Harmonics Wheel

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The Theory












Harmonics Wheel

Harmonics Theory

HARMONICS WHEEL combines the principle of natural harmonics with the cycle of 4ths and 5ths. However, it uses equal temperament tuning - the harmonics have been slightly detuned to conform to J.S. Bach’s Equal Temperament Tuning system.

Using the “Play Bar” and the “Cycle Pie” it is very easy to create musical structures that modulate from key to key smoothly without the need to learn complex fingering patterns that a standard keyboard or fretboard normally require nor does it need years of practice and music theory study in order to produce beautiful music.


The first 7 ODD Harmonics (1, 3, 5, 7, 9, 11, 13) of the Dominant Note of the Major Scale of a key form a Dominant 13th chord. The 15th Harmonic is the Major 7th of the Dominant Note and is often referred to as the Dominant Note’s “Leading Tone”. The First 6 EVEN (2, 4, 6, 8, 10, 12) Harmonics of the Dominant Note of the Major Scale of a key form a Dominant Major Chord.

Adding the 14th harmonic forms a Dominant 7th Chord

The Dominant 7th Chord of a key resolves to the Tonic Chord (the “AMEN Cadence” heard at the end of almost every major classical composition in the history of music).

For example G Dominant 7th resolves to C.

THE CYCLE OF 4ths AND 5ths:

Going clockwise, each note in the cycle is the third harmonic of previous note and “resolves” downward to it. For example, G resolves downward to C which in turn resolves downward to F and so on round the cycle. It takes 12 notes to form a closed cycle. J.S.Bach discovered this while tuning the organ.

Technically the cycle will never close (see website for a more detailed mathematical explanation) but Bach found that by very slightly de-tuning each note he could form a closed cycle. He called this “Equal Temperament Tuning” and it is used universally in Western Music today. Prior to J.S.Bach’s discovery, musical instruments used ‘Just Intonation” which adhered strictly to the harmonic series, however, it was not possible to modulate between keys using this tuning and transposing melodies and harmonies into other keys changed their character significantly.

Bach’s discovery allowed melodies and harmonies to be transposed freely into any key without changing their character and gave birth to the Baroque style of music with its constant modulations from key to key. This approach was refined during the Classical and Romantic periods that followed and is still used today.

In the cycle of 4ths and 5ths notes that are directly opposite each other divide the cycle into two semicircles, each of which are the notes of a major scale. These two scales are a flattened fifth apart and are known as “Complimentary Keys”. They share the two notes that form the diameter but all other noes are different in each scale, however, all the notes in the entire chromatic scale are utilized in these two scales.

The two notes that form the diameter form a flattened fifth interval that is the Major 3rd and the 7th of the Dominant 7th chords of both scales, however, the interval is inverted in each key.

For example Major Keys of C and Gb are complimentary keys.

Their Dominant 7th chords are G7 and Db7.

The 3rd of G7 is B and the 7th is F which forms a flattened fifth interval The 3rd of Db7 is F and the 7th is B (technically Cb) which is the same flattened fifth interval but with the notes inverted.

It is also interesting to note that for either key the notes on the cycle of 5ths and 4ths that are not part of that key form a pentatonic scale.

For example the scale of C Major when looked at on the cycle of 5ths and 4ths has all the notes in the semicircle whose diameter is B to F that is:- B, E, A, D, G, C and F. The remaining notes (Bb Eb Ab Db and Gb) form a pentatonic scale. The traditional piano keyboard is laid out so that the white notes form the diatonic scale of C Major while the black notes form a pentatonic scale.

For a more in depth explanation of Malcolm Cecil’s Theory of Harmonics and Subharmonics go to www.harmonicswheel.com

We hope you enjoy Harmonics Wheel and look forward to continue "Expanding" the musical experience.