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What interval is this?

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Perfect 4th.

It's a lot easier to get your head around if you play the 2nd string B at the 4th fret of the 3rd string.

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Alan's answer is the simple one - but music theory isn't always simple.

It will sound like a perfect fourth, yes... but it might not be. That's because notes involved can have more than one name, and the name of the interval depends on the names of the notes used, not the sound they produce.

Your fourth string note could be F# - or it could be Gb. Your first string note could be B, or it could be Cb - and it could even be Ax (A double sharp).

An interval name has two parts: the second part identifies the size, and the first part tells you the quality of the sound based on that size. When Alan says "perfect fourth", the fourth part says the higher letter is four up from the lower one (if the lower note is F#, F is 1, G is 2, A is 3, and B is 4), and the "perfect" part tells you how that fourth sounds.

But if the lower note is called Gb, then G is 1, A is 2 and B is 3 - so it's some kind of third. It would be an "augmented third" (which sounds exactly like a perfect fourth).

So there are really several answers to the question, and only one will be right in context:

F#-B = perfect fourth
F#-Cb = doubly-diminished fifth
F#-Ax = augmented third
Gb-B = augmented third
Gb-Cb = perfect fourth
Gb-Ax = triply-augmented second

That last one is rare enough that you'll only see it in theory books. But the first five do occur in music - for example, F#-Cb is the distance between the third and seventh of a D diminished seventh chord (D-F#-Ab-Cb).

The reason we have so many names for the same sound is that music theory started way back when - and note names like F# and Gb did not always represent the same sound. Five or six hundred years ago, F#-B sounded different than Gb-B, so they needed different names. As our tunings evolved, the sounds became the same, but the different labels are still used, because certain aspects of advanced harmony grew out of the earlier tunings - if you can't identify the difference (in written music) between enharmonic intervals, the way some complex chords are used won't make sense.

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I'd have said 11th

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It depends on why you need to name the interval.

If you want to construct a chord, yes - it's probably an 11th. That's because chords are constructed by stacking thirds, so chord tones end up being odd numbers (with two exceptions: 4 if you're making a suspended chord, and 6 if you have no 7th).

If you're using it for interval identification, when the two pitches lie in the same octave they'll have a number of 7 or less. We don't hear an 11th when the two are played together - you'd hear an 11th if you played 2xxx0x, placing them an octave and a fourth apart.

But even in interval identification, we don't normally use distances over a 10th. Anything larger than an octave is called a "compound" interval, and we typically raise the lower note or lower the upper note until they lie in the same octave. That's because register doesn't affect the names used in harmony: 0xxxx5 is considered a fourth (E-A) rather than an 18th. And x30010 would be a Cadd9 chord, even though the raw distance from the low C to the D is just a second.

Outside of chord construction, the only time we really need to deal with compound intervals is in arranging - you typically don't want a space of greater than a 10th between any two upper voices, or the chord produced starts to sound thin. So arrangers/orchestrators might look for raw 11ths, 12ths, 13ths etc. and move one of the notes an octave (or assign it to a different instrument) to get a better sound.

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