TonalityGUIDE - basic tonal music theory and analysis for undergraduates
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Key and Modulation

introduction major and minor the circle of fifths ways of modulating spotting modulations

fifth-related major keys | series and circles | minor keys

key and modulation
longer progs.

The perfect fifth - the first interval in the harmonic series - is crucial in tonal music. It is the interval between the roots of the chords in the progression V - I - the perfect cadence (V - I) that is so important for defining a sense of key. The theory is explained on these pages, whilst some examples can be found in the section on longer progressions (follow the link in the blue triangle).

As explained in chords and scales, the perfect fifth is also the only interval by which you can cycle all the way through the whole major scale. In the example below, two scales a fifth apart are arranged as a series of fifths: D major and A major. The notes of each scale are circled in red and the tonic is marked in blue.

When you arrange a scale as a series of fifths, the tonic is second note from the bottom. The interval between the leading note and subdominant of a major scale is a diminished fifth, so these notes have to be at the top and bottom respectively (C# and G in D major). Remember to look in the basics section of the Toolkit if you are uncertain of functional note names such as leading note and subdominant

Arranging the notes of these scales as a series of fifths makes clear the close relationship between them. D and A major consist of the same notes except for G, which is sharpened as the leading note of A major. In order to modulate a up fifth (from D to A), you take the bottom note of the scale arranged as a series of fifths, raise it by a semitone and move it to the top of the series. Conversely, in order to modulate down a fifth (from A to D), you take the top notes of the scale arranged as a series of fifth, lower it by semitone, and move it to the bottom of the series.

Here is another way of thinking about it. All major scales a perfect fifth apart are related in this way, and if you imagine the notes above as part of a longer series of fifths, D and A represent two of many overlapping groups of seven notes. Modulating up a fifth means moving up one overlapping group, modulating down a fifth means moving down.

Just so that we don't forget that the whole point of all this is to explain what happens in actual music, here is a short extract that modulates from D to A. In the second bar, there is a G# - the composer has started using the the group of seven notes that make up A major rather than D.

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