
The Circle of Fifths
A detailed discussion - how to construct and use the Circle Of Fifths
Includes discussions and video tutorials
Includes discussions and video tutorials
Terms used in this discussion
Scale or key, tonal structure, tonic, Intervals, perfect fifth, perfect fourth, enharmonic, sharps, flats, relative minor, major and chromatic.
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Introduction to The Circle of Fifths
There
is nothing mysterious about the circle of fifths. Think of the Circle
of Fifths as a chart of major and minor scales arranged vertically. The
chart is subdivided into two sections, the upper section of the chart
tabulates scales that have sharps, in their key signatures. The
lower section of the chart tabulates scales that have flats in their key
signatures. Our discussion includes videos and textual content spanning
the following topics :
- The unit of measurement
- The enharmonic
- The chromatic scale
- The major scale and its unique tonal structure
- The intervals of a perfect 4th and 5th
THE UNIT OF MEASUREMENT IN MUSIC
The semitone and tone are the
terms used to describe the measurement of the interval between two
notes. For example, C to C# is a semitone, while the interval, C to D,
is a tone. C first moves to C# then moves over to the note D. C to C# is
the first semitone, while C# to D is the second semitone. Two
semitones, are equal to one tone, therefore, the interval C to D has a
measurement of two semitones or 1 tone. (semitone + semitone = tone).
Spend time on the piano. Mark off the tone and semitone intervals in other keys. While in our discussion we will refer to the tone and semitone only, there are many other terms to measure intervals that are way smaller than the semitone. An example is the microtone which is smaller than the semitone.
THE ENHARMONIC
Notice that each of the black keys
has two names, e.g. C# and Db, which is the first black note in the illustration
above. We call this the enharmonic equivalent and they sound the same.
Here are a few examples.
Here are a few examples.
C# is the enharmonic equivalent of
Db.
Db is the enharmonic equivalent of C#
Another example is,
D#, which is the enharmonic of Eb.
A white key may also have an enharmonic.
The note, A, is the enharmonic equivalent of B double flat.
The pitch B is the enharmonic of, A double sharp.
In some contexts, it is necessary to refer to the pitch, F, as E#, or, Fb, as E natural. Another example is B# which is the note, C natural, and Cb, which is the note B natural.
We will discuss other enharmonic equivalents within the context of the scale.
THE CHROMATIC SCALE
The tonal structure of major
and minor scales is best understood by learning the chromatic scale.
There are rules to follow when writing the chromatic scale. In our
example we are going to keep it simple at first. You can refer to a more
comprehensive account of the chromatic scale in our online tutorials.
An important feature of the chromatic scale is the fact that the distance between adjacent notes is always an interval of a minor second. The minor second interval on the piano will be played from a white key then moving to the adjacent black key. In other words, it has an interval of a semitone. Example, C to Db is a semitone interval.
Notes such as B to C, and E to F, are already semitone intervals and do not have a black key in between.
An important feature of the chromatic scale is the fact that the distance between adjacent notes is always an interval of a minor second. The minor second interval on the piano will be played from a white key then moving to the adjacent black key. In other words, it has an interval of a semitone. Example, C to Db is a semitone interval.
Notes such as B to C, and E to F, are already semitone intervals and do not have a black key in between.
SEMITONE INTERVALS
There are special instances where
two white notes on the piano, will form an interval of a semitone or
minor second. The two examples are E to F and B to C. You will also
note that the black key does not feature between E to F and B to C. As mentioned earlier, E# is enharmonic of F natural and Fb is the enharmonic of E natural.
B# is the enharmonic of C natural and Cb is the enharmonic of B natural.
B# is the enharmonic of C natural and Cb is the enharmonic of B natural.
The major scale
The major scale has five tones and two semitones. The intervals in all diatonic major scales are specifically arranged as follows: Tone, Tone, Semitone, Tone, Tone, Tone, Semitone. Take a look at the illustration below. Notice that the diatonic scale has only 7 unique notes and the the chromatic scale has 12 unique notes.
The C Major Scale
The semitones or half-steps in a major scale are always located between notes, three and four & seven and eight. This will always be the case with every major scale. In order to maintain the tonal structure of the major scale, some notes have to be raised using sharps and lowered, with the use of flats.
There are seven intervals in the C major scale which contribute to it's characteristic sound. They are arranged as follows:
Tone, tone, semitone, tone, tone, tone and semitone.
The semitones or half-steps in a major scale are always located between notes, three and four & seven and eight. This will always be the case with every major scale. In order to maintain the tonal structure of the major scale, some notes have to be raised using sharps and lowered, with the use of flats.
There are seven intervals in the C major scale which contribute to it's characteristic sound. They are arranged as follows:
Tone, tone, semitone, tone, tone, tone and semitone.
This arrangement of intervals is used for every major scale.
In the examples that follow you will see the same arrangement.
In the examples that follow you will see the same arrangement.
The G major scale
Although the notes are different, the tonal structure of the G major scale, remains the same as any other major scale; Tone, tone, semitone, tone, tone, tone and semitone. The seventh note becomes F#, to keep the semitone interval between the seventh and eight notes.
The entry in the chart of scales will read: ' G has 1# - F#
The entry in the chart of scales will read: ' G has 1# - F#
The scale of F major
The scale of F major is illustrated below. Notice that the note, B natural, has become Bb (B flat). This, again, has to be done for the tonal structure to match that of the major scale. The entry in the chart of scales will read: ' F has 1b - Bb'
Major scales and accidentals
Generally, we do not use accidentals with notes that are included in the key signature. For example, in the key of G, the seventh note is F# (F sharp). The note, F# is included in the key signature. This means that we will not use an accidental with the note F. The note is played as F# due to its inclusion in the key signature.
The note, Bb, in the key of F major, is written without a flat due to its inclusion in the key signature. This rule applies to all scales, including the minor scales, which we will discuss later. Take another look at the keys illustrated above and all will become clear.
In an examination, you may be asked to write a scale with our without the key signature. 'Without' key signature, means that the candidate will use accidentals next to appropriate notes in the scale.
In an examination, you may be asked to write a scale with our without the key signature. 'Without' key signature, means that the candidate will use accidentals next to appropriate notes in the scale.
The key signatures for major scales that have sharps
The discussion above has shown us that we find the key signature from the accidentals used in the scale. The scale of F major had one flat, which is Bb. The scale of G major has one sharp which is, F#. It is good practice to write scales by hand, with key signatures, and without the key signature, using accidentals.
The key signatures for major scales that have flats
This is a summary of scales that have flats.
The interval of a perfect fifth and a perfect fourth
The interval of a perfect fifth and a perfect fourth
In the scale of C major, the interval C to G is a fifth, since we traverse five notes to arrive at G from C: C D E F, and G. This answers the fifth part of the mystery, what about the word, perfect. We have a perfect 5th interval when the semitone count is seven.
The perfect fourth in the key of C major is C to F. The semitone count for any perfect fourth interval is five semitones.
The perfect fourth and fifth are needed to create the table of scales / the circle of fifths as illustrated above.
The perfect fourth in the key of C major is C to F. The semitone count for any perfect fourth interval is five semitones.
The perfect fourth and fifth are needed to create the table of scales / the circle of fifths as illustrated above.
Finding the major scales that have sharps
The first scale that we have is C Major and it has no sharps or flats
The first scale that we have is C Major and it has no sharps or flats
Example C D E F G A B C - C major
To find the next scale, move up a perfect fifth from the tonic, C D E F, and G.
To find the next scale, move up a perfect fifth from the tonic, C D E F, and G.
This means the next scale up the chart from C major, is, G major.
Example: G A B C D E F# G - G major
We find the next scale in the chart by moving up a perfect fifth from the tonic; G A B C, and D.
The next scale in our chart will be D major.
Example: D E F# G A B C# D - D major
Find the next scale by moving up a perfect fifth from the tonic D; D E F# G, and A.
Example: A B C# D E F# G# A - A major
The next scale in our chart will be D major.
Example: D E F# G A B C# D - D major
Find the next scale by moving up a perfect fifth from the tonic D; D E F# G, and A.
Example: A B C# D E F# G# A - A major
We have arrived at the following scales using the 'perfect fifth method'
C major - 0 sharps
G major - 1 sharp - F#
D major - 2 sharps - F#, C# (notice that the interval from F# to C# is also a perfect fifth)
A major - 3 sharps - F#, C#, G#
A major - 3 sharps - F#, C#, G#
Let's, move on! The next scale will be found a perfect away from the tonic A; A B C# D, and E.
The next scale is E major.
Example: E F# G# A B C# D# E
The next scale is found a perfect fifth away from the tonic. E F# G# A, and B.
Example: B C# D# E F# G# A# B
The next scale is E major.
Example: E F# G# A B C# D# E
The next scale is found a perfect fifth away from the tonic. E F# G# A, and B.
Example: B C# D# E F# G# A# B
As can be seen from the B major scale a perfect fifth above the tonic, B, is F#.
We have our next scale F# major.
Example: F# G# A# B C# D# E# F#
Example: F# G# A# B C# D# E# F#
The final scale in the list of scales that have sharps is a perfect fifth away from F#, and that is C#.
Example: C# D# E# F# G# A# B# C#
Example: C# D# E# F# G# A# B# C#
This is the scale of C# major with seven sharps.
The final summary of scales with sharps
C major - 0 sharps
G major - 1 sharp - F#
D major - 2 sharps - F#, C#
A major - 3 sharps - F#, C#, G#
C major - 0 sharps
G major - 1 sharp - F#
D major - 2 sharps - F#, C#
A major - 3 sharps - F#, C#, G#
E major - 4 sharps - F#, C#, G#, D#
B major - 5 sharps - F#, C#, G#, D#, A#
F# major - 6 sharps - F#, C#, G#, D#, A#, E#
C# major - 7 sharps - F#, C#, G#, D#, A#, E#, B#
We can write key signatures from the summary. This will be illustrated in the following section.