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. If, for example, two adjacent strings are tuned a fourth interval apart, the Tone played open on the higher string is the identical Tone as that played on the lower string at the fifth 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 using three strings tuned to an open G chord.

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.

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

The Scale Analyzer allows the user to specify the area of interest on the Fretboard by selecting a Position. The Position options that are offered fall into two categories; Fret Range Positions, for which the Notes are bounded by a span of frets, and Note Range Positions, for which the Notes are bounded by different Root Notes in the Scale.

Fret Range Positions

For fretted Instruments, Fret Range Positions represent a section of the Fretboard where Scales can be played without moving the left hand. These include the Open Position, and as many as seven Closed Positions. Within a given Position, the number of alternative Methods for playing the Scale is small and often unique, so it is feasible to generate the Scale Methods for such Positions programatically.

The procedure used for defining Fretboard Positions is based on the Mandolin and Fiddle, for which Positions are well defined. These Instruments are tuned with a perfect fifth interval between adjacent strings, and the neck is short enough to allow four consecutive Notes from the Diatonic Scale to be played without repositioning the left hand. For a given Key, a Note in the Scale on the lowest string is selected and the next three Notes in the Scale are located on that string. The next Note in the Scale is located on the next higher string and the next three Notes are located on that string. The process is repeated for each string as illustrated in the following diagram.

Mandolin Positions Image

In the above diagram, the first illustration represents an unspecified section of the Fretboard identifying the Notes in some Key. Each following illustration shows the various Positions, which are identified by the Scale Degree of its starting Note (e.g., Position 3). An interesting property of this positioning scheme is that placement of any finger on any string on any Note in the Scale unambiguously defines one of the Positions illustrated above, and thus, the finger to be used for each tone when playing in that Position. This is only be true for Instruments that are tuned in fifths.

This process is used for Instruments that are not tuned in fifths with one additional stipulation. Notes are located on a given string until four Notes are found or until the next Note can be located on the next higher string at or above the starting fret of the Position. Consequently, there are often alternative places to play one or more Notes within the range of frets spanned by the Position, and thus, multiple alternative Methods to play the Scale.

Scale Methods for Fret Range Positions are automatically determined in the Scale Anlyzer for any selection of Instrument Type (standard tuning or user defined tunings), and for any Scale Type/Mode, including user specified Scale Types.

Note Range Positions

Although the term "Position" is used for Note Ranges, they often span portions of two or more Fret Range Positions, and therefore can involve Position Shifts. The number of possible Methods by which one might play a Scale in a given Note Range can be very large, and most of them would not be efficient Methods for playing the Scale. Thus, it is not feasible to generate them automatically. Information describing these Scale Methods must be provided by an author, one with expertise on the given Instrument. Although, much can be accomplished by learning the Scales in Fret Range Positions, the ability to smoothly transitions between them is the essence of mastering an Instrument. Methods for Note Range Positions are not currently provided for all Instrument Types, because this author lacks the expertise, but hopefully they will be provided by others in the future. When available, the Note Range Positions are 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.