2.2.2: dissonances

This tuning gives you lovely pure major 3rds; but the 'black' notes of the keyboard are without any question c#, e-flat , f#, g# and b-flat, and you have no d-flat, d#, g-flat, a-flat or a#. You can play a whole lot of music without feeling the need of a d-flat, g-flat or a# but having to manage without d# and a-flat may be a nuisance.

You can of course choose to tune d# instead of e-flat (you get it as a pure third above b-natural, or a tempered 5th above g#): and you can choose a-flat instead of g# (a 3rd below c, or a tempered 5th below e-flat); and once you're used to it, you can do it between pieces in a few seconds. But make sure you don't ruin a special effect by doing so:

Roger North:

"It is observed that the defects that will fall in the use of some keys, as F with a flat 3rd... and others, by meer out-of-tuned-ness have certein caracters, very serviceable to the various purposes of Musick; so, to instance in one for all, F with a flat 3rd hath somewhat that more resembles a dolorous melancholy than any of the rest..."

In one of Dowland's songs, for instance, he uses the dissonant interval f-g# as if it were f-a-flat to express the word 'Hell' in the poem.

We have established that the 3rds and octaves are in tune in this temperament, and that the flatness of the 5ths is small enough to be accepted: the 4ths are sharp by the same amount, as are the minor 3rds (they are tuned as major 3rds below the tempered 5ths): and the sixths are as in tune as the thirds.

What of the 2nds? They are dissonant and produce beats even when they're in tune, so how can you say whether they're in tune or not? Well, if they're not right they will sound more dissonant than they need to: and even if they are dissonant, they are still intended to be usable, as a contrast to all those cloying consonances. Look at ex.1 again. At a first glance you may notice that the notes in this natural scale get closer and closer together the higher you go; at a second glance you may notice that that's not quite right, that the progression is a bit uneven - there seem to be two intervals of one-and-a-half semitones in a row, and as many as four whole tones one after the other. Actually, as you might guess, it's not that nature is inconsistent, but that people's thinking - and therefore their writing - is not subtle enough to show the consistency of the pattern.