keystring That puts us on the same page. Good enough.
We're on the same page now K.S. The centimetre (distance) units is equivalent to the integer multiple of semitone units.
When we use the definitions of major and minor intervals in the form of unison, major second, minor second, major third, minor third etc --- there is a direct but non-linear mapping. Eg. unison maps to zero semitone. Minor second maps to 1 semitone. Major second maps to 2 semitones. Minor third maps to three semitones. Major third maps to four semitones. Perfect fourth maps to FIVE semitones. Perfect fifth maps to SEVEN semitones etc.
Some people do take advantage of the above mapping.
I don't have a problem with you or teachers teaching what you want to teach.
And earlier, I was only pointing out that when you wrote 'A' is sixth one over from 'C', it should be 'A' is the sixth one in the set of notes 'C to A' in C major scale, which is the application of the SPAN-of-notes method.
Another example of that is E4-sharp and C5. Since E4-sharp is the lower note, we go for E4-sharp major scale, which has this sequence E♯, F, G, A♯, B♯, C, D -- and then finally back to E# of course. And the E4-sharp and C5 spans six notes. Major sixth interval. Here, we can say that from E4-sharp to C5, we have a span of notes equal to six. We have a major sixth interval.
I think it was great that we had this conversation, and also the discussion in this thread and the other thread about the diminished third interval. It looks like everyone has learned something - which benefits all of us.
keystring You and I seem to be on the same page, where you've decided to use the word "span" to describe what I call "1st house, 2nd house, 3rd house..." which is less abstract than the word "span" which frankly I'd have to look up and might still get wrong.
Once you have been taught what span-of-notes means --- which probably takes 10 seconds or less to convey (ie. span of notes being the number of notes covered/contained in a set/sequence of notes) --- then you will never forget it for the rest of your life.
