well tempered temperaments

[Bec and John]

Hi Ed,

Thanks so much, I'm an anxiously awaiting trying some of this out! 
Would you say the Kirnberger is a more mild temperament?

- John


>   Yes,  The Young temperament was an ideal of perfect balance, 
> however, on
> the piano, it may be that the 21 cent F#-A# is too much for some.  I 
> used to use
> this as an introduction to temperaments for the uninitiated, but found 
> that
> too high a percentage of customers were put off by it.  If you want to 
> try it,
> I would suggest that you follow Thomas Young's abreviated version of
> instruction as published by Owen Jorgensen.
>
>  "In practice, nearly the same effect (temperament),  may be very 
> simply
> produced, by tuning from C to F, Bb, Eb, Ab, Db, Gb,  six perfect 
> fouths; and
> again, from C, tune six equally imperfect fifths, (ie, C-G-D-A-E-B-F#) 
> .   This
> results in a Valotti that is transposed up a fifth, which leaves C as 
> the most
> consonant key rather than Valotti's F.
> Notice that you end up with a Gb when tuning by perfect fourths from 
> C, and
> that same note is an F# when you approach it from C by imperfect 
> fifths.  This
> will leave a rather active third between F# and A#, but that will be 
> the
> widest third in the temperament.
>
> Now,  if you would like to excercise control over how strong the 
> temperament
> is, the following is a magical procedure from Jorgensen that allows 
> the tuner
> to make decisions in regard to allotting the dissoannce.
>
> Tuning To Personal Taste (Jorgensen)
>
> All fourths are wide or Just,  all fifths are narrow or Just
>
> 1.   tune C to fork
> 2.   tune C4-E4 according to taste  (Just or wide)
> 3.   tune E4 - E3    Just
> 4.   tune G#3 between E3 & C4 so   Ab-C is 1.25 times as fast as  E-G#
>
> Tune the following intervals Just for Well temperament, (or very 
> slightly
> tempered for Victorian if C-E is beating at least 4 bps).
> 5.  G#3-C#4
> 6.  C#4 - F#4
> 7.  F#4 - F#3
> 8.  Ab3 - Eb4
> 9.  Eb4 - Bb3
>
> 10.  tune D4 between Bb3 & F#4 so D -F#  is1.25 times as fast as Bb-D
> 11.  tune G3 from C4 & D4 so G-C beats 1.3 as fast as G-D
> 12.  tune A3 from E3 & D4 so A-D beats 1.3 times as fast as E-A
> 13.  tune B3 between F#3 and E4 so B-E beats 1.3 times as fast as F#-B
>
>     Check
> G3-D4 is slower than A3-E4
> G3-C4 is faster than A3-E4
> A3-D4 is faster tahn G3-C4
>
> 14.  tune F4 from Bb3 & C4 so C-F beats 1.5 times as fast as Bb-F
> Beat rates should increase in order from
> E3-B3
> Bb3-F4
> B3-F#4
> B3-E4
> E4-A4
>
>     If steps 5 - 9 are tuned in Just intonation, the C-E third 
> controls the
> harmonic balance.  If it is Just, a temperament like Kirnberger(Prinz) 
> results.
>  If C-E is tuned faster than 4 bps and less than7 bps, only F#-A# is 
> 21.5
> cents wide and the results are more "Victorian".
>
> Enjoy!
>
>
> Ed Foote RPT