"Key Signature Math"
How to Use Simple
Math to Find The Sharp and Flats
Key Signature Math is a fundamental principal that
is used
in creating a new key signature that adds one
sharp at a time or one flat at a time.
Each key
change that adds one new
sharp is done by moving a perfect fifth from our current key
signature root.
If we start with the key of C, where we have
no
sharps or flats, and move to the perfect fifth, which is G, it will add
one sharp.
So what would be the new sharp?
How to Add Sharps and Change Keys
Let's look at it a couple of different ways to
apply Key Signature math.
The
sharp will be defined by the major seventh interval which
is 11 half steps
from the key name, or the M7th of the scale.
The second way is to simple think of it
as a
half step down
from the root note that is an octave above.
So for G it will be F#. The M7 or a half step
down from G.
Look at how the scale is built for the G major scale. For review these
concepts are covered in intervals and
is expanded upon in the music theory of scales.
Interval:
1 2
3 4 5
6 M7 8
Scale steps: W + W +
W + H + W + W + W + H
Notes:
G
- A - B - C - D - E - F# - G
The Major 7 (M7) is F#.
Review How the Key
Signature Math Works for Sharps
- To obtain the
next key signature that adds a sharp - it is called the name of the
perfect
fifth from where you
started. ( C to G ),
- the sharp added was the major seventh interval
of
the new key, which is a half step down from the octave of the new key,
(F# is the M7 or a half step down from G).
Considering Flats
The fundamental way to consider flats is actually a continuation of the
sharps once you have added all seven sharps. It would involve changing
all the sharps to flats and then reducing the flats one at a time.
You will see how that is done when we work with our circle of fifths
in the next segment.
However, for building the flat keys there is another way of doing it if
we start with the key of C and add one flat at a time. That involves
using the idea of fifths and fourths again.
The first flat key will be the key of F it is a fifth down from C, (or
alternately a fourth up from C) as shown on this keyboard.
F Major Scale, by default has the Bb as the perfect fourth. That is our
first flat.
Look at how the scale is built for the F major scale using the same
formula as before:
Interval:
1 2
3 4 5
6 M7 8
Scale steps: W + W +
W + H + W + W + W + H
Notes:
F
- G - A - Bb - C - D - E - F
Review How the Key
Signature Math Works for Flats
-
To obtain the
next flat key signature that adds a flat - it is called the name of the
perfect
fifth below where you
started. ( C to F ),
-
The flat added was the perfect fourth
interval
of
the new key, (Bb is the P4 from F).
Alternate
Method of Math for Flats
-
Another
way to look at it is the 4 + 4
method. If you look at the keyboard
above and consider that if you started at C went a 4th up you are at F,
the new key, another 4th and you have the Bb that is in the key.
- A
pattern you will become familiar with is that the new flat to be added
for the next key change will be a fifth down, just like the key. (or a
fourth up)
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