Scale Theory

Introduction

This page explains various musical concepts involved with Scales, provided to clarify the intended meaning of the jargon that is used. It is by no means a course in music, but rather a brief overview.

Notes And Tones

Throughout the text on this website, the words "Note" and "Tone" are often used. For the descriptions and definitions to be clear, it is worthwhile to precisely define what these words are intended to mean.

A Tone implies a specific frequency. A particular Tone can only occur once in a Scale. The same Tone can often be played at multiple places on the Fretboard. For example, for the standard tuned Resonator Guitar, the Tone played on the open first string is the identical Tone played on the second string at the third fret.

A Note is one of the 12 members of the Chromatic Scale. It can be referenced specifically, by it's letter name (e.g., A, Bb, F#, etc.) or relatively, by it's Scale Degree as a member of a Diatonic Scale. The Note played on the open sixth string is a G, and is the same Note as played on the open third string. These are not the same Tone, however, since the frequency of the third string is twice that of the sixth.

It can be confusing when the word "Tone" is used with its alternate meaning in discussing intervals. On fretted instruments a "Whole Tone" is an interval of two frets, a "Half Tone" is an interval of one fret, etc. On this website, the use of the word "Tone" by itself means a "frequency" and the interval usage will always include a modifier (Half, Whole, etc).

Chord Numbering

Throughout the information on this site, chords will often be referred to using a chord numbering system. The following brief explanation is provided for those unfamiliar with this system.

In a given Key, the primary chord for which the Key is named (also called the Root), is designated by the roman numeral "I". The chord named for each Note in the the Diatonic Scale of the Key is designated by the roman numeral for its order in the Scale. For example, in the Key of G, a C chord (corresponding to the 4th Note in the Scale) is designated as the IV chord.

The natural progression of chords that are used in a Key can be generated by starting with the three Notes that comprise the I chord, and progressing to the next Note in the Diatonic Scale from each of those Notes. The resulting 3 Notes comprise the II chord. This is repeated to produce the other chords in the Key. The following diagram illustrates the process.

Chord Numbering Image

A common practice in using the numbering system is to designate Major chords with "M" and Minor chords with "m" (e.g., IIIM or VIm). But in the discussion on this website, it will be assumed that the I, IV, and V chords are Major, the II, III, and VI chords are Minor, and the VII chord is Diminished, as in the above diagram. It is also sometimes necessary to reference chords for which the Root Note is not in the Scale of the Key, which are Ab, Bb, Db, Eb, and F# for the Key of G. These can be referenced using the prior numeral with a "+" or the next numeral with a "-". Thus, Bb is the III- chord in the Key of G. All such chords are assumed to be Major. In any case where a chord does not follow these rules an "M" or "m" designation will be included (e.g., Bmaj in the Key of G would be designated IIIM).

The chord numbering system is very convenient because it can make most discussions apply to any Key.

Scale Types

Why do we care about Scales? Scales are not just a construct of music theory, they are the Notes you need to play. A great number of melodies draw from a palette of only seven Notes. Standard musical notation is set up to identify those seven Notes (the Scale) at the beginning of the staff. If a melody requires a Note that is not in the defined Scale, a temporary Scale change notation (flat, sharp, or natural) is required, which is called an "accidental". When playing in the Key of G Major, one plays Notes from the G Scale while the chord behind the tune is G. When the chord changes to a C, D or some other related chord, one does not play Notes from a C or D Scale, but continues to use the same seven Notes of the G Scale. So if one is very familiar with the locations of the 7 Notes for a given Key, he/she is likely to be able to play most tunes in that Key with relative ease.

In the music of Western Culture, there are twelve Notes, each separated by a "Half Tone". The most basic Scale Type is the Chromatic Scale, which includes all twelve Notes. This Scale Type is not formally addressed by the Scale Analyzer because there is not much information to be gained by doing so. However, there are Chromatic Note sequences in other Scales Types. Western music is primarily based on the Diatonic Scale and all other Scales Types are described in terms of this Scale Type.

Diatonic Scales

The Diatonic Scale is defined by a sequence of Whole Step and Half Step intervals as follows:.

Diatonic Intervals Image

After the last Half Step, the pattern repeats. The above sequence defines a Major Diatonic Scale. If one looks at the keyboard of a Piano, the Diatonic Sequence is apparent by examining the intervals between the white keys, which comprise the Notes in the C Major Scale:

Keyboard Image

The Note for each black key is designated as the sharp (#) of the Note before it or the flat (b) of the Note after it, depending upon the Key of the Scale you are working with. By starting on a given Note, and using the interval sequence described above, the Major Scale for the Key (designated by the starting Note) can be determined. The following diagram identifies the Major Scale for each of the twelve Keys.

Keys Image

The reason some Keys use flat (b) designation versus sharp (#) is explained by the nature of standard musical notation. Notes are designated by 5 lines and the spaces between them. For example, the following identifies the Notes represented by the lines and spaces on the treble staff for three different Key signatures:

Clef Image

Each line and space must represent a consistent letter name for its Note, which may be designated to be sharp or flat, depending on the Scale. For example, the second line from the bottom can only represent a G, Gb, or G# Note. If the Key of F were to use sharp designations and the Key of A were to use flats, those Scales would have ambiguous Note name references, as is shown in the following diagram:

Bad Sharps Image

Notice that if sharp designations were used for the Key of F, there would be two Notes named with the same letter (A and A#). Thus, the second space from the bottom would have to represent both A and A#. Since there is no contention for Note letters when using flat designations, those are used for the Key of F. The converse is true for the Key of A.

Scale Degree

When playing in a given Key, it is usually more convenient to refer to a Note by its relative order in the Major Scale than by its letter name. This is called the Scale Degree:

Scale Degree Image

As shown above, in the Key of D, the D, E, F#, G, A, B, and C# Notes are the Root, 2nd, 3rd, 4th, 5th, 6th, and 7th, respectively. The Notes that are not included in the D Major Scale, D#, F, A#, and C are the Minor 2nd, Minor 3rd, Minor 6th, and Minor 7th of the Key. The G#, which is also not in the Major Scale, is referred to as the augmented 4th or diminished 5th. In discussion on this website, "3-" is shorthand for "Minor third", "4+" for "augmented fourth", etc. By using the Scale Degree, one can refer to any Note in any Key, without having to memorize the absolute (lettered) Notes that make up each Key.

Diatonic Modes

A Scale that is constructed using the Diatonic Sequence described above is the Major Scale of the Key named by the starting Note, which is also called the Ionian Mode. The order of the intervals in the Diatonic Sequence cannot change and still be Diatonic, but one may begin on a different interval in the sequence. Since there are seven intervals in the sequence, there are seven intervals on which one can begin. Each starting interval defines a different "Mode" of the Key. The following diagram illustrates the process for the Key of G.

Modes Image

In the above diagram, the top line illustrates two cycles of the Diatonic Sequence.

The Modes are formally defined by the changes to the Major Scale that are needed to produce each Mode for the same Key. For example, the Dorian Mode contains a Minor 3rd, and a Minor 7th (Bb and F, for G Dorian) instead of a natural 3rd and 7th, and all other Notes are the same as in the Major Scale. The following diagram summarizes.

Ionian (Major) 1 2 3 4 5 6 7
Dorian 1 2 3- 4 5 6 7-
Phrygian 1 2- 3- 4 5 6- 7-
Lydian 1 2 3 4+ 5 6 7
Mixolydian 1 2 3 4 5 6 7-
Aeolean (Minor) 1 2 3- 4 5 6- 7-
Locrian 1 2- 3- 4 5- 6- 7-

The Notes in a given Major Scale also comprise the Scales of Diatonic Modes in other Keys. So if one begins on another Note in the Scale (other than the Root), a different Mode is played in the Key designated by the beginning Note. The following diagram illustrates the process using the G Major Scale as an example.

Modes Image

In the above diagram, the top line illustrates two cycles of the G Major Scale.

Related Key

The Key of G is the Related Key for the A Dorian, B Phrygian, C Lydian, D Mixolydian, E Minor, and F# Locrian Scales. This is because the Notes for each of these Scales are drawn from the G Major Scale, as shown in the previous diagram.

If one needs to determine the Notes that are needed to play in a given Mode, he can memorize the Notes (Scale Degrees) that comprise the Mode. Another, possibly easier way comes from the recognition that there are only twelve sets of Notes that make up all the Modes of the Diatonic Scales of which there is a total of 84 (12 Keys x 7 Modes). For example, an A Minor Scale consists of the same seven Notes as the C Major Scale, but the A Minor Scale begins and ends on the A Note.

If one can determine the Major Key that includes the same set of Notes as the desired Mode, that is, the Relative Key, and he/she has learned that Major Scale, it should be simple to play in the desired Mode. The following illustrates a method for determining the Relative Key for each Diatonic Mode:

Mode Play Notes from. . . # frets from the Root. . .
Ionian (Major) I
Dorian VII- +10 -2
Phrygian V+ +8 -4
Lydian V +7 -5
Mixolydian IV +5 -7
Aeolean (Minor) III- +3 -9
Locrian II- +1 -11

To illustrate how to use this diagram, suppose one wanted play an A Lydian Scale. Locate an A (second string, second fret), go up the Fretboard seven frets to find the E (or just locate the V chord). The Notes in the E Major Scale are the same Notes used in the A Lydian Scale, with the Scale beginning and ending on the A Note. Notice that the fret sequence going down the Fretboard (-2, -4, -5, -7, -9, -11) is the Diatonic Sequence in reverse.

Why do we care about Modes? Each of the Diatonic Modes has a distinct "mood" or "feel" that can be applied to a tune or song. The following describes each Mode from my subjective point of view.

Knowing the kind of mood you want to produce and using the above information, one can determine the Scale that needs to be played. Most players (including myself) do not regularly use all of the Modes, nor do they play in all of the Keys. Consider a player who only plays out of the G and D positions (capoing when needed) and only uses the Major, Minor, and Mixolydian Modes. That player could benefit greatly from practicing Scales in the Keys of G, D, and C. These would help him play in G Mixolydian, D Mixolydian, D Dorian, A Minor, and B Minor in addition to the three Major Keys. These are not all the Modes that these three Scales support, but they are the more commonly used. Familiarization with the F Scale would add significant capability, notably D Minor and G Dorian. Knowledge of a few Scales can go a long way.

Arpegios

Arpegios are not actually Scales, or could be considered "sparse" Scales. They consist of the Notes that make up a chord. The Scale Analyzer offers Arpegios as a Scale Type Selection for Major Keys. These consist of the Root, third, and fifth of the selected Key. It is useful to be familiar with where the Notes that comprise the Root chord lie on the Fretboard because it helps one to recognize Positions. The following diagram identifies them for the Key of G.

Chords Image

From the diagram above, it can be seen that, besides being able to play a G chord open or at the 12th fret, there are several "approximations" of a G chord that can be played near the 5th and 7th frets:

If you associate either of the first two of these "chords" with Position IV, the third with Position V, and a straight bar with Position I, it is easier to visualize the pattern of Notes in the Scale for each Position:

Chords Image

The diagrams above display background Note patterns representing one of the possible methods of playing the Scale for each Position.

Pentatonic Scales

Pentatonic Scales, as is implied by the name, consist of five Notes. The Pentatonic Scale is defined by a sequence of Whole Step and Three Half Step intervals as follows:

Pentatonic Intervals Image

Pentatonic Modes

The order of the intervals in the pentatonic sequence cannot change and still be pentatonic, but one may begin on a different interval in the sequence. Since there are five intervals in the sequence, there are five intervals on which one can begin. Each starting interval defines a different pentatonic "Mode" of the Key. The following diagram illustrates the process for the Key of G.

Pentatonic Modes Image

In the above diagram, the top line illustrates two cycles of the pentatonic sequence.

These Scales could be considered "partial" Diatonic Scales. The following diagram identifies the Notes that comprise each Pentatonic Mode.

Mode I (Major) 1 2 3 5 6
Mode II 1 2 4 5 7-
Mode III 1 3- 4 6- 7-
Mode IV 1 2 4 5 6
Mode V (Minor) 1 3- 4 5 7-

By comparing this with the corresponding diagram for Diatonic Modes, one can determine the Diatonic Modes for which each pentatonic Mode can be substituted. For example, the Minor Mode (V) has all five Notes in common with both the Aeolian and Dorian Modes, and therefore, could be used in place of either. The following diagram suggests some possible substitutions.

Mode I (Major) 1 2 3 5 6
Ionian 1 2 3 4 5 6 7
Mode II 1 2 4 5 7-
Mixolydian 1 2 3 4 5 6 7-
Mode III 1 3- 4 6- 7-
Phrygian 1 2- 3- 4 5 6- 7-
Aeolean 1 2 3- 4 5 6- 7-
Mode IV 1 2 4 5 6
Ionian 1 2 3 4 5 6 7
Mode V (Minor) 1 3- 4 5 7-
Dorian 1 2 3- 4 5 6 7-
Aeolean 1 2 3- 4 5 6- 7-

There are many other substitutions of Pentatonic for Diatonic Modes that could be made just on the basis of having Notes in common, but it does not make sense to substitute a Scale that loses the "character" of the Diatonic Mode. For example, the Major Pentatonic Mode has all Notes in common with the Lydian Mode, but does not include the augmented 4th, which is the "defining" Note for the Lydian Mode.

Pentatonic Scales are simpler and generally easier to play than Diatonic Scales, and can be very effective for improvisation. There are other five Note Scales that are used in Rock and Jazz that include Half Tone intervals, but these will not be described here at present.

Blues Scales

The common Blues Scale consists of six Notes. It is defined by a sequence of Whole Step, Half Step, and Three Half Step intervals as follows:

Blues_Intervals Image

The Blues Scale can be played over a Minor or Major Root chord. It is most closely related to the Pentatonic Minor Scale, differing only by the inclusion of the augmented fourth (1, 3-, 4, 4+, 5, 7-). The Scale is also related to the Diatonic Dorian Mode. Notice the brief Chromatic passage of the third, fourth, and fifth Notes in the sequence. This Scale has no associated Modes.

Fretboard Positions

For guitars, fiddles, and other fretted instruments, there are well defined hand positions for playing Scales which determine the finger to be used to fret a given Tone. On the Resonator Guitar, hand positions are not clearly defined, since we only use one "finger" to play all the Notes. In an attempt to understand the Resonator Guitar Fretboard, I have devised "Fretboard Positions" for playing Scales, so that at any given time, I visualize myself playing in a particular position. When moving up or down the Notes of a Scale, there is often need for a "shift" between positions. The following is a diagram of the first 17 frets, indicating all Notes that belong in the G Major Scale:

G Notes Image

The relationship of Notes for a Key other than G can be acquired by shifting the above diagram to the right or left by the appropriate number of frets. Notice that the frets of most significance to the G Major Scale are the open position, and the 5th, 7th, 12th and 17th frets. This is because the Notes on all six strings at those bar positions are in the Scale. These correspond to the bar positions where the main chords in the Key of G are played: Root (I) - open, 12th fret; subdominant (IV) - 5th fret, 17th fret; dominant (V) - 7th fret.

From this Note arrangement, the following Fretboard Positions are defined: open, I-, I+, IV-, IV+, and V. In the position names, the roman numerals refer to the fret where the indicated chord is played for the Key in which one is playing. The plus/minus sign indicates whether the Scale is played "in front of" (+) or "behind" (-) the bar. The following associates the Notes in the G Scale with the various Fretboard Positions.

G Postions Image

The above diagram identifies six sections of the Fretboard which overlap. As is shown, there are many cases where a Note at a given fret is used in two different positions. This is one way to organize the Fretboard for the purpose of constructing Scales, which is used throughout this website. Certainly, there are other valid ways to view the Notes on the Fretboard.

Open Position

The Open Position has a different Note pattern for each Key and can have Notes in common with the next higher position. As can be seen in the diagram above, for the Key of G, the Open Position differs from Position I+ (12th fret) because of the lack of accessible 7th Notes "behind the nut".

Open Position Scales are easiest to play in the Keys that contain the open Notes, G, B, or D. The following identifies which Keys include which open Notes.

Open Notes Keys that include the Open Notes
G B D G, C, D
B D A
G B Bb, Eb, F
G D
B B, E, F#
G Ab
D
Db

Those Keys whose Scale contains all the open Notes provide the best opportunity to use Melodic Technique.

Closed Positions

There are five Closed Positions (I-, I+, IV-, IV+, and V), each of which defines a pattern of Notes. The reference to roman numerals implies, e.g., that the I- Position is a pattern of notes behind the fret where the I chord is played (as defined in the Chord Numbering system). For Major Modes, this is true. But it is important to understand that Closed Positions are defined for the Related Key as opposed to the Key. Different Modes of a given Key have differing Note patterns at a given Fret, but identical patterns can be found at a different Fret. This is illustrated by the following diagram.

A and Am Postions Image

The IV- Position for A Major (behind the fifth fret above the A Chord) has a specific Note pattern. For A Minor, the pattern of Notes to be used behind that fret differs from that of A Major. But Notes of the IV- Position of the Related Key, C are also used for A Minor. When using this Position for Am, the Scale Degrees change as shown. Notice that the pattern of the Notes of the VI- Position in A is the same shape as the VI- Position for C/Am. For each mode, the reference frets (I, IV, and V) are at different locations relative to the Root chord.

Closed Position Scales are the most difficult to play accurately at high speed with good Tone. This is because they consist of all Closed Moves, which involves a lot of bar movement. However, if they are learned at any speed, they contribute significantly to knowledge of the Fretboard. If they are mastered, they are the most useful of the Scales, because they can be used in any Key. Playing well in Closed Position requires the ability to cleanly perform consecutive Closed Moves.

I- Position

In this position, all Notes can be acquired at or behind the fret where the Root is played. Since there are two places in this Fret Range to access the 3rd, there are two methods for playing the Scale in the I- Position.

Position I- Image

I+ Position

In this position, all Notes can be acquired at or in front of the fret where the Root is played, except the 7th, which must be acquired from behind the fret.

Position I+ Image

IV- Position

In this position, all Notes can be acquired at or behind the fret where the IV chord is played. Since there are two places in this Fret Range to access the 6th, there are two methods for playing the Scale in the IV- Position.

Position IV- Image

IV+ Position

In this position, all Notes can be acquired at or in front of the fret where the IV chord is played, except the 3rd, which must be acquired from behind the fret. Since there are two places in this Fret Range to access the 7th, there are two methods for playing the Scale in the IV+ Position.

Position IV+ Image

V Position

In this position, all Notes can be acquired at or in front of the fret where the V chord is played. Since there are two places in this Fret Range to access the 2nd, there are two methods for playing the Scale in the V Position.

Position V Image

Octaves

When analyzing the Fretboard, it often important to examine one or more complete Scales (octaves) even if these span multiple Positions. Therefore, the Scale Analyzer allows the user to specify the range of Notes of interest in addition to specifying the Fretboard Position of interest. These Note Ranges are specified by the Low Octave, Middle Octave, High Octave, Low&Mid Octave, and Mid&High Octave. In some keys, the two octave ranges can involve as many as three Position Shifts.