30 different key signatures exist (15 for major scales and 15 for minor scales). Most theory students are expected to memorize all 30.
Fortunately, using the key signature calculation method, one only has to memorize seven.
In the calculation method, each key signature is assigned a numeric value based on the number and type of accidentals. Sharps are positive; flats are negative.
The key of C Major has no accidentals; therefore, its numeric value is 0.
The key of D Major has two sharps; thus, its numeric value is 2.
The key of E Major has four sharps - a numeric value of 4.
The key of F Major has one flat; therefore, its numeric value is -1. (Remember: flats are assigned negative numbers)
The key of G Major has one sharp. Its numeric value is 1.
The key of A Major has three sharps - a numeric value of 3.
Finally, the key of B Major has five sharps - giving it a numeric value of 5.
These seven values must be memorized before we can proceed.
Next, let's compare Cb, C, and C# Major.
If we start at C Major and subtract 7, we end up at Cb Major.
If we start at C Major and add 7, we end up at C# Major.
These two numeric relationships can help us calculate keys that we do not know.
Let's figure out Eb Major. First, start with E Major, which has a numeric value of 4.
To convert to Eb Major, subtract 7.
The result is -3; thus, Eb Major has 3 flats.
Let's try F# Major. Start with F Major, which is -1.
To convert to F# Major, add 7.
The result is 6; thus, F# Major has 6 sharps.
Next, we will examine minor scales. Compare C Major and C Minor.
To convert a major scale into its parallel minor, simply subtract 3.
Let's calculate D Minor. We will start with D Major, which is 2.
Next, simply subtract 3.
The result is -1. Therefore, D Minor has one 1 flat.
Next, let's try F Minor. We will start with F Major, which is -1.
Next, subtract 3.
The result is -4. Thus, F Minor has 4 flats.
Some key signatures require two conversions. For example, let's calculate G# Minor.
Start with G Major, which has a numeric value of 1.
Next, add 7 to get to G# Major.
Finally, subtract 3 to convert to G# Minor.
The result is 5. G# Minor therefore has 5 sharps.
Using the calculation method, it is possible to calculate key signatures which have more than seven accidentals.