of
course the 3rd and the 6th from the same root form a 4th and if this 4th is
ever so slightly wide, ie you can't quite count the beats (on a piano) your
C# and F# are properly (probably) tempered from A.

    So hear <g> is an Aural Tuning exercise.   Tune a major 3rd from A
strictly by beats, (C#) and then a 6th from A--(F#) by beats only.  Now
listen to the 4th...C#--F#.  If it is right, then C# and F# are right, as
long as C# is right.
Hint.... to get the A--C# 3rd right, tune the rest of the sequence of
contiguous 3rds in the A3--A4 octave.  That is tune A--C#--F--A  until the
beats progress evenly, (egalement?).   If you have these right you are way
ahead of the game.  Now if you tune the A--F# 6th and F# agrees with C#
(4th) you are that much further along.  You can tune D down from A4 and
listen to its 3rd with F#.  You can tune Bb down from F and listen to Bb--D
3rd   and Bb--D--F# as well. You have A3--C#--F--A4, right? Now listen to
Bb--D--F#--Bb.