Title:           Music theory lecture two: harmonic motions and scales
Author:          Anonymous
Pastebin link:   http://pastebin.com/3JC9Z6uH
First Edit:      Sunday 5th of May 2013 06:11:12 PM CDT
Last Edit:       Sunday 5th of May 2013 06:11:12 PM CDT

We're going to be looking at stacking 5ths and what sorts of scales they create.
 
        If you take a starting pitch, which C will be the example, and go up a fifth, you get G. This was pointed out in the last lecture. So, if you treated those as a pseudo-scale, you'd get C-G-C (I-V-I). This is an authentic motion. If you take your starting pitch, and use the note a 5th below, you get F, and together, you'd get C-F-C (I-IV-I) which is known as a plagal motion. This is often used in old church music as an ending gesture. They'd end on tonic, move up to pre-dominant, than back down to tonic.
        That's all we can do with one stacked 5th. Let's see what we can do with two stacked 5ths. So, starting on C, and going up a 5th, we get G, and going down a 5th, we get F. So, put those in order, and we get C-F-G-C (I-IV-V-I). We can do two 5ths up. C up a 5th is G, and up another 5th is D. C-D-G-C (I-ii-V-I). We can even go down two 5ths C down a 5th is F, and down a 5th is Bb. C-F-Bb-C (I-IV-bVII). These are known as the tetractys scales. The only one that isn't that common is the I-IV-bVII. It isn't used frequently until videogames. Seriously, go play a C-F-Bb-C chord progression. It isn't necessary, but it is cool.
        If you stack five 5ths, you'll get the pentatonic scale. C to G to D to A to E. Put those in order and you have C-D-E-G-A-C (I-ii-iii-V-vi-I). You can keep stacking 5ths, and eventually, you'll get the diatonic, and chromatic scales. E up a 5th is B, and B up a 5th is F#, but for the sake of following the tetractys scales, F# is just going to be F.
 
We have:
C-G-C     Authentic
C-F-C     Plagal
 
C-F-G-C  -]
C-D-G-C   | Tetractys
C-F-Bb-C -]
 
C-D-E-G-A-C  Pentatonic
 
C-D-E-F-G-A-B-C  Diatonic