Working Out Keys

[fuel925]

I thought it was time I brushed up on my knowledge of keys, so i've been going through some reading material on how to work out keys from the sheet music. I have successfully learned how to work out the name of the key by looking at the key signature, however I am looking for methods on how to work out what #'s or b's are necessary when given the name of the key. For instance, if someone asked you "Write the key signature of C Minor", how would you work this out? (assuming you had NOT memorised this key).

We all know about the circle of fifths diagram, and I also have a different table memorised that gives all this information. This is all very good for exams, where I can draw out the table at the beginning of the exam, and I can use it throughout, however i'd like to know if there was a quick way of working out keys when I just need to know one, and don't want to spend time drawing out a table. Is there a method to work out keys using the piano keyboard?

[charleyg]

I noticed quite early on that the relative minor scale starts on the 6th degree of the major scale.  If you invert a major 6th, you get a minor 3rd.  Somewhere along the line I noticed that inverting intervals gave you a sum of 9 (6+3=9), that perfects stayed perfect but that majors alternated with minor.  Anyway, getting back to this point, if the key signature was G, then a minor 3rd down from G is E, so it's also the key signature for Em.  Vice versa, if I wanted the key signature for Dm, I know that the minor 3rd is F, so I'd use the key signature for F major.

I'm sure there's a million other good ways to work this out too.

[tac-tics]

It's a simple math game of sharps (flats are counted as negative sharps). This method is from www.musictheory.net

Find the base letter (counting up by even numbers)
C: 0 (even numbers, counting up by 2 from 0)
D: 2
E: 4

F: -1 (odd numbers counting up by 2... but starting at -1 =-)
G: 1
A: 3
B: 5

Apply Sharp/Flat (the difference of 7)
If the key is natural, +0 (no change)
If the key is sharp, +7
If the key is flat, -7


Apply Minor (the difference of 3)
If the key is major, +0 (no change)
If the key is minor, -3

So if you can remember the counting by two step, and the magic numbers 7 and 3 (which are traditionally lucky numbers in many Western cultures), you can always figure out the key sig.

Example: F# minor.
1) F is -1 sharps by the table above
2) F# is sharp, so +7 for a total of 6
3) F# minor is minor, so -3, for a total of 3.

To get the name from the signature, just work the process in a backwards, keeping the number of sharps between -7 and 7. Note, though, one signature is used for many keys.

Reduce Minor to Major
If the key is major, +0 (no change)
If the key is minor, +3

Reduce Sharp/Flat
If the key is natural, +0 (no change)
If the key is sharp, -7 (negative... the opposite of above, since we're working backwards)
If the key is flat, +7 (again, the opposite of above)

Look up Base Letter
Use the table above to find the letter.

Example: 4 flats (-4)
If you add +7 to make it a flat key, you get, 3. Since 3 is A, the key is A flat major.
However, you can start with -4, and add +3 for a minor scale, the total is -1, so the key also acts as F minor.

[abell88]

Example: 4 flats (-4)
If you add +7 to make it a flat key, you get, 3. Since 3 is A, the key is A flat major.
However, you can also apply the minor modifier of -3, for a total of 0, so the key is C minor as well.

But the key signature of C minor is 3 flats...the minor key with 4 flats is F minor.

For major # keys: the last # is one semitone lower than the name of the key. Example: B major-- the last # will be A#. If you know the order of #s (F C G D A E B), you can see that B major will have 5 #s.

For major flat keys: the last flat is a 4th higher than the key name. Example: A-flat major -- the last flat will be a 4th higher than A flat, which is D flat. If you know the order of flats (B E A D G C F), you can see that A-flat major will have 4 flats.

Minor keys: as noted above by charleyg, find the minor key's relative major by going up a minor 3rd (count 3 semitones and make sure you have a letter name in between). Then use the above rules to find the major key's key signature, which is shared with its relative minor. Example: B-flat minor - count up 3 semitones to D flat (not C#, because you must have a letter name between the two names). The last flat will be a 4th higher than D flat, so it's G flat. Using the order of flats, you can see that the key signature will be 5 flats.

To use these rules, all you have to do is memorize the order of the #s and flats:
sharps: Father Charles Goes Down And Ends Battle
flats: Battle Ends And Down Goes Charles' Father

[tac-tics]

But the key signature of C minor is 3 flats...the minor key with 4 flats is F minor.

Indeed. This is why your math teachers tell you to double check your work! I corrected my mistake above (I had subtraced 3 instead of adding it).

[abell88]

Well, tac-tics, I'm afraid I wouldn't call your method "simple"...but, as my father used to say, "There's more than one way to skin a cat!"

Not that I believe in skinning cats...

[tac-tics]

Well, tac-tics, I'm afraid I wouldn't call your method "simple"...but, as my father used to say, "There's more than one way to skin a cat!"

Not that I believe in skinning cats...

I'm sure I could find a number of much, much more comlicated ways to do it, noting that the "base" values above form a residue number system modulus 7 

What about languages which don't use the Latin alphabet? Your mnemonics would be just as complicated to explain as my system =-P

[abell88]

What about languages which don't use the Latin alphabet? Your mnemonics would be just as complicated to explain as my system =-P

Very true...but on this forum we all do use the Latin alphabet, and even the same language. I wonder though, how those who use "Do Re Mi" for the letters manage it?

I'm sure I could find a number of much, much more comlicated ways to do it, noting that the "base" values above form a residue number system modulus 7

I'm sure you could! (Were you in on that contest some months ago with questions like, what are the notes of the iiiflat3 chord in the minor key with 47 sharps?) I haven't been in a math class for nearly 30 years, so I'm a little rusty...even the terminology has changed in that time, I find, so I look at my kids' math homework and don't even recognize it as something I used to be able to do (I was quite good at math in those days).

[Bob]

Just memorize them.  There are only 15 or 30. 

Memorize the order of flats and sharps.

Relate the relative Major and minor together like everyone is saying.

I assume you know how to play all these scales already?

If it's major and sharp, go up a half-step from the last sharp to find the major key center. 
If it's major and flat, the second to last flat is the key center.

Take a look at the piece, esp the first and last areas of notes.  Look for a V I to tell you what key you're in.  Look at the bass note. 

[Tash]

if you're really stuck you could just remember that C major (A minor for minor keys, but remember to raise your 7th) has no black keys, then work your way up chromatically til you reach your chosen key and figure out what the #'s and b's are