My friend Josh and I have been working through the book The Intellectual Devotional together. The book is a pretty neat idea; it's a series of short articles on a variety of topics. Each day of the week has a different theme. The book is patterned after a religious daily devotional, but covers secular/intellectual topics. Josh and I have already discussed the first few articles offline, so I'll start off the blog with my thoughts for Day 5: The Basics of Music.
Like the other articles we've read so far, this has been a bit basic. The article covers what you might expect out of the first couple days of a junior-high music class, just the bare basics of Western music theory. There are a few footnotes that hint at more interesting facts, including one that has a tidbit about the differences between Indian and Western music theory, which was new to me. But overall, anyone who knows much of anything about music theory has heard all of this multiple times before. That said, I'm hopeful that future articles are going to be more interesting, as the book devotes every Friday to a discussion of music.
One topic I hope to see discussed is the relationship between music and math; for example things like the Circle of Fifths always reminds me of the fact that the 12-tone system is an example of modular arithmetic.
While I don't have the background in music that PM does, most of this information is at least passingly familiar to me. I would have appreciated an example of the major key and minor key.
ReplyDeleteModular arithmetic is interesting to me at the moment. We've been discussing at work how to operate on integer matrices (e.g. finding the solution) in the integer domain while constraining intermediate values. It turns out that the answer is to constrain the matrices to a finite field, which in our case is probably a modular field. I'm not quite using the correct math terms here, though....
Well, it only took me about five attempts to figure out how to comment on my own post. HOW IS BLAG WORK? HOW COMMENT GET PUBLISH?
ReplyDeleteI had typed up a couple versions of the relationship between major and minor keys, and how you get one from the other, but I'm too lazy to recreate them, so here's the tl;dr:
You can rotate a major scale by different amounts to get different modes. The 6th mode (rotated 5 places) is the basic minor scale. For example, C major (C D E F G A B C) becomes A minor (A B C D E F G A).
You can also get a minor key by lowering th 3rd, 6th, and 7th notes of the scale by a half step. C major becomes C minor (C D Eb F G Ab Bb C).
So is there an A major scale? If so, then how do you resolve lowering the 3, 6, and 7th notes to get a minor key (presumably A minor) with the A minor you obtain from the rotation?
ReplyDeleteYeah so you take the W W H W W W H pattern starting at A to get A major = A B C# D E F# G# A. Dropping the 3rd, 6th, and 7th of that scale gets rid of the sharps, so A minor = A B C D E F G A.
ReplyDeleteHmm, now I see that I never talked about that pattern. Anyway, the basic major scale is a scale starting at any note with a pattern of increments equal to whole step, whole step, half step, etc.
ReplyDelete