bandcoach
Zukatoku - Mod Scientist
Circle of Fifths
Circle of fifths because you circle around it.
It is the relationship of key signatures as you move through them, pure and simple.
In all there are 21 key signatures. This is because each note can be named as flat (b), natural or sharp (#)
Ab-Bb-Cb-Db-Eb-Fb-Gb
A-B-C-D-E-F-G
A#-B#-C#-D#-E#-F#-G#
If we were to arrange these key names in sequence from Fb to B#, like so:
where each key is a fifth above the previous one, we can see how we can begin to call this a circle of fifths.
We can conceivably bend both ends of this sequence to create a circle that wraps around itself:
But notice that the two ends are not lined up. In fact, they wrap, spiral like, around to reach the start again at B#.
Generally we only use 14 of keys Cb-C# from the above, as the rest are overkill (you end up with 12# for B#).
Upper and lower tetrads
When we construct major scales we start from the concept that there is a fixed pattern of notes applied to every possible starting note:
Let's break that down a bit, because it looks like there might be some symmetry inside of that:
Consider the C Major scale
CDEF
GABC
The distance between C and D is the same as between G-A; between A and B is the same as between D and E; the distance between E and F the same as the distance between B and C. Each of these four note scale fragments, called tetrads (literally 4 notes from the Greek tetra - four), has the same pattern: TTS. In any major scale we separate the lower and upper tetrads by a tone, hence our original pattern TTSTTTS.
Now let's go back to the original circle of fifths. Filling in each of the scales, we can see the upper and lower tetrad pattern being continually updated as we move from Fb to C#. Looking more closely, we see that each new key after Fb uses the upper tetrad of the preceeding key as the lower tetrad of the new key, i.e. each scale is prefaced in the upper tetrad of the scale before it in the Circle of 5ths. This is a partial explanation of why there is such a strong link between the dominant (the key a 5th above) and sub-dominant (the key a 5th below) to the main key.
The table is colour-coded to show where the same tetrads (regardless of actual note name) occur.
Looking closely at the table we can also see the following two features
Language use
T(one) = Whole-step
S(emitone) = Half-step
Circle of fifths because you circle around it.
It is the relationship of key signatures as you move through them, pure and simple.
In all there are 21 key signatures. This is because each note can be named as flat (b), natural or sharp (#)
Ab-Bb-Cb-Db-Eb-Fb-Gb
A-B-C-D-E-F-G
A#-B#-C#-D#-E#-F#-G#
Fb-Cb-Gb-Db-Ab-Eb-Bb-F-C-G-D-A-E-B-F#-C#-G#-D#-A#-E#-B#
where each key is a fifth above the previous one, we can see how we can begin to call this a circle of fifths.
We can conceivably bend both ends of this sequence to create a circle that wraps around itself:
But notice that the two ends are not lined up. In fact, they wrap, spiral like, around to reach the start again at B#.
Generally we only use 14 of keys Cb-C# from the above, as the rest are overkill (you end up with 12# for B#).
Upper and lower tetrads
When we construct major scales we start from the concept that there is a fixed pattern of notes applied to every possible starting note:
T(one)-T-S(emitone)-T-T-T-S.
Let's break that down a bit, because it looks like there might be some symmetry inside of that:
T-T-S
T
T-T-S
T
T-T-S
Consider the C Major scale
CDEF
GABC
The distance between C and D is the same as between G-A; between A and B is the same as between D and E; the distance between E and F the same as the distance between B and C. Each of these four note scale fragments, called tetrads (literally 4 notes from the Greek tetra - four), has the same pattern: TTS. In any major scale we separate the lower and upper tetrads by a tone, hence our original pattern TTSTTTS.
Now let's go back to the original circle of fifths. Filling in each of the scales, we can see the upper and lower tetrad pattern being continually updated as we move from Fb to C#. Looking more closely, we see that each new key after Fb uses the upper tetrad of the preceeding key as the lower tetrad of the new key, i.e. each scale is prefaced in the upper tetrad of the scale before it in the Circle of 5ths. This is a partial explanation of why there is such a strong link between the dominant (the key a 5th above) and sub-dominant (the key a 5th below) to the main key.
The table is colour-coded to show where the same tetrads (regardless of actual note name) occur.
Looking closely at the table we can also see the following two features
- When we move up from Fb-C# the seventh note in each successive scale is sharpened or raised a semi-tone
- When we move down from C#-Fb the fourth note of each successive scale is flattened or lowered by a semitone.
Language use
T(one) = Whole-step
S(emitone) = Half-step
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