Are there any tuning differences between the C# Major Scale and Db Major Scale? [duplicate]

Question

I am looking for a little clarification related to the differences between sharp (♯) and flat (♭) notes in music theory.

1. Some people say C♯ and D♭ are the same, but some say they are not. Some say they both have the same frequency in the 12 tone system. Is there any other music system where these notes have different frequencies? I've also heard that C♯ actually has a lower frequency than D♭.

2. I saw that the C♯ Major and D♭ Major scales have the same notes in them. So, can we say both are the same?

3. I've heard that there are pianos with separate keys for sharps and flats. Is that true? If so, how are the sound frequencies calculated?

Answer 1

In 12edo, there are only 12 notes, and C# and Db have the same pitch and same sound on instruments which are tunes thus - like pianos.

The difference comes, and I think this is what you're asking, in other tunings, such as just tuning, which were common before the compromise of 12et became regularly used, to enable instruments to play more melodiously in any key.

On a violin, for example, where notes can be changed very slightly in pitch quite easily, in some keys, playing a Db will not be exactly the same as playing a C# in other keys. The difference is not great, but by playing 'in the cracks', melodies will sound more in tune.

As far as your example of Db and C# notes or scales is concerned, since they both start from the same note, the intervals will be the same, thus they will sound identical. And on piano, that's all they can do.

In answer to your header, I'd go as far as to say assuming the scales start at exactly the same pitch, played on a 12et, the only difference is going to be the names of the notes played. Being both major scales, there can't be any other differences. And even on instruments like violins, even playing just intonation, again assuming the same start pitch, there will be no differences in what is heard.

Never come across a piano with different sharps and flats - the main problem being where would they all fit?!

Answer 2

This question is quite similar to Tuning of Accidentals & Scales, and you may find some useful information there.

Some people say C# and Db are same, but some say they are not.

The most precise way to say it is that they are 'enharmonic equivalents'. Whether you think they are the same 'note' is a matter of opinion, and depends on your definition of 'note'.

Often they are the same pitch; sometimes they aren't.

Some say, they both have same frequency in 12 tone system.

As you mention in your question, just knowing the note name doesn't define a frequency (or pitch). You need to know the note name, the reference concert pitch, and the temperament and intonation to which the instrument is tuned (for a fixed pitch instrument like a piano), or with which it is being played (for a continuous pitch instrument like a violin).

Is there any other music system where those have different frequency?

Simplistically speaking, you can think of an infinite number of combinations of situations where a C# played with one combination of concert pitch, tuning and temperament would have a different pitch to a Db played with another.

One a single given instrument on any given day, they might have a different frequency any time a player can play them differently, and chooses to.

I also heard that C# is actually have less frequency (Hz) than Db

That may be true in some situations, but it's not true as a general rule. As above, you need to define more than just the note name to be able to calculate the frequency of a note.

I saw that C# Major Scale and Db Major scale have same notes in it. So, can we say both are same. ?

It's the same as my answers above for a single note. Are you talking about an instrument where the player can't play the enharmonically equivalent notes differently? If so, they will have the same frequency. If not, then players may choose to play them differently.

Generally, singers and players of continuously-pitched instruments tend (consciously or unconsciously) towards using just intonation in the key that they're playing in. In those cases, it might be very common for a given note that we're calling C# to have a different frequency to one we're calling Db.

I heard that there exist piano for separate keys for sharps and flats ?

I think there are some historic instruments that do - I'm not personally an expert, but hopefully someone will be. It's not commonly-found in modern instruments though.

Answer 3

They have the same pitches, they do not have the same notes (Important distinction)

C# major has seven sharps, where Db has 5 flats. They may all be enharmonic equivalents of each other, but that does not make the notes the same.

Even on the piano, where the fingering for the two keys are the same, there is still quite the paradigm shift when you think about five flats vs seven sharps.