Is my answer the following question is correct:

Q: What is the augmented seventh from E?

A: D double sharp

Method

  1. Write down the note (of your choosing) on the bottom line of the treble staff which is E.

  2. Note down the same note a generic seventh from above. This will be positioned on the second line of the staff which is D.

  3. On a keyboard, count 12 half steps from E and you end up at E.

Thus an augmented seventh from E is D double sharp.

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Correct. A seventh up from E will be 7 letter names up, i.e. some sort of D. Then you can count semitones if you like, though I think most of would relate it to the scale of E major, which has D# as its (major) 7th note. Sharpened again, that's Dx.

(I've got through 50+ years as a professional musician without consciously thinking how many semitones were in a given interval. But I know my scales!)

Not that you often (if ever) FIND an augmented 7th in the wild. It's pretty hard not to hear it as an octave. But you're technically correct.

  • I'd love to see a score that uses an augmented seventh in a harmonically useful way! – leftaroundabout Sep 13 at 15:55
  • Let me know if you find one! – Laurence Payne Sep 13 at 16:24
  • @LaurencePayne I think we both answered the same exact thing at the same exact time :) yours hadn't shown yet when I posted mine, or else I would've just let you cover it, since you pretty much word for word said what I wanted to say. Great answer! – Kevin H Sep 13 at 22:22
  • @Kevin H nothing wrong with your answer either! Yes we seem to have overlapped. – Laurence Payne Sep 14 at 9:47
  • @leftaroundabout I think there are some examples in the last movement of Ligeti’s Musica Ricercata. At any rate, that piece contains many similarly unusual intervals such as doubly-diminished intervals, augmented octaves, etc. – Pat Muchmore Sep 14 at 12:07

Your answer is correct. Intervals are counted by letter names, so a seventh starting on E is (disregarding accidentals) E, F, G, A, B, C, D. So you know it will be a D note of some kind.

You then can note that a major seventh is E to D#, because D# is diatonic to the E major scale. To find the augmented seventh, you merely raise the major seventh by a semitone (while keeping the same letter name). Thus, D sharp becomes D double-sharp.

It's worth noting that augmented sevenths aren't common. By ear you would just identify them as octaves.

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