Fundamentals of Scales
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Fundamentals of Scales
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FUNDAMENTALS OF SCALES

 

This section presents the rudiments of Diatonic Scales for those who know little or nothing about them. This will by no means be an in depth lesson in music theory. Those who are familiar with these concepts should skip this section.

  Why do we care about scales? A great number of melodies draw from a palette of only seven notes. Standard musical notation is set up to identify those seven notes, that is, the scale, at the beginning. If a melody requires a note that is not in the defined scale, a temporary scale change notation (flat, sharp, or natural) is required. It’s called an “accidental” (as if you didn’t mean to do it). 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 all the notes for a given key, he is likely to be able to play most tunes in that key with relative ease. Scale exercises are a means of gaining that familiarity.  

  Diatonic Scales

  The Diatonic Scale is defined by a sequence of Whole Step (W) and Half Step (H) intervals as follows: 

        W  W  H  W  W  W  H

  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: 

       Black keys      C#   D#      F#   G#   A#

       White keys    C    D    E  F    G    A    B  C 

  Notes between the lettered notes are designated as the sharp (#) of the note before it (as shown above) 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.

              C  C# D  D# E  F  F# G  G# A  A# B  C  C# D  D# E  F  F# G  G# A  A# B  C

                 Db    Eb       Gb    Ab    Bb       Db    Eb       Gb    Ab    Bb    C  

Key of C      C     D     E  F     G     A     B  C 

Key of Db        Db    Eb    F  Gb    Ab    Bb    C  Db

Key of D            D     E     F# G     A     B     C# D 

Key of Eb              Eb    F     G  Ab    Bb    C     D  Eb

Key of E                  E     F#    G# A     B     C#    D# E 

Key of F                     F     G     A  Bb    C     D     E  F 

Key of F#                       F#    G#    A# B     C#    D#    E# F#

Key of G                           G     A     B  C     D     E     F# G 

Key of Ab                             Ab    Bb    C  Db    Eb    F     G  Ab

Key of A                                 A     B     C# D     E     F#    G# A 

Key of Bb                                   Bb    C     D  Eb    F     G     A  Bb

Key of B                                       B     C#    D# E     F#    G#    A# B   

The reason some keys use flat (b) designation versus sharp (#) is explained by the nature of standard musical notation. In this notation, notes are designated by 5 lines and the spaces between them. For example, the following indicates the notes for the lines and spaces on the treble staff:

    Key of C  --------- F   Key of F  --------- F   Key of A  #-------- F#

                        E                       E                       E

              --------- D             --------- D             --------- D

                        C                       C               #       C#

              --------- B             b-------- Bb            --------- B

                        A                       A                       A

              --------- G             --------- G             #-------- G#

                        F                       F                       F#

              --------- E             --------- E             --------- E

Each line and space indicates a consistent letter name for its note, which may be designated to be sharp or flat for the scale. If the key of F were to use sharp designations and the key of A were to use flats, the scales would be as follows:

              Key of F      F     G     A  A#    C     D     E  F 

              Key of A      A     B     Db D     E     Gb    Ab A 

Notice that there are two notes named with the letter A for the key of F, which are A and A#. Thus, if sharp designations were used, the second space from the bottom on the treble staff  would have to represent both A and A#, which is ambiguous. 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.

               Key of F      F     G     A  Bb    C     D     E  F 

              Key of A      A     B     C# D     E     F#    G# A 

When playing in a given key, it is usually more convenient to refer to a note by its relative order in the major scale, or scale degree, than by its letter name.

                             1   2-  2   3-  3   4   4+  5   6-  6   7-  7   1

              Key of F      F       G       A   Bb      C       D       E   F 

                                 Gb      Ab          Cb      Db      Eb

Thus, in the key of F, the F, G, A, Bb, C, D, and E notes are the root, 2nd, 3rd, 4th, 5th, 6th, and 7th, respectively. The notes between the notes in the scale, Gb, Ab, Db, and Eb are the minor 2nd, minor 3rd, minor 6th, and minor 7th of the key of  F. The Cb, which is also not in the major scale, is referred to as the augmented 4th or diminished 5th (don’t ask). In this paper, “3-“ is shorthand for “minor third”, 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.  

MODES

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 sequence defined above defines the Major mode, which is also called Ionian. The following diagram illustrates the interval sequence for each mode.

       Ionian (Major)       W  W  H  W  W  W  H

       Dorian                  W  H  W  W  W  H  W

       Phrygian                   H  W  W  W  H  W  W

       Lydian                        W  W  W  H  W  W  H

       Mixolydian                       W  W  H  W  W  H  W

       Aeolean (Minor)                     W  H  W  W  H  W  W

       Locrian                                H  W  W  H  W  W  W

 

For a given key, the seven scale modes can be constructed by using each of the above sequence variations, starting from the root.  The following diagram illustrates that process for the key of G.

Ionian (Major)       G     A     B  C     D     E     F# 

Dorian                     G     A  Bb    C     D     E  F     G

Phrygian                         G  Ab    Bb    C     D  Eb    F     G

Lydian                              G     A     B     C# D     E     F# G

Mixolydian                                G     A     B  C     D     E  F     G

Aeolean (Minor)                                 G     A  Bb    C     D  Eb    F     G

Locrian                                               G  Ab    Bb    C  Db    Eb    F     G

 

                           W     W  H     W     W     W  H     W     W  H     W     W     W  H

In the above diagram, the bottom 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 example, the Dorian mode contains a minor 3rd, and a minor 7th 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-

 

If one needs to determine the notes that are needed to play in a given mode, he can memorize the above information for the modes he commonly uses. Another (possibly quicker) 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). The seven notes that make up a C Major Scale are the same set of notes used in the D Dorian, E Phrygian, F Lydian, G Mixolydian, A minor, and B Locrian scales. These are played by starting and ending the C Major Scale on a different note than the root. 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.

So if one can determine the major key that includes the same set of notes as the desired mode (and he has learned that major scale), it should be simple to play in the desired mode. The following identifies, for a given key, the relative key from which the notes are used to form each diatonic mode:

         Mode                 Play notes from…     # frets away 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 neck 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 neck (-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.

Ionian: Major, upbeat, “happy” sound.  

Lydian: Similar to Major. The augmented 4th gives it a slightly brighter sound  

MixoLydian: Similar to Major. This mode is commonly used in Celtic, Old Time, and Bluegrass music. Examples of tunes that use this scale are Red Haired Boy, June Apple, and Big Mon. The minor 7th gives it a slightly more somber sound than the Major Mode.  

Aeolian: Minor, sad or “dark” sound.  

Dorian: This scale works when played against either a major or minor G chord. When played against a major chord, it produces a “bluesy” sound. The Bill Monroe tune Evening Prayer Blues is played primarily using this scale. When this mode is used against a minor chord, it sounds very nearly minor, differing from the Aeolian mode by only the natural 6th.  

Phrygian: Exotic, Spanish sound. This mode is often used in Flamenco pieces.  

Locrian: Exotic, middle eastern sound. This mode differs most from the Major Mode, with only the root and 5th in common. This mode is often used in Klezmer music.

Knowing the kind of mood you want to produce and using the above diagram, you can determine the scale/mode 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. So 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 C Mixolydian, D Minor and G Dorian. So knowledge of a few scales can go a long way.    

Pentatonic Scales

Pentatonic Scales, as is implied by the name, consist of 5 notes instead of 7. The Pentatonic Scale is defined by a sequence of Whole Step (W) and Three Half Step (W+) intervals as follows:

       Mode I (Major)             W   W   W+  W   W+

       Mode II                        W   W+  W   W+  W    

       Mode III                           W+  W   W+  W   W    

       Mode IV                                W   W+  W   W   W+

       Mode V (Minor)                             W+  W   W   W+  W 

These scales could be considered “partial” diatonic scales. This is illustrated by the following diagram, which leaves a space where a note number is omitted.

       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, you 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. These will not be described here.

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