By the late 1600s, composers were beginning to make much greater use of transposition between keys and the existence of wolf notes in tunings such as 1/4 comma Meantone were becoming unacceptable. However, the need remained for consonant 3rds and 5ths a seemingly insoluable dilemma. The only answer was to compromise and the compromise chosen was to flatten only some of the 5ths rather than all of them. If we take an early example French Ordinaire it may be seen that this creates two different intervals for the 5ths, with some 5 cents flatter than the natural pitch and some 5 cents sharper. It has reduced the wolf to 14 cents, from 36 and kept a significant number of the 3rds at their perfect ratios.
Such temperaments are not meantones, since a further effect is to create different size tones, an example being the key of Bb with its major 2nd at 204 cents and its major 3rd at 397 cents (only 193 cents higher). Instead, with their attempt to resolve all of the above needs, these temperaments are called 'well-temperaments'
Two further examples, Kirnberger III and Werckmeister spread the syntonic comma (22 cents) and the Pythagorean comma (24 cents) respectively, across 4 intervals (each choosing a different set of intervals) removing the wolf altogether at the expense of some sharper 3rds.
Lastly, in this set of examples, Vallotti/Young spreads the Pythagorean comma across 6 intervals (4 cents) to remove the wolf, creating a narrower range of 3rds in the process.
The is one further, very important difference with the well-temperaments which has not revealed itself so far. If 1/4 comma Meantone and Werckmeister are compared not with natural tuning but relative to themselves, a very interesting difference appears. The meantone tunings are identical in each of the playable keys but the well-temperaments are different! This means that modulating to different keys will not only have the effect on the listener which we recognise today, but there will be a 'colour' difference as well with different interval sizes in different keys. To look at this a different way, a piece of music may be composed for a particular key because of the way that key sounds, relative to others even with the same tuning.
This takes the discussion neatly to J.S. Bach and the Well-Tempered Clavier. This set of keyboard pieces is deliberately written in each of the 24 major and minor keys. Because music was Bach's medium, rather that words, he neglected (or didn't see the need to) write down two very important facts. The first is that he doesn't tell us which of well-temperaments he used, though the smart money appears to be on Werckmeister. The second and much more fascinating fact, which remains the subject of academic debate to the present day, is whether he wrote the 24 preludes and fugues as a celebration of the fact that these keys were available on one 'clavier' or wether he was celebrating the subtle differences in colour created by the new well-temperaments.
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