Tutorial 2

MUSI 1023 (1A)

Copyright © KWOK MAN HO MARCO 2021. All rights reserved.

Warm-up exercise
● What is the interval between these two notes?
Intervals
● Measurement of the vertical (pitch) distance between two notes
○ Harmonic interval - the notes are played at the same time
○ Melodic interval - the notes are played successively

Intervals
● Two parts to any interval name
○ First part: numerical value (number of letter names spanned)

A Letter names F G A
No. of letter
1 2 3
F names spanned
3rd

○ ALWAYS count from the lower note to the higher note

Intervals
○ What is the numerical value of the intervals below?

E Letter names A B C D E
No. of letter
1 2 3 4 5
names spanned
A
5th

Intervals
○ The numerical value of the intervals WON’T be changed by
any accidentals

E
Letter names A(♯) B C D E

No. of letter
1 2 3 4 5
names spanned
A♯
Accidentals are:
1. Always on the LEFT of the note
2. Place on the SAME space/ line of the note

Intervals
○ The numerical value of all the intervals below are 5ths

○ To describe the differences of the 5ths above,

we need the modifier



Intervals
○ Second part: Modifier that precedes the numerical value
■ Major, Minor, Perfect, Augmented and Diminished
■ Requires the knowledge about steps and major key
signatures

Steps
● Half step (semitone)
○ Distance from a key on the piano to the very next key
○ Examples:

C♯ D G A♭

Steps
● Whole step (whole tone/ tone)
○ 2 half steps
○ Examples:

F♯ G♯
C D

Major key signatures

● A pattern of sharps or flats that appears at the
beginning of staves
● Indicates that certain notes are to be consistently
raised or lowered
● There are seven key signatures using sharps, and
also seven key signatures using flats

Major key signatures

Major key signatures
● Pattern of the key signatures with sharps

B C D E F#

GABCD DEFGA ABCDE EFGAB F# G A B C#

FGABC CDEFG GABCD DEFGA ABCDE EFGAB

F♯ C♯ G♯ D♯ A♯ E♯ B♯
○ 5th above the previous one
Major key signatures
● Pattern of the key signatures with flats

BbA G F E b
DbC B A G b

F E D C Bb EbD C B Ab AbG F E D b G bF E D C b

BAGFE EDCBA AGFED DCBAG GFEDC CBAGF

B♭ E♭ A♭ D♭ G♭ C♭ F♭

○ 5th below (or 4th above) the previous one

Major key signatures
○ You can simplify the major key signatures with the table below:
+5 letter names

Sharps
F♯ C♯ G♯ D♯ A♯ E♯ B♯
(in order)
Major Keys G D A E B F♯ C♯
-5 (or +4) letter names

Flats
B♭ E♭ A♭ D♭ G♭ C♭ F♭
(in order)
Major Keys F B♭ E♭ A♭ D♭ G♭ C♭

Intervals
● Modifiers for intervals:
○ Group A: 2nd, 3rd, 6th and 7th

Diminished Minor Major Augmented

(d) half step (m) half step (M) half step (A)
wider wider wider

○ Group B: unison (1st), 4th, 5th, octave (8ve)

Diminished Perfect Augmented

(d) half step (P) half step (A)
wider wider

Intervals
● “Major” and “Perfect” intervals in a major scale
○ Relating them to the intervals contained in the major scale
○ E.g. C major

M2
M3
P4
P5
M6
M7

Intervals
● Steps for working out the intervals:
1. Find out the letter names of two notes
2. Work out the numerical value (ignore the accidentals)
B♭ Numerical value:
6th
D
Letter names D E F G A B(♭)
No. of letter
1 2 3 4 5 6
names spanned

Intervals
3. Form a major scale with the LOWER note

B♭

D E F♯ G A B C ♯
○ In this example, form a “D major scale”
■ Write the letter in order (starting from D)
■ Add ♯ /♭ according to the key signature
(F ♯ and C ♯ for D major)



Intervals
4. Find out the Major/ Perfect interval with the same letter
name (in the major scale)

B♭

D E F♯ G A B C♯
6th
M6
○ For 6th, we use diminished, minor, major and augmented
as modifiers
Intervals
5. If the letter names circled in orange have different accidentals,
find out the intervals by counting step(s) between them

A half step
NARROWER than M6
B♭

Half step D E F♯ G A B C♯
lower 6th
M6

M6
Intervals
● Modifiers for intervals:
half step
○ Group A: 2nd, 3rd, 6th and 7th narrower
Diminished Minor Major Augmented
(d) half step (m) half step (M) half step (A)
wider wider wider

○ Group B: unison (1st), 4th, 5th, octave (8ve)

Diminished Perfect Augmented

(d) half step (P) half step (A)
wider wider

Intervals
5. Answer: Minor 6th (m6)

A half step
NARROWER than M6
B♭

Half step D E F♯ G A B C♯
lower
m6 M6
(Minor 6th)
M6

Intervals
○ You may not be abled to form a major scale directly with
the lower note sometimes:

G
D♯?
Sharps
F♯ C♯ G♯ D♯ A♯ E♯ B♯
(in order)
Major Keys G D A E B F♯ C♯

Intervals

G → G♭ HS lower
D♯ → D E F♯ G A B C♯
Diminished 4th (D4) P4

1. Lower or raise both notes (canceling the accidentals of the lower note)
2. DO NOT change the letter names!
3. The interval won’t be changed when you move both notes together
4. Form the major scale with the new bottom note (i.e. “D major scale”)

Intervals ♭
E → E♭ → E♭
● Notate the specified interval above the given note.
HS HS

♭
♭ E♭♭ Diminished → Minor → Major → Augmented

G A B C D E F♯
M6

1. According to the numerical value, find out the letter name and note above
2. According to the modifier provided, find out how many half step(s) do you
need to lower/ raise (by adding accidentals)

 (♭) (♭)
Letter names D E F G A B C D E F G A B

Intervals No. of letter

names spanned
1 2 3 4 5 6 7 8 9 10 11 12 13

● Intervals smaller than an octave are called simple intervals

● Intervals larger than an octave are called compound intervals

B♭

D
Minor 6th Compound Minor 6th
(m6) (Compound m6)
Or
Minor 13th (m13)

Common mistakes - enharmonic intervals

● What is the name of the interval below?

Augmented 4th (A4)?

Diminished 5th (D5)?

○ ALWAYS count the numerical value first!

Common mistakes - enharmonic intervals

● What is the interval below? Tritone = D5 or A4
Half step lower =

F D5

B C♯ D♯ E F♯
P5

Half step higher =

E♯ A4

B C♯ D♯ E F♯ Enharmonic:
Notes that have the same
P4 pitch but that are spelled
differently


Common mistakes - notation
● Notation of “major 2nd” (M2) above the given note
○ the positions of the notes and accidentals are little tricky
○ E.g. E and F#

♯ ♯ ♯ ♯

Harmonic interval Melodic interval Poor position of Poor position of

(vertically) (horizontally) the note the sharp

END