Depends on your language use - hrs talking in terms of semitones throughout the article, so thats correct; you're thinking in terms of whole /half steps (so you would be correct if the article was written in those terms).

I think talking in semitones helps clear up any misunderstanding over the explicit intervals present in a chord (and I've found that very useful when talking to guitar pupils who only know guitar and want to understand theory, particularly because the guitar neck is made of semitones), but if someone knows more scale theory (or plays piano), then talking in scale steps makes more sense.

> Depends on your language use

'Step' has a specific meaning in music and it doesn't mean 'semitone'. Why not just use semitone seeing as that precisely describes what's intended? Conflating meanings seems like it could be confusing. "The tritone of this note is 6 steps up" "Gotcha, so the tritone of C is B" "No no, by step I currently mean tones, not semitones" "Ah, so 3 scale tones, ok" "No just 3 tones, or 6 steps" "Ok, I'll count 6 steps, 1,2,3,4..."...just use the correct word.

"Step" refers to an interval gap of "half step" or "whole step". In a way, I could see this as a "specific meaning", but since it refers to a group of intervals and not a single one, I would be quite open to a definition where '1 step' is always '1 half step', since both 'semitone' and 'half step' imply a less useful fundamental value of 2 half steps, even though music that involves only whole steps is quite dissonant and uncommon (the whole tone scale).

Your entire hypothetical dialogue is confusing as well, since your hypothetical person isn't using correct words either. The situation where C + 6 of something = B is with scale degrees (C moved 6 scale degrees up is B). And then you say "I currently mean tones", when 6 "tones" has the exact same grouping problem you are criticizing (because 'whole tone' and 'semitone' have the exact same meaning as 'whole step' and 'half step', only now 'scale tone' is in the group too). This artificially lengthens the example.

"The tritone of this note is 6 steps up" "Gotcha, so the tritone of C is B" "No, that's scale degrees, by 'step' I mean 'half step'." "Oh, so it's F# then." Done.

> "Step" refers to an interval gap of "half step" or "whole step"

Right, but it does not mean 'half step'. It means one or other depending on the harmonic context, not the language context as said above. In the case in the article, a "step" down from the third is the second, not the minor third as the article says.

> I would be quite open to a definition where '1 step' is always '1 half step'

I don't understand this, sorry. Why not just use semitone?

> Since both 'semitone' and 'half step' imply a less useful fundamental value of 2 half steps

Western music isn't fundamentally chromatic either, so talking in semitones isn't particularly useful.

As you imply with reference to wholetones and dissonance, the words tone/semitone also give useful melodic information that we've all already learned. E.g. raising the 5th a tone is consonant, raising the major 3rd a tone is dissonant. Of course you could teach students that not all steps/two steps are the same, depending on scale degree, but then you're back to square one, just with different words for semitone/tone.

> Your entire hypothetical dialogue is confusing as well, since your hypothetical person isn't using correct words either.

Yeah it's meant to be confusing, my point is that overloading terms gets confusing quickly, at least for me.

I realized when reading your response that you use "tone" for "whole tone". So from my perspective you're overloading "tone", which could mean semitone, whole tone, or scale degree tone, to only mean two half-steps, but to me, it's like your perspective that in the article the word "step" is overloaded to mean one half-step. I think it is more useful, if you were to define fundamental unit of pitch as one half-step, since there are of course many intervals that you cannot describe with just a number of whole-tones. It's one syllable and corresponds to one note = 1, instead of the notion of "half" and then you have to explain how the difference between E and F is '1 half', I think it is a mess.

And - I personally analyze music in semitones, not scale degrees. I find it much more useful. Even though that's not considered "standard" there are some things even standard theory has to use chromatic language to describe, like the tritone (you could get into "#4 or b5" but that would require a lot more than just saying 6 semitones).

> "Step" refers to an interval gap of "half step" or "whole step"

What? I'm lost. How can a step possibly mean a half step? A step is a whole step. Anything else is madness.

Pshh... Unfortunately things aren't that consistent or that would have been pointed out much earlier. C to C# and C to D are both considered 'steps' (see 'stepwise motion'). That is to say, "half" and "whole" are treated like two different types of steps in traditional theory. (that and "whole" is a much less useful fundamental unit as I said before)

Today I learned...

Good point, it is ambiguous. I changed it to "semitone."