Key Signature Calculation
  • 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 C# Minor.
  • Start with C Major, which has a numeric value of 0.
  • Next, add 7 to get to C# Major.
  • Finally, subtract 3 to convert to C# Minor.
  • The result is 4. C# Minor therefore has 4 sharps.
  • Using the calculation method, it is possible to calculate key signatures which have more than seven accidentals.
  • While these exist in theory; in practice, they would not be used.
  • For example, let's calculate G# Major.
  • Start with G Major, which has a numeric value of 1.
  • Next, add 7 to get to G# Major.
  • The result is 8. G# Major therefore has 8 sharps - a double sharp and six normal sharps.
  • Again, this key is strictly theoretical. In practice, a composer would use the enharmonic equivalent of Ab major.
  • Use this chart for reference to the key signature calculation method.
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