General Scale Theory


This lesson is on scales. What are scales? What can we do with them? We are looking at the general things that we can say about all (or mostly all) scales.

A preview of the lesson:
Scales:
1.) as melodic templates
2.) a basic definition
3.) as collection of intervals, defined by intervals
4.) chromatic and major scales as basis for analysis
5.) types of scales
6.) with relation to chords/ harmonized to chords
7.) defined by step pattern
8.) families of scales/ definition of modes
9.) a small syllabus of scales
10.) applied to standard tuning
11.) applied to standard notation, keys and key signatures

Scales as Melodic Templates
Scales are collections of pitches from which we create melodies.

Scales are templates from which we create melodies.

Scales: a Basic Definition
We define a scales as a collection of tones within an octave usually not played at the same time.

In the western music system we are using, there are 12 tones to choose from to create a scale. The scale (collection of tones) with all 12 tones is calles the chromatic scale.

The 12 tones are described using 7 letters and accidentals. They 12 tones are called: A, A#/Bb, B, C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab. Note: The names with slashes are two different names for the same tone, these are called enharmonic equivalents (C# is the enharmonic equivalent of Db, etc.). When using letters to refer to a scale, we are refering to a specific scale (ex. A,B,C,D,E,F,G# is the A-harmonic minor scale).

Scales are a collection of intervals. They are defined by intervals.
In the above example, A is the root note, all the other notes in the scale relate to the root note. The distances between the other notes are called intervals, and we can define our scales in terms of their intervals. generally, we use simple intervals (intervals within an octave) to define our scales. The interval definition of the scale (type of scale) remains constant no matter what key (root note, tonic, starting frequency) you are in.
The intervals we use can be written as a combination of letter and number or as number and accidental.
More info on intervals at http://simianmoon.com/snglstringtheory/scales/intervals.html

But here's a brief summary of the info:

distance from	name		letter/#	#/accidental
root in 
half-steps
0		Pefect unison	P1		1
1		minor second	m2		b2
2		Major second	M2		2
3		minor third	m3		b3
4		Major third	M3		3
5		Perfect fourth	P4		4
6		augmented 4th/	aug4		#4
		diminished 5th	dim5		b5
7		Perfect 5th	P5		5
8		augmented 5th	aug5		#5
		minor sixth	m6		b6
9		Major sixth	M6		6
		diminished 7th	dim7		bb7
10		minor seventh	m7		b7
11		Major seventh	M7		7
12		Perfect octave	P8		8

All compound intervals are generally reduced to within an octave for practical applications, except when necessary , for scales. (when discussing scales we note that the scale repeats itself in the next octave, the 6 and 13 are the same pitch but in different octaves. There are some "exotic" scales which do not repeat beyond the octave but that is beyond the scope of this lesson)[ We can refer to pitches, or pitch classes].

So for example, the major scale is defined as having the intervals M2, M3, P4, P5, M6, M7, P8 (and all their octaves). We can write this as :
Major scale = 1,2,3,4,5,6,7.

The major scale (also called the Ionian mode) is the only scale to have this exact intervallic definition.

So the Bebop scale (=1,2,3,4,5,6,b7,7) is NOT the major scale because it has an extra interval that the major scale does not have.

Likewise the Major pentatonic scale (=1,2,3,5,6) is NOT the major scale because it is missing intervals.

All 3 of the above are major scales (more on that below - under scale types), but only one of them , the Ionian mode, is THE major scale.

We call the scale with all of the aforementioned intervals (and their octaves) the Chromatic scale, and we can write it as Chromatic scale = 1,b2,2,b3,3,4,b5,5,b6,6,b7,7 . We can write it as including all enharmonic equivalents, some or none. So we could also write it these ways.
Chromatic scale = 1,#1/b2,2,#2/b3,3,4,#4/b5,5,#5/b6,6,#6/b7,7 (all enharm.equiv.)
Chromatic scale = 1,b2,2,b3,3,4,b5,5,b6,6,b7,7 (no enharm.equiv.)
Chromatic scale = 1,#1,2,#2,3,4,#4,5,#5,6,#6,7 (no enharm.equiv.)
Chromatic scale = 1,b2,2,b3,3,4,#4/b5,5,b6,6,b7,7 (some enharm.equiv.)

Scales are basis of analysis

In western music, we use the major scale and the chromatic scale to analyze music, and musical structures. The major scale (=1,2,3,4,5,6,7) is the standard against which all other structures (chords, scales, progressions, etc.) are compared. We do NOT build all structures off the major scale, we COMPARE all structures to the major scale.

For example, the minor chord (m = 1,3,5) is not built off the root note of the major scale and then altered. But rather the collection of intervals is compared to the major scale and we find that the root and 5th intervals match up with the major scale (making them tonic[1], and perfect 5th respectively), while the 3rd is halfway between the 2nd and 3rd of the major scale , and we call this a minor third.

What we DON'T do is say "to make a minor chord, we take the major scale, use the 1,3,5, and then make the 3rd a minor 3rd (b3)".

Any chord (or scale) is a collection of intervals. Although we can derive chords from scales (and scales from chords), we don't NEED to do so. It helps us to undertsnad patterns and relationships to analyze the intervals with respect to some reference, and the major scale has been chosen (in western music) to do that.

The major scale contains only (and all) Perfect, and Major intervals (as determinied from the root).

Any interval that is a half-step lower than the major interval is a minor interval. A half-step lower than a minor interval is a diminished interval. A half-step higher than a Major interval is an augmented interval.

For Perfect intervals, a half-step lower is diminished, and a half-step higher is augmented.

Compare this with the above chart, and note that there are several missing names (for consideration of space). For example, the m2 could also be considered aug1, and the M2 could also be considered dim3, etc. I've listed the main ones in the chart.

Types of Scales
We can classify our scales by their intervals. We refer to what types of chords can built off their root notes.

Recall,
Major chord = 1,3,5
minor chord = 1,b3,5
diminished chord = 1,b3,b5
augmented chord = 1,3,#5

We classify THE major scale as a major scale because it contains the same intervals as the major chord.
Major scale = 1,2,3,4,5,6,7
major chord = 1,3,5

We classsify the minor scale as a minor scale because we find the minor triad occuring within it (built off the root note).
Minor scale = 1,2,b3,4,5,b6,b7
minor chord = 1,b3,5

We classsify the locrian mode as a diminished scale because it contains the intervals of a diminished chord (triad) within it (based off the root).
locrian = 1,b2,b3,4,b5,b6,b7
dim chord = 1,b3,b5

We classsify the 3rd mode of the harmonic minor scale as augmented because it has the same intervals as the augmented chord within it.
3rd mode of the harmonic minor scale (ionian#5) = 1,2,3,4,#5,6,7
augmented chord = 1,3,#5

etc. (some players find it handy to discuss dominant scales [scales containing dom7 chord {1,3,5,b7}])

A list of scales by chord type can be found at http://simianmoon.com/snglstringtheory/scales/scalesyl.html#chords

With relation to chords
We can build chords off of scales, and scales off of chords.

From chords to scales:
We can create scales from chords, it's often done in jazz. Take a chord and add some more notes to it, and play these as a scale.

ex.
Take a 7#9 chord (7#9 = 1,3,5,b7,#9), write the compound interval #9 as a simple interval #2, this gives us (1,#2,3,5,b7) and we add some more notes if we like. Let's say i want a 7-note scale, I would need to add 2 more notes and I can choosebetween any of the remaining notes in the chromatic scale. I'll choose 4 and 6 to give the scale: 1,#2,3,4,5,6,b7.

How about we take 2 chords ( maybe from a progression) and fill in the missing notes.
ex.
Am7 and D7 (i7 and IV7); Am7=A,C,E,G (i7=1,b3,5,b7) and D7=D,F#,A,C (IV7=4,6,8,b10). Add them together (1,b3,4,5,6,b7,8,b10) and reduce to one octave (1,b3,4,5,6,b7) and we have a six note scale. I could add another note to have a seven-note scale:
1,2,b3,4,5,6,b7 = Dorian scale
1,b2,b3,4,5,6,b7 = Javanese scale (Dorianb2, 2nd mode of the melodic minor scale).
(other possibilities exist).

From scales to chords:
We can create chord from scales. We can take a scale and pick any 3 or more notes out of it to make a chord.
Ionian = 1,2,3,4,5,6,7
example chord = 1,4,6
this happens to be an inversion of 4,6,8 (the IV chord) but it is a chord nonetheless.

It is common to talk about harmonizing scales to derive chords. see http://simianmoon.com/snglstringtheory/chords/harmtri.html and the most common harmonization scheme is tertian harmonization (harmonizing in thirds, previously described at the above link). In this process we would take every 3rd note and use it in our chord.

ex. Ionian = 1,2,3,4,5,6,7
1,3,5,7 = major seven chord can be said to be harmonized (derived) from the Ionian mode (major scale).

* When looking at 3rds, the first note is counted as 1, the next note as 2, and the note after that as 3 (3rd).

We need not harmonize in 3rds, we could use a different scheme (4ths, 5ths, other).

ex.
4-note Dorian chord harmonized in 4ths.
Dorian = 1,2,b3,4,5,6,b7
??? = 1,4,b7,b10 = 1,b3,4,b7 = m7/11(no5) or m7(4)

ex. 4-note chord harmonized in 5ths from Ionian
Ionian = 1,2,3,4,5,6,7
??? = 1,5,9,13 = 1,2,5,6 = 6/9(no3)

Besides being able to harmonize in other intervals, several other schemes exist to harmonize with (beyond the scope of this lesson).

Scales are definied by Step Pattern

Not only can scales be defined as intervals from a root note, but we can define it by the intervals from note-to-note.

We will refer to the following terms:
half-step (1/2, same as semitone, or minor 2nd, distance of one fret)
wholestep (W, same as wholetone, or major 2nd, distance of two frets)

We take for example the C major scale.
C major scale = C,D,E,F,G,A,B,C.
C to D is a whole step (W). D to E is a whole step (W-W). E to F is a half step (W-W-1/2). F to G is a whole step (W-W-1/2-W). G to A is a whole step (W-W-1/2-W-W). A to B is a whole step (W-W-1/2-W-W-W). B to C is a half step (W-W-1/2-W-W-W-1/2). So the major scale has the step pattern W-W-1/2-W-W-W-1/2. All major scales (ionian scales/modes, c-major, D-major, etc.) have the step pattern W-W-1/2-W-W-W-1/2. No other type of scale has the step pattern W-W-1/2-W-W-W-1/2 (the Ionian mode and THE major scale are the same scale).

Scales can be defined by their step pattern.

So we can define the major scale as
major scale = W-W-1/2-W-W-W-1/2.

Famalies of Scales/ Definition of modes

Using the step pattern of a scale, we can create modes.

By taking a scale, and starting on the next note, we can create a mode (this is the same as taking the first step and placing it at the end).

ex. C-D-E-G-A-C (C-major pentatonic scale = W-W-m3-W-m3)
D-E-G-A-C-D (D-2nd mode of maj. pent. = W-m3-W-m3-W)

If we continue doing this until we return to our original scale, we can create all of the modes of that scale (a family of scales)
W-W-m3-W-m3 - pent.maj. (1st mode)
W-m3-W-m3-W - 2nd mode of pent. maj.
m3-W-m3-W-W - 3rd mode of pent. maj.
W-m3-W-W-m3 - 4th mode of pent. maj.
m3-W-W-m3-W - 5th mode of pent. maj. (pentatonic minor)

Scales having the same pitches but being different modes are said to be realated (relative) scales.

Different scales starting on the same pitch are said to be parallel scales.

C-Ionian and D-Dorian are relative scales.
C-Ionian and C-Dorian are parallel scales.

A Small Scale Syllabus
A list of common scales follows defined by intervals, step patterns, and pitches (starting on C).

Pentatonic Major
= W-W-m3-W-m3
= 1,2,3,5,6
= C,D,E,G,A

Pentatonic Minor
= m3-W-W-m3-W
= 1,b3,4,5,b7
= C,Eb,F,G,Bb

Major (Ionian)
= W-W-1/2-W-W-W-1/2
= 1,2,3,4,5,6,7
= C,D,E,F,G,A,B

Minor (Aeolian)
= W-1/2-W-W-1/2-W-W
= 1,2,b3,4,5,b6,b7
= C,D,Eb,F,G,Ab,Bb

Harmonic Minor
= W-1/2-W-W-1/2-m3-1/2
= 1,2,b3,4,5,b6,7
= C,D,Eb,F,G,Ab,B

Melodic Minor
= W-1/2-W-W-W-W-1/2
= 1,2,b3,4,5,6,7
= C,D,Eb,F,G,A,B

Gypsy Minor
= W-1/2-m3-1/2-1/2-m3-1/2
= 1,2,b3,#4,5,b6,7
= C,D,Eb,F#,G,Ab,B

Dorian
= W-1/2-W-W-W-1/2-W
= 1,2,b3,4,5,6,b7
= C,D,Eb,F,G,A,Bb

Phrygian
= 1/2-W-W-W-1/2-W-W
= 1,b2,b3,4,5,b6,b7
= C,Db,Eb,F,G,Ab,Bb

Lydian
= W-W-W-1/2-W-W-1/2
= 1,2,3,#4,5,6,7
= C,D,E,F#,G,A,B

Mixolydian
= W-W-1/2-W-W-1/2-W
= 1,2,3,4,5,6,b7
= C,D,E,F,G,A,Bb

Locrian
= 1/2-W-W-1/2-W-W-W
= 1,b2,b3,4,b5,b6,b7
= C,Db,Eb,F,Gb,Ab,Bb

Whole Tone
= W-W-W-W-W-W
= 1,2,3,#4/b5,#5/b6,#6/b7
= C,D,E,F#,G#,A#/Bb

chromatic scale
1,b2,2,b3,4,#4/b5,5,b6,6,b7,7
1/2-1/2-1/2-1/2-1/2-1/2-1/2-1/2-1/2-1/2-1/2-1/2
C,C#/Db,D,D#/Eb,E,F,F#/Gb,G,G#/Ab,A,A#/Bb,B

Applied to standard Tuning

STANDARD TUNING (EADGBE)

E-I-F-|F#/Gb|-G-|G#/Ab|-A-|A#/Bb|-B-|-C-|C#/Db|-D-|D#/Eb|-E-|
B-I-C-|C#/Db|-D-|D#/Eb|-E-|-F-|F#/Gb|-G-|G#/Ab|-A-|A#/Bb|-B-|
G-IG#/Ab|-A-|A#/Bb|-B-|-C-|C#/Db|-D-|D#/Eb|-E-|-F-|F#/Gb|-G-|
D-ID#/Eb|-E-|-F-|F#/Gb|-G-|G#/Ab|-A-|A#/Bb|-B-|-C-|C#/Db|-D-|
A-IA#/Bb|-B-|-C-|C#/Db|-D-|D#/Eb|-E-|-F-|F#/Gb|-G-|G#/Ab|-A-|
E-I-F-|F#/Gb|-G-|G#/Ab|-A-|A#/Bb|-B-|-C-|C#/Db|-D-|D#/Eb|-E-|
0  1      2   3     4   5    6    7   8     9   10   11   12

in F this becomes

7|-1|b2|-2|b3|-3|-4|b5|-5|b6|-6|b7|-7|
T|-5|b6|-6|b7|-7|-1|b2|-2|b3|-3|-4|b5|
2|b3|-3|-4|b5|-5|b6|-6|b7|-7|-1|b2|-2|
6|b7|-7|-1|b2|-2|b3|-3|-4|b5|-5|b6|-6|
3|-4|b5|-5|b6|-6|b7|-7|-1|b2|-2|b3|-3|
7|-1|b2|-2|b3|-3|-4|b5|-5|b6|-6|b7|-7|
0  1  2  3  4  5  6  7  8  9 10 11 12

E shape (root notes on the 6th, 4th, and 1st strings)

-7|-1|b2|-2|b3|
b5|-5|b6|-6|b7|
-2|b3|-3|-4|b5|
-6|b7|-7|-1|b2|
-3|-4|b5|-5|b6|
-7|-1|b2|-2|b3|
0   1  2  3  4

D shape (root notes on 4th and 2nd strings)

|b2|-2|b3|-3|-4|b5|
|b6|-6|b7|-7|-1|b2|
|-3|-4|b5|-5|b6|-6|
|-7|-1|b2|-2|b3|-3|
|b5|-5|b6|-6|b7|-7|
|b2|-2|b3|-3|-4|b5|
 2  3  4  5  6  7

C shape (root notes on 1st and 3rd strings)

|-3|-4|b5|-5|b6|
|-7|-1|b2|-2|b3|
|-5|b6|-6|b7|-7|
|-2|b3|-3|-4|b5|
|-6|b7|-7|-1|b2|
|-3|-4|b5|-5|b6|
  5  6  7  8  9 

A shape (root notes on 5th and 3rd strings)

|b5|-5|b6|-6|b7|-7|
|b2|-2|b3|-3|-4|b5|
|-6|b7|-7|-1|b2|-2|
|-3|-4|b5|-5|b6|-6|
|-7|-1|b2|-2|b3|-3|
|b5|-5|b6|-6|b7|-7|
  7  8  9 10 11 12

G shape (root notes on 6th, 3rd, and 1st strings)

|b6|-6|b7|-7|-1|b2|
|b3|-3|-4|b5|-5|b6|
|-7|-1|b2|-2|b3|-3|
|b5|-5|b6|-6|b7|-7|
|b2|-2|b3|-3|-4|b5|
|b6|-6|b7|-7|-1|b2|
  9 10 11 12 13 14 

Applied to Standard notation, keys and key signatures

There is a correlation between the major scale (major = 1,2,3,4,5,6,7 = W-W-1/2-W-W-W-1/2) , major keys, and key signatures.

We define a major key as the collection of notes that are contained within the corresponding specific major scale.

A key signature is a symbol that tells how many sharps or flats a particular key has (how many of the notes contain a sharp or flat).

Ex.
the C-major scale contains the notes: C,D,E,F,G,A,B
so the key of C contains the notes: C,D,E,F,G,A,B
and there are NO sharps or flats,
so the key signature of C has no sharps or flats.

Ex.
the D-major scale contains the notes: D,E,F#,G,A,B,C#
so the key of D contains the notes: D,E,F#,G,A,B,C#
and there are 2 sharps,
so the key signature of D has 2 sharps.

Ex.
the Ab-major scale contains the notes: Ab,Bb,C,Db,Eb,F,G
so the key of Ab contains the notes: Ab,Bb,C,Db,Eb,F,G
and there are 4 flats,
so the key signature of Ab has 4 flats.

In standard notation, the key signature is written after the clef and before the time signature.

For those interested, here's a brief outline of scale studies.
(one way to approach it, other teachers might emphasize things at different times, etc.)

---Beginner's studies---
- Be able to read diagrams and TAB
- Know how to place fingers down on the fretboard
- Learn/ memorize basic scales (pent. min., pent.maj., major)
- Learn simple picking (plectrum) and fingerpicking techniques
- Learn the chromatic scale
- Know how to use a chord book

---Intermediate studies---
- Locating root notes
- How to play and use moveable scales
- Learning intervallic spellings of scales
- Learning how chords and scales relate to each other
- Knowing how to play various articulations, ornaments
- understanding and applying dynamics
- Learning to make your own scale diagrams/ fretboard maps
- Knowing how to make the most out of scale books
- Understanding modes
- reading scales from standard notation and sight-read in open position
- some more common scales (minor, harmonic minor, melodic minor, blues)

---Advanced studies---
- Soling over chords and progressions
- Playing "outside"
- Sightreading scales and melodies in standard notation in higher positions
- Chord-melody studies
- Modal famalies of scales
- composing from motifs

---Beyond that?---
- Creating a personal style
- Polyphony, counterpoint
- Improvisation, being able to play what's in your head
- Manipulating emotions, understanding the effect of tone on the psyche
- Music therapy, using tones to cure body, mind, and spirit
- Allowing the music to use you as it's tool
- Finding the instruments/tunings voice, and allowing it to speak

Next lesson is on the dominant ninth chord.

Peace,
Christopher Roberts
snglstringtheory@aol.com


How do I change all those numbers to letters (for notes, chords, etc.)? Here's a transposition chart simianmoon.com/snglstringtheory/guitar/8theory3.html

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Last updated July 18, 2002
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