Why do black keys on a piano have 2 names?

Question

I’m a complete novice to music and am learning piano, I just bought some stickers with the notes and letters for my keys but the black keys have 2 notes and letters, do they make a different sound when you hit them higher up vs lower on the key?

In: Other

Answer 1

C# and Db (two names for the black note in between the C and D white notes) are not necessarily the same thing. One (Db) is a minor second *above* C, the other (C#) is a minor second *below* D.

In the typical tuning for modern instruments in the West – twelve-tone equal temperament – the two happen to correspond to the same frequency. But in other tuning systems, they don’t.

If you tune an instrument to a specific key (“just intonation”), the sound of each note is defined by ratios of the key note (“tonic”)’s frequency. If, for example, your key is C, then you define other notes as ratios of the frequency of C. For example, the perfect fifth of the key of C (which happens to be G) is tuned to 3/2 the frequency of C. In just intonation, the minor second – in this case, Db – is 16/15s the base frequency, or 1.0666… times the base frequency. C#, on the other hand, doesn’t exist in the key of C, and its frequency depends on what key it *is* tuned to – but in any event, in just intonation, it won’t be 16/15ths the frequency of C.

In equal temperament, however, the notes are equally spaced. Each note is 2^(1/12) = about 1.0594 the frequency of the previous one. In equal temperament, the notes aren’t tuned to a specific key, and you can use any note in any key and get the same relative ratios between keys – at the cost of those ratios not being quite perfect. In equal temperament, C# is 2^(1/12) the frequency of C, D is 2^(2/12) the frequency of C, and C# is 2^(1/12) *below* the frequency of D, which happens to be…2^(1/12) above the frequency of C. So in this tuning, C# and Db are the same sound.

We call these kinds of notes that are the same in equal temperament but not just intonation, *enharmonically equivalent*. In equal temperament you can freely swap one for the other. In just intonation, swapping one for the other changes the quality of the interval between notes, creating a dissonant [wolf interval](https://en.wikipedia.org/wiki/Wolf_interval).