I'm trying to look at the fret board in distance vs notes, I know that going up from the low E string to the A string is a perfect 4th, but going from the A string to the low E string is a perfect 5th. Why is this? I would think there is some symmetry between the strings (excepting the G string)

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    "going from the A string to the low E string is a perfect 5th" - no, it's a fourth, same as it was coming up! – topo Reinstate Monica Aug 23 '19 at 20:40
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    A to E does make a perfect fifth, but only when the A is going up to the E. Going from the A down to the E is a perfect fourth (interval inversion). The guitar's strings are all a perfect fourth higher/lower than their neighbors (except, as you noticed, the G string and B string are a major third apart). Going up a fourth and then down a fourth will put you back on the same note, so the intervals going downwards are exactly the same, but descending. – user45266 Aug 24 '19 at 0:49
  • I get your confusion. Intervals are always measured from low to high, so the direction A up to D or D down to A is immaterial, the interval stays the same. , . – PeterJ Aug 24 '19 at 12:13
  • @PeterJ -- your confusion is confusing. Intervals aren't measured from low to high; intervals are just a measure of distance. It doesn't matter if I am 2 meters from the door or the door is 2 meters from me, the interval is the same: 2 meters. It doesn't matter if an E is a third above C or a C is a third below E, the interval is the same: a third. – ex nihilo Aug 25 '19 at 0:08
  • @DavidBowling - yes, this is what I said. I thought the OP was making the mistake of counting up from A to E, therefore counting it as a fifth rather than a fourth. But perhaps there's another explanation for the mistake. . – PeterJ Aug 25 '19 at 11:21

The question is asked with slightly wrong premises. Any interval is named from bottom to top - lower note being the start point. So E to A will always be P4 - count up - E F G A in letter names. count down in letter names, it's the same P4!

Start with A underneath, and it's P5. A B C D E, so it's never going to be P4. No need to worry about number of semitones for this particular case, honest!

You've also confused the issue - header is about A and D, whereas question is about E and A - although exactly the same applies. Try counting the other two.

With intervals, there's the 'rule of 9' It concerns inversions. A>E is P5, whereas E>A is P4. major intervals become minor, and vice versa, as in M3 inverts to m6. Augmented and diminished are likewise - C>F♯ is aug4, whereas F♯ >C is dim5.

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It's all about the direction in which you're moving.

If you're moving from A up to E, it's a fifth, because A–B–C–D–E is five pitches. But if you're moving from A down to E, it's suddenly a fourth, because A–G–F–E is only four pitches.

This is because the perfect fifth doesn't actually split the octave into two equal halves. Since the perfect fifth is itself inherently asymmetrical, some intervals won't seem to match up if we're not careful about direction.

Similarly, moving from the D (up) to the A string is a fifth. If we want that same fifth from A to D, we have to move A down to D; otherwise, moving A up to D is only a fourth.

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    I wonder if the concept of inversion would be a good thing to bring up in this context. – Todd Wilcox Aug 24 '19 at 4:59
  • @ Todd: It is! What OP not may know is that to define the intervals we always have to count the first and the last tone and why the sum of a P4 and P5 is a P8 while adding 4+5=9. Preety confusing thing for beginners. – Albrecht Hügli Aug 24 '19 at 6:00
  • Thanks everybody, you answered my question. I am a new player, I played folk songs and "campfire music" with chords on the Acoustic for years. Now I'm taking lessons on the electric guitar and studying theory. I like to know the theory behind the shortcuts so that I don't merely play by rote memorization. – thegrons Aug 24 '19 at 23:03

The best illustration of the tonal system is the representation in the piano or keyboard.enter image description here

As we can see there are 2 symmetries in the 12 keys. But there will be augmented fourths and diminished fifths from g#/ab to d and d to g# or ab. And it shows clearly that the interval e to a is 5th (down) or 4th (up).

On the guitar you play efga on the E - string in the bends 0135 and abcde 02357 and you see there is fourth and a fifth.

Or you play the whole major scale doremifasolatido on one single string E or A: whole steps you have to skip a bend!

0-2-4-5-7-9-11-12 WWHWWWH w=whole steps h=half steps

We can see and hear that there us no symmetry but 4ths and 5ths.

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