Well, here goes. I’ve never yet found any correlation between readership and what I write about, so what have I got to lose.
If you take a piano with a fairly standard seven octave keyboard, you can of course play the C near the bottom of the keyboard and make seven steps, C to the next C, and finally reach the C that is the top note of most pianos; the one that to many people including myself often sounds more like a click than a proper note: our perception of very high notes as notes drops off with age and in any case is subject to variations according to the time of day, our mood and so on.
You could also get from that low C to the high one in smaller steps; steps of a perfect fifth: C, G, D, A, E, B, F#, C#, G#(Or A flat), E flat, B flat, F, and finally that top C. And that top C is the same top C you reached before by octaves. Isn’t it? Yes of course it is; it’s the same ‘key’ (in the sense of keyboard lever): that’s the way pianos are made.
But it only works like that as the result of a compromise: if our fifths were real perfect fifths, having the frequency ratio of 2 to 3, that is, if a note has a frequency of 200 Herz then the note a perfect fifth higher has a frequency of 300 Herz, if, as I say, we insisted on such perfection, then we would find that the high C we finally arrived at, (and of course we would need an audio signal generator rather than a piano to do it), was distinctly sharp compared to the high C we arrived at by the octave method. Sharp, in fact, by about an eighth of a tone; a painful amount known as the Pythagorean Comma.
The Pythagorean Comma almost certainly has nothing directly to do with Pythagoras: there were no pianos then, and ancient Greek music, about which we know very little, used a completely different scale system. The name is probably more to do with the fact that Pythagoras notoriously had an Asperger’s-ish obsession with precision and wanted things to work out just right, so this anomaly would have freaked him out. We all know how upset he was by the failure of the ratio between the circumference and diameter of a circle (known as Pi, π,) to come to a neat fraction.
In fact, on a modern piano all the fifths are tuned just a teensy bit flat; not enough for anyone to notice. The accumulated little bits of flatness mean that the C you come out at, going up in fifths, is the ‘right’ one; exactly seven octaves above the piano’s bottom C.
Now in the early days of keyboard instruments, (not actually pianos because at the time I’m talking of Cristofori was still working on his invention, but rather harpsichords, clavichords and so on, but let’s for convenience call them all pianos) they hadn’t worked all this out; the tuner might tune someone’s piano, starting with a C, to have all its fifths really perfect ones. The thing would then play beautifully in C major and still be OK in the closely related dominant of G major and subdominant of F major. But getting a bit more adventurous and going into D or B flat, people with sensitive ears would notice some oddity; a sourness or sweetness not perhaps amounting to real out-of-tuneness. If the player got really clever and went into B major it would sound pretty off, and I should think D flat major would have been ghastly. So a good tuner might ask the player which keys he most liked, and tweak a few notes so that things weren’t too bad. But no amount of tweaking could hide the fact, as it most definitely was in those days, that different keys had different qualities: if C were neutral, then B flat might seem to most people a touch martial, and D rather bright. D flat was positively funereal, and E a bit ethereal. Though people might disagree about the characters of different keys, these were real differences, which would have been measurable had the necessary scientific instruments been available.
Some composers and players — including JS Bach himself — were discontented with this. Wouldn’t it be nice, they thought, to have a piano that played really well in all keys, so that you didn’t have to get up and go to a friend’s house when you wanted to play in A, because your own piano only really sounded right in, say, B flat? Just flattening the fifths wasn’t enough; really one needed many much finer adjustments to ensure that the relations between the notes of the scale would be identical in all keys. Work on this went on for many years, centuries even, before the present system of equal temperament was arrived at, but there was a breakthrough in the time of Bach, and he celebrated by writing one of the greatest of all keyboard works: The ‘Well-Tempered Clavier’, also known as the ‘48’; two sets of 24 preludes and fugues in all possible keys, and all playable (if you’re good enough; I can do precisely 1/96th of the thing) on the one instrument.
But what of ‘Key Mood’? Surely there can now be no such thing? Indeed there are many who insist that because there is now no ‘scientific basis’ for a belief in different moods for different keys, there can’t be any such thing. I know of a university professor who has even developed a galumphingly crass set of tests, which ‘prove’ (to his satisfaction, if to no-one else’s) that Key Mood is just a persistent myth. Nevertheless there have always been, and still are, many people who believe in it, including composers from Mozart to the present day. Berlioz once wrote an exposed passage for trombone in D flat and then panicked; could trombonists reasonably be expected to play in such a key? He dashed out to find a trombone player, who laughed and said that actually it’s quite a comfortable key on the trombone. Believers in Key Mood are not all new-agey airy-fairy types who are so open-minded their brains have dropped out. I certainly believe in key mood, also that it is something so delicate and evanescent that it hides when you try to prove or disprove it. Sure, in the current state of science there is no explanation for it. Yet.