In a continuing harmony rant - because I'm feeling like writing a bit...
I'm going to start explaining how to transfer some of the ideas to the piano, or at least beginning to familarise ourselves with harmonic transitions at the piano rather than just in theory.
Firstly, I want to briefly outline 'modes' because sooner or later I'm going to feel like using the terminology here and you'll need to know what I'm on about - I don't really think you need to memorise this right now, its just to avoid later confusion.
The major scale has 7 'modes' - they each have their own name. The standard major scale that we all first learn is the "ionian" mode of the scale. Below I have written them all out and highlighted the chord tones within each mode. - continuing to work in F major..
F G A Bb C D E (F) - F major - Ionian mode.
The scale can also be built upon each degree, the same way we built the chords -
G A Bb C D E F (G) - Dorian mode
A Bb C D E F G (A) - Phrygian mode
Bb C D E F G A (Bb) - Lydian mode
C D E F G A Bb (C) - Mixolydian mode
D E F G A Bb C (D) - Aeolian mode (natural minor scale)
E F G A Bb C D (E) - Locrian mode
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After that crash course in major scale harmony - lets take it to the piano..
We might start my familiarising ourselves with the 3rds, through each mode/chord using the pattern we worked out earlier..
So the left hand will play the chord root, and the RH will play the thirds. The left hand will stay more or less within the octave range of middle C, to the C below. The RH from middle C, to the C above (this is rough, they can move outside, its just to keep you changing direction and not playing straight up the keyboard like a scale/arp). Additionally, to keep inline with the consolation/polyrhythms, I'm going to do 2 vs 3 between the hands. This way we learn harmony and our technical challenge.
To better explain what I mean I've attached a score, I've done it in F major, don't ask me why the bar lines are positioned the way they are, i have no idea.. the notation software had a fit it seems. - anyone trying this needs to transpose it and play it in multiple keys. The objective of practice here is not to learn/memorise each pattern here - so you wouldnt repeat a given key, rather, work through a key once, then move onto a new key. You are practicing the process of thinking through the harmony (and covertly practicing polyrhythms at the same time)
This is still fairly dull at the moment with all the repeated notes, but it should still be plenty to think through for those that haven't studied harmony at all.. we would soon start adding notes, such as using all the notes within each chord (1, 3 and 5 to begin with) to form the LH part, and talking about how to use other scale notes/chord notes to transition between chords in the RH.