Some had a different opinion from that of Roger North, however, and - to extend his metaphor - carried on like Robin Hood: instead of having six keys rich in consonance and six quite destitute, they shared things out somewhat so that all keys had part of the richness and part of the poverty.

The normal thing was still to share out the dissonance unequally, so that C-major was still rather well in tune, F-and G-major slightly less so, and so on round to the extreme 'black' key, which could work as either F#-or G-flat major, and which although worst could nevertheless be listened to.

In this system - unequal temperament - each key has objectively and demonstrably its own characteristic sound; and this became part of l8thC. consciousness, together with the well-established rhetorical ideas that a composer flattens a note to express softness, sadness etc., and sharpens it to express hardness, cruelty and the like.

Many writers described different ways of carrying out this 'well-tempering'. The names quoted most often today are Werckmeister and Kirnberger: they wrote in quite a lot of detail, but we can express one such system here very simply: "temper the four 5ths between C and e' to give a pure 3rd (plus an octave), as in mean-tone tuning: and set all the other 5ths in tune":

* there will be sound examples here soon *

More normal, however, was simply a brief observation like Peter Prelleur's, that

all sharp Thirds must be as sharp...and all the Fifths must be as flat as the Ear will permit (48).

click for a closer view fig 3: Peter Prelleur's voilin intonation

Many people who were taught years ago that c# is the same as d-flat can have difficulty accepting that they are different in the world of practical reality. The most convincing proof is to hear it, but it may help to be able to 'see how it sounds': notice that on the a string, for example, while c# is taken with th 2nd finger, d-flat is taken with the 3rd; and while D# is taken with the 3rd finger, e-flat is taken with the 4th.

The idea of sharing out the dissonance equally has also been known and discussed since at least renaissance times: it is intellectually satisfying, and one can find a kind of balance in the idea of all semitones being equal, all keys equally out of tune. But this balance only works in practice if all keys are used equally often, which has never been the case, of course: and since - given a normal repertoire - the sum total of out-of-tuneness is much greater with equal temperament than with mean-tone or unequal temperament, it was never normal to use it until recent times. It is particularly inappropriate for works which exploit a whole cycle of keys, like J.S. Bach's 48 preludes and fugues, 'The well-tempered Clavier' since it removes the differing degrees of out-of-tuneness which are an essential part of each piece's individual character: and so sad that many people these days believe 'well-tempered' to mean 'equal tempered' in this context, completely missing the central point.

There are other important losses arising from the use of equal temperament. One is that a sharp note which is in tune a 3rd above its bass note exerts a very clear pull upwards, an in-tune flat note pulls downwards - rhetorical effects which were used routinely by all composers before, say, Brahms, and which are entirely absent in equal temperament. Another is that in unequal temperaments and in mean-tone tuning the various dissonances all make different effects, and the performer clearly understood this as part of his repertoire of means of expression. Quantz was one of the few who bothered to point out how it worked in detail, but it is quite clear that baroque and renaissance musicians regarded such things as self-evident rhetorical devices.

ex.10: hierarchy of dissonances (Quantz, Versuch, XVII,vi,§l4)

In equal temperament these differences are almost completely lost: a diminished 5th is identical with an augmented 4th, for example, and the augmented second Dowland used for 'Hell' is identical with the minor 3rd he used elsewhere for 'Love'.

It must by now also be evident that a choir which sings in tune with a piano cannot be in tune with itself - although it may regard the prize of keeping a constant pitch worth the loss of intonation: as the Doge of Venice said in a recent radio play, "We left 2000 dead on the beach, but we got the grapes..." Similarly with two recorders and a piano playing together - if any two of them are in tune with one another, they must be out of tune with the third.

The situation in an average modern orchestra could only be experienced by a baroque musician as barbaric, since the concept of 'schizophrenic' didn't exist then - the woodwind tune to some sort of equal temperament, the strings tune to perfect 5ths starting from an a , the brass play perfect 5ths but starting from a b-flat an equal-tempered semitone above the violinists' a... Of course, the better players try to adjust, but no-one has a very clear idea of who to adjust to - unless it's a piano concerto, of course, in which case the whole orchestra can relax in its mutual agreement that only the octaves are in tune. Little wonder that the normal reaction of a modern musician meeting mean-tone for the first time is to laugh with relief.