Technical Library TEMPERAMENTS XXI: Bach/Barnes Entire Contents Copyright © 2005 CBH

The late John Barnes, onetime curator of the famous Russell Collection in Edinburgh, published an article in the April 1979 issue of Early Music, titled “Bach’s keyboard temperament — Internal evidence from the Well-Tempered Clavier”.

Using statistical analysis and weighting thirds by their perceived prominence in Bach’s musical use, Barnes arrived at a very useful temperament. When you study the diagram, you can observe that it is very similar to Vallotti, except with with the fifth E–B tuned pure and one tempered fifth tucked further around the circle. What effect does this have? With the B raised somewhat from Vallotti, the intonation of the B Major triad is improved at the expense of the G Major triad.

If you’ve just tuned Vallotti, you can easily try Bach/Barnes by simply retuning your b a pure fifth above e. Naturally enough, to work from the beginning the tuning method will be very similar to Vallotti. Again, let’s work from the a':

1. Tune your usual a' to a tuning fork, and tune a in absolute perfect tune an octave below it.

2. Now we want to find the f a third below that a: Tune it pure first of all, but then widen the interval by flattening the f until you hear three distinct beats per second.

3. Tune all the fifths from the flat side of F around the circle of keys absolutely pure until you hit F♯.

4. Tune e' initially pure to a, then lower it a little, squeezing the interval so it has a perceptible beat. (If you’ve been tuning Vallotti, you are already used to the sound of sixth-comma fifths. If you are a piano tuner, these sixth-comma fifths beat exactly twice as fast as you expect from the same intervals in Equal Temperament). Drop down the octave now to e, which of course must be tuned pure.

5. Find b by making a pure fifth up from e. The 5th made from the b to your already-tuned f♯' will not be perfect, but again a sixth of a comma narrow.

6. Middle c' comes next. Tune it a pure fifth above your f, and then squeeze the interval a little.

7. Find your g' above middle c', again tuning the fifth pure and then squeezing it. Drop down the octave to place the pure g.

8. Your d' must now be positioned between g and a'. First of all, tune it pure to g, then flatten it little by little until your fifth g–d' sounds about the same as your f–c'.

9. Again, if all your tempered fifths beat a little more rapidly in turn as you ascend the keyboard, you’ve done a good job: f–c', g–d', a–e', b–f♯', c'–g' & d'–a'. All the other intermediate ones are pure: f♯–c♯', a♭–e♭', etc.

10. Bring the rest of your instrument in tune with your bearings area, try some Bach and see what you think.

Further discussion
Anonymous [Kayano, Moxzan] Dodecagon — Chi-s akt temo Tokyo 2012, p89
Padgham, Charles The Well-Tempered Organ Positive Press, Oxford 1986, p71

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