Music and Geometry: Intervals and Scales

It does seem that I include all Chapman's scales (while saying nothing about chords), although oddly enough he's chosen to use the modes of harmonic major but not those of its inversion, harmonic minor?

Edit: In fact I found the second link (first one's pretty vague and wasn't enough for me to follow the diagram) relevant enough that I added a paragraph to point out the connection!

Don't say "dissonance" (or explain what dissonance is)- that much is obvious, looking for something a bit more detailed, e.g. why 1-2-5 sounds brighter than 1-4-5

You can use the geometric representation ("necklace") to explain modulation of e.g. diatonic scales as axial mirroring. This can be regarded as a geometric operation. When you look at harmony in this way, some interesting insights open up. I've even built a tool to explore it: https://github.com/rochus-keller/MusicTools/tree/master.

Besides aesthetics, though, there might be educational value given that the equal temperament tuning is a cornerstone of western music education.

<3

Although there have been some claims in these comments to the contrary, harmony is particularly mathematical. Symmetry and the breaking of within the integers mod 12 form the foundational principles of harmony.

Using a 6-string bass as an example: https://bradleyfish.com/the-notes-on-the-6-string-bass-guita...

You can find a 2D pattern in the white notes (green notes in the pic) that you can use to understand how the pattern will extend from a given point. For example notice EF+BC always appear in the same 2x2 box shape. Also how those boxes repeat in a diagonal line, and how boxes are connected vertically by a "strip" of 3 notes ADG

The only difference for guitar is that you have to correct for the G/B strings which are separated by a 3rd instead of a 4th, by scooting the pattern on the B+E strings up by one fret

- those 5 chords are the first you learn, and mechanically easy to play in open position, so you know them by heart

See this diagram (https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2F...):

- the CAGED 'order' (C then A then G etc) matches the order in which octaves of the same root appear as you go up the neck, therefore CAGED is a good way of visualising octaves (see how in the 'C-shapes' column the chords 'share' root notes when played in that order up the neck)

- each chord matches a root note position (C: top part of the neck box on the 5th string, A: bottom part of the neck box on the 5th string, etc), therefore if you're playing a scale, no matter what position you're playing it in, you can choose a CAGED chord to overlay on it and easily find the root, third, and fifths (see how in the 'C major scale' column, you can overlay each chord onto one way of playing the C major scale)

- learning these mnemonics should eventually help you 'unlock' the guitar neck, ie have an intuitive knowledge of what intervals you're playing and how to build melodic lines with them

Generally, music theory 'works' because it describes why things sound good. It's not theory that informs what sounds good, rather theory attempts to describe what sounds good and build patterns which will help theory learners, in turn, make music which sounds good.

By the way I think the most difficult thing about CAGED is that it's way too overhyped. It promises too much (scales?) but delivers too little. (Doesn't even have minors)

You can't make music without learning an instrument.

Maybe the instrument is a computer with PD or DAW software but it is still a musical instrument that you have to learn to play.

There is no way around spending hours learning and practicing whatever instrument you pick.

What makes a computer hard to learn to play is that it has too many options. You don't learn anything playing trumpet for a month, then changing to piano for 2 weeks, then trying a new guitar that just came out for 2 months. That though is basically what many computer musicians do.

You need to pick the software setup and then spend a long time learning it and don't switch instruments.