Constructing Music Theory Scales with Scale Formulas
We use the 12 notes with their corresponding sharps and flats
to build a music scale.
The music theory scales are developed mathematically using whole,
half and
minor third steps.
If we assign a numeric value to each note, this provides an interval to
each note. with in the math pattern producing the scale formulas.
Notation for exploring scales.
W = whole step: such as C to D
H = Half Step: as in C to D#
m3 = minor 3rd which is a whole and a half step together: C to Eb
We will use the S to indicate the 'Start'
position or tonic root, then add the steps to construct a scale.
Chromatic Scale:
The Chromatic scale is produced using all half steps and uses
all 12 notes. This is the most basic of all scales. Used to make a type
of fill in special applications to move from one point to another.
S 
H 
H  H  H  H  H  H  H  H 
H  H  H
C

C#  D  D#  E  F  F#  G  G#  A  A#  B  C
Scale FormulasEach is given in Interval steps and notes for the scale primarily
starting on C.
Major Scale:
Mathematically the major scale is produced using the following
formula.
1  2 
3  4  5  6  7  8
S W 
W  H  W  W  W  H
C
 D  E  F  G  A  B  C
Harmonic Minor Scale:
Mathematically the Harmonic minor scale is produced using the following
formula. (flat the 3rd and 6th)
Notice the 3 half steps (m3) in the 6th
to 7th position.
1  2 
m3  4  5  m6  7  8
S W 
H  W  W  H  m3  H
C
 D  Eb  F  G  Ab  B  C
Natural or Relative Minor Scale:
Mathematically the Natural minor scale is produced using the following
formula. (flat the 3rd, 6th, and
7th) the A natural minor is shown here
also, it has no sharps or flats the same as the C major scale.
1  2 
m3  4  5  m6  m7  8
S W 
H  W  W  H  W  W
C
 D  Eb  F  G  Ab  Bb  C
A
natural minor
A
 B  C  D  E  F  G  A
Melodic Minor Scale:
Mathematically the melodic minor scale is produced using the following
formula. (flat only the
3rd )
1  2 
m3  4  5  6  7  8
S W 
H  W  W  W  W  H
C
 D  Eb  F  G  A  B  C
Diminished Scale:
Mathematically the diminished scale is produced using the following
formula of whole  half combinations.
Notice we have 9 notes to complete
the sequence instead of 8. This music scale is used in jazz a lot.
1  2 
m3  4  d5  +5  6  7  8
S W 
H  W  H  W  H  W  H
C
 D  Eb  F  Gb  G#  A  B  C
Polytonal Scale:
Mathematically the Polytonal scale is an inversion of the diminished
scale. Using the the half
 whole repeating pattern. 1, b3, 4, b5, 5 b7
1  m2 
m3  b4  #4  5  6  m7  8
S
H  W  H  W  H  W 
H  W
C
 Db  Eb  Fb  F#  G  A  Bb  C
Pentatonic Scale:
Mathematically the Pentatonic scale is produced with 5 notes using the
following formula. Using the 1, 2, 3, 5, 6
1  2 
3  5  6  8
S W  W  m3  W  m3
C  D 
E  G  A  C
Blues Scale:
Mathematically the Blues scale is produced with 6 notes using the
following formula. Using the 1, b3, 4, b5, 5 b7
1  m3 
4  d5  5  m7  8
S m3 
W  H  H  m3  W
C
 Eb  F  Gb  G  Bb  C
Gospel Scale:
Mathematically the Gospel scale is produced with 6 notes using the
following scale formula. Using the 1, 2, b3, b4, 5, 6
1  2 
m3  d4  5  6  8
S  W 
H  H  m3  W  m3
C
 D  Eb  E  G  A  C
So there is just a quick review to math of scale formulas. Go to the lessons to explore further the scale development and use.
Learning Resources
Scales Workshop
Learning scales is intimidating for the beginning
student.
Don't let them get the best of you. This Getting
It Down Cold Key and Scale Workshop easily leads
you through the process step by step.
Learn
More...
Lessons
in Scales:
Next: Chords
