Key Signature Calculation (via MusicTheory.net)

Lesson from MusicTheory.net

Recently I found myself in a situation quite common for me: purposelessly browsing musictheory.net and aimlessly clicking through the site's many lessons and exercises (yes, really). One lesson I came across was called Key Signature Calculation, and it explained a handy method of calculating key signatures with minimal rote memorization required.

I have previously written about key signatures in a post where I shared a visual aid (a variation on the standard Circle of Fifths) that can be used to remember the number of sharps or flats in a particular key. This tool covers 12 major keys, and by extension, 12 minor keys. That's a total of 24 keys, and when you account for enharmonic keys, there are actually 30 possible key signatures.

Instead of struggling to memorize all these key signatures, this calculation method can be used with minimal memorization. All the information that must be memorized to use this method is summarized in the following image, which I lifted from musictheory.net:

The Method

The top row of the image shows the seven notes of a C major scale (C, D, E, F, G, A, B) with their respective key-signature-numbers. The absolute value of the numbers refers to the number of sharps (positive) or flats (negative).

The next few bits of information (bottom row) show three possible calculations you can use to get from a key from the top line to a different key not on the top line:

• Major key to parallel minor: subtract 3  (C major to c minor: 0-3=-3
• Key to half step lower: subtract 7 (C major to Cb major: 0-7=-7)
• Key to half step higher: add 7 (C major to C# major: 0+7=7)

The method is simple: apply the appropriate operation (from the image's bottom row) to a (top-row) numeric value.

Application

Once that information is committed to memory, it is now possible to quickly and easily calculate any key signature. Let's practice:


1. Desired key signature: Eb major

• E's numeric value is 4, then we subtract 7, yielding -3
• -3 translates to 3 flats (Bb, Eb, Ab). Voila.

2. Desired key signature: G minor

• G's numeric value is 1 (1 sharp). To get to its parallel minor, subtract 3, yielding -2.
• -2 translates to 2 flats (Bb, Eb). Boom.

3. Desired key signature: F# major

• F's numeric value is -1 (1 flat). To go up a half step, add 7, which yields 6.
• 6 translates to 6 sharps (F#, C#, G#, D#, A#, E#). Piece of cake.

Final Words

That's about it. Commit those seven key-signature-numbers (from the top row of the image) to memory, then either subtract 3 (to get to the key's parallel minor), add 7 (to go up a half step), or subtract 7 (to go down a half step). The resulting number tells you the number of sharps (positive number) or flats (negative number) in your desired key. If you want more key signature information, check out this circle of fifths visual I made.

Visual Aid for Key Signatures

The visual aid

One late night I began doodling around the topic of key signatures. I had fun interweaving note names with numbers, and when I was finished, I found that I had created a musical tool that perhaps you might find handy.

The end result, in effect, is a visual fusion of a key (letter name) with its respective number of sharps or flats. Here I have posted the tool in two forms (click to enlarge each image):

• Vertical (black and white), progressing in ascending fourths as you move from the top of the image to the bottom.
• Circular (with color), as in the circle of fifths. As you move clockwise, you are moving up by fifths. As you move counter-clockwise, you are moving up by fourths.

Circle of fifths

*Click here for a larger version of the vertical image (left).

*Click here for a larger version of the circular image (right).

 To use the visual tool...

1. Locate your desired major key.
2. Observe its corresponding number. This is the number of sharps/flats in a particular key.
3. If you are in a flat key (the blue half of the circle), add that number of flats to the key signature by following the order of flats (B E A D G C F).
4. If you are in a sharp key (the green half of the circle), add that number of sharps to the key signature by following the order of sharps (F C G D A E B).

 *Keep in mind this tool is designed for finding the key signatures of major keys. That said, it's easy enough to figure out the key signature for a minor key if you know its relative major key.

• Relative keys share the same key signature. In the same way you and your relatives share similar DNA, relative keys share the same number of sharps/flats.
• To go from a minor key to its relative major key, simply move up three half steps.
• Example: To get from F minor to its relative major, walk up three half steps (F#, G, Ab). We arrived at Ab, which means the relative major of F minor is Ab major. Therefore, we can say that both F minor and Ab major have the same key signature!

**In these visuals, I included only one of the common enharmonic key spellings (Gb and F#). Other enharmonics include Db/C# and Cb/B.

If you found these visuals helpful or if you know someone who might find them helpful, please feel free to share!