Music is about the interaction of sounds. 2 pitches played together create a specific flavour of sound, only determined by how "far apart" they are ... explained below.

An interval always involves 2 pitches ... these maybe identical, or not. . Physically, playing a string causes air to move backwards and forwards some number of times a second (hold a fret down nearer the bridge shortens the string, so it vibrates faster as there is less string mass to move) ... those vibrations in the air hit our ears, and our ear drums vibrate to match The faster this back-and-forward motion, the higher pitch we hear. This number of times back and forward per second is known as the frequency of the sound. Some body of musicians chose to give certain frequencies "names". For example, the frequency of 440 Hz (Hz is "hertz", or cycles per second ... effectively number of times the air moves backwards and forwards per second).

A guitar pick up creates an electric signal that mimics the vibrations caused by the string ... when this is plugged in to an amp, which in turn is plugged into speakers, the amp drives the speakers to vibrate, matching the original string vibration, and again ... the air vibrates, it hits our ears, and we hear these vibrations as pitches.

Guitar makers these days build instruments so that adjacent frets on the same string produce sounds so that the frequency of the higher pitch is 1.0594 times that of the lower pitch. (There's a mathematical reason for this). The effect of this is that, after moving up 12 frets (e.g. from fret 1 to fret 13), the upper pitch frequency is double the lower.
When one frequency is double an other, we say they are an octave apart.. Physicists, sound engineers, and musicians, all use this term. In music, we refer to an interval of an octave ... two pitches whose frequencies are an octave part. In music, we name these pitches the same (same letter).

So, with A (440 Hz) ... this is produced at the 5th fret, on treble E string (provided the guitar is in concert tuning). Then an "A" an octave higher is found at the 17th fret (5 + 12). Effectively, the octave is chopped into 12 pieces.

Pianos are made similarly ... the pitch of adjacent piano keys (e.g. black and white) follow this same mathematical prinicipal, so 12 piano keys to the right produces an octave higher.

The difference in pitches produced by two adjacent frets on the same string is known as a "semitone" ... there are 12 semitones per octave. Ditto, two adjacent piano keys produce pitches a semitone apart,

An interval is the number of semitones between 2 pitches.

An interval named the "5th" (also known as "perfect 5th") is made by two pitches 7 semitones apart. (e.g. fret 1 and fret 8 on any same string).

The term "3rd" is generic ... there are two types of "3rds". A "major 3rd" is made by two pitches 4 semitones apart. A "minor 3rd" is made by two pitches 3 semitones apart.

When you play a chord, you are combining intervals, For example, a major chord has pitches found at 4 and 7 semitones above some pitch you chose.

E.g. if you chose open E (fret 0, open string), then we can add the 4th fret and the 7th fret. We have three intervals: 0 -> 4. 4 -> 7. 0 -> 7.

When you combine intervals, the ear detects one of the pitches as the strongest ... this is the ROOT of that combination.

We care very much about these intervals ... the chord's that are built from these are the basis of Western music.

We can write "recipes" to indicate a given combination of intervals, and give the recipe a name (such as a scale name, or a chord name). These names are short hand for the recipes. When the recipe is adhered to, we get a particular sound palette to use. Doesn't matter where we decide to apply the recipe, we still get the same sound palette ... the actual pitches involved will change, depending on choice of starting pitch ... but the overall sound is determined by the various distance, the various intervals, from this starting pitch.

Music is about RELATIONS between pitches (intervals), NOT the specific pitches themselves.
Last edited by jerrykramskoy at Jan 4, 2017,
Might this have been inspired by a recent thread here in MT?

Quote by jerrykramskoy
Music is about RELATIONS between pitches (intervals), NOT the specific pitches themselves.

I agree with you on this. But some people with perfect pitch might not
Quote by Jet Penguin
Theory: Not rules, just tools.

Quote by Hail
*note that by fan i mean that guy who wants his friends to know he knows this totally obscure hip band that only he knows about with 236 views on youtube. lookin' at Kev here
Absolutely inspired by other thread! As for perfect pitch ... I had a friend with trhis ability ... could repeat back anything I played (so long as it wasn't too fast so he'd miss some detail). But he had no clue what he was doing, and couldn't improvise at all. Even with this ability (which I don't have), I'd still use knowledge of relationships to try stuff out with my hands/brain.
There are people who have perfect pitch but also have a highly trained sense of relative pitch y'know? The world is bigger than we think.
Quote by GoldenGuitar
There are people who have perfect pitch but also have a highly trained sense of relative pitch y'know? The world is bigger than we think.

I agree! I don't have perfect pitch, but I have a "highy trained sense of relative pitch". You can blast any intervals and I'll name them. Any chords and I'll name them. I think anyone can learn how to do that, but some have an easier time, and some a harder time...