Do difference in octaves matter for the intervals?

Question

Should I account difference in octaves between different guitar strings, like between 5th (octave A2) string and 4th string (octave D3), when I'm looking for intervals (for example perfect 4th) ? I mean, technically from theory standpoint, because I understand that they sound a bit differently.

Also, for example If I play P4 of G which is G-C notes, and if I play notes in reverse order and C and G are in different octaves is that considered a different interval? I think not, but what confuses me is that being in different octaves the actual half-step distance between notes change (if G is in the next octave then the distance is 7 half-steps, or P5), while the definition of P4 says that half-step distance should be 5 half-steps.

So, the rule is that if notes of some interval are in the same octave then the order they are played doesn't matter, but if notes are in different octaves then the order may matter?

Answer 1

Two important ideas:

1. Intervals are defined from the lower pitch to the higher pitch.
2. The numerical octave designation by itself does not affect the interval type.

Given the example of A2 to D3:

1. A2, being the lower pitch, is our starting point for naming the interval.
2. Counting up from A2, there are five semitones between it and D3 (A#2 B2 C3 C#3 D3).
3. Thus, the interval is a P4.
4. Even if we count from D3 down to A2, of course, it's still five semitones — P4.
5. However, if we invert the interval, DX to AX, the number of semitones from lower pitch to higher pitch is now 7, a P5.

Where the octave matters is in compound intervals, intervals in which the pitches are more than a diatonic octave apart. A2 to D4 and C3 to D4 are both compound intervals. A2 to D4 is a compound P4 or an P11; C3 to D4 is a compound M2 or a M9.

The guitar string(s) on which the notes are played doesn't matter in itself in determining the interval, only the actual pitches involved.

Answer 2

Intervals make sense when counted from lower to upper note. Not the only way, but that works.

Thus, if the lower note is G, and upper the very next C going up, we have a P4. Using that same C, and going up to the very next G (an octave above the original), the interval is now a P5.

Be very careful with intervals, though - the number of semitones is literally half the story, the other half being what the notes are being called. For example G>B♯ (which will sound the same, and be the same number of semitones apart), is not P4, it's actually A3.