# Is a doubly augmented seventh a compound interval?

A compound interval is an interval spanning more than one octave.

Does "spanning" in this case refer to the number of staff positions or to the number of semitones?

Wikipedia lists the diminished ninth (12 semitones) as the smallest compound interval, so I'm guessing that the distinction between simple and compound intervals is based on staff positions instead of semitones: intervals encompassing 8 or less staff positions are simple, those with more are compound. Hence a double augmented ninth would still be a compound interval, whereas the doubly augmented seventh mentioned in the title would be simple.

Is my understanding correct?

Standing at what the article says:

Any compound interval can be always decomposed into one or more octaves plus one simple interval.

You cannot split a double augmented 7th in an octave + something else (basically because you haven't even reached the octave by staff positions), while you can express a 9-- as an octave plus a diminished second.

So yes, it is staff positions that matters.

Perhaps a simpler way to look at it is letter names. C4>C5 anything is simple, even if the space is more than an octave. C4>D5 anything is compound, even if the space is less than an octave.

• Thanks for your input! I'm not sure I understand your "C4>C5" / "C4>D5" notation. Could you elaborate on that? Commented Feb 15, 2019 at 13:03
• C4 is middle C. C5 is an octave above. D5 is the next note above that.
– Tim
Commented Feb 15, 2019 at 13:04
• I'm aware of that, but I still don't understand what "C4>C5" is supposed to mean within the phrase "C4>C5 anything is simple". Commented Feb 15, 2019 at 13:07
• C4>C5 is an interval. One octave. C4>Cb5 is a dim octave. C4>C#5 is an aug octave. All simple. C4>D5 is M9. C4>Db5 is m9. C4>Dbb5 is dim9. All compound.
– Tim
Commented Feb 15, 2019 at 13:10