Pinpointing intervals: Perfect fifth or Perfect fourth?

Question

a shower thought occurred to me and as a non-formally trained musician I wonder if someone could quell my queries regarding this.

Say I have an interval, a G note followed by a C note, where the C is higher than the G. We can all unanimously agree that the interval is a perfect fourth. However, if we take reference to the C note instead, G would be the perfect fifth instead and we would call it a perfect fifth?

My confusion comes from the fact that the G is actually lower than C in this case.

Do we always take reference to the lowest note (G in this case) when pinpointing an interval, or are there any sort of rule in terms of which note to reference such that we could call the specific example a perfect fifth instead?

Answer 1

...a G note followed by a C note, where the C is higher than the G

You can add octave numbers to letters...

G3 to C4

...melodically you would call that an ascending perfect fourth.

If the notes are simultaneous...

...you just call it a perfect fourth. It does not really matter the order of the note references other than to change the relative position words: above or below. C4 is a perfect fourth above G3, or G3 is a perfect fourth below C4. Whichever way it's stated the relationship between the two notes is always a perfect fourth.

...However, if we take reference to the C note instead, G would be the perfect fifth

The only G a perfect fifth from C4 is G4 not the original G3...

...which I think you can now see is a different G, in a different octave.

So, first you must give the octaves if you want a specific interval.

Second, either simply state the interval (perfect fourth) or if relative position matters say something like 'above' or 'below', 'before' or 'after', 'acending' or descending, etc.

I think part of your confusion is assuming that if someone says notes C and G that it means the movement ascends to the nearest octave. Don't assume that. Either say it explicitly or if someone else is speaking ask them to explain.

This can be frustrating (to me at least) when people talk about root progression by fifths. In which direction?!? Root progression by descending fifth or ascending fifth are very different kinds of progressions!

Answer 2

The interval is the frequency different between the notes. This can also be expressed in terms of the number of half steps it takes to walk from the lower pitch note to the higher pitch note.

In your example from G up to C is a perfect 4th. You can think of this in terms of walking up the major scale starting at G (Do). C is then the 4th note (Fa), which is also 5 half steps.

From C up to G is a perfect 5th. Start walking up the major scale from C (Do). Then G is the 5th note in that scale (Sol). It is also 7 half steps.

Based on the example I'd say that we do describe intervals from bottom up.

However, you can say that G is a 5th above C or a 4th below C. In other words I can get from C to G by walking up in pitch by 7 half steps or down in pitch by 5 half steps. But I think the interval definition is based on a bottoms up approach (low pitch to high pitch). This is related to the idea of an inversion, or inverted interval. We invert an interval by swapping the order of the notes. (C, G) is a 5th and its inversion (G, C) is a fourth. There is a similar relation between 2nd and 7th, and 3rd and 6th though in those cases minor becomes major and vice verse.

Lastly note that interval is a relative term. We use the same numbers to describe degrees of a scale. That can be confusing to a beginner. In the Key of C G is the 5th degree. So in the example (G, C) I evaluated the interval by walking up the G major scale. But if someone asked "what is the 5th of the key of C" that would always be G regardless of placement above or below the root note of the key. So it is correct to say "G is the 5th of C and it is a 4th below C". The number referring to different concepts.

Answer 3

To cut down on ambiguity, intervals are always calculated from lower to higher note. Thus G>C is P4 - you go up P4 (G A B C) from G to C. Or you go down P4 (C B A G) from C to G - backwards. But counting up is generally easier!

The 'rule of nine' is important, as when inverted - C>G here, C now being the lower note - the P4 as was becomes P5. C D E F G: 5 steps alphabetically. Perfect intervals retain their perfectness!

The only other perfect interval is P8/P1 - the octave (or unison). Rule of 9 again.

Worth mentioning that alongside the alphabet count, the number of semitones always comes into the equation. P4 has 5 semitones and P5 has 7. If you like, there's a 'rule of twelve' here. The same applies to maj/min intervals: m3 gets inverted to M6. As in C>E♭ = m3, so E♭>C = M6. And apply the semitones rule - m3 = 3, M6 = 9. Augmented and diminished also follow the swapping rule. No need to go into that here though!