Holy Grail

[Paul N. Bailey]

>Yes, so tell us what the Holy Grail temperament is purported to be?  

>ab

Anne,   
        This is a temperament that came to me in 1992. Took another year to
figure out exactly what it really is.
        Since then I've run across the Kellner well temperament , which I 
think is a bit better than the pb'93, although the two are very similar.


                                Bearing Plan
                                   for the
                        P.B.  '93   Well Temperament    

1) TUNE C to a pitch source.

2)TEMPER F a 1/12 comma narrow fifth below C.
        (This could be done with no estimating by going one round of the
E.T 
thru Just Intonation bearing plan of John Farey,1807;[see O.J.'s TUNING, 
SEC.85-86.] Very careful testing of all the fifths and fourths  and the
just 
third would be required for accuracy, and any working tuner will almost
surely
use direct tempering with one or two tests instead. It is very interesting
to 
me that if one goes the long way 'round for the 1/12 comma fifth, this
becomes
a complete just intonation and/or exact copy of beat rate temperament, with

absolutely no estimate-guestimate tempering.)

3) TUNE Bb a just fifth (or fourth) from F; keep going by just fifths or 
fourths to Eb, Ab, Db and Gb. Spread this around the keyboard enough so
that 
you can-

4)TEMPER B a wide fourth above F#(Gb)  so that the third B-D# beats at the 
same rate as the third  F#-A# a fourth lower.

5) TUNE E just to B.

6) TEMPER  A a wide fourth above E so that A-C# beats at the same rate
asE-G# 
a fourth lower.

7) TEMPER  D between  Bb and  F#  so that two conjunct equal beating thirds

are formed.

8)  TEMPER  G  so that  Eb-G beats at the same rate as Bb-D a fifth higher.

                        Cents Deviation from Equal Temperament

C=+6.2  C#=-1.6         D=+1.4  D#=+2.3         E=-2.1          F=+6.2  

F#=-3.6 G=+49   G#=+0.3         A=0.0           A#=+4.2         B=-0.1


Paul Bailey RPT
103445.713@compuserve.com