Ok, if there are any of you out there that have a fundamental understanding of the circle of fifths, I need some help. I have a friend that's trying desparately to get it to sink in but music theory is one of those things that my brain shuts down upon. Actually he is not only being very patient with me, but doing a good job of explaining it. It's just very complex and interconnected and I had the thuoght that a different perspective may help me. I'm more visually oriented, it's hard for me to think of things in terms of sound, which is why I changed majors to begin with.13 responses total.
What do you mean by 'understanding' the circle of fifths? Are you just looking to be able to play in all keys? Are you looking to learn some music theory? Do you (god forbid) want to understand the tuning issues it brings up?
C G G D D A A E E B B F# F# C# (aka Db) Db Ab Ab Eb Eb Bb Bb F F C
Hmm. The way I remember it is with F# converting to Gb (6 sharps = 6 flats).
Does this have something to do with the Comma of Pythagoras?
(Yes. Twelve fifths are not _quite_ seven octaves, if you tune them justly. The Comma of Pythagoras is the very slight difference between twelve perfect fifths and seven perfect octaves. In equal temperment, one-twelfth of the comma is added to each fifth, so the circle of fifths ends up being a perfect circle.)
So, is "Circle of Fifths" the same as "Equal Temperment". Or, what does one do with the "Circle" in addition?
Re: #3: You are probably right. Me, I didn't care *too* much where the enharmonic substitution was made! :-)
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Pythagorean Comma was how I remember it referred to . .
But we are hardly any help to Carla.
Back to our meta-questions: what is it you want to
understand?
If you keep ascending by a fifth, that is, 5 notes
up the scale, you hit all twelve tones. We only have
12 notes. Then you are back to your starting point:
like going around a circle. You can stop there,
if you want.
But the real starting point is the harmonic series.
Any uniform material, like a string or a column of air,
vibrates in a series of frequencies called 'partials'.
Let's say you have a string you can pluck or bow and
it vibrates back and forth 100 times a second. A low
note.
Each half is also vibrating independently, at
twice the frequency (200 cps, cycles per second).
Each third is also vibrating independently, 300
times a second, aka 300 Hertz, 300Hz. And these
partial overtones keep going, 400, 500, 600,
theoretically to infinity, but they get quieter and
quieter so it's really only the bottom dozen or so
that we hear.
Grab a guitar, pluck any open string and let it ring
out. Now gently touch the string with your fingertip,
at it's exact center. Hey! At the 12th fret!
Touch it for the shortest instant.
You will cancel out the bottom frequency, and cancel all
the odd numbered partial overtones that are vibrating
the string at that spot. For the even ones, that spot
is right where they are not vibrating, so you are
not damping them. So this subset of overtones will
seem to jump out at you.
This harmonic series, starting at any frequency X,
and including 2X, 3X, 4X, etc., is where all our
scales and harmonies come from. There's stuff built
into your ear, and your brain, and the cableing
in between, to help you notice that two different
frequencies you are hearing happen to be integer
multiples of each other. Is that going to happen
by accident? Not often.
I'll get it right someday.
(John? are you scribbling and reposting for a resaon?)
mistakes.
You have several choices: