Why is the interval between C# and F a diminished 4th?

Wouldn't it be the major third as well?

• It's all about the note names! C# to E# would be a major third. C# to F is a diminished 4th even though it sounds the same – Aric Feb 3 at 21:57

The number of an interval is always determined by how many letter names (or staff positions if you think about written music) they encompass. C to F encompasses four letter names (C, D, E, and F) - therefore it has to be a fourth of some kind (note, it doesn't matter if one or both of the notes has a sharp or flat). After that we have to count semitones to determine the quality of an interval (i.e. if it's Perfect, Diminished etc.). For the number of semitones needed for each interval, you can look at this chart (ignore the bit about tuning systems)

You are of course right that the diminished fourth sounds the same as a major third. They are, as we say, enharmonic, but for theoretical reasons we distinguish between the two. This is similar to how we do with notes as well. C# and Db, sound the same but they get different names based on the context they appear in. Incidentally, the distance from a Db to F would actually be called a major third, since D to F encompasses three letter names (D, E and F).

• This is helpful. Steps from the tonic doesn't matter, but the number of notes do. Why, in this instance, do we call the major third E#, rather than F? – ppadru1 Feb 3 at 22:20
• @ppadru1 Again, it comes down to counting letter names - if you want a third above C (weather it be C#, Cb or C natural) - you will need an E of some sort because C to E makes three letter names (C, D and E). To make a major third specifically we need 4 semitones (see added link above) so we start from C# and go up four semitones which lands us on the note E#. We can't call it F, because then we'd have a fourth of some kind, so it needs to be an E, and since it is a semitone higher than E natural, we just call it E#. – user57228 Feb 3 at 22:32
• What if I were to call the scale a Db? How does that change the nomenclature? – ppadru1 Feb 3 at 22:45
• @ppadru1 I'm not sure I understand your question? Do you mean what if we called the starting note Db? It's the same procedure. If you want to find a major third above Db, you count up three letter names, i.e. D - E - F . Which means your second note needs to be an F of some kind. Then you count four semitones and you land on an F natural. So that would be your major third. So there are always two parts to finding/naming an interval: the number of the interval, determined by how many letter names. and the quality of the interval determined by distance in semitones. – user57228 Feb 3 at 22:53

If you spell it Db - F (or C# - E#) it's a major 3rd. Spell it C# - F then it's a diminished 4th.

Same sound. Very likely a different harmonic function. We hope the composer chose the spelling that best clarifies the harmony, not the one that looked 'easier'.

If you have no problem with being scene at the seen of an accident, or sending your mail a Valentine in the male, I'll allow you to spell a major triad as B#, Fb, G. Otherwise, don't!

• ...and B-double-sharp-to-F is a triply-diminished fifth. Horrors! – phoog Feb 4 at 19:27