CIRCLE OF FIFTHS (PART TWO)

From our last lesson, we've looked at what circle of fifths are, how they are formed and how they move. Before concluding the previous lesson, we started to look at the structure of circle of fifths and how it is used in different ways. This lesson is a continuation from there. If you're lost or you missed the last lesson, I'll strongly recommend that you go back to the first lesson "CIRCLE OF FIFTHS (PART ONE), then you can come back to this. The following are some others ways the circle of fifths is used. DIATONIC KEY SIGNATURES The circle is commonly used to represent the relationship between diatonic scales. Here, the letters on the circle are taken to represent the major scale with that note as tonic. The numbers on the inside of the circle show how many sharps or flats the key signature for this scale has. Thus a major scale built on A has 3 sharps in its key signature. The major scale built on F has 1 flat.

For minor scales, rotate the letters counter-clockwise by 3, so that, e.g., A minor has 0 sharps or flats and E minor has 1 sharp, e.t.c. A way to describe this phenomenon is that, for any major key [e.g. G major, with one sharp (F#) in its diatonic scale], a scale can be built beginning on the sixth (VI) degree (relative minor key, in this case, E) containing the same notes, but from E – E as opposed to G – G. Or, G-major scale (G – A – B – C – D – E – F# – G) is enharmonic (harmonically equivalent) to the E- minor scale (E – F# – G – A – B – C – D – E). When notating the key signatures, the order of sharps that are found at the beginning of the staff line follows the circle of fifths from F through B. The order is F, C, G, D, A, E, B. If there is only one sharp, such as in the key of G major, then the one sharp is F sharp. If there are two sharps, the two are F and C, and they appear in that order in the key signature. The order of sharps goes clockwise around the circle of fifths. (For major keys, the last sharp is on the seventh scale degree. The tonic (key note) is one half-step above the last sharp.) For notating flats, the order is reversed: B, E, A, D, G, C, F. This order runs counter-clockwise along the circle of fifths; in other words they progress by fourths. Following the major keys from the key of F to the key of C flat (B) counter- clockwise around the circle of fifths, as each key signature adds a flat, the flats always occur in this order. (For major keys, the penultimate (second to last) flat in the key signature is on the tonic. With only one flat, the key of F does not follow this pattern.) MODULATIONS AND CHORD PROGRESSIONS Tonal music often modulates by moving between adjacent scales on the circle of fifths. This is because diatonic scales contain seven pitch classes that are contiguous on the circle of fifths. It follows that diatonic scales a perfect fifth apart share six of their seven notes. Furthermore, the notes not held in common differ by only a semitone. Thus modulation by perfect fifth can be accomplished in an exceptionally smooth fashion. For example, to move from the C major scale F – C – G – D – A – E – B to the G major scale C – G – D – A – E – B – F♯, one need only move the C major scale's "F" to "F♯". The circle can be easily used to find out the common chord progression for basic keys. The circle of fifths shows every major key with its corresponding minor key (of the Aeolian mode). This can be used as the vi chord in a progression. The V and IV chord can be found by moving clockwise and counterclockwise from the root chord respectively. The corresponding minor keys of the V and IV are the iii and ii respectively. The major and minor chords in each major key: I ii iii IV V vi C major: C Dm Em F G Am G major: G Am Bm C D Em D major: D Em F♯m G A Bm A major: A Bm C♯m D E F♯m E major: E F♯m G♯mA B C♯m B major: B C♯m D♯mE F♯ G♯m F♯ major: F♯ G♯mA♯m B C♯ D♯m G♭ major: G♭A♭m B♭mC♭ D♭E♭m D♭ major: D♭E♭m Fm G♭A♭ B♭m A♭ major: A♭ B♭mCm D♭E♭ Fm E♭ major: E♭ Fm Gm A♭ B♭Cm B♭ major: B♭Cm Dm E♭ F Gm F major: F Gm Am B♭C Dm In Western tonal music, one also finds chord progressions between chords whose roots are related by perfect fifth. For instance, root progressions such as D–G–C are common. For this reason, the circle of fifths can often be used to represent "harmonic distance" between chords.

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