Introduction to music theory for guitar

v0.2

(C) 1994, by Dimitris Dranidis

Guitar is a very nice instruments for a lot of reasons. One can play all kinds of songs, and music. One can learn to play the instrument without a teacher too. And I guess most of the people out there haven't had a teacher, just like me. It is really fun to learn and explore the instrument all by yourself. (Though with a teacher it would go faster :-)

Playing is great! Understanding what you're playing improves playing and brings you closer to your instrument, your songs or music. I believe that it does not need a lot to understand music theory. [Theory is not a bad word. Get used to it.] Most guitar players are interested in chords. Accompanying songs with the guitar is great! Well all you have to do in order to play all the chords of this world is to learn the intervals and then the chord construction. Then you don't need any chord charts any more. If you want to understand furthermore why a particular chord sounds good in a particular part in a song then you must learn some harmony too. Harmony is based on scales and chords. It has simple rules and is easy to understand if you catch the main idea.

So let us begin… This introduction covers:

Email:dranidis@informatik.uni-muenchen.de

URL: http://www.pst.informatik.uni-muenchen.de/~dranidis/

Dimitris Dranidis (10.11.1994)


Music Material

Notes, tones, semitones

In well-tempered instruments (the guitar is one) we have 12 distinct notes in an octave. These build the chromatic scale: (starting from c)

        c  ♯c d  ♯d e  f  ♯f g  ♯g  a  ♯a b  c
        1  2  3  4  5  6  7  8  9  10 11 12 1

Notes are noted with the first 7 letters of the latin alphabet:

        a b c d e f g

and symbols for chromatic alterations: ♯ (sharp) and ♭ (flat). More on these comes later. The following is a diagram of the frets and the notes on the guitar. All the 12 tones and only these can be found on the fretboard. The instrument is called well-tempered since it is fretted and the intervals are not the physical intervals (those found in the nature) but "well tempered" so that music in every key is sounded as good as on any other key. If we exclude bending, then no other notes can be played on this instruments. For example, there is no note between c and ♯c.

      e ||--f-|-♯f-|--g-|-♯g-|--a-|-♯a-|--b-|--c-|-♯c-|--d-|-♯d-|--e-|...
      b ||--c-|-♯c-|--d-|-♯d-|--e-|--f-|-♯f-|--g-|-♯g-|--a-|-♯a-|--b-|...
      g ||-♯g-|--a-|-♯a-|--b-|--c-|-♯c-|--d-|-♯d-|--e-|--f-|-♯f-|--g-|...
      d ||-♯d-|--e-|--f-|-♯f-|--g-|-♯g-|--a-|-♯a-|--b-|--c-|-♯c-|--d-|...
      a ||-♯a-|--b-|--c-|-♯c-|--d-|-♯d-|--e-|--f-|-♯f-|--g-|-♯g-|--a-|...
      e ||--f-|-♯f-|--g-|-♯g-|--a-|-♯a-|--b-|--c-|-♯c-|--d-|-♯d-|--e-|...
           1st       3rd       5th       7th       9th           12th fret

The distance between two succeeding notes is a half-tone (H). Two half-tones build a whole-tone (W). On the guitar each fret is a half-tone.

Diatonic

If we leave the sharped notes apart, then we get the 7 natural notes.

      e ||--f-|----|--g-|----|--a-|----|--b-|--c-|----|--d-|----|--e-|...
      b ||--c-|----|--d-|----|--e-|--f-|----|--g-|----|--a-|----|--b-|...
      g ||----|--a-|----|--b-|--c-|----|--d-|----|--e-|--f-|----|--g-|...
      d ||----|--e-|--f-|----|--g-|----|--a-|----|--b-|--c-|----|--d-|...
      a ||----|--b-|--c-|----|--d-|----|--e-|--f-|----|--g-|----|--a-|...
      e ||--f-|----|--g-|----|--a-|----|--b-|--c-|----|--d-|----|--e-|...
           1st       3rd       5th       7th       9th           12th fret
      

Starting from c they build the C major scale:

       c d e f g a b c
       1 2 3 4 5 6 7
        W W H W W W H
       \_____/ \_____/

Observe this on the second string:

      b ||--c-|----|--d-|----|--e-|--f-|----|--g-|----|--a-|----|--b-|--c-|...

These notes build a diatonic scale. A diatonic scale consists of 7 notes, arranged so, that they (usually) build 5 whole-tones and 2 half-tones. The first and the last tone of a diatonic scale is called tonic. The seventh tone is called leading tone because it leads to the tonic. There are names for the rest but we'll leave them for later.

Accidentals

There are two types of accidentals. The sharp and the flat. The sharp (♯) raises the tone of the note by a half-tone. In the guitar that's the next fret. The sharp produces 7 sharped notes: (♯c, ♯d, ♯e, ...). because ♯e ~ f and ♯b ~ c only 5 notes are new. the flat (b here noted as !) lowers the tone of the note by a half-tone. in the guitar that's the previous fret. the flat produces 7 flatted notes: (!c, !d, !e, ...). again because ♭c ~ b and ♭f ~ e only 5 of them are new, and these are the same which are produces by sharped notes, i.e. #c ~ ♭d, #d ~ ♭e, #f ~ ♭g, #g ~ ♭a, #a ~ ♭b.

Chromatic

The chromatic scale consists of all the 12 notes, 7 from the diatonic and 5 flatted or sharped.

Solfege

I find the alphabetic system very difficult to keep in mind or "sing". I use solfege when I want to sing a melody, a chord, a scale or to name a note. I might still write "c" but say "do". So what you should learn is the sequence:

        do re mi fa sol la ti do
        c  d  e  f  g   a  b  c
        

Unfortunately the only easy to remember is f (fa) therefore one must memorize this sequence. Altered notes are easy to remember too:

        di ri fi si li
        #c d# #f #g #a
        

and

        ra ma -- lo ta
        !d !e !g !a !b
        

though you won't need them a lot.

Intervals

By intervals we mean the distance between the notes in the diatonic scale:

         _____________________13th_____________________
        /_________________11th_________________        \
        /______________9th______________       \       |
        / __________octave__________    \      |       |
        /                           \   |      |       |
        c   d   e   f   g   a   b   c'  d' e'  f'  g'  a'
        \2nd/   |   |   |   |   |
        \__3th__/   |   |   |   |
        \____4th____/   |   |   |
        \______5th______/   |   |
        \________6th________/   |
        \__________7th__________/

So d is a second away from c, e is a third away from c and so on. c' is an octave away from c and d' is a ninth away from c and so on. So d is either a second or a ninth away from c, f is either a fourth or an eleventh away from c. If we begin from e, then f is a second away from e and g is a third away form e and so on. Notice however that the second c-d is a whole-tone, while the second e-f is a half-tone; the third c-e consists of two W's (four H's), while the third e-g consists of one H and one W (three H's). In order to distinguish between "small" and "big" intervals we need to declare types of intervals. In the following we use the letter H for half-tones. By an interval of 5 H we mean five half-tones or equivalently 5 frets on the guitar.

Types of intervals

There are five types of intervals:

1. Perfect (p)
Perfect intervals are the unison or octave, the perfect fourth and the perfect fifth. These are noted as u, o, p4 and p5 respectively. A perfect fourth consists of 5 H, and a perfect fifth of 7 H.
         Ex. c-c, d-d, ...                           : u or o, (0 H or 12 H)
             c-f, d-g, e-a, f-!B, g-c, a-d, b-e,  ...: p4, (5 H)
             c-g, d-a, e-b, f-c,  g-d, a-e, b-#f, ...: p5, (7 H)
         
2. Major (M)
Major intervals are the major second, third, sixth, and seventh. These are noted as M2, M3, M6 and M7 respectively. Ex. c-d, d-e, e-#f, f-g, g-a, a-b, b-#c,... : M2, (2 H) c-e, d-#f, e-#g, f-a, g-b, a-#c, b-#d,... : M3, (4 H) c-a, d-b, e-#c, f-d, g-e, ... : M6, (9 H) c-b, d-c#, e-#d, f-e, g-#f,... : M7, (11 H) (At this point notice that all the intervals in the major scale [Ionian mode] are either perfect or major)
3. Minor (m)
Minor intervals are the minor second, third, sixth, and seventh. These are noted as m2, m3, m6 and m7 respectively. Ex. c-!d, d-!e, e-f, f-!g, g-!a, b-c : m2, (1 H) c-!e, d-f, e-g, f-!a, ... : m3, (3 H) c-!a, d-!b, e-c, f-!d, ... : m6, (8 H) c-!b, d-c, e-d, f-!e, ... : m7, (10 H) (You should not associate minor intervals with flatted notes. If we start the diatonic scale from the note E then all the natural intervals are either minor or perfect: e-f : m2, e-g : m3, e-a : p4, e-b : p5, e-c : m6, e-d : m7 [by the way, that's the E phrygian mode])
4. Augmented (#)
Augmented intervals are perfect or major intervals which are raised a half-note step. Most used are the augmented fifth (#5) and ninth (#9). Ex. c-#g : #5, (8 H) c-#d : #9 (15 H) (Notice that the second and the ninth are the same notes an octave away: c d e f g a b c' d' e' f' g' a' .. 1 2 3 4 5 6 7 8 9 10 11 12 13 .. the same is true for the fourth and the elfth or for the sixth and the thirteenth.)
5. Diminished (b)
Diminished intervals are perfect or minor intervals which are lowered a half-note step. Most used are the diminished fifth and seventh which are noted as b5 and b7 respectively. Ex. c-!g : b5, (6 H) c-!!b : b7 (9 H) (Notice the double-flatted b; we could write a instead, but a is the sixth in the diatonic and we want the seventh which is b)

If we put these intervals in a sequence and tidy them up, we get the following nice table:

        chromatic   c  !d d  !e e  f  !g g  !a a  !b b  c
                    --------------------------------------
        diatonic    c     d     e  f     g     a     b  c
        sharps         #c    #d       #f    #g    #a
        flats          !d    !e       !g    !a    !b
                    ======================================
        perfect     u              p4    p5             o
        minor          m2    m3             m6    m7
        major             M2    M3             M6    M7
        augmented            #2    #3 #4    #5    #6
        diminished        b3    b4    b5 b6    b7
                    --------------------------------------
                    u  m2 M2 m3 M3 p4 b5 p5 m6 M6 m7 M7 o

Notes on the same column are equivalent and interchangeable. These notes are called enharmonic. For example C# is enharmonic with Db.

On the fretboard

The first thing you should notice are the intervals between succeeding open strings: e-a : p4, a-d : p4, d-g : p4, g-b : M3, b-e : p4 So all the intervals are perfect fourths except the one between g and b which is a major third.

So take two stings, fret on the second (third in the case of b) fret of the second string and you get a perfect fifth. Ex. e-b, a-e, d-a, g-d, b-#f.

        e ||----|-f#-|----|...
        b ||----|----|--d-|...
        g ||----|--a-|----|...
        d ||----|--e-|----|...
        a ||----|--b-|----|...
        e ||----|----|----|...

In the following one can see all the intervals on the fretboard. One must start from a fret noted as R(oot). Roots are found on all strings so this is a complete diagram. Note that it is circular too.

    e ...|-M6-|-m7-|-M7-|--R-|-m2-|-M2-|-m3-|-M3-|-p4-|-b5-|-p5-|-m6-|-M6-|...
    b ...|-M3-|-p4-|-b5-|-p5-|-m6-|-M6-|-m7-|-M7-|--R-|-m2-|-M2-|-m3-|-M3-|...
    g ...|--R-|-m2-|-M2-|-m3-|-M3-|-p4-|-b5-|-p5-|-m6-|-M6-|-m7-|-M7-|--R-|...
    d ...|-p5-|-m6-|-M6-|-m7-|-M7-|--R-|-m2-|-M2-|-m3-|-M3-|-p4-|-b5-|-p5-|...
    a ...|-M2-|-m3-|-M3-|-p4-|-b5-|-p5-|-m6-|-M6-|-m7-|-M7-|--R-|-m2-|-M2-|...
    e ...|-M6-|-m7-|-M7-|--R-|-m2-|-M2-|-m3-|-M3-|-p4-|-b5-|-p5-|-m6-|-M6-|...
    

How to use this diagram? Say you got the following chord with three open strings:

        e ||--f-|----|----|...
        b 0|----|----|----|...
        g 0|----|----|----|...
        d 0|----|----|----|...
        a ||----|--b-|----|...
        e ||----|----|--g-|...
        

Say you want to find out what's the name of this chord (Assuming you do not already know it). Place this pattern on the diagram, so that the fretted g on the sixth string, falls on the R on the sixth string. Then notice where the rest of the notes fall:

        e  ||-m7-|----|----|...
        b M3|----|----|----|...
        g  R|----|----|----|...
        d p5|----|----|----|...
        a  ||----|-M3-|----|...
        e  ||----|----|--R-|...
        

So, if you know that M3, p5 and m7 build the dominant seventh (more on building chords comes later) , then you tell that this is the G7 chord. Example To demonstrate the use of intervals let's take any note, say F, and name all the intervals. That's relatively easy if we write down the chromatic scale, starting from F, and placing the interval sequence below it (see table):

            f !g  g !a  a !b  b  C !d  d !e  e  f
            -------------------------------------
            u  m2 M2 m3 M3 p4 b5 p5 m6 M6 m7 M7 o
            

The same for !a:

           !a !!b !b !c  c !d !!e !e !f  f !g  g !a
            ----------------------------------------
            u  m2  M2 m3 M3 p4 b5  p5 m6 M6 m7 M7 o
            

(If you are puzzled with the double flatted notes: the minor second of !a is a natural, but we call it !!b which is enharmonic to a, because b is the second of a in the diatonic)

Table 1 gives the interval between two notes.

Table 1.
            c  #c d  #d e  f  #f g  #g a  #a b

        c   -- m2 M2 m3 M3 p4 b5 p5 m6 M6 m7 M7
        #c  M7 -- m2 M2 m3 M3 p4 b5 p5 m6 M6 m7
        d   m7 M7 -- m2 M2 m3 M3 p4 b5 p5 m6 M6
        #d  M6 m7 M7 -- m2 M2 m3 M3 p4 b5 p5 m6
        e   m6 M6 m7 M7 -- m2 M2 m3 M3 p4 b5 p5
        f   p5 m6 M6 m7 M7 -- m2 M2 m3 M3 p4 b5
        #f  b5 p5 m6 M6 m7 M7 -- m2 M2 m3 M3 p4
        g   p4 b5 p5 m6 M6 m7 M7 -- m2 M2 m3 M3
        #g  M3 p4 b5 p5 m6 M6 m7 M7 -- m2 M2 m3
        a   m3 M3 p4 b5 p5 m6 M6 m7 M7 -- m2 M2
        #a  M2 m3 M3 p4 b5 p5 m6 M6 m7 M7 -- m2
        b   m2 M2 m3 M3 p4 b5 p5 m6 M6 m7 M7 --

Inversion of intervals

An interval is inverted if we change its sequence. So c-d is inverted to d-c. c-d is a M2 and d-c is a m7.

Rules of inversion:

  1. minor intervals become major and vice versa,
  2. augmented intervals become diminished and vice versa,
  3. perfect intervals remain perfect,
  4. 2nds become 7ths, 3rds become 6ths, 4ths become 5ths and vice-versa.

Ex. m6 → M3, p4 → p5, m2 → M7, …


Chords

If you understood the intervals then you will easily understand the chords. Chords are three or more tones which sound simultaneously. The character of a chord and its name depends upon the intervals of the tones from a concrete tone which is called root and is (usually) self present in the chord.

Triads

Triads are chords consisting of exactly three notes. There are four kind of triads: major, minor, augmented and diminished.

Major

The most common chord is the major chord. It consists of a major third and a perfect fifth.

        Ex. C major, simply C : c   e   g
                                \M3/ \m3/
                                \___p5__/
        

Note all the intervals involved in this chord:

                  c  e  g
        from c    -- M3 p5
        from e    m6 -- m3
        from g    p4 M6 --
        

So if the chord has the third e at the bass note then the intervals are a m3 to g and a m6 to to c. That's the first inversion of C. If the chord has the fifth g at the bass note then the intervals are a p4 to c and a M6 to to e. That's the second inversion of C.

Minor

The second most common chord is the minor chord. It consists of a minor third and a perfect fifth.

        Ex. C minor, simply Cm : c   !e   g
                                 \m3/  \M3/
                                 \___p5___/

Intervals:

                  c  !e g
        from c    -- m3 p5
        from !e   M6 -- M3   (1st inversion)
        from g    p4 m6 --   (2nd inversion)
        

Augmented

That's a major chord with an augmented fifth.

        Ex. C augmented, simply C+5 or C+ : c   e   #g
                                            \M3/ \M3/
                                            \___#5__/

Intervals:

                  c  e  #g
        from c    -- M3 #5
        from e    m6 -- M3    (1st inversion)
        from #g   b4 m6 --    (2nd inversion)

Diminished

A diminished triad is a minor triad with a diminished fifth.

        Ex. C diminished, simply Cm-5 or Cmb5   :    c   !e  !g
                                                     \m3/ \m3/
                                                     \___b5__/

Intervals:

                  c  !e !g
        from c    -- m3 b5
        from !e   M6 -- m3   (1st inversion)
        from !g   #4 M6 --   (2nd inversion)
        

Figured bass notation

All the triads consist of a third and a fifth. Their 1st inversion consists of a 3rd and a 6th and is notated as "6" in the figured bass notation. The second inversion consists of a 4th and a 6th and is notated as "46" [Note that "4" is below "6" in the normal (not-ASCII) notation].

Stacked thirds

Seen from another point of view every triad consists of two stacked thirds:

              Major triad: M3 and m3,
              minor      : m3 and M3,
              augmented  : M3 and M3,
              diminished : m3 and m3.
              

On the fretboard

See the appendix for chord patterns on the fretboard.

Enharmonic chords

If you experiment with the chord patterns by transposing them then you might notice something about the augmented chords. If not, follow: Play the G+ by using the "E"-pattern:

        e ||----|----|--g-|----|----|----|...
        b ||----|----|---->-#d-|----|----|...
        g ||----|----|----|--b-|----|----|...
        d ||----|----|----|----|--g-|----|...
        a X|----|----|----|...
        e X|----|----|----|...
             1st       3rd       5th    fret
             

Now play the B+ by using the "A"-pattern:

        e ||----|---->-##f|----|----|----|...
        b ||----|----|----|-#d-|----|----|...
        g ||----|----|----|--b-|----|----|...
        d ||----|----|----|---->-##f|----|...
        a X|----|----|----|...
        e X|----|----|----|...
             1st       3rd       5th    fret
             

Now play the Eb+ by using the "C"-pattern:

        e ||----|----|--g-|----|----|----|...
        b ||----|----|----|-!e-|----|----|...
        g ||----|----|---->--b-|----|----|...
        d ||----|----|----|----|--g-|----|...
        a X|----|----|----|...
        e X|----|----|----|...
             1st       3rd       5th    fret
             

The same notes are played in all chords. (Note that ##f ~ g, #d ~ !e). So G+, B+ and Eb+ are the same chords. You could also find out that C+, E+ and Ab+ are also the same chords. The same for F+, A+ and C#+ and for D+, F#+ and Bb+. Observations:

Sevenths

A triad consists of 2 thirds. 3 thirds make a seventh. There are 6 kinds of seventh chords:

Dominant 7TH

It is a major triad with a minor seventh.

           Ex. G dominant 7th, simply G7 : g   b    d    f
                                           \M3/ \m3/ \m3/
                                           \___p5__/
                                           \_____m7_____/
                                               \___b5___/

Note all the intervals involved in this chord:

                  g  b  d  f
        from g    -- M3 p5 m7
        from b    m6 -- m3 b5
        from d    p4 M6 -- m3
        from f    M2 #4 M6 --
        

Characteristic interval of this chord is the diminished 5th between the major third (b) and the minor seventh (f). If you notice the construction of the chord, it consists of two triads sounding together: a major triad (g b d) and a diminished triad (b d f)

Major 7TH

It is a major triad with a major seventh.

           Ex. G major 7th, simply Gmaj7 : g   b    d   #f
                                           \M3/ \m3/ \M3/
                                           \___p5__/
                                           \_____M7_____/
                                               \___p5___/

Note all the intervals involved in this chord:

                  g  b  d  #f
        from g    -- M3 p5 M7
        from b    m6 -- m3 p5
        from d    p4 M6 -- M3
        from #f   m2 p4 m6 --
        

If you notice the construction of the chord, it consists of two triads sounding together: a major triad (g b d) and a minor triad (b d #f)

Minor 7TH

It is a minor triad with a minor seventh.

           Ex. G minor 7th, simply Gm7 :   g   !b   d    f
                                           \m3/ \M3/ \m3/
                                           \___p5__/
                                           \_____m7_____/
                                               \___p5___/

Note all the intervals involved in this chord:

                  g  !b d  f
        from g    -- m3 p5 m7
        from !b   M6 -- M3 p5
        from d    p4 m6 -- m3
        from f    M2 p4 M6 --
        

This chord consists of two triads: a minor triad (g !b d) and a major triad (!b d f).

Minor triad major seventh

It is a minor triad with a major seventh.

           Ex. G minor, major seventh, simply Gm(maj7) :
                                           g   !b   d    #f
                                           \m3/ \M3/ \M3/
                                           \___p5__/
                                           \_____M7_____/
                                               \___#5___/
                                               

Note all the intervals involved in this chord:

                  g  !b d  #f
        from g    -- m3 p5 M7
        from !b   M6 -- M3 #5
        from d    p4 m6 -- M3
        from #f    m2 b4 m6 --

Characteristic interval of this chord is the augmented 5th between the minor third (!b) and the major seventh (#f). If you notice the construction of the chord, it consists of two triads sounding together: a minor triad (g !b d) and an augmented triad (!b d #f).

Half diminished 7TH

It is a diminished triad with a minor seventh.

           Ex. G half diminished 7th, simply Gm7b5 :  g   !b   !d   f
                                                      \m3/ \m3/ \M3/
                                                      \___b5__/
                                                      \_____m7_____/
                                                          \___p5___/
                                                          

A half diminished appears in the seventh degree of the major scale: B7b5 : b d f a Note all the intervals involved in this chord:

                  b  d  f  a
        from b    -- m3 b5 m7
        from d    M6 -- m3 p5
        from f    #4 M6 -- M3
        from a    M2 p4 m6 --

If you notice the construction of the chord, it consists of two triads sounding together: a dim. triad (b d f) and a minor triad (d f a)

(Full) Diminished 7TH

It is a diminished triad with a diminished seventh.

           Ex. G diminished 7th, simply Gdim :   g   !b   !d   !f
                                                 \m3/ \m3/ \m3/
                                                 \___b5__/
                                                 \_____b7_____/
                                                     \___b5___/
               Bdim : b d f !a
               Ddim : d f !a !c  (d f !a b)
               

Note all the intervals involved in this chord:

                  b  d  f  !a
        from b    -- m3 b5 b7
        from d    M6 -- m3 b5
        from f    #4 M6 -- m3
        from !a   #2 #4 M6 --
        

Characteristic intervals of this chord are the two diminished 5ths and the diminished 7th. If you notice the construction of the chord, it consists of two diminished triads sounding together: a dim. triad (b d f) and a dim. triad (d f !a)

Another thing to notice is that Bdim, Ddim, Fdim and Abdim are all enharmonic chords. Remember the observations we made about the augmented chords and the major thirds. We can make similar observations about the diminished sevenths and the minor triads. Observations:

Figured bass notation

All the sevenths consist of a third, a fifth and a seventh. Their root position has the notation "7". Their 1st inversion consists of a 3rd, a 5th and a 6th and is notated as "56" (remember "5 below 6"). The second inversion consists of a 3rd, a 4th and a 6th and is notated as "34". The third inversion (seventh in bass) consists of a 2nd, a 4th and a 6th and is notated as "2". Stacked thirds or simult.triads Every seventh consists of three stacked thirds, OR every seventh consists of two triads:

                            thirds             triads
         diminished 7th       :  m3 m3 m3     OR    dim dim
         half diminished 7th  :  m3 m3 M3     OR    dim min
         minor 7th            :  m3 M3 m3     OR    min maj
         minor, major 7th     :  m3 M3 M3     OR    min aug
         dominant 7th         :  M3 m3 m3     OR    maj dim
         major 7th            :  M3 m3 M3     OR    maj min
         

QUESTION : Are there any augmented sevenths chords?

Circle of thirds

You surely noticed how important are the thirds for the chord construction. Therefore you must know fluently the circle of thirds in the diatonic:

           c   e   g   b   d   f   a   c
           do  mi  sol ti  re  fa  la  do
           

If you know this sequence fluently, then you can immediately tell which notes consist for example the Fmaj7: f a c e, or every other chord. You must however be able to alter the sequence if needed. For example F7: f a c !e. This sequence is also valuable by music-reading. A stuff with the key of C consists of 5 lines. On these lines fall the notes E,G,B,D,F. Between these lines fall the notes F,A,C,E.

Ninths

(Almost) All the sevenths can become ninths by stacking another triad on their top. The ninth must be a major ninth from the root. For example:

         Ex. G dominant 9th, simply G9 : g   b    d    f    a
                                         \M3/ \m3/ \m3/ \M3/
                                         \___p5__/
                                         \_____m7_____/
                                         \________M9_______/

If the added ninth is not a M9, that must be noted with an alteration sign. For example:

           G7b9 : g b d f !a   has a minor ninth (not a diminished!)
           G7#9 : g b d f #a   has an augmented ninth.
           

QUESTION : Well, which sevenths cannot have a ninth on top of them?


Harmony

In this section we will learn some simple classical harmony which also applies to western folk music, or rock music, or simple jazz.

Index

Major scale

Classical harmony is based on two scales. The major and the (harmonic) minor scale. Let us begin with the major scale. C major scale:

          W   W   H   W   W   W   H
        c   d   e   f   g   a   b   c'
        i  ii  iii  iv  v   vi vii

All the notes in the scale have a name:

i : tonic
ii : supertonic
iii : mediant
iv : subdominant
v : dominant
vi : submediant
vii : leading tone

For the moment memorize the tonic (i), subdominant (iv), dominant (v) and leading tone (vii).

Triads

The following three triads are the most important chords in classical harmony: tonic, dominant, subdominant.

Tonic

The triad over the tonic note (in C major the C major chord : c e g) is also called tonic. We will note the tonic as I. A piece (written in the C major) usually begins with the tonic (C major) tonic and almost always ends with the tonic tone.

Dominant

The triad over the dominant note (in C major the G major chord : g b d) is also called dominant and is noted as V. The dominant chord contains the leading tone which tends to resolve to the tonic.

Subdominant

The triad over the subdominant note (in C major the F major chord : f a c) is also called subdominant and is noted as IV.

Note that the notes in these three chords cover the whole scale:

               IV
          +-----+---+
          |     |   |
          c d e f g a b
          | | |   |   |
          +---+---+   |
          I |     |   |
            +-----+---+
                  V

Also note that all of them are major triads.

The most important seventh is the dominant seventh:

Dominant seventh

If we build the seventh on the fifth degree of the scale then we get a dominant seventh chord (that's why this kind of seventh is called dominant) (in C major the G7 : g b d f) and is noted as V7. The dominant seventh contains a diminished fifth (b - f) which is considered as dissonance and must be resolved. In the classical resolution the leading tone (b) goes to the tonic (c) and the seventh of V7 (f) goes to the third of I (e):

            Resolution
            ----------
         *   f  → e
             d  → c (or e)
         *   b  → c
             g  → g

V7 forces I to come. Try playing C | G | C and then C | G7 | C to note the difference. How does C | G7 | F sounds? The tonic I, the subdominant IV and the dominant (seventh) V7 are the main chords for (all the) songs of western music. Some songs do not have any other chords. I will list these chords for the more important keys:

              Key | I   IV  V7  |     notes of the diatonic
              ----+-------------+---------------------------
              Eb  | Eb  Ab  Bb7 |   !e  f  g !a !b  c  d !e
              Bb  | Bb  Eb  F7  |   !b  c  d !e  f  g  a !b
              F   | F   Bb  C7  |    f  g  a !b  c  d  e  f
        -     C   | C   F   G7  |    c  d  e  f  g  a  b  c
              G   | G   C   D7  |    g  a  b  c  d  e #f  g
              D   | D   G   A7  |    d  e #f  g  a  b #c  d
              A   | A   D   E7  |    a  b #c  d  e #f #g  a
              E   | E   A   B7  |    e #f #g  a  b #c #d  e
              B   | B   E   F#7 |    b #c #d  e #f #g #a  b

Check out some popular songs you know and watch out for the presence and use of these chords.

Subdominant sixth

Another fairly often used chord is the major sixth on the 4th degree, the subdominant sixth (f a c d) which is noted as IV6 when the fifth is not present and as IV56 (5 below 6) if the fifth is present. [Note that it is the same chord with a minor seventh on the second degree]. From now on we will only note it as IV6 and enclose the fifth in parenthesis if optional.

ii-V-I progression

With the use of tonic, subdominant sixth and dominant seventh we can play the most played progression in the world of modern music, the so called ii7-V7-I progression, which is actually a IV6-V7-I progression. Why don't we call it then IV-V-I progression? A lot do. We saw that IV6 is the same with the seventh on the second degree. People like ii-V-I more because sevenths are more common than sixths and moreover the movement in the bass is better because of the fourth fall: d falls to g and g falls to c.

The other degrees

We introduced chords on the 1st, 4th and 5th degree of the diatonic scale. We can do the same with the rest notes of the scale. Before we do so we introduce the notion of parallel chords.

Parallels

A chord is parallel to another chord if it is a third away. For example Am is the parallel minor of C. The same way C is the parallel major of Am.

Tonic parallel

On the sixth degree of the scale is the parallel minor of the tonic. This is noted as Ip or simply vi. (Am in C major). I is capital because the tonic is major and p is small because the parallel is minor.

Dominant parallel

On the third degree of the scale is the parallel minor of the dominant. This is noted as Vp or simply iii. (Em in C major)

Subdominant parallel

On the second degree of the scale is the parallel minor of the subdominant. This is noted as IVp or simply ii. (Dm in C major)

Dominant seventh without root

On the seventh degree of the scale one finds the diminished triad which is a part of the dominant seventh. Therefore we denote the chord on this degree as V/7 or vii (The slash should come over V but that's not possible in ASCII). This chord relatively often replaces the V7 chord.

Now we have triads on all degrees of the diatonic major scale:

              (c)         (d)   (f)
         g     a     b     c     d     e     f
         e     f     g     a     b     c     d
         c     d     e     f     g     a     b
         --------------------------------------
         C   Dm(7)  Em    F(6)  G(7)   Am   Bmb5
         I   ii(7)  iii  IV(6)  V(7)   vi   vii-

[Note that the parentheses are not part of the notation. They should be erased if the optional note is present.] The dominant seventh V7 has the property that it establishes the key. One can find a (unaltered) G7 only in the key of C major, a C7 only in the key of F major, a D7 only in the key of G major and so on.

Secondary dominants

Each chord can be reinforced by playing its dominant seventh before it. A commonly used chord is the double dominant which is the dominant of the dominant. In C major, G is the dominant so D7 is the double dominant seventh. A double dominant coincides with II7, ie with the major second degree (Notice that normally the second degree is minor).

Play:

            chords :      C   D7   G7  C  (in C major)
        or  chords :      F   G7   C7  F  (in F major)
            -----------------------------
            harmony:      I   II7  V7  I

to get an idea of how it sounds. Note that a double dominant contains notes which are not in the scale. For example D7 is d #f a c, whereas #f is not in the C major scale.

Dominants of the rest of the chords are called simply secondary dominants. In the following we give all the secondary dominants of the C major scale. Secondary dominants are noted with a V in parentheses before the chord.

          A7  Dm  ,  B7  Em  ,  C7  F  ,  E7  Am
         (V7) ii  , (V7) iii , (V7) IV , (V7) vi

As secondary dominants we can also have secondary subdominants. They are noted as (IV) before the chord. Double subdominant is the subdominant of the subdominant. In C major, F is the dominant and Bb is the double dominant. A double subdominant coincides with bVII, i.e with the major lowered seventh degree.

Indeed any degree can appear as secondary. As we said a common progression is the ii-V-I progression. This progression can be played before any minor or major chord in a scale:

          Dm7 G7 C  ,  Am7 D7  G
          ii7 V7 I  , (ii7 V7) V
          Em7 A7  Dm  ,  F#m7 B7  Em  ,  Gm7 C7  F  ,  Bm7 E7  Am
         (ii7 V7) ii  , (ii7  V7) iii , (ii7 V7) IV , (ii7 V7) vi

Minor scales

If we now take the natural minor scale:

          W   H   W   W   H   W   W
        a   b   c   d   e   f   g   a
        i  ii  iii  iv  v  vi  vii

then we notice that

  1. 1. the tonic (a c e) is a minor chord and is noted as i.
  2. 2. the subdominant (d f a) is also a minor chord and is noted as iv.
  3. 3. the dominant (e g b) is also a minor chord and is noted as v.

The natural minor scale has no leading tone. Therefore it has no dominant seventh. The seventh in the fifth degree is a minor seventh. In order to restore this scale harmonically we raise the seventh (g -> #g); then we get a scale with a leading tone:

          W   H   W   W   H   WH   H
        a   b   c   d   e   f    #g  a
        i  ii  iii  iv  v   vi  #vii

this is called the "harmonic" minor. That's why the name. We can now build a major dominant (e #g b) which is noted as V. The seventh on the fifth degree is also a dominant seventh (e #g b d) and noted as V7. With the help of the V7 we can establish the tonic t. The invented harmonic minor has an augmented second interval (WH) between the sixth and the seventh note. This does not sound melodically correct (I find it good sounding :-) so the sixth is raised too. Then we get the following scale:

          W   H   W   W   W   W   H
        a   b   c   d   e   #f  #g  a
        i  ii  iii  iv  v  #vi #vii

which is called (guess why) "melodic" minor. Notice that within this scale we have a major subdominant too. Chords on all degrees of the diatonic natural minor scale:

         e     f     g     a     b     c     d
         c     d     e     f     g     a     b
         a     b     c     d     e     f     g
         --------------------------------------
         Am   Bmb5   C     Dm    Em    F     G
         i    ii-   III    iv    v     VI   VII

Note that all the chords are the same with those of C major scale. But their function is different. Here is Dm iv, in C major it was ii and so on. Chords on all degrees of the diatonic harmonic minor scale:

                      (b)   (d)
     e     f    #g    (a)    b     c     d
     c     d     e     f    #g     a     b
     a     b     c     d     e     f    #g
     --------------------------------------
     Am   Bmb5  C+   Dm(6)  E(7)   F   G#mb5
     i    ii-  III+  iv(6)  V(7)   VI  #vii-

Chords on all degrees of the diatonic melodic minor scale:

          (a)         (b)   (d)
     e    #f    #g    (a)    b     c     d
     c     d     e    #f    #g     a     b
     a     b     c     d     e    #f    #g
     --------------------------------------
     Am    Bm   C+    D(6) E(7) F#mb5 G#mb5
     i    ii(7) III+ IV(6) V(7)  #vi-  #vii-

The minor scales offer a big repertoire of chords to play.

Other chords

The dominant ninth on the V degree. Noted as V9. In C major : G9 (g b d f a), in A melodic minor : E9 (e #g b d #f).

The half-diminished seventh on the vii degree. Noted as V/9 or vii7-5. It is a dominant ninth with no root. In C major : B7b5 (b d f a). In A melodic minor : G#7b5 (#g b d #f).

The (full) diminished seventh on the vii degree of the harmonic minor. Noted as V/b9 because of the lowered (minor) ninth wrt to the dominant or viio (The circle o denotes a full diminished seventh). In A harmonic minor : G#dim (#g b d f)

Altered chords

The following chords are called altered because not all of their notes belong to the scale they appear.

Neapolitan sixth

The lowered subdominant sixth of the (harmonic) minor scale. Noted as iv-6 or N6. In Am : Dm-6 (d f !b) is the same chord with Bb. Note that we don't include the fifth (a) in the Dm-6. As a seventh chord the neapolitan appears as a dominant seventh, i.e. Bb7 (!b r f !a), which means that the fifth of subdominant Dm is altered too.

Note that one can have a neapolitan sixth in a major scale. In this case one has to take the lowered sixth of the minor subdominant. For example in C major, iv-6 : Fm-6 (f !a !d) same with Db. The seventh Db7 is used too.

The neapolitan sixth can be noted as bII or bII7. This chord is a substitute for the dominant V7 both in major and minor mode. It is called the tritone substitution since the roots of bII7 and V7 are a tritone (diminished 5th) away from each other. Actually the chords V7b5 and bII7b5 are identical to each other.

 
   Example: G7b5 : g b !d f and Db7b5 : !d f !!a !c. Check this out!
  

Altered dominants

The notes that should be raised or lowered are noted with # or b, or sometimes with + or - respectively. Examples: D7#5 or D7+5, D7b9 or D7-9, …

The symbol "alt" is used to notate a dominant seventh with both altered fifth and ninth: Galt = G7b5b9 or G7#5#9.

Modulation

Sometimes a piece written in the key of C major modulates in the key of its relative minor Am or dominant G major or subdominant F major or whatever key you want. We say that a piece modulates in another key when it has changed the tonic to another key for some relatively long part of the piece. However changes of keys can be short too. A short change is noted with parenthesis when it ends to the tonic and with angle parenthesis when it does not end to the tonic (though excepted). Examples (these are right out of my head, I didn't even play them; who knows? they may sound good :-) :

             D7  Gm (Em7 A7) D7) G7 C.
        C: ((V7) iv (ii7 V7) V7) V7 I

            [Bb Gm F7]  F C G7 C.
        C:  [I  vi V7] IV I G7 I.
                     ^ here is Bb excepted

Songs for harmony exploration

Wonderful tonight by Eric Clapton (in G major)

--

[Simple harmony: I V IV V I IV V I V vi IV V I]

G                D       C                     D
It's late in the evening, she's wondering what clothes to wear
I                V       IV                    V
...
C            D       G     D        Em
And then she asks me, do I look all right
IV           V       I     V        vi

          C             D           G
And I say yes, you look wonderful tonight
          IV            V           I
---------------------------------------------------------

THE BOXER by Simon & Garfunkel (in C major)

--

[Simple harmony: I vi V V7 I....]

C                                             Am
I am just a poor boy though my story's seldom told
I                                             vi

       G
I have squandered my resistance
       V

      G7                               C
For a pocket full of mumbles, such are promises
      V7                               I

             Am            G                 F
All lies and jest, still a man hears what he wants to hear
             vi            I                 S

                   C     G  G7   C
And disregards the rest
                   I     V  V7   I

Am G Am G F C
Lie la lie Lie.....
vi V vi I IV I
---------------------------------------------------------

Let It Be by the Beatles (In C major)

--

[Simple harmony, use of ii7]

       C              G                Am          F
When I find myself in times of trouble Mother Mary comes to me,
       I              V                vi          S

C                 G              F  C/E Dm7 C
speaking words of wisdom, let it be.---
I                 V              IV  I  IV6 I
                                        ii7*
.....
G      Am            G             F             C
Let it be,--- let it be,--- let it be,--- let it be.----
V      vi            V             IV

C                G              F  C/E Dm7 C
Whisper words of wisdom, let it be.---
I                V              IV  I  IV6 I

--
* IV6 = ii7. For example F6 = Dm7
---------------------------------------------------------

American Pie (in G major)

--

[Use of (V7)]

G   C        G        D
bye bye Miss American Pie
I   IV       I        V

(same ...
Drove my chevy to the levy But the levy was dry
And them good old boys were drinking whiskey and rye
)
        Em                        A7
Singin' this'll be the day that I die
        vi                       (V7)

Em                        D7
this'll be the day that I die.
vi                        V7

(Note that each strophe ends with a dominant. Therefore we feel that this song never finishes. It rolls and rolls... Play a tonic at the end to feel satisfied.)


All My Loving The Beatles (in C major)

--

[Use of bVII, ii-V-I progression, short change to relative harmonic minor]

           Dm            G7         C           Am
Close your eyes and I'll kiss you tomorrow I'll miss you,
           ii            V7         I           vi
           ii  --------  V -------- I

  F           Dm        Bb    G
remember I'll always be true.
  IV          ii        bVII  V

         Dm         G              C          Am
And then while I'm away I'll write home every day,
         ii         V              I          vi

         F           G7        C
and I'll send all my loving to you.
         IV          V7        I

       Am      Caug               C
All my loving - I will send to you
       vi      I+*                I
  Am :(i      III+               III)

       Am      Caug            C
all my loving, Darling I'll be true.
       vi      I+              I

* Caug is a chord of A harmonic minor.


Yesterday The Beatles (in F major)

[Short changes to relative minor, or dominant. Extensive use of ii-V-I progression. Use of V/9]

F         Em7       A7                 Dm   Dm/C
Yesterday    all my troubles seemed so far away.
I       ( ii7       V7               ) vi
          ii ------ V ---------------- I

Bb     C7                      F
Now it looks as though they're here to stay,
IV     V7                      I

C/E  Dm7 G7       Bb    F
Oh   I believe in yesterday.
V  [ ii7 V7 ]*    IV    I
            C
     ii--V--

 Em7 A7  Dm  C  Bb Dm      Gm6      C7       F
 Why she had to go I don't know she wouldn't say.
(ii7 V7) vi  V  IV vi      V/9**    V7       I
 ii--V---I                (ii-------V7-------I)

...

* Note the short change of scale: G7 implies C major, the dominant.

** Note that Gm6 (: G Bb D E) is a C9 (: C E G Bb D) with no root.


Hotel California By The Eagles (in A minor)

[Simple minor scale harmony]

Am                        E
On a dark desert highway, cool wind in my hair
i                         V

G                     D
Warm smell of colitas rising up through the air
vii                   IV
[I                    V]*

F                         C
Up ahead in the distance, I saw a shimmering light
VI                       III
[I                        V]*

Dm
My head grew heavy and my sight grew dim
iv

E
I had to stop for the night
V**

....

F                        C
Welcome to the Hotel California.
VI                      III
[I                       V]*

       E                    Am
Such a lovely place, such a lovely face
       V                    i

F                               C
Plenty of room at the Hotel California
VI                             III
[I                              V]*
    Dm                                      E
Any time of year (any time of year) you can find it here
    iv                                      V**

* Note the relation tonic-dominant in each strophe, with a different tonic.

** This song ends to the dominant too. Therefore it cannot be abruptly interrupted, instead it fades....

Chord patterns appendix

There are two main chord construction patterns. I'll call them the E major and the A major patterns or simply "E" and "A", because these are the chords in the first position.

Triads on the fretboard

"E"-pattern

The E major chord (E) consists of root E, major third G# and perfect fifth B. The following six-string chord is a way to play E:

        e  R|----|----|----|... E
        B p5|----|----|----|... B
        G | |-M3-|----|----|... G#
        D | |----|--R-|----|... E
        A | |----|-p5-|----|... B
        E  R|----|----|----|... E
             1st       3rd   fret

On the right of each string we write the note. On the fret we write the interval. Try to learn which interval you have on each string. This will help when you build complicated chords. If you leave the 3rd string unfretted then you get a G natural instead of a G#. That will make a minor third and consequently the E minor (Em) chord:

        e  R|----|----|----|... E
        B p5|----|----|----|... B
        G m3(----|----|----|... G (==
        D  ||----|--R-|----|... E
        A  ||----|-p5-|----|... B
        E  R|----|----|----|... E
             1st       3rd   fret

The signs "(" or ")" in the place of a fret indicate which note should be lowered or raised from the original major pattern to obtain the desired chord. To get the augmented E (E+) you should begin with the E major and raise the fifth a fret. The fifth is B and it appears on two strings: the open second and the fretted fifth. You should raise both of them:

        e  R|----|----|----|... E
        B  |)-#5-|----|----|... B# (==
        G  ||-M3-|----|----|... G#
        D  ||----|--R-|----|... E
        A  ||----|----)-#5-|... B# (==
        E  R|----|----|----|... E
     1st       3rd   fret

That's really difficult and impracticable to play as a six-string chord. You should either play only the 4 notes starting from bass, or the four higher strings starting from the D-string.

To get the diminished triad E (Eb5) you should begin with the E minor and lower the fifth a fret. It is impossible to lower an open string so this will only work on the 4 top strings (B should not sound!):

        e  R|----|----|----|... E
        B  X|----|----|----|...
        G m3(----|----|----|... G
        D  ||----|--R-|----|... E
        A  ||-b5-(----|----|... Bb (==
        E  R|----|----|----|... E
             1st       3rd   fret

Well if you transpose these patterns and use your first finger as a barre you can play the F chords (barre on 1st fret), the G chords (barre on 3rd fret) and so on... That's why I call it a pattern.

"A"-pattern

The A major chord consists of A, C# and E. (Note that we leave the first string because be strumming all the strings, three fifths (Es) in the chord will give it an E chord character. In fingerpicking however one can play it)

        e p5|----|----|----|... E
        B  ||----|-M3-|----|... C#
        G  ||----|--R-|----|... A
        D  ||----|-p5-|----|... E
        A  R|----|----|----|... A
        E  X|----|----|----|...
             1st       3rd   fret

Well now you know how it goes... Fret C instead of C# to get the minor chord (Am):

        e p5|----|----|----|... E
        B  ||-m3-(----|----|... C (==
        G  ||----|--R-|----|... A
        D  ||----|-p5-|----|... E
        A  R|----|----|----|... A
        E  X|----|----|----|...
             1st       3rd   fret

Take the major and raise the fifth to get the augmented A (A+):

        e  ||-#5-|----|----|... E# (==
        B  ||----|-M3-|----|... C#
        G  ||----|--R-|----|... A
        D  ||----|----|-#5-|... E# (==
        A  R|----|----|----|... A
        E  X|----|----|----|...
             1st       3rd   fret

Take the minor and lower the fifth to get the diminished triad A (Ab5). Notice the X's!:

        e  X|----|----|----|...
        B  ||-m3-(----|----|... C
        G  ||----|--R-|----|... A
        D  ||-b5-|----|----|... Eb (==
        A  R|----|----|----|... A
        E  X|----|----|----|...
             1st       3rd   fret

Transpose these patterns and get all the chords you need...

More patterns

There are two more useful patterns. These are not so easily transposed with a barre finger, but I will list them:

"C"-pattern

C major (C E G):

        e 0|----|----|----|... M3
        B ||--C-|----|----|... R
        G 0|----|----|----|... p5
        D ||----|--E-|----|... M3
        A ||----|----|--C-|... R
        E X|----|----|----|...
             1st       3rd   fret

C minor (C Eb G):

        e X|----|----|----|...
        B ||--C-|----|----|... R
        G 0|----|----|----|... p5
        D ||-Eb-(----|----|... m3 (==
        A ||----|----|--C-|... R
        E X|----|----|----|...
             1st       3rd   fret

C augemented (C E G#):

        e 0|----|----|----|... M3
        B ||--C-|----|----|... R
        G |)-G#-|----|----|... #5 (==
        D ||----|--E-|----|... M3
        A ||----|----|--C-|... R
        E X|----|----|----|...
             1st       3rd   fret

C diminished cannot be played with this pattern.

"D"-pattern

D major (D F# A):

        e ||----|-F#-|----|... M3
        B ||----|----|--D-|... R
        G ||----|--A-|----|... p5
        D 0|----|----|----|... R
        A 0|----|----|----|... p5
        E X|----|----|----|...
             1st       3rd   fret

D minor (D F A):

        e ||--F-(----|----|... m3 (==
        B ||----|----|--D-|... R
        G ||----|--A-|----|... p5
        D 0|----|----|----|... R
        A 0|----|----|----|... p5
        E X|----|----|----|...
             1st       3rd   fret

D augmented (D F# A#):

        e ||----|-F#-|----|... M3
        B ||----|----|--D-|... R
        G ||----|----)-A#-|... #5 (==
        D 0|----|----|----|... R
        A X|----|----|----|...
        E X|----|----|----|...
             1st       3rd   fret

D diminished (D F Ab):

        e ||--F-(----|----|... m3
        B ||----|----|--D-|... R
        G ||-Ab-(----|----|... b5 (==
        D 0|----|----|----|... R
        A X|----|----|----|...
        E X|----|----|----|...
             1st       3rd   fret

The last pattern. OK! There is one more. It is only a major chord pattern.

"G"-pattern

G major (G B D):

        e ||----|----|--G-|... R
        B 0|----|----|----|... M3
        G 0|----|----|----|... R
        D 0|----|----|----|... p5
        A ||----|--B-|----|... M3
        E ||----|----|--G-|... R
             1st       3rd   fret

or

        e ||----|----|--G-|... R
        B ||----|----|--D-|... p5
        G 0|----|----|----|... R
        D 0|----|----|----|... p5
        A ||----|--B-|----|... M3
        E ||----|----|--G-|... R
             1st       3rd   fret

It is rather difficult to finger the minor or the diminished from this pattern. You can try the augmented: G+ (G B D#)

        e ||----|----|--G-|... R
        B 0|----|----|----|... M3
        G 0|----|----|----|... R
        D |)-D#-|----|----|... #5
        A ||----|--B-|----|... M3
        E ||----|----|--G-|... R
             1st       3rd   fret

Sevenths on the fretboard

We won't give all the patterns for all the sevenths. It is easy and good practice to find them out alone by alternating thirds, fifths and sevenths. In each pattern we will give the dominant seventh and the most important alterations.

"E"-pattern

E7

        e  R|----|----|----|... E           e  R|----|----|----|... E
        B  ||----|----|-m7-|... D           B p5|----|----|----|... B
        G  ||-M3-|----|----|... G#          G  ||-M3-|----|----|... G#
        D  ||----|--R-|----|... E     OR    D m7|----|----|----|... D
        A  ||----|-p5-|----|... B           A  ||----|-p5-|----|... B
        E  R|----|----|----|... E           E  R|----|----|----|... E
             1st       3rd   fret

Em7

        e  R|----|----|----|... E           e  R|----|----|----|... E
        B  ||----|----|-m7-|... D           B p5|----|----|----|... B
        G m3(----|----|----|... G           G m3(----|----|----|... G
        D  ||----|--R-|----|... E     OR    D m7|----|----|----|... D
        A  ||----|-p5-|----|... B           A  ||----|-p5-|----|... B
        E  R|----|----|----|... E           E  R|----|----|----|... E
             1st       3rd   fret

Edim

        e  R|----|----|----|... E
        B  ||----|-b7-(----|... Db
        G m3(----|----|----|... G
        D  ||----|--R-|----|... E
        A  ||-b5-(----|----|... Bb
        E  R|----|----|----|... E
             1st       3rd   fret

"A"-pattern

A7

        e p5|----|----|----|... E             e  ||----|----|-m7-|... G
        B  ||----|-M3-|----|... C#            B  ||----|-M3-|----|... C#
        G m7|----|----|----|... G             G  ||----|--R-|----|... A
        D  ||----|-p5-|----|... E     OR      D  ||----|-p5-|----|... E
        A  R|----|----|----|... A             A  R|----|----|----|... A
        E  X|----|----|----|...               E  X|----|----|----|...
             1st       3rd   fret

Am7

        e p5|----|----|----|... E             e  ||----|----|-m7-|... G
        B  ||-m3-(----|----|... C             B  ||-m3-(----|----|... C
        G m7|----|----|----|... G             G  ||----|--R-|----|... A
        D  ||----|-p5-|----|... E     OR      D  ||----|-p5-|----|... E
        A  R|----|----|----|... A             A  R|----|----|----|... A
        E  X|----|----|----|...               E  X|----|----|----|...
             1st       3rd   fret

Amaj7

        e p5|----|----|----|... E             e  ||----|----|----|-M7-|.G#
        B  ||----|-M3-|----|... C#            B  ||----|-M3-|----|...   C#
        G  ||-M7-|----|----|... G#            G  ||----|--R-|----|...   A
        D  ||----|-p5-|----|... E     OR      D  ||----|-p5-|----|...   E
        A  R|----|----|----|... A             A  R|----|----|----|...   A
        E  X|----|----|----|...               E  X|----|----|----|...
             1st       3rd   fret

Adim

        e  ||----|-b7-(----|... Gb
        B  ||-m3-(----|----|... C
        G  ||----|--R-|----|... A
        D  ||-b5-(----|----|... Eb
        A  R|----|----|----|... A
        E  X|----|----|----|...
             1st       3rd   fret

How to correctly tune your guitar

There are several ways to tune a guitar. One is to use a set of pipes for all six strings. I do not recommend this since a single pipe can have the same result, and moreover alternate tunings are not covered by the 6pipes-set. The second way is to use a single pipe as already mentioned. This is usually a "A"-pipe with frequency of 440 Hz. On the guitar it matches (unison) the 5th fret of the 1st string. The third way is to use an "A"-fork. Well that's identical to a "A"-pipe and it is a matter of taste which to use. Pipes are not expensive and handy to carry with.

What about harmonics?

No! Tuning with harmonics —other than the 1st harmonic on the 12 fret which is an octave above the open string— are not correct well-tempered tunings. The fequencies of natural harmonics (notes as found in the nature) which are based on the length of vibrating strings (1/2, 2/3, 3/4, ...) do not match the frequencies of the artificial well-tempered tuning which is used in the western music.

Octave based tunings

A tuning is called octave based tuning when we are comparing unisons or octave intervals while tuning all the strings. Every octave based tuning tunes a guitar correctly, if it is correctly done.

The following tuning is the most popular one and it is entirely based on unisons.

  1. Tune the 5th string with the A-pipe.
  2. Tune the 6th string: Fret the 6th string on the 5th fret and compare to the open 5th string.
  3. Tune the 4th string: Fret the 5th string on the 5th fret and compare to the open 4th string.
  4. Tune the 3rd string: Fret the 4th string on the 5th fret and compare to the open 3rd string.
  5. Tune the 2nd string: Fret the 3rd string on the 4th fret and compare to the open 2nd string.
  6. Tune the 1st string: Fret the 2nd string on the 5th fret and compare to the open 1st string.

The diagram illustrates the procedure.

      e ||----|----|----|----|----|----|-
      b ||----|----|----|----|--e-|----|-
      g ||----|----|----|--b-|----|----|-
      d ||----|----|----|----|--g-|----|-
      a ||----|----|----|----|--d-|----|-
      e ||----|----|----|----|--a-|----|-
           1st       3rd       5th

A better tuning

Well an even better kind of tuning is based on octaves of the same note for all the strings. You can tune all the six strings by comparing A tones at different octaves and different strings with the open 2nd string (A). This approach has the advantage that all the strings are compared to the same string (2nd) and not to each other. So errors on tuning of one string does not propagate.

Procedure:

  1. Tune the 5th string with the A-pipe.
  2. Tune the 6th string: Fret the 6th string on the 5th fret and compare to the open 5th string.
  3. Tune the 4th string: Fret the 4th string on the 7th fret and compare to the open 5th string.
  4. Tune the 3rd string: Fret the 3rd string on the 2th fret and compare to the open 5th string.
  5. Tune the 2nd string: Fret the 2nd string on the 10th fret and compare to the open 5th string.
  6. Tune the 1st string: Fret the 1sy string on the 5th fret and compare to the open 5th string.
      e ||----|----|----|----|--a-|----|----|----|----|----|----|----|...
      b ||----|----|----|----|----|----|----|----|----|--a-|----|----|...
      g ||----|--a-|----|----|----|----|----|----|----|----|----|----|...
      d ||----|----|----|----|----|----|--a-|----|----|----|----|----|...
      a ||----|----|----|----|----|----|----|----|----|----|----|----|...
      e ||----|----|----|----|--a-|----|----|----|----|----|----|----|...
           1st       3rd       5th       7th       9th           12th fret