<< > Greetings, > << Just wondering if anyone can point a web link or a book on tuning well > temperaments. >> 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 http://www.uk-piano.org/edfoote/index.html www.uk-piano.org/edfoote/well_tempered_piano.html
This PTG archive page provided courtesy of Moy Piano Service, LLC