My eventual goal, is to be able to play up and down the Chromatic in numerous scales using the most efficient hole selections. But it make sense to begin with the C major scale. You might think, well that is because there are no flats and sharps so we don't have to use the slide. But as you will see that is not true.
First looking at the keyboard layout below, remember that it is important to think about scales as interval patterns. The Major scale has the following pattern beginning on the first note of the scale in this case C.
Whole - Whole - Half - Whole - Whole - Whole - Half
As you can see the EF and BC intervals are half steps.
Now looking at the harp note lay out it would appear the way to play a major scale would be as follows: 1 blow - 1 draw - 2 blow - 2 draw - 3 blow - 3 draw - 4 draw - 4 blow
And that indeed would work, BUT when playing up and down the harp in the C major scale, there will be times when this note/whole assignment is not the most efficient.
The Chromatic Slide in action
Know that the slide always raises the pitch you are playing by one half step, whether you are blowing or drawing. So Blow C - slide would produce a C# (C sharp). Draw D, would produce a D# (also called an Eb or E flat) So knowing that the slide raises the pitch one half step, what would E Slide be? Looking at the piano keyboard above, 1/2 step up from E is F. That means that 6 blow is an E, and E blow - slide is an F . So there are 2 ways to play an F, 6 Draw and 6 Blow-Slide. Now look at B which is 4 Draw. Press the slide in and you will be one half step up. Look at the piano keys to see that one half step up from B is C. This means that 4 Draw - Slide is a C note. So there are 2 notes C & F that have "alternate" ways to reach them using the slide key.
C = 4 blow OR 4 Draw - Slide (yes 1 blow also gives you a C an octave down)
F = 2 Draw OR 2 Blow - Slide
So, alternate way to play the C scale will be
1 blow (C) - 1 draw (D) - 2 blow (E) - 2 blow/slide (F) - 3 blow (G) - 3 draw (A) - 4 draw (B) - 4 draw/slide (C)
Why play the F and the C alternate holes? Anytime you can keep from switching directions of air flow between 2 notes it will sound smoother. Try alternating as fast as you can with blow 2, draw 2, this is EF. Now play EF by playing blow 2 and blow 2/slide. As you can see, you can play much faster and smoother using the slide note for F.
The following video is where I am currently at in learning to play the C major scale. Still working on the top 3 holes and trying to get faster.