Hacienda de Ville wrote:
> What exactly is the purpose of the circle of 5ths
It has no purpose. It simply exists, and it's a good thing to know it
exists as well as what it is.
And it's only a true *circle* if you're working within the 12 tone
equally tempered scale. This is because it's only in 12TET tuning that
the following enharmonically equivalent note pairs are truly the same
pitch:
Fb-E, Cb-B, Ab-C#, F#-Gb, E#-F, etc.
I.e. It is only in 12tet tuning that after we've traversed 12 Perfect
5ths we arrive back at the *exact same* pitch class (i.e. a note with
the same letter name) and pitch (i.e. a true octave double for) the note
that we started at:
B E A D G C F Bb Eb Ab Db Gb |Cb/B
In 12tet tuning, Cb and B are the exact same pitch.
So are E and Fb, C and B#, F and E#, Bb and A#, Eb and D#, Ab and G#, Db
and C#, Gb and F#.
That is not true in most other tuning systems.
Note: C F Bb Eb etc. (i.e. moving down by P5ths/up by P4ths) is
sometimes called the cycle of 4ths while C G D A etc. (i.e. moving up by
P5ths/down by P4ths) is called the cycle of 5ths.
I learned them as positive and negative cycle 5, respectively, myself.
In a tuning system based on pure Perfect 5ths, like the type of Perfect
5th found in the harmonic overtone series, there would be no circle. The
cycle of 5ths could go on to infinity in both directions without ever
arriving back at the *exact* same pitch-class/octave double:
......Cx Fx B# E# A# D# G# C# F# B E A D G C F Bb Eb Ab Db Gb Cb Fb Bbb
Ebb..... etc.
This is because it's only in 12tet tuning that, for example, B# and C
natural, etc., are the *exact* same pitch. In a system of pure 5ths, B#
and C nat are tuned to slightly different pitches.
But even in a pure 5ths tuning system (like the one in the example
above) the following note pairs work out to be *real* close to each other:
Cb/B, B#/C, C#/Db, D#/Eb, Fb/E, E#/F, F#/Gb, G#/Ab, A#/Bb
So we usually stop the cycle at 12 P5ths/P4ths anyway.
Cb/B Fb/E A D G B#/C E#/F Bb/A# Eb/D# Ab/G# Db/C# Gb/F# |Cb/B
1 2 3 4 5 6 7 8 9 10 11 12 1
Note: Technically speaking, the interval Cb-E is not really an ascending
P4th interval. It's an ascending augmented 3rd interval. But in 12tet
tuning, aug 3rds are audibly indistinguishable from P4ths. Etc.
> and how essential is
> it to know?
It's pretty handy for a lot of things.
1. When practicing scales, arpeggios, etc. through all 12 keys it's
often a good idea to go use the cycle of 5ths as a guide.
Eg. When practicing major scales you might first work on the C major
scale, then G major, then D major, etc., until you've covered all 12
possible tonics.
(You could also traverse all 12 keys by going chromatically too. Eg. C
C# D Eb, etc. But lots of music where keys change just happens to change
key quite often along the cycle of 5ths. By practicing your scale
through the cycle of 5th you prepare your ears better for this type of
thing.)
2. Familiarity with the cycle of 5ths helps one to remember the various
key signatures in written music.
C (no sharps or flats), F (1 flat), Bb (2 flats), Eb (3 flats), etc.
G (1 sharp), D (2 sharps), A (3 sharps), etc.
Not only that, but the way the sharps or flats are written within a key
signature follows the cycle as well.
1 flat (Bb), 2 flats (Bb Eb), 3 flats (Bb Eb Ab), etc.
1 sharp (F#), 2 sharps (F# C#), 3 sharps (F# C# G#), etc.
3. There are other ways that the cycle is used by musicians too. But I
can't think of any worth mentioning right now.
> Also, can you recommend a good "beginners" book on music theory,
<http://www.amazon.com/Music-Theory-Dummies-Michael-Pilhofer/dp/0764578383>
> something easy to understand for those of us who are newbies?
>
> Thanks!
>
> Haci
--
Joey Goldstein
<http://www.joeygoldstein.com>
<http://homepage.mac.com/josephgoldstein/AudioClips/audio.htm>
joegold AT sympatico DOT ca
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