well tempered temperaments

[Bec and John]

Hi Ed,

Thanks for the instructions, I was indeed asking how to tune a well 
temperament for an aural tuner, though all that didn't seem to come out 
:)

A few questions if you don't mind:

- What is 1/12 of a comma?

- When doing step 3 in the P.B. '93 well temperament (and step 3 of 
Kirnberger) where tuning the Eb, Ab, etc. via just fifths I presume you 
are to cover over 2 octaves? And when it says "Spread this around the 
keyboard" I presume that is tuning those notes in different octaves 
around the keyboard?

- I am particularly interested in the Young 1799 temperament, which 
seems to be highly regarded. Does anyone have a details that could help 
an aural tuner?

Thanks!

- John


> Umm,  Ok,  you were asking HOW to tune a well temperament...??  There 
> is a
> lot on the web, but here is one that you may be interested in trying,
> compliments of Paul Bailey RPT.
>
>
>                                 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
>
> Now, for a more traditional approach,  this is a plan for the 
> Kirnberger,
> compliments of Carey Beebe:
>
> Here's how you go about setting Kirnberger III:
> 1. Tune your c'' (that's the c one octave above middle c'!) to
> a tuning fork, and tune middle c' in absolute perfect tune
> below it.
> 2. Now we want to determine the e' a perfect third above
> middle c': This will be a revelation if you have never heard
> a perfect third before--Your violinist friends are going to
> find it unbearably flat, but we want it in perfect tune. (Hint-
> -if you split your interval over the octave, you will find it
> easier to hear because the speed of the beats is halved.)
> 3. Next, the hard part. Make all the fifths around the circle
> between C and E equally narrow and rough. We are
> dividing the comma among these four fifths, instead of the
> twelve of equal temperament, so they are going to be three
> times as out of tune as the equal tempered fifths we know
> and love on the piano. To tune a narrow fifth, first tune it
> perfectly, then lower the top note (or raise the bottom note)
> until you can't bear it any more. That's probably about a quarter of a 
> comma!
> All your fifths C-G, G-D, D-A and A-E should sound equally rough. 
> Don't move
> your c' or e'--you've already tuned them, and must keep that interval 
> as the
> beautiful perfect third. (Actually, it wasn't that hard, was it?)
> 4. Tune all the fifths from the flat side of C around the circle of 
> keys
> absolutely perfect. Stop about the Eb, and begin again working around 
> the sharp
> side of E, tuning all those fifths absolutely perfect. (In theory, 
> you'll
> end up with one fifth a little narrow, in fact very close to an equal
> tempered fifth, but in practice, they should all sound perfect.)
>             When you are happy with your middle octave, you must bring 
> the
> rest of your instrument into tune with what you have done. Tune down 
> in octaves,
> and up in octaves.
>
> When you feel you've mastered Kirnberger, it's an easy
> matter to change it into something else, so now it's time
> for Werkmeister III. He proposed his third temperament
> in 1691 (Those Darwinists reading this will, I trust, forgive
> me working backwards in history for ease of tuning--in
> musical terms, what came later was not always better!),
> and this is how you can accomplish it on your i
> nstrument:
> 1. From your nicely tuned Kirnberger, sharpen that e' that
> your violinist friend so much despised, so that instead of
> the beautiful perfect third with middle c', it makes a
> perfect fifth with a.
> 2. Tune down the octave to e, and raise the b so it is a
> perfect fifth with the e.
> Congratulations--You're done! You've tucked that last
> narrowed fifth a little bit further around the circle,
> improving the sharp keys. And you will be forever loved
> by your string-playing colleagues because they needn't detune the top 
> string
> on their fiddles.
>
>
>
> Ed Foote RPT