TÂ is for Temperament
The physics of sound can't cope with the demands of Western music. If you do it mathematically, a keyboard instrument will only be playable in a few keys, creating an extraordinarily rich, warm sonority. But reach further into the twelve notes of our scale and the 12 major/minor keys, and things go horribly awry. For example, tune a beautifully pure-sounding third, from C up to E, another from E to G#, and finally G# to B#. B# looks like C on your piano - but it isn't, and these three pure thirds equal a horrendously flat 'octave'. To put it another way, if you go round what's called a circle of fifths, going up five notes each time (CGDAEBF# etc...), the C you eventually get back to will be horrendously out of the tune with the one from which you started!
When composers stuck to simple keys rather than exploring further, they selected a tuning system in which made a few keys sound great - and it's indeed a wonderful experience to hear chords in such a 'mean-tone temperament'. Mind you, a semitone scale can sound quite bizarre.
As music ventured further, into more remote keys, musicians compromised with tunings in which everything was just about playable, but some keys sounded relatively pure while others sound doleful, aggressive, snarling... Bach certainly knew about so-called 'equal temperament' where all keys are indistinguishable from each other. However, there's evidence that the 'Well-Tempered Clavier' was intended for one of the 'compromise' tunings (or 'temperaments'). In Book I at least, you can hear the Preludes matching the characters of the keys. The first Prelude has slow, sustained harmony in sonorous C major while the third skitters around a rather twitchy C#.
But you gain something and lose something else... With the way we normally tune keyboard instruments nowadays, we make all our semitones exactly the same - it's called 'equal temperament'. We can play equally in any key - but we have lost kaleidoscope of colour in which every key had a different character, and when to change key was not simply to change pitch.
George Pratt & Graham Dixon
December 2005
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Read what others have said..
I have been impressed by Bradley Lehman's research and logic and am about to tune the instruments at Hammerwood Park to his Bach temperament. It's looks a useful deviation from Equal Temperament without looking as though it will "get in the way" of listening to music in distant keys. I'm intrigued by Mr Mander's comment: " Indeed as a number of people have pointed out, a more simple interpretation of the squiggles can be made by *not* turning them upside down. " and wonder what that interpretation might be - I have not seen one, and would appreciate alternate enlightenment.
David Pinnegar, East Grinstead Sussex
For further information regarding Bach's keyboard temperament, please download my online paper at: http://tinyurl.com/dgqvl
John Charles Francis, Ostermundigen, Switzerland
A follow-up article by me, about the clavichord (not bending the tangents etc), is in the November 2005 issue of _Clavichord International_ giving more information about this Bach temperament. And my research methods have nothing to do with numerology! The body of primary evidence is Bach's extant music, played and analyzed...not merely his diagram or any interpretation thereof.
Bradley Lehman, Virginia, USA
Hear hear, Mr. Mander! If it was important, Bach would never have hidden it at all - especially in what was intended from the start to be a pedagogical collection! Lehman may be a far more accomplished musicologist than I, but the explanation of his tuning scheme falls into all the familiar numerologist's traps. Of course, you can't change temperament on a fretted clavichord at all without bending the tangents, which is not a good practice to get into. All of Bach's contemporaries had a whole portfolio of temperaments, and it seems pretty unlikely that he didn't have the same. He almost certainly expected solo keyboard works to be performed in a variety of temperaments. In addition, As Ross Duffin has pointed out in "Why I hate Valotti" (which used to be available on the Web) temperaments which are suitable for solo keyboard works may not be suitable for ensemble or choral works, because of the large number of differently-sized intervals. It seems pretty clear to me that the idea of one single one-size-fits-all "Bach temperament" is wishful thinking.
Ian Kemmish, Biggleswade, UK
Subsequent letters in Early Music have cast considerable doubt on Bradley Lehman's conclusions and as a practical organbuilder with experience in unequal temperaments, I am doubtful as well. It may be a useful temperament (of which there are a significant number) but to suggest it is Bach's is far fetched and too complex. Indeed as a number of people have pointed out, a more simple interpretation of the squiggles can be made by *not* turning them upside down. But why would Bach "hide" his idea for a temperament at all if he had one?
John Pike Mander, London
How true, the comments about loosing something with equal temprament. Although I have not yet set this temprament, the very convincing set of articles on Bach's own temprament, (Early Music) as extrapolated from the title-page of the '48 (bk.1) should leave no one in any doubt. Of course this only applies to the harpsichord, and if set on a modern piano, it just sounds like a modern piano - muddy and unexciting, and can carry nothing of wonderful rhythmic drive and haunting resonance of an 'authentic' harpsichord.
Michael Taylor, Elsworth, Cambridge
I have just retuned my Virginal in the Bach temperament newly rediscovered by Bradley Lehman (see www.larips.com) and was amazed by all keys being playable yet all subtly different. A whole new sound experience - try it!
Patrick Perry, Tamworth
Are there any recorded examples of the different temperaments (perhaps on line), so as to demonstrate what you say about the different characters of the keys?
Caroline Agarwala, Hatfield, Hertfordshire.
It has been suggested that the strange graphic on the title page of the autograph manuscript of the Well Tempered Clavier book 1 represents Bach's own temperament. An interpretation by American musicologist Bradley Lehman, described at www.larips.com and in "Early Music" journal earlier this year, is now being used by many performers for recordings and by several organ builders.
Dr John Pike, Bristol