In a theory test, I got this marked wrong.

E to A# is an augmented fourth. (The clef is treble, by the way.)

So... What gives?

E to A is a perfect fourth.

Raise the A to A# and you get a tritone. AKA an augmented fourth, since you raised the fourth instead of lowering a fifth. Right?

I asked my teacher, who asked her daughter who just graduated college with a music major. She thinks I should contest. I don't know that I care enough to, but I need to know, was this a mistake on their part, or a lack of knowledge on mine?

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    It might all lie in the "... AKA a tritone" - if you're supposed to call it such, then another (albeit equivalent) nomenclature would be wrong. Apr 9 '18 at 22:59
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    @Stinkfoot - as much as I hate to endorse Wikipedia... It's defined as an interval. And it was an acceptable answer in my music theory class 15 years ago. Apr 9 '18 at 23:04
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    The page for musical interval identifies the [quality, ordinal number] system as the most common, but it's not the only naming convention. Apr 9 '18 at 23:07
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    @TheChaz2.0 That's super interesting. I highly doubt that Certificate of Merit would accept "tritone" as an interval though. Their pretty... rigid? I guess what it is is that "tritone" is descriptive of an interval, but doesn't actually define it. You can't major/minor/augment/diminish tritone... Apr 9 '18 at 23:07
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    Just to play Devil's Advocate: is this in treble clef?
    – Richard
    Apr 10 '18 at 0:31

Raise the A to A# and you get a tritone. AKA an augmented fourth, since you raised the fourth instead of lowering a fifth. Right?

Right. Your explanation is perfect. E->A is P4th, adding the # makes it augmented.

One of the ways a perfect interval becomes augmented is by raising the higher note half a step, while keeping the same note name, as in your case. A->A#. If we use the enharmonic, Bb, then E->Bb would be a diminished 5th.

Whoever marked that is an ignoramus, or quite possibly it is simply a mistake, as @jdjazz has pointed out in the comments.

  • @GeneralNuisance - and you don't have to graduate college with a music major to know this. It's basic theory - very basic.
    – Stinkfoot
    Apr 9 '18 at 23:18
  • @NeilMeyer - Understood, but what I said is entirely, correct: A perfect interval becomes augmented when it is raised by half a step. I did not say that was the only way it can become augmented. I addressed the case in question. Tnx.
    – Stinkfoot
    Apr 10 '18 at 11:08
  • @Tim So did you ever try to make a mistake on purpose only by mistake you got it right? :-) Apr 10 '18 at 12:47
  • @Tim - at my age, I now call them "senior moments"... nobody can have a problem with that!
    – Stinkfoot
    Apr 10 '18 at 12:53
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    @jdjazz I feel like I'd better clarify that I don't actually think the person who graded my test is an ignoramus, I was being jocular. It was actually a Certificate of Merit theory test, and they probably just have people trying to pump these out with all of their submissions. So while I probably won't be able to find that grader specifically, I'm glad to know that it wasn't a mistake on my part. Apr 10 '18 at 15:41

My comment of "is it in treble clef?" was largely a joke, but I thought it would be interesting to take it a bit further. Here's that interval in all clefs (or, at least, in as many clefs as necessary to exhaust all possible staff locations):

enter image description here

You'll actually notice that every single one of these is an augmented fourth except for one: in alto clef, the pitches are F and B♯, which actually creates a doubly augmented fourth.

This is an outgrowth of the fact that, with perfect intervals, the accidentals always match, unless it's the fourth/fifth between F and B. In all other cases, matching accidentals create a perfect interval, and therefore seven of the above clefs create the augmented fourth. The only clef that doesn't is the one that results in the F to B fourth.

This just shows that the only way this is the student's error is if this example is in alto clef. If it's in any other clef, then the student is correct. QED


It would have been good to have been shown the full page width, containing the complete rubric to the question. But from what you've shown us, yes you've been wrongly marked. It's an augmented 4th.

(It would be in bass clef too, @Richard)


It is definitely an augmented 4th. There is an easy way of checking. Starting with the E major scale (since E is the first note), we know that the first four notes in the E major scale are: E, F#, G#, A.

A# is a semitone higher than A, therefore the interval is an augmented 4th.

Another example is an interval from C to E flat. From the C major scale, we know that the first three notes of the scale are C, D, E.

E flat is a semitone lower than E, so the interval is a minor 3rd.

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