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Math, Music and Memory Fall 2014
Handout for Sections 2.2 and 2.3: Scales and Intervals
Scale # of Notes H-W Sequence
Chromatic 12 All half steps
Whone Tone 6 All whole steps
Major 7 W W H W W W H
Natural Minor 7 W H W W H W W
Harmonic Minor 7 W H W W H WH H
Figure 1: The five types of scales discussed in Section 2.2 and their defining sequences of half (H) and whole (W) steps.
Examples
F
!
"!
"
"^!
"
!
!
E
!
!
F
!
A
!
!
A
"
!^ "
G
!
!
G
"
"
!!
!
B
!
!
C
! !
! C
$
"
"
!
!
D D
!
!^!
! C
Figure 2: An ascending chromatic scale beginning on C. The scale has twelve notes, with consec- utive notes always separated by a half step.
A
"^!
G
(^) "!
C
"^!
E
!! D
! F
! C
F
" D
! B
!
A
!
G
! "
C!
! !
"
C
!
A
"^!
G
(^) "!
C
"^!
E
!! D
! F
! C
F
" D
! B
!
A
!
G
! "
C
!!^
"
C
!
Figure 3: The two different whole tone scales, one beginning on C and the other on C]. In each case, the interval between consecutive notes is always equal to a whole step (two half steps).
A
G
C
B
E
D
F
C
W
H
H
W
W
W
W
F
D
B
A
G
C
C
D
G
F
B
A
G C
Figure 4: The C major scale. Notice the pattern of whole (W) and half (H) steps between consecutive notes. This same pattern holds for any major scale.
A
G
C
B
E
D
F
C
4
W
3
H
2 7
H
6
W
5
W
1
W
W
8 = 1
4
G
3
F
7
C
6
B
5
A
"!^
1
D
2
E
8 = 1
D
D
G
F
B
A
G C
Figure 5: The D major scale in the treble clef.
F
"^!
E
D
B
"^!
A
G
C
C
4
W
"^!
3
W
7
W
"^!
6
W
5
H
1
W
2
H
8 = 1
4
G
3
F
7
C
6
B
5
A
#!^ $
1
D
2
E
8 = 1
D
"^!
4
D
3
C
7
G
F
"^!
5
E
1
A
2
B
A
8 = 1
D
G
F
B
A
G C
Figure 6: The natural C minor scale. Notice the pattern of whole (W) and half (H) steps between consecutive notes. This same pattern holds for any natural minor scale.
F
"^!
E
D
B
"^!
A
G
C
C
4
W
"^!
3
W
7
W
"^!
6
W
5
H
1
W
2
H
8 = 1
F
"^!
E
D
B
"^!
A
G
C
C
4
W
"^!
3
W
7
H
"^!
6
WH
5
H
1
W
2
H
8 = 1
4
G
3
F
7
C
6
B
5
A
#!^ %
1
D
2
E
8 = 1
D 8 = 1
Figure 7: The harmonic C minor scale. The only difference from the natural C minor scale is that the seventh scale degree has been raised up a half step.
Scale Deg. Interval Half Steps Name Musical Example(s)
1 Uni. 0 Tonic
2 M2 2 Supertonic Fr`ere Jacques Happy Birthday to You
3 M3 4 Mediant Oh, When the Saints Kumbaya
4 P4 5 Subdominant Here Comes the Bride Oh Christmas Tree
5 P5 7 Dominant Twinkle Twinkle Little Star My Favorite Things
6 M6 9 Submediant My Bonnie Lies over the Ocean It Came upon a Midnight Clear
7 M7 11 Leading tone Take on Me
8 = 1 Oct. 12 Octave Somewhere over the Rainbow
Table 1: The major (M) and perfect (P) intervals within the octave, including the number of half steps in each interval, and some sample musical examples.
Notes Interval Half Steps Musical Example(s)
C – D[^ m2 1 Theme from Jaws
C – E[^ m3 3 “Air-ball!” (the heckle interval) Greensleeves
C – F]^ Tri. 6 Maria Theme from The Simpsons
C – A[^ m6 8 Theme from Love Story Go Down Moses
C – B[^ m7 10 There’s a Place for Us
Table 2: The tritone (Tri.) and the minor (m) intervals within the octave, including the number of half steps in each interval, and some sample musical examples.
Exercises (blank piano keyboard provided below for assistance)
- Write an ascending whole tone scale (one octave) using only flats in the bass clef beginning on G. Use whole notes and write the letter name below each note.
Music engraving by LilyPond 2.12.3—www.lilypond.org
- Write an ascending E[major scale (one octave) in the treble clef. Use whole notes and write the letter name below each note.
Music engraving by LilyPond 2.12.3—www.lilypond.org
- Write an ascending C]^ natural minor scale (one octave) in the treble clef. Use whole notes and write the letter name below each note.
Music engraving by LilyPond 2.12.3—www.lilypond.org
- Write an ascending B[^ harmonic minor scale (one octave) in the bass clef. Use whole notes and write the letter name below each note.
Music engraving by LilyPond 2.12.3—www.lilypond.org
- Notate each of the following musical intervals, including major, minor and perfect designations.
! #^ "!!!
Tri.
P
P
m
%!^!
Oct.
M
m
m
m
m
m
Tri.
m
m
% "^!
