Intervals - explanation (let's see how it goes)

K.S. I know what you mean. It was a long time ago - I thought the issue was me - but the issue is actually with the system. The way that people are teaching it - which is messed up.

For example, for intervals - people are often teaching things like ---- 'From C to E'. And students are always thinking the obvious -- and intuitively -- sure -- from C --- in C major scale, the 'E' is two notes 'away' from 'C', right?

Well ---- of course --- yes it is. E is TWO notes away from C. In other words, that is TWO houses from C. Not three houses from C.

Although, if we think of it as --- houses on a street, with the first house (labeled number 1), second house (labeled number 2), third house etc. Then we can say things like the 'third house'. We don't need to introduce uncertainty by saying 'from'. So when we say sixth house - we know EXACTLY which one it is .... it's the sixth one. And this is extremely clear. This is the 'span' method.

For the span method -- we say eg. C and E. The C being the lower note. The E being the higher note. The lower note sets the scale, and is also assigned temporarily to be the tonic (root note of that scale). In this case - C major scale, which goes C, D, E etc.

E happens to exist in the C major scale. C to E spans THREE notes in the C major scale. Major third.

Had E been an E-flat instead. Then we can just go with C to E-flat is one semitone less than the major third. So -- that would be a minor third interval. But to get formal about it -- C minor scale goes C, D, E-flat. So E-flat exists in C minor scale. C to E-flat is a minor third interval, because C to E-flat spans three notes in the C minor scale. It spans three notes in the minor scale --- minor third.

K.S. --- the two 'proper' ways they generally use to define intervals is a 'distance' approach -- measured as an integer multiple number of semitones. The other proper way -- is the SPAN method.

Ok ...... I do know there is the way that a lot of people try to teach or push onto the students, which involves people telling students things like 'G is FIVE notes from C'. And then they will START their count AT C, Beginning the count AT C is not an example of FROM C.

In C major scale, beginning the count (1) at 'D' is the correct example of 'FROM' C. But the issue there is -- G is four notes from (ie. away from) C in the C major scale.

It's ok to use the 'FROM' method if we're using SPAN of notes though. That works excellently. Eg. in the C major scale, from C to D, this pair of notes spans (including themselves) 2 notes. Major 2nd.

K.S. - also --- very importantly, I totally understand what the teachers have been teaching. I notice there is a fundamental issue with that approach. But on the other hand, I definitely know that if the students are prepared to accept the 'G is 5 notes away from C' thing (and begin the counting from the tonic) --- then it obviously isn't going to ruin them. And the thousands of people that learned it that way certainly have not been ruined at all - and in fact are very successful. The main thing is that there is an understanding that teachers saying things like 'G is five notes from C' (and starting the count from C) is ----- I think we all know that it's 'technically' wrong. But I don't mind at all. I'm just trying to point that out only.

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.

keystring We have some common ground but I'm afraid you slipped up on the "E# major scale"

Earlier .... I was meaning to write e-flat major scale.
E♭, F, G, A♭, B♭, C, and D.

The two notes I was meaning to set the example for is ... E-flat and C.

So now we see the value of myself laying out the foundations ... and explaining my procedure comes in handy.

The interval E5-flat and C5 in the E-flat major scale is a major sixth. Spanning 6 notes.

keystring It's fine K.S. In my post .... I did mention the pattern .... tone, tone, semitone etc. So you will know that the sequence I had earlier doesn't follow that pattern. And you know full well my example intention is to demonstrate a major 6 interval. And as I told you .... it should have been E-flat and C as the example pair. I was thinking of E-flat ...... not E-sharp, since E sharp is an F in absolute terms.

Hence the importance of me writing the process ... so it's easy to see that cross checking indicates that my example really was to meant to be what I wrote. E4-flat and C5.

Likewise .... when you make mistakes like writing A is 6 notes over from C ..... same deal.

Almost done. E# major scale will be F major scale. F, G, A, B♭, C, D, E

If considering F4 and C5, then the procedure is to take the lower note. It is F. So use F major scale. If the lower note had been F# instead, then would use F# major scale. But we're dealing with the lower note being F. So F major scale.

In this case .... F4 and C5 interval spans 5 notes in F major scale. Perfect fifth interval.

Better cover F4-sharp and C5 as well. Lower note is F#, so choose F# major scale.

F♯, G♯, A♯, B, C♯, D♯, E♯

F# and C# spans five notes ... perfect fifth, while we want F# and C, which is 1 semitone less than the perfect fifth interval. So F# and C is associated with a diminished fifth interval.