That's interesting, I think you get to the core of what prompted my original question here.
I agree completely about terminology: it's important to learn the same language as everybody else.
Where we seem to differ is on learning the concepts to which those terms are attached. Though people vary, I think it's not merely a matter of taste whether it's better to start by "digging into some basic terminology" or learning missing concepts to which terminology can be attached: the latter is better. Once you have a concept you can immediately attach a word to it without much effort. That isn't a claim that learning is ever a simple process of pouring knowledge into people's heads, it isn't and always involves guesswork and backtracking. But there is such a thing as an elementary explanation, and they're very useful for people starting out in an area of knowledge new to them!
That's true. I'm guess I'm just trying to avoid overloading you with information.
You can get VERY deep into chords, scales and intervals but it is a mouthful when you're just starting out. Perhaps it would be better to say, start out by learning intervals, scales and chords with some basic explanations of what they are and why they work the way they do. But if you feel more motivated by getting deeper explanations, of course there should be sources out there that can provide
Here we go: I've read terms like "fifth" (not sure whether I mean "perfect fifth" or just fifth - I won't try and google any of this to make my train of thought apparent) being defined as "the interval between N white notes" (probably it was seconds and thirds rather than fifths where I read that). But of course the interval in semitones between N white notes depends on where you start on the keyboard: 7 semitones * 2 ** (1/12) is about a ratio of 1.5 in your example of C to G, but B to F is only six semitones, so 2 ** (1/2), about 1.41. Are intervals (fifths, thirds, seconds etc.) constant intervals in log(frequency), or do they refer to different physical intervals depending on where you start on the keyboard?
frodo1 gave you an overview of the intervals already. I think it illustrated the point I was trying to make in that you kinda just look at the list which says "this is what it is" and you quickly get the basic gist. But I'll give you a deeper explanation about the naming convention. It's correct that a perfect fifth is always 7 semitones, so B to F is not a perfect fifth, however B to F# is. (B to F is called a diminished fifth, assuming it's notated as a B and F; if it's notated as a B and E# it's an augmented fourth, but all of this is another whole can of worms).
Are you familiar with scales? A scale in general is basically defined as a sequence of notes in ascending order. In western music, there is a set of specific scales that are used as a basic building block from which to construct music, divided into two types called major and minor, both which feature seven individual pitches before you come back to the first pitch again an octave up, perhaps you have heard of this? The simplest scale to remember is perhaps C major so I'll use that one to explain interval naming conventions - it starts on C and uses only the white keys on the piano:
C D E F G A B C
If you look at the piano, you'll see that the scale is made from a series of 2nds, either major or minor, ie either 2 semitones (a whole tone) or one semitone, starting from C and then going to D, E and so on:
whole whole semitone whole whole whole semitone
This is the pattern we call a "major" scale. You can start from any note on the piano, and as long as you play following the pattern above, it'll be a major scale. For example, B major is B C# D# E F# G# A# B
The minor scale exists in three variants, but we'll use the simplest one for now, the "natural minor". (The other two variants, "harmonic" and "melodic" minor, feature minor changes to the scale to better suit the ways chords and melodies are typically used/written in traditional western music). The simplest minor scale to remember is natural A minor, which also uses just the white keys, starting from A:
A B C D E F G A
The natural minor scale instead follows the pattern
whole semitone whole whole semitone whole whole
If you look at frodo1's summary of the intervals you'll see that they all either are, or are some type of second, third, fourth, fifth, sixth, seventh or octave. This "generic" name is taken from how the intervals fit into the scales western music uses, for example in the C major scale above
C to D is called a second, because D is the 2nd step (often called degree) of the scale
C to E is called a third, because E is the third step of the scale
C to F is called a fourth, because F is the fourth step of the scale
C to G is called a fifth, because G is the fifth step of the scale
etc.
Regardless if you start from the C in the C major scale or A in the A minor scale and play each interval in turn, they're all seconds, thirds, fourths, fifths, sixths, sevenths and octaves. The fourth, fifth and octave consist of the same amount of semitones in both the C major and A minor scale, we call them "perfect". Take any major or minor scale (using the patterns outline above) and go up to the fifth step, and you'll have a perfect fifth between the first step and the fifth step. For example, in F major:
F G A Bb C D E F ----- F and C are a perfect fifth.
Compare, however, the third, sixth and seventh in the C major vs the A minor scale - they're major thirds, sixths and sevenths in the major scale, and minor thirds, sixths and sevenths in the natural minor scale. Take any major scale, and the interval between the first and third step will be a major third, and take any natural minor scale and the interval between the first and third step will be a minor third, etc. The only exception to this "rule" is the first second, which is a major second both in the major and minor scale.
In fact, the difference between a major chord and a minor chord, ie C major, which consists of CEG played simultaneously, and A minor, which consists of ACE, is if the third above the starting note is a major third or a minor third. So C major is kinda short for "the scale or chord which starts on C and has a major third", and A minor is kinda short for "the scale or chord which starts on A and has a minor third". It's this difference mainly between the major/minor thirds and sixths, around the framework of the perfect fourths, fifths and octaves, which gives the major vs minor keys their distinct flavor/color.
Why intervals called perfect, diminished/augmented, or major/minor is answered better than I can here by Rita Karpati:
https://www.quora.com/Music-Theory-Why-do-we-call-a-fifth-perfect-but-other-intervals-%E2%80%9Cmajor%E2%80%9DI
hope this was helpful and not confusing, because it became a bit longer than I thought it would
Topic: Beginner music theory for people OK with some maths?