A.P. Music Theory

I'm taking musci theory next year and have started on my summer work early but i'm confused, how would I write an essay describing on how to read and memorize the circle of fifths.

Wait, wait, wait.

The circle of 5ths is... 12 note names in a row. Just count 1,2,3,4...5 from every note and you go it. Or visualise the piano, 2 octaves and start walking up the notes, or walking down the notes, 5 every time...

CGDAEBF#C#G#D#A#F

End of story. I doubt there's any room for an "essay" for something like that...

Wait, wait, wait.

The circle of 5ths is... 12 note names in a row. Just count 1,2,3,4...5 from every note and you go it. Or visualise the piano, 2 octaves and start walking up the notes, or walking down the notes, 5 every time...

CGDAEBF#C#G#D#A#F

End of story. I doubt there's any room for an "essay" for something like that...

Well this teaches is strict and this summer work counts as 75% percent of the first quarter so i'm going to have to give an essay., but thank you that helps little more, like I've only seen the circle of fourths I know all the flats and sharps there is to know beyond the forths but I guess that's not good enough.,lol

If you need to write an essay on it I would just go through some of the general ways in which it's useful. For instance, you can talk about how it can help figure out key signatures, how closely related different keys are, how it can point you towards the relative minor of a key, etc..

I see what you mean

Is there any online notational programs?, like what's that are web-based

An "essay" is a too general term. If you give the exact info we could help further I think...

But yes, you could enter the tonality issues, the why the circle is important in tonality, how it was used in classical time, in jazz maybe, what other circles are there (of 2nds, of 3rds, of 4ths as you say), examples, etc...

Well this teaches is strict and this summer work counts as 75% percent of the first quarter so i'm going to have to give an essay., but thank you that helps little more, like I've only seen the circle of fourths I know all the flats and sharps there is to know beyond the forths but I guess that's not good enough.,lol

You realize that there's no real difference between a circle of fourths and a circle of fifths? It's the same, just going in the other direction. C-G-D-A-E etc. can be a series of fifths going upwards, or fourths going downwards. So if you know the circle of fourths, you know all there is to know.

I also don't quite understand what you mean with "flats and sharps there is to know beyond the fourths", since by going round the circle of fourths/fifths you'll cover all sharps and flats. There are none "outside" of it.

EDIT: The only case where there would be a difference between a circle of fourths and a circle of fifths would be in non-equal temperament, by using just intervals: An "octave" built out of fifths results in a ratio of 2.0273 (((3/2)^12)/64) and is thus slightly too large, whereas an octave built out of fourths only has a frequency ratio of 1.9731 (((4/3)^12)/16) - if I calculated correctly. Thus a tuning system built out of fourths would be quite different from a tuning system built out of fifths, but I don't think that matters in your case, since the concept of a "circle of fifths" requires equal temperament to make any sense in the first place (as without equal temperament it won't result in a circle where both ends meet in one point, but in a spiral). I suppose though that this last paragraph has nothing at all to do with what you're looking for, so feel free to just ignore it.

EDIT: NUMBERS NUMBERS NUMBERS

How do you DO that. You got a piece of paper with you at all times with the pythagorean coma nonsense written on it and all the formulas???? Woah~!

PS: I've done the temperament based on 4th things before, electronically. It sounded interesting, buuuut too much work to be of any use.

How do you DO that. You got a piece of paper with you at all times with the pythagorean coma nonsense written on it and all the formulas???? Woah~!

No, but I got a calculator on my computer :P

It's not that hard: 12 fifths add up to a couple of octaves, so to get from, say, C to B# you have to multiply the frequency by the ratio for a fifth (3/2) 12 times, i.e. (3/2)^12. Then divide that by two a couple of times until you get in a reasonable range, i.e. a value near 2 (perfect octave). For fourths you do the same, just using the fourth ratio 4/3. And if you forget the interval ratios, just imagine the harmonic series and see where the interval you're looking for first appears. (Which would be between the third and fourth note in the case of the fourth, and the second and third note in the case of the fifth. As a further example: a just major third would be between the fifth and fourth note of the harmonic series, so the ratio is 5/4. You need three major third steps to go from C to B#, so an octave built out of major thirds would have a frequency ratio of (5/4)^3 = 1.9531). But sorry, I'm derailing.

No, but I got a calculator on my computer :P

It's not that hard: 12 fifths add up to a couple of octaves, so to get from, say, C to B# you have to multiply the frequency by the ratio for a fifth (3/2) 12 times, i.e. (3/2)^12. Then divide that by two a couple of times until you get in a reasonable range, i.e. a value near 2 (perfect octave). For fourths you do the same, just using the fourth ratio 4/3. And if you forget the interval ratios, just imagine the harmonic series and see where the interval you're looking for first appears. (Which would be between the third and fourth note in the case of the fourth, and the second and third note in the case of the fifth. As a further example: a just major third would be between the fifth and fourth note of the harmonic series, so the ratio is 5/4. You need three major third steps to go from C to B#, so an octave built out of major thirds would have a frequency ratio of (5/4)^3 = 1.9531). But sorry, I'm derailing.

I'll keep this in mind, thanks.

No, but I got a calculator on my computer :P

It's not that hard: 12 fifths add up to a couple of octaves, so to get from, say, C to B# you have to multiply the frequency by the ratio for a fifth (3/2) 12 times, i.e. (3/2)^12. Then divide that by two a couple of times until you get in a reasonable range, i.e. a value near 2 (perfect octave). For fourths you do the same, just using the fourth ratio 4/3. And if you forget the interval ratios, just imagine the harmonic series and see where the interval you're looking for first appears. (Which would be between the third and fourth note in the case of the fourth, and the second and third note in the case of the fifth. As a further example: a just major third would be between the fifth and fourth note of the harmonic series, so the ratio is 5/4. You need three major third steps to go from C to B#, so an octave built out of major thirds would have a frequency ratio of (5/4)^3 = 1.9531). But sorry, I'm derailing.

geek! :D

And I'm one too for understanding it. I have a good book on piano tuning that REALLY goes in to all of those details on temperaments and tuning and calculation. Dreadfully interesting, and it's quite logical, really.

You don't write an essay for the AP test. I took the test, what you'll get instead is what they call the free-response portion. The first part of this is with "aural stimulus." They will play a melody and you have to write it down. Also known as melodic dictation.

Then you will listen to a 4-part writing piece. You will have to notate the soprano and bass line, but they will just be playing half-notes, so you don't have to worry about rhythm. This is called harmonic dictation. If I remember correctly, that's all for "aural stimulus."

Now you get a harmonic progression, and you have to write a 4-part harmony. You have to follow all the rules (ex no parallel fifths). I think there are 8 chords you have to fill. They determine your base line (they tell you your inversions), but you do have to fill it in.

I'm forgetting something that goes here, but you'll figure it out in the class hopefully. It has something to do with 4-part writing.

Then you have to write a base line and a harmony. They give you the soprano voice and a portion that has the base line a harmony, and you kind of have to follow the pattern. Just make sure to use common chord progression (up a second, down a third, down a fifth) when you write it.

So you don't have to write an essay, this is the equivalent to the essay portions of the other AP tests.