# What key has 30 sharps?

Musical keys typically have 0 to 7 sharps or flats, but we can imagine adding any number of sharps or flats.

When you go up a fifth (seven half steps) you add a sharp. For example, the key of C has no sharps or flats, G has one sharp, D has two, etc. Starting from C and adding 30 sharps means going up 30*7 half-steps. Musical notes operate modulo 12 since there are 12 half-steps in an octave. 30*7 is congruent to 6 modulo 12, and six half-steps up from C is F#. So the key with 30 sharps would be the same pitches as F#.

But the key wouldn’t be called F#. It would be D quadruple sharp! I’ll explain below.

Sharps are added in the order F, C, G, D, A, E, B, and the name of key is a half step higher than the last sharp. For example, the key with three sharps is A, and the notes that are sharp are F#, C#, and G#.

In the key of C#, all seven notes are sharp. Now what happens if we add one more sharp? We start over and start adding more sharps in the same order. F was already sharp, and now it would be double sharp. So the key with eight sharps is G#. Everything is sharp except F, which is double sharp.

In a key with 28 sharps, we’ve cycled through F, C, G, D, A, E, and B four times. Everything is quadruple sharp. To add two more sharps, we sharpen F and C one more time, making them quintuple sharp. The note one half-step higher than C quintuple sharp is D quadruple sharp, which is enharmonic with F#.

You could repeat this exercise with flats. Going up a forth (five half-steps) adds a flat. Or you could think of a flat as a negative sharp.

## 4 thoughts on “What key has 30 sharps?”

1. Dave Tate

Now repeat the exercise in some temperament other than equal temperament… Ouch!

2. patfla

John, you might know.

Charlie Parker’s “higher intervals”: in what are the 9th, 11th and 13th different from the 2nd, 4th, and 6th?

3. I think the difference is how people think about them. For example, 9th implies there’s a 7th as well. Sometimes you’ll see a 2 to indicate just adding the 2nd to a triad.

11th implies there’s a 7th and 9th as well, and often the 11th is raised. 4th implies a suspended chord, e.g. CFG resolving to CEG.

4. patfla

I think you’re right and I’ll keep that in mind as I study Parker solos.