Trjtdtk

This is a very theoretical question but it's confusing me a little.

So intervals overlap - That's why I can call a major 3rd a diminished 4th, and such.

However, from what I understand, a perfect 5th only overlaps with a diminished 6th. You cannot refer to a 7 semitone interval using a 4th because the "biggest" fourth, augmented fourth, is a diminished 5th.

So consider this (treble clef):

What would you call the interval here? From what I understand it should be called a 4th because of the distance between the notes. But that's impossible.

You're correct; it should be called a fourth!

But since "augmented fourth" won't be big enough for this, we kind of had to make up a term, and the world of music theory collectively decided upon calling this interval a doubly augmented fourth. This just means that it's one half step larger than an augmented fourth. (As such, the augmented fourth is not really the "biggest" fourth possible.)

The same is true for diminished intervals; a half step smaller than a diminished sixth will be a doubly diminished sixth.

Any interval can overlap with (or, in more academic terms, "be enharmonic to") another interval. A perfect fifth could, in theory, be enharmonic to a triply augmented third—not that you'll encounter those very often!

Just my 2 cents after the great Richard's answer.

1) It's a fourth because there are 4 letters from the lower note to the higher (A, B (or H if you're using German note names, just like me), C, and D).So, A<some accidental> to D<some accidental> will always be a 4th, regardless of the actual accidentals or their absence.

2) Since A to D (without any accidentals) is a perfect 4th, and this must be 2 half-steps wider than A-D (since A&flat; is 1 half-step lower than A, and D&sharp; is 1 half-step higher than D), so A&flat; to D&sharp; would be a doubly augmented 4th (because we augment the perfect interval twice).

And another 2 pence following on from Richard's and trolley813's answers:

1) First, you name the interval according to the note names.  So an A​<something> up to a D​<something> will always be a fourth of some kind.  (This is the diatonic bit, based on how the interval looks.)

2) Then, you adjust it so it covers the right number of semitones.  (This is the chromatic bit, based on how the interval sounds.)

That second step is always possible, as you can squash or stretch any numbered interval as much as you need, by diminishing or augmenting.

For the ‘perfect’ intervals — unisons, fourths, fifths, and octaves — the range of interval sizes goes:

• …


• triple-diminished


• double-diminished


• diminished


• perfect


• augmented


• double-augmented


• triple-augmented


• …

And for other intervals:

• …


• triple-diminished


• double-diminished


• diminished


• minor


• major


• augmented


• double-augmented


• triple-augmented


• …