Unit8-Numerical Representation of Scales

MUSC 101 Music Fundamentals - Spring 2012

Unit 8 - Numerical Representation of Scales

Major Scale as Reference Scale

We'll use the major scale as our reference scale. We'll number the notes of the major scale 1 2 3 4 5 6 7 1. Note 3 of the C major scale is E, note 3 of the G major scale is B, note 3 of the F major scale is A, etc. The note F is note 1 of the F major scale, note 2 of the Eb major scale, note 4 of the C major scale, etc.

We can compare other scales to the notes 1 2 3 4 5 6 7 of the major scale. We'll use sharps and flats to indicate which notes are altered from the corresponding note of the major scale. Any number can be preceded by a sharp or flat which will raise or lower the note by one half step compared with the Major Reference Scale.

Symbol	Meaning	Example
2	note 2 of the major scale	note 2 of the C major scale is D
#2	note 2 of the major scale raised by a half step	note #2 relative to the C major scale is D#
3	note 3 of the major scale	note 3 of the D major scale is F#
b3	note 3 of the major scale lowered by a half step	note b3 relative to the D major scale is F
etc.

When the major scale is compared to its corresponding three parallel minor scales we get the following table.

Major	1	2	3	4	5	6	7	1
Natural Minor	1	2	b3	4	5	b6	b7	1
Harmonic Minor	1	2	b3	4	5	b6	7	1
Melodic Minor Ascending	1	2	b3	4	5	6	7	1
Melodic Minor Descending	natural minor in reverse

Here's the table using the notes for G Major and the three forms of G Minor.

G Major	G	A	B	C	D	E	F#	G
G Natural Minor	G	A	Bb	C	D	Eb	F	G
G Harmonic Minor	G	A	Bb	C	D	Eb	F#	G
G Melodic Minor Ascending	G	A	Bb	C	D	E	F#	G
G Melodic Minor Descending	natural minor in reverse

From the tables we see that:

The notes that differ between the major and minor scales are notes three, six, and seven.
The third note of all minor scales is a half step lower than the third note of the major scale.
In natural minor the third, sixth and seventh note are a half step lower than the major scale.
In harmonic minor the third and sixth note are a half step lower than the major scale.
In melodic minor ascending the third note is a half step lower than the major scale.
In melodic minor descending the third, sixth and seventh note are a half step lower than the major scale.

Scale Conversion Formulas

You should be able to quickly convert notes to and from any combination of major and minor scales. The examples below use the parallel major and minor scales of A Major and A minor. However, these formulas are true for all parallel major and minor scales.

Major to Any Other Scale

Major to Natural Minor

	Lower notes 3, 6, and 7 by a half step.
Major to Harmonic Minor
	Lower notes 3 and 6 by a half step.
Major to Melodic Minor Ascending
	Lower note 3 by a half step.

Natural Minor to Any Other Scale

Natural Minor to Major

	Raise notes 3, 6, and 7 by a half step.
Natural Minor to Harmonic Minor
	Raise note 7 by a half step.
Natural Minor to Melodic Minor
	Raise notes 6 and 7 by a half step.

Harmonic Minor to Any Other Scale

Harmonic Minor to Major

	Raise notes 3 and 6 by a half step.
Harmonic Minor to Natural Minor
	Lower note 7 by a half step.
Harmonic Minor to Melodic Minor Ascending
	Raise note 6 by a half step.

Melodic Minor Ascending to Any Other Scale

Melodic Minor Ascending to Major

	Raise note 3 by a half step.
Melodic Minor Ascending to Natural Minor
	Lower notes 6 and 7 by a half step.
Melodic Minor Ascending to Harmonic Minor
	Lower note 6 by a half step.

[Overview] [Syllabus]

Revised by John Ellinger, Spring 2012.