Del Vento Del ----- I'm totally with you on the first approach, as in a more clear and correct way of teaching. When I first started looking at information to learn about intervals, and the teachers/sources started to teach things like (eg. the wrong way of teaching) ---
'interval is a "distance between notes/pitches" eg. major third, choose any major scale, and then begin with the first note - aka tonic - and then go to second note, and then to the third note, and "so" the distance between the first note and the third note is "3"'
While we can understand that distance is fine for a different mapping, such as distance in number of semi-tones, it doesn't apply or work at all with the 'degree' counting system, as in first degree to third degree is not a 'distance' of three at all, while - even if technically is wrong - they usage of 'span of notes' will definitely work, and at least aligns with the counting system. Or at least it works a heap better than telling students to count to three, and then make somebody do some hoop-jumping by tell them that they start from one, and then end at three, so that it is (very misleading) 'distance' of three.
The semi-tones intervals approach (where distance actually works) - can then always be taught later if needed. On a piano, which seems to have an incredibly convenient layout on the keyboard - allows people even physically 'see' semitone steps - after they're taught what to look for - as in two next-door neighbor keys are a 'semitone' apart on that particular perspective. So as long as they know (on a piano for starters) what a semitone is on that particular perspective, then they can then get another qualitative feel for 'minor thirds etc'. Where, whenever they encounter minor, they can generally or maybe always just knock one semitone off a major (eg. third or second, or fifth).
There's always going to be other stuff that could start to confuse people again though, such as terms like 'perfect fifth', where it may become ok again once they get more into 'the system', as in learn more about it. But the teaching of 'distance' between notes based on the degree counting system really threw me. It just doesn't 'add up'.
Most people would 'assume' - distance between first degree note and third degree note is three minus one, equals two. Major Second? (wrong hehehehe). So they should throw 'distance' out the door completely, and just consider getting student to hypothetically consider spans of notes, in order to then get numbers to align with their existing system. So, first degree note to the third degree note spans three major scale notes. The number 3, which at least can be conveniently linked to the three in 'third' (or major third).
