MUSIC THEORY— Circle of Fifths

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 OK, that’s all nice and fine but what can you do with it? First of all, if we draw a line from the between F and Bb to in between B and F#, everything on the right side is in the key of C. Rotating the line to the right by one degree gives you the key of G and so on. It’s very easy to see how many sharps and flats the key has in it. G has 1—F#. If we bisect the circle from Ab to A, we can determine that the Key of Eb has 4 flats, Eb, Ab, Db and Gb (F#) and that the Key of E has 2—Eb and Bb.

 

Now to get into a little geometry, if we trace a triangle starting with C then going to E (the major third—always the 4th node clockwise from the root and then finish with G (immediately to the right of C), we’ve spelled a C major chord. Keeping the triangle in the same configuration and moving it around the circle will spell out all the major chords. Replacing the E with an Eb (minor 3rd—3 nodes counter-clockwise), we get the C minor chord. Again, keeping the triangle in the same orientation and moving it from C to D, spells out D minor -( D, F, A). This can be done with any chord, including diminished, augmented, etc. Dominant, major and minor 7ths will have 4 sides since they have 4 notes. It is easy to see how the 6 (the third node to the right) chord of the root note of the scale is the same chord as the minor 7th chord of the 6th note of the scale since they contain the exact same notes. The same holds true for diminished 7ths since all four notes in a diminished 7th can act as a root note.  Combining 2 or more major and minor triangles will yield extended chords such as 9ths, 11ths and 13ths.  For instance, C13 is C major combined with G major and D minor. (all the notes in the C major scale).

 

From a composition standpoint, you can use the circle of fifths to come up with chord progressions. Let’s go back to drawing the line bisecting the circle from D to Db. This is the key of A and the first 2 chords (D, A and E) are major with the next 4  (E, B, F# and Db) being minor. The Ab chord is, of course, always diminished. As a rule, the more notes two chords share, the easier the transition will be and the chords immediately to the right or left of any chord will be the smoothest. For example, going from G (G B D) to D (D F# A) or C (C E G) will sound smoother than G (G D B) to F#  (F# Db Bb) or Db (Db Ab C). You can also see how the C7 resolves to the G since they have 2 notes in common. In general , the further away a chord is on the circle, the more dissonant it will sound.  This can help you with chord substitutions (again, in a future article) in the sense that you have work your way from G to F# by putting some chords in between that will be smoother transitions. So instead of 2 measures of G followed by a measure of F#,  the progression could change on the 1/4 notes and go something like G, D7/F#, Em7, D7, G6/C, Bm, Adim7, F#maj7  with the root notes for each chord in a descending pattern as noted by the slash notes.

 

Next month—composing bass lines

      Now we’re going to get into some math and geometry (sorta) as it relates to music. The circle of fifths (properly named The Circle of Fourths and Fifths—you’ll see why in a bit) is a contraption that can illustrate all sorts of relationships between notes, scales, modes and chords. It was first described by John David Heinichen in 1728 but was in use prior to that.

 

Imagine, if you will, a circle around which all the notes of a chromatic scale are arranged. The arrangement is not in chromatic fashion but proceeds in clockwise fashion from node to node in intervals of a fifth. So starting at the top with the note C and proceeding clockwise, the next note is G, then D, then A, then E and so on until you get to F#. The sharps are all on the right side (Keep in mind that every note can be spelled as a sharp or a flat. Gb is F# as Cb is B or E is Fb). Then starting at the bottom of the circle and continuing clockwise, you have Gb (F#), Db, Ab, Eb, Bb and F before coming full circle to C again. As you can see the flats are all on the left side.

 

Going counter-clockwise, the intervals are fourths. The fourth and fifth of a scale are inversions of each other. This is a construct that is very easy to illustrate on guitar. Pressing down the low E string at the fifth fret yields the note A. The note directly next to it on the 5th string is D (the 4th). The note on the 7th fret of the 4th string is A one octave higher than the original, which just so happens to be the 5th of D. (we’ll get into some more of this in a later article). 

 

 

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