Temperament selection

[Brad Lehman]

> 
> I've had our church piano set in the Bach since June 2005, all the time, 
> and it works beautifully for everything.  (Of course it does, since it 
> comes from the Well-Tempered Clavier, using all 24 keys!)
(...)
> Seven of the twelve notes happen to be the same as in Vallotti's.  I 
> have cent charts at the bottom of the page here, showing details and 
> instructions:
> http://www-personal.umich.edu/~bpl/larips/comparison.html


Let's make this even easier by describing it this way.

"Setting the Bach from a Vallotti base" (like folding a nicely refined 
origami bird, and not just one more ordinary crane....)

- Set all the following notes at the same places they are in Vallotti: 
C, D, E, F, G, A, and Eb.

- The remaining steps are by ear.

- From the E, tune three pure fifths/fourths: E-B-F#-C#.

- From the Eb, tune a Bb that makes a very slightly narrow fifth...and 
check this Bb also as a fifth with F, being just barely *wide* enough 
(sic) to start beating slowly.  (Among other things, this helps the 
F#-A#-C# triad not to be raucous....)

- From the C# and the D#, tune the G# at an average position so both the 
C#-G# and the G#-D# are slightly narrow fifths.

That's all there is to it.  Then play music in all 24 keys.  :)

=====

Comparing the results, the two recipes:

Vallotti: F-C-G-D-A-E-B 1/6 comma; B-F#-C#-G#-D#-A#-F all pure.

Bach: F-C-G-D-A-E 1/6 comma; E-B-F#-C# pure; C#-G#-D#-A# 1/12 comma.


Brad Lehman
http://www.larips.com