question about theory, notation, intervals

Yep, your question makes lots of sense.

When you're working in the key of F, the major chord works out exactly the same - up a major third to F, up a minor third to C. That's going to be true of any major chord in any key... and the same with the minor chords: up a minor third, then up a major third.

Key is synonymous with I, the first note of the scale. That's called the 'tonic', or 'key note'.

Where you screw up a little bit is when you move to the key of E... scale degrees are intervals from the tonic. The II would be a major second above I, and III would be a major third above I - so in the key of E, you'd have E-F#-G# for I-II-III. If you'd kept those major second/third relationships intact, you would have transposed from the key of C to the key of E.

ok now it is a little confusing... your post makes perfect sense, but now calls into question this from the article:

"
Let's make sure we're on the same page:
I II III IV V VI VII VIII
C D E F G A B C

So you see that the interval from C to E is called a third. C to A is sixth.
"

he is using the notation in a different way? Above, it looks like the roman numerals are for each note, regardless of number of semitones.

So in an E scale...

I II III IV V VI VII VIII
E F G A B C D E

(is that correct?)

He is calling F a II, where you explain that II is actually "a 2nd from E", or F#. I can deduce that a 2nd is "two semitones up from the tonic". So, my above E scale is wronge? It should be:

I II
E F# ...

?

I perhaps incorrectly assumed that any major scale was just the series of natural notes after the root.

I'm probably getting ahead of myself somehow.

Using roman numeral can be a little confusing - they're usually reserved for chords. Scale degrees are usually talked about in Arabic ('normal') numbers... 1-2-3-4-5-6-7-8 is the pattern for a major scale.

Each of these scale degrees represents a specific interval from the tonic. The 2nd is two half-steps (one whole step) above the tonic; the 3rd is two whole steps; the 4th is two whole steps and a half step; the 5th is three whole steps and a half step; the 6th is four whole steps and a half step; the 7th is five whole steps and a half step. The octave is six whole steps.

So the pattern 1-2-3-4-5-6-7-8 in E would be E-F#-G#-A-B-C#-D#-E. If you wanted to write a different pattern, you'd use accidentals - sharps and flats - to create the pattern. E harmonic minor would be 1-2-b3-4-5-b6-7-8, etc.

There is a really great article David Hodge has that I think explains the part that is confusing, and I think it is "Theory Without Tears". Try reading that, then see if it is more clear. :wink:

I think you're getting lost on the basic concept of a scale. A major scale is made up of two identical halves (known as tetrachords), separated by a whole tone. A major tetrachord consists of the intervals Whole, Whole, Half. So, if we take 2 of them and separate them with a whole tone we get:

W, W, H - W - W, W, H or WWHWWWH.

This applies to all and any major scales.

So:
1 2 3 4 5 6 7 8
W W H W W W H

Taking the chromatic scale:

C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C

Starting at C an applying the WWHWWWH, we get

C, -, D, -, E, F, - G, -, A, -, B, C

Applied to E, we get

E, -, F#, -, G#, A, -, B, -, C#, -, D#, E

The root or tonic is always the "1"

Thanks all, I'm getting it now...

Yes it was confusing to see Roman Numerals, which I was using to correlate to the chord progressions I've seen written that way, such as I-IV-V etc.

Also, now I see why the C scale is always used in examples, it is special in that it has all natural notes. I think that should be mentioned whenever it is hauled out: "we will be using the C scale since it is in some ways simpler than others" etc.

So, should I memorize each scale, or just be able to calculate it?

Thanks again, I am surprised at how learnable (if complex) this stuff is.

The learning goes on and on. Even after you think you already know something about a topic.