Music Material

Index

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 b (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 me se le te
        !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:

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)

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)

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])

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 eleventh or for the sixth and the thirteenth.)
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:

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

Ex. m6 ==> M3, p4 ==> p5, m2 ==> M7, ...

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