What key is this?

In Lesson Two of basic music theory I was told that there are two scales, major and minor. Well, two if you counted the melodic “natural” minor and ignored the inconvenient harmonic minor. And, for our continued convenience, let’s ignore harmonic minor for a little while longer.

It turns out that “C major” and “A minor” scales can both be played on the piano’s white keys; you just start from C (or A) and go up (or down) playing one white key at a time until you reach the same note an octave higher (or lower). “A minor” is called the relative minor of “C major”.

This pattern propagates simply and elegantly through all keys. When we change key from C to G, we add one sharp (F#) and discover that we can play both “G major” and “E minor” in the same key. Using one more sharp (C#) you can play “D major” and “B minor”. Next we add a G# with A major and its relative minor, F# minor, both played using the same three sharps.

After Lesson One we were asked what key has no sharps or flats, and the single correct answer was C major. But after Lesson Two we were asked, “What key has no sharps or flats?” and the double correct answer was “C major and A minor”.

We had accepted that a scale consists of a sequence of full-tone or semi-tone intervals which are defined by the position of the piano’s black keys.

Now we know that there are seven modes that are related to (or generated from) seven scales that can be played on the piano’s white keys:

  • We can start on a D and get a Dorian Scale;
  • We can start on a E and get a Phrygian Scale;
  • We can start on a F and get a Lydian Scale;
  • We can start on a G and get a Mixolydian Scale;
  • We can start on a A and get an Aeolian Scale;
  • We can start on a B and get a Locrian Scale;
  • We can start on a C and get an Ionian Scale.

So we could answer the question, “What key has no sharps and no flats?” with a pedantic response, “C (Ionian major) and A (Aeolian minor)”. In fact we could answer the question, “If you allow the existence of seven scales, then any key can have no sharps and no flats, see the list above.

In the tabulation below you see a column for each key (A, B, C, D,..) and a row for each mode (from Lydian to Locrian). Every position in the table shows the number of sharps or flats that corresponds to a valid mode in that key. For example, we can use the table to answer the question, “What key has 3 sharps?” and the answer is A (if you mean Ionian). The answer is also B (if you mean Dorian). The answer is also C# (if you mean Phrygian). The answer is also D (if you mean Lydian). And so on.

Tabulation of the seven church modes in all possible keys
Tabulation of the seven church modes in all possible keys