Relativity


(entry for 11/8/24)


One of the things about music that is confusing to non-musicians (and, sadly, to some musicians as well) is the idea of Keys.

“What Key are you playing that in?” one pianist or guitarist will ask another.

(This whole problem isn’t made any easier by the fact that the physical notes on a piano or on a woodwind instrument such as a flute or clarinet are also called ‘keys.’ But the two uses of the same word do not mean the same thing! Though they’re a tiny bit related.)

What we mean when we say that we’re playing in the Key of G Major, for example, is that the G Major Triad is the Home Chord (the Tonic Chord) of the piece. Any song or other composition will usually have the Tonic Chord as its first chord and also as its last one, especially as the last one.  When that is the case, it’s usually very easy to figure out what key the piece is in! (You can’t count on it, though. There aren’t many exceptions, but there are a few.

There’s another way, too, which always works: the key signature. If you know how to read it, the key signature tells us what key you’re in. Or, rather, it almost tells us. Each key signature is correct for two different Keys, one major and one minor. For example, a key signature of one sharp means that the piece is either in the key of G major or in the key of E minor. A key signature of two flats means that the piece is in either B-flat major or G minor. (This would be a good place to mention that in most traditional writing about music, at least about classical music, a major key is spelled with a capital letter, and a minor key is spelled with a lower-case letter. From now on, we’ll follow that tradition. So that last sentence before the parentheses would be: A key signature of two flats means that the piece is in either B-flat major or g minor.) The example at the head of this post is of the key signature of two flats, which is the one we just talked about.

The question arises, then, if you don’t have all your key signatures memorized, how do you figure out what the Key is for a given signature that you’ve never seen before? And the answer is (if we’re talking sharps): the right-most sharp is one-half step below the name of the major key, or a whole step above the name of the minor key. That sounds confusing until we put it into practice, so let’s do so right now: In a key signature of three sharps, the sharp farthest to the right of the signature is the note G-Sharp. What is a half-step up from G-Sharp? The answer is: A. Therefore, the Key for a key signature of three sharps, if we’re talking major, is: ‘A major.’ 

Here’s what a key signature of three sharps looks like:



What about minor? A whole step below G-Sharp is F-Sharp. Therefore the Key for a piece in minor with three sharps as the key signature is: f-sharp minor. Another word to learn is the word ‘relative.’  A relative key is one that has the same key signature as another key. To use the example we’ve just been working on, it follows that f-sharp minor is the relative minor of A-major. And A-major is the relative major of f-sharp minor.

Got it?

There’s another term we should learn also. “Enharmonic.” Enharmonic keys are ones that share the same letter name. For example: C major, and C minor. These do NOT have the same key signature, but they do share the same note-name, so they are enharmonically related rather than key-signature (or harmonically) related. The key of C major is the enharmonic major to the key of c minor. And vice versa.

Let’s try it with a 'flat' signature. Let’s say we have a four-flat signature.

The rule for flats is: the name of the major key is a perfect fourth below the right-most flat symbol in the key signature. 

When a key signature has four flats, the one farthest to the right is D-flat. What’s a perfect fourth below D-flat? Answer: A-flat. Therefore the major Key for a key signature of four flats is: A-flat major.

What about minors? The minor Key for a flat key-signature is either a major 3rd above the farthest-right flat in the signature, or a minor 6th lower, whichever is easier for you to think about. So, going back to our four-flat signature, where the farthest right flat symbol is for the note D-flat, the minor key for that signature is f minor, because the note F is a major third above D-flat, and it’s also a minor sixth lower than D-flat. (Remember, music is not math!)

Here’s what a key signature of four flats looks like:



There’s one key signature that you just have to memorize, because there are no sharps or flats in it, to work from. I’m talking about the so-called empty key signature, where there’s nothing to see at all! (It’s sometimes also referred to as the ‘invisible’ key signature.)

The major key for the empty key signature is ‘C’ major. The minor is ‘a’ minor. These are the equivalent of the Ionian and Aeolian modes that we talked about last time, provided we are talking about Natural minor, and not one of the other two kinds. (We will get to the three kinds of minor in our very next post.)

Which brings us to a related subject, which some musicians find even harder to learn than how to figure out what key they’re in. Namely, how do you construct a key signature correctly?

The first sharp in any sharp signature is F-sharp. (Remember in the chromaticism post we mentioned that F-sharp was one of the first two ‘black notes’ invented? And the only sharp one of those two? That’s why it’s the first sharp in any sharp signature. It came first in time, so it comes first in ‘rank.’

For each additional sharp in a signature, you go up a perfect 5th from the one before. So to make a signature of two sharps, you go up a 5th from F-sharp and land on C-sharp, and that’s the order you put them in to make a two-sharp signature: F-sharp on the left and C-sharp on the right. In treble clef, it looks like this (be aware that though we went up a perfect fifth to get the C-sharp we needed to write next, we wrote it lower on the page, because putting it higher would have put it way above the staff):


Quick review: What major key does that put us in? Remember, go up a half-step. A half-step above C-sharp is D, so the major key for two sharps is D major.

To add each additional sharp to the signature, you simply go up another perfect 5th, till you have used up all five black keys. (If you follow carefully each step in the process, you will discover that five sharps equals B major and g-sharp minor.)

Remember that we said the first flat note invented was B-flat? (Unless you’re in Germany or Austria, where it’s called just plain B.) Logically, it follows that the one and only flat, for a key signature of one flat, is B-flat. To get the additional flats you go down a perfect 5th each time, instead of up. The five black notes, in order from left to right in the signature, and also the order in which they were invented, is:

B E A D G

Quick review: What would the minor be for five-flats? The right most flat symbol in the key signature is G-flat. A major third above G-flat is B-flat. Therefore the minor key for five flats is b-flat minor. (I’ll let you figure out what the relative major is.)

The only thing left to worry about is: When you’re constructing a key signature, where do you put the sharps or flats? Which space or line? When do you go up? When do you go down?

The answers are (using sharps, for treble clef): 1. Place the first symbol as high as possible within the staff. (Don’t go above or below the staff.) 2. Always place the second symbol lower than the first one for sharps. 3. As you add sharps or flats, alternate going up and down, whenever possible. (For sharps, it is OK to go above the staff, but only just touching it, not by using ledger lines.) For example, the third sharp in treble clef is placed on the G-space above the treble clef, because that doesn’t require a ledger line, but the fifth sharp is placed on the space within the staff because it would need a ledger line to put it above the staff.

Once you have worked out the correct placement for the sharps, using the treble clef, you simply copy that pattern onto the bass clef, whether that follows the rules for the treble clef or not.  (But of course adjusting for the proper bass clef pitches.)

Here’s the key signature for five sharps, in both of the two most common clefs. If you need to see what fewer sharps would look like, just cross out the ones you don’t need, from right to left. (Not left to right!)



Note that even though you could have placed the fifth sharp on the top line of the bass staff (using the treble clef rules), you don't.  You keep the pattern the same.

The treble clef rule is almost exactly the same for flats, except that the second flat is placed higher than the first one, not lower. Also, while it’s now OK to use the space immediately below the staff, it’s not OK to use the space right above the staff.

Here is the key signature for five flats.




Again, you keep the pattern the same for the bass clef, even though you could have put the fifth flat on the top space and been within the rules.

Also, please note: you never have both sharps and flats in the same key signature.  It's one or the other.  (Or neither, in the case of the 'empty' signature.)

Since there are seven different letter names available (in non-Teutonic language countries), it's possible to have key signatures of up to seven sharps or seven flats.  This involves the concept of white-note sharps and flats, which we will cover later.


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