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 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.
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.
- 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.
- 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.
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.