Sunday, October 2, 2016

Beginner Guitar player with Clairnote and M3 tuning - Lesson 1

1 Introduction

This series of blog posts is intended for complete guitar beginners, and also for people who may have played the guitar for a bit with tablatures, but who do not really understand how harmony works. It is also suitable for more advanced players who would like to try a different approach.

This series aims to propose an alternative to traditional teaching, by using:

  • an alternative guitar tuning: The Major Third (M3) tuning
  • an alternative music notation: Clairnote
  • a non-conventional terminology for notes and intervals: integer numbers

I strongly believe that these three items are easier to understand compared to the traditional ones. They allow to play music more naturally by having fewer things to remember. I think that playing an instrument should be as natural and straightforward as singing.

1.1 My Background

I have been playing the guitar for 10 years, but as I have not played very regularly, I would think my level is intermediate. I learned to play the guitar using tablatures for many years, concentrating on the technique rather than the theory.

More recently, I learned a bit about music theory and harmonization and how it translates to the guitar. However, with my Maths/Computer science background, I found it striking that many concepts could be explained much more succinctly and logically using numbers and arithmetics rather than letters and roman numerals !

My musical inclination is towards blues / rock / heavy metal, but I also fancy a bit of pop and classical music from time to time.

1.2 My first student

My 14-years old daughter had taken guitar lessons for a few years and then stopped. She is now keen on playing again, and I proposed to teach her using the non-conventional items outlined above. She is not a true beginner, therefore some of the lessons might be too fast paced for complete beginners. I will try to keep this in mind and maybe add additional lessons depending on your feedback.

1.3 Links

  • Music for geeks and nerds is a very interesting short book. Highly recommended if you like programming
  • M3 Guitar describes how to tune your guitar in Major Thirds, and provides useful chords and scales diagrams
  • Clairnote is an alternative music notation which works very well with the Major Third tuning.
  • Wikipedia: pitch class describes the theoretical background behind the integer notation that I will use in the lessons.

1.4 Feedback

If you like this blog, if you do not understand something, if you think I should explain things differently, or if you think my approach is completely wrong, I would welcome your feedback ! Please leave a comment below.

2 Integer notation

In all the lessons, I will use integer numbers from 0 to 11 for the names of the notes, instead of the traditional C, D, E, F, G, A, B or Do Re Mi Fa Sol La Si.

The reason for this unorthodox choice is that I find it much easier to do arithmetics with numbers rather than with letters !

Integer English Latin
0 C Do
1 C# / Db Do# / Reb
2 D Re
3 D# / Eb Re# / Mib
4 E Mi
5 F Fa
6 F# / Gb Fa# / Solb
7 G Sol
8 G# / Ab Sol# / Lab
9 A La
10 A# / Bb La# / Sib
11 B Si

In this notation, there is one semitone between 2 consecutive notes. 12 seminotes constitute an octave. Two notes separated by 12 semitones (or one octave) have the same name.

3 Tune your guitar

We are going to use a special tuning, called "Major third tuning". It means that there is a "Major Third" interval = 4 semitones, between two strings. But we will come back later to these terms in more details.

You do not need a special device for this, these days a phone or tablet does the job very well. I would recommend PitchLab lite (here for Android, here for iPhone), but you can use any tuner as long as you can change the default notes for each string.

You need to tune the strings with the following notes, from the highest pitched string to the lowest :

4 / C  |-------------| 6th string (highest pitch)
8 / Ab |-------------| 5th string
4 / E  |-------------| 4th string
0 / C  |-------------| 3rd string
8 / Ab |-------------| 2nd string
4 / E  |-------------| 1st string (lowest pitch)

You can check that the guitar is well tuned by playing one string on the 4th fret and the following string open. The two pitches must be exactly the same. Then do the the same for the 5th and 4th string, 4th and 3rd, …

0 / C  |----------0--| 
8 / Ab |-------0--4--|
4 / E  |-------4-----|
0 / C  |----0--------|
8 / Ab |-0--4--------| 2nd string: open, do not press any fret
4 / E  |-4-----------| 1st string: 4th fret with left index

It is important to always play with a guitar in tune. I would recommend to always tune your guitar before a practice session. At this stage of your learning, you are creating connections between your different senses. Your ears, fingers, and eyes are all learning the guitar. If you get used to the guitar sounding out of tune, then you will take longer to overcome that.

OK, now that our guitar is in tune, we are going to use Clairnote to play some scales.

4 Clairnote

Clairnote music notation is an alternative music notation system designed and introduced by Paul Morris in December 2013. If you are already familiar with the Traditional Notation (TN), you can go to the Clairnote website to understand the differences in more details.

But given that this blog is intended for beginners, I will give you just enough information to get started. The clairnote music sheet below is a 0 / C chromatic scale, it starts with the note 0 / C and has 12 notes. In this scale, each note is one "semitone" above the preceding one.

4.1 Chromatic scale

4.2 Features

  • Hollow and solid note heads alternate to help indicate a note’s pitch and to make interval patterns easy to see.
  • The staff line are regularly spaced by 4 semitones.
  • The 0 / C staff line is invisible to make the staff less cluttered.

4.3 On the guitar neck

When we tuned our guitar earlier, we tuned it so that two consecutive strings are also separated by 4 semitones. This correspondance means that you can almost treat the clairnote notation as a tablature, each staff line representing one string.

Let's play the chromatic scale on the guitar. We must start with a 0 / C, and add one semitone each time. On the guitar neck, one semitone = one fret. Here is the corresponding tablature:

0 / C  |--------------------------------------| 
8 / Ab |-------------------------0--1--2--3---|
4 / E  |-------------0--1--2--3---------------|
0 / C  |-0--1--2--3---------------------------|
8 / Ab |--------------------------------------| 
4 / E  |--------------------------------------|

You can appreciate how close the tablature matches the clairnote staff, and how you can play the entire scale without moving your left arm.

One of the great features of the guitar is that you can play the same notes at different places on the neck. Let's play the same scale starting on the 4 / E string. Here is a trick to instantly find any note on a given string:

  • take the open string's note s = 4 / E
  • take the target note n = 0
  • calculate f = n - s = 0 - 4 = -4
  • if the resulting number f is negative, add 12 to it => fret = -4 + 12 = 8
  • that means that if we play the 8th fret on the 4 / E string, we will get a 0 / C note !
0 / C  |--------------------------------------| 
8 / Ab |--------------------------------------|
4 / E  |--------------------------------------|
0 / C  |-------------------------8--9--10-11--| 
8 / Ab |-------------8--9--10-11--------------|
4 / E  |-8--9--10-11--------------------------|

5 The major scale

The major scale or Ionian scale is one of the most commonly used musical scales, especially in Western music. Like many musical scales it is made up of seven notes.

Here is a 0 / C major scale. Its name comes from the first note on the scale.

You should be able to play it on the guitar without a tablature. Observe the number of semitones between two notes:

  • when there is only +1 semitone, the note head changes from black to white, or from white to black.
  • on the guitar, play +1 fret. If you played a note n with your index, play n+1 with your middle finger. If you played n with your pinkie, play n+1 on the following string with your index.
  • when there are +2 semitones, the note head is the same, but it slightly higher on the staff
  • on the guitar, play +2 frets. Use the same rules w.r.t fingering: your left arm should not move.

Here is the tablature for reference, but try to play by just looking at the clairnote staff.

0 / C  |---------------------------|
8 / Ab |---------------------------| 
4 / E  |---------------------------|
0 / C  |----------------9--11------|
8 / Ab |-------8--9--11------------|
4 / E  |-8--10---------------------|

6 Exercise 1

Play the 9 / A major scale, starting on the 4 / E string, and then starting on the 8 / Ab string.

7 Exercise 2

Play a simple song that you already know which only uses the major scale. For instance you can try "Happy Birthday", "Jingle Bells", "Au clair de la lune", …

Start playing it in the 0 / C Key, which means that you will use only the notes of the 0 / C major scale. Once your have found the right notes and the right rythm, try playing it in another key, and/or try playing it in the same key, but start from a different string.

Saturday, November 1, 2014

Chords

Major chords

A chord is a set of 3 or more notes played simulteanously. A triad is a chord composed of 3 notes. A tetrad is composed of 4 notes.
Major triad chords are composed of a root note, a note 4 semitones above the root (the major third), and a note 7 semitones above the root (the fifth). We notate the intervals composing the chord using curly brackets:
Major chord = { 0 4 7 }
We also notate the sequence of intervals between notes of the chord in square brackets []. We obtain it by subtracting each number with the previous one:
Major chord = { 0 4 7 } = [ 4-0, 7-4, 12-7] = [ 4 3 5 ]

Using our clock notation, a 0 (C) Major chord looks like this:

C Major =  0 + { 0 4 7 } = (0 4 7) = (C E G)
If we want to find the notes composing a 2 (D) Major chord, we just have to add  { 0, 4, 7 } to the root note 2.
D Major = 2 + { 0 4 7 } = ( 2 6 9 ) = (D F A)
Interestingly, the shape of the triangle is exactly the same. When we transpose the root note, we are actually doing a rotation of the triangle.

Minor chords

Using the previous notation,
Minor chord = { 0, 3, 7 } = [ 3, 4, 5 ]

C Minor = 0 + { 0 3 7 } = ( 0 3 7 )

Seventh chords

  • A Major seventh chord is constructed by adding a fourth note to a major triad, 4 semitones above the last note (a major seventh). A C major seventh is noted C7M
  • In a Minor seventh chord, the fourth note is 3 semitones above the third note (minor seventh).  A C minor seventh is noted C7m.
  • A Dominant seventh chord is a major triad with a fourth note 3 semitones above the third note. (minor seventh). A C dominant seventh is noted C7.
M7 chord = { 0 4 7 11 } = [ 4 3 4 1 ]
m7 chord = { 0 3 7 10 } = [ 3 4 3 2 ]
7 chord = { 0 4 7 10} = [ 4 3 3 2 ]

C7M = 0 + { 0 4 7 11 }
 


C7m = 0 + { 0 3 7 10 }

This is quite interesting: both 7M and 7m chords have a trapezoid shape when drawn in the note clock. This shape has symmetry axe, but I am not sure whether this has any relationship with the harmony of the chord.
On the other hand, the dominant seventh is asymmetric:

C7 = 0 + { 0 3 7 10}


Application to the guitar fretboard

 

Major triad, E shape

Here is a method to to find any major triad (3 notes) on the fretboard. Bear in mind that in any operation, we may have to add or substract 12 to always stay in the [0, 11] range.
  1. Find the root note. We know from the previous post that the standard tuning is ( 4 9 2 7 11 4 ), so if I want to play a 4 Maj (E Maj) chord, the first note of the chord can be on the open 6th string, or on the 7th fret of the 5th string (9+7 = 16, 16-12 = 4), or .... For this example let's use the open 6th string.
  2. Find a note on the 5th string that is part of the chord and that can be played without stretching fingers too much. We know that our chord structure is { 0, 4, 7 }, and the that the 5th string is 5 semitones above the 6th string.
    • Can I play the root note, +0 semitones above the root ? +0 (interval to play) - 5 (number of semitones between 6th and 5th string) = -5, -5 + 12 = 7th fret. I have not used any of my fingers yet, so I could play it. But let's carry on and see if we could play other notes of the chord.
    • Can I play the major third, +4 semitones above the root ? +4 -5  = -1, -1+12 = 11th fret. It's even further away, let's continue
    • Can I play the fifth, +7 semitones above the root ? +7 -5 = 2nd fret. This fret is much closer to the open string on the 6th string, so it looks like it is the best fit, let's use this.
  3. Find a note on the 4th string. The 4th string is 5 semitones above the 5th string, hence it is 10 semitones above the 6th string. Let's repeat the same process.
    • Play a root +0 ? +0 -10 (number of semitones between 6th and 4th string) = -10, -10 + 12 = 2nd fret.
    • Play a major third +4 ? +4-10 = -6, -6+12 = 6th fret.
    • Play a fifth +7 ? +7 -10 = -3, -3+12 = 9th fret.
  4. Find a note on the 3rd string, which is 15 semitones above the 6th string. 
    • +0 ? +0 -15 = -15, -15+12 = 3rd fret. 
    • +4 ? +4 -15 = -11, -11+12 = 1st fret.
    • +7 ? +7 -15 = -8, -8+12 = 4th fret
  5. Find a note on the 2nd string, which is 19 semitones above the 6th string. 
    • -19 is equivalent to -19 + 12 = -7
    • +0 ? +0 -7 = -7, -7+12 = 5th fret
    • +4 ? +4-7 = -3, -3+12 = 9th fret
    • +7 ? +7-7 = 0th fret (open string)
  6. Find a note on the 1st string, which is 24 semitones above the 6th string.
    • -24 is equivalent to -24 + 12 + 12 = -0
    • +0 ? +0 -0 = 0th fret
    • +4 ? +4-0 = 4th fret
    • +7 ? +7-0 = 7th fret
  7. Let's play it !
4 Maj (E Maj)
 
This is the E-type shape of chord in the CAGED system. Notice that the +0 and +7 intervals are played many times on several strings. This explains why this shape of chord sounds more full than other types.
As you probably already know, you can use the same chord shape to play other chords, by just moving your hand down the neck.
For instance if you want to play a 7 Maj (G Maj) chord, just move your hand by 3 frets (7 Maj - 4 Maj = 3)

7 Maj (G Maj)

 

 Major triad, C shape

Using the same method, we can work out other chord shapes.
Here are the details for finding the C shape:
  1. We want to play a 0 Maj (C Maj) chord, starting from the 5th string. The 5th string played open is 9, so if I want to play a 0, I need to press a finger on the 0 - 9 = -9, -9+12 = 3rd fret
  2. 4th string
    • Play a root +0 ? +0 -5 (number of semitones between 5th and 4th string) +3 (fret played on the 5th string) = -2, -2+12 = 10th fret. Impossible to play unless you have huge hands !
    • Play a major third +4 ? +4 -5 +3 = 2nd fret. This is the closest to the 3rd fret
    • Play a fifth +7 ? +7 -5 +3 = 5th fret
  3. 3rd string:
    • +0 ? +0 -10 +3 = -7, -7+12 = 5th fret
    • +4 ? +4 -10 +3 = -3, -3+12 = 9th fret
    • +7 ? +7 -10 +3 = 0th fret (open string)
  4. The 2nd string is 14 semitones above the 5th string. We can simplify the calculations by always adding -14 + 3 = -11, -11+12 = +1
    • +0 ? +0 +1 = 1st fret
    • +4 ? +4 +1 = 5th fret
    • +7 ? +7 +1 = 8th fret
  5. The 1st string is 19 semitones above the 5th string. With the simplification we need to add -19 + 3 = -16, -16+12 = -4 to each chord interval.
    • +0 ? +0 -4 = -4, -4 + 12 = 8th fret
    • +4 ? +4 -4 = 0th fret
    • +7 ? +7 -4 = 3rd fret
  6. The resulting chord looks like this on the fretboard:
0 Maj (C Maj)









 

Other chords

As an excercise, you can work out the other CAGED shapes by solving the same puzzle and this information:
  • The A shape starts on the 5th string
  • The G shape starts on the 6th string
  • The D shape starts on the 4th string
Minor chords are obtained by using { 0 3 7 } intervals, M7 by using {0 4 7 11}, ... (see above)

Sunday, October 5, 2014

Clock notation

I am a guitar player, who has learned playing exclusively with tablatures. Now I am a bit tired of playing like a robot without understanding why the songs I like are written as they are. I can feel that there is an underlying structure and logic common to many songs. I have tried to read and understand some material on music theory and harmony, but I generally find it non-logical, confusing, and difficult to apply to guitar playing.
In this blog I will try to explain harmony by using numbers and geometric figures, which in my opinion is more natural, logical, and easy to remember. I hope this will be helpful for guitarists or keyboard players without a background in music theory.

Rock around the clock

You probably already know the major scale, C D E F G A B C, or Do Re Mi Fa Sol La Si Do. The distance or interval between two notes is expressed in tones and semitones.  2 semitones = 1 tone. You may also know that there are two semitones (one tone) between most notes, such as C (Do) and D (Re), but just one semitone between E and F and between B and C:
  • C 2 D 2 E 1 F 2 G 2 A 2 B 1 C
This notation maps nicely to the white keys of the piano keyboard:

  • When there is a black key between two white keys, the keys are separated by 2 semitones. 
  • When there is no black key (B - C and E - F), the keys are separated by 1 semitone. 
  • A black key is 1 semitone above the preceding white key. The note's name is suffixed with a sharp #.
Therefore, unlike the guitar, the piano keyboard is not uniform: two adjacent white keys can be separated by 1 or 2 semitones, depending on their position. This is why some people build alternative keyboards: http://www.altkeyboards.com

Now, why on earth do we use consecutive letters, which look like a regular interval, when the intervals between letters are not all the same ? This makes calculating intervals between two notes quite cumbersome. For example the interval between C and F (3 letters "above" C) is 2.5 tones, but the interval between F and B (3 letters "above" F) is 3 tones...
Playing music with traditional notation looks like doing arithmetic with roman numerals !

Fortunately, there is a simpler notation, called clock or integer modulo 12 notation:

Each note is named with a number, from 0 to 11. With this notation, calculating intervals between two notes is as simple as doing additions and subtractions:
  • The interval between 0 (C) and 5 (F) is 5-0 = 5 semitones (2.5 tones). 
  • The interval between 5 (F) and 11 (B) is 11-5 = 6 semitones (3 tones).
  • The interval between 11 (B) and 2 (D) is 2 + 12 - 11 = 3 semitones (1.5 tones). 
Whenever an operation's result is above 12 or below 0, just subtract / add 12 to stay in the 0 to 11 range.
The 0 (C) major scale becomes:
0 2 2 2 4 1 5 2 7 2 9 2 11 1 0

Now, try to memorize 2 2 1 2 2 2 1, the sequence of intervals of the major scale. Start with any key note, add these numbers, and you obtain the notes of the major scale in any key.
For example, the 5 (F) major scale is:
5 2 7 2 9 1 10 2 0 2 2 2 4 1 5
F   G  A   A#  C   D   E   F

Interval names

Now we know how to calculate the interval between two notes, using the number of semitones. However most musicians prefer to use these awkward names:

SemitonesNamePosition of the note in the C major scale
0Unison1st - C
1Minor second
2Second2nd - D
3Minor third
4Major third3rd - E
5Perfect fourth4th - F
6Augmented fourth or Diminished fifth
7Perfect fifth5th - G
8Minor sixth
9Major sixth6th - A
10Minor seventh
11Major seventh7th - B
12Octave8th - C

Which one do you prefer ? Names or numbers ? I personally find the names of the intervals quite confusing. When someone talks about a "fifth", I hear 5, so I tend to think that there are 5 semitones or 5 tones, when there are in fact 7 semitones in a fifth... Admittedly, there is a logic behind these names: they are named in relation to the position of the note in the C major scale.

 Now, I am not going to change the way millions of musicians call intervals, but as a coping strategy I memorized the table above and mentally translate an interval name into its number of semitones.

Application to the guitar fretboard

The guitar fretboard is divided in semitones, which means that we can again do simple arithmetic to work out how to play the major scale in any key.
The standard guitar tuning is E A D G B E, from the 6th (biggest) string to the 1st (thinnest) string. Using the clock diagram above, this tuning translates into 4 9 2 7 11 4 in the clock notation.
By subtracting these numbers in pairs, we can work out the intervals between the strings:
  • Between 6th and 5th: 9 - 4 = 5 semitones
  • Between 5th and 4th: 2 - 9 = -7, -7 + 12 = 5 (when we obtain a negative number, add 12)
  •  ...
  • Between 3rd and 2nd: 11 - 7 = 4 
  • Between 2nd and 1st: 4 - 11 = -7, -7 + 12 = 5
  • 4 5 9 5 2 5 7 4 11 5 4
We can see that the interval between two strings is 5 semitones, except between the 3rd (G) and 2nd (B) strings, where we have 4 semitones. This is why some people prefer to tune their guitar in "All fourths" (5 semitones between every string), or in "Major thirds" (4 semitones between strings).

Using this knowledge, let's play the 5 (F) major scale on the guitar. As mentioned above, the intervals of the major scale are 2212221.
  • We need to find the root note of the scale, 5 or F or Fa. The 6th string of the guitar is the note 4 (E). So if I press the 1st fret, I am going to play a 4 + 1 = 5 (F)
  •  The second note of the scale is 2 semitones above the root, so I play the 1st fret + 2 semitones = 3rd fret
  • The third note is again 2 semitones above the previous note. I can play the 3rd fret + 2 semitones = 5th fret on the 6th string. But since the 6th and 5th strings are separated by 5 semitones, I can also play the 5th string open, because 5th fret - 5 semitones = 0
  • The fourth note is 1 semitone above the previous note. We play it on the 0th fret + 1 semitone = 1st fret of the 5th string.
  • ... and so on. When your fingers are stretching, you can play a note on the following string if you subtract 5 to the number of frets, or 4 if you are going from the 3rd to 2nd string. 
The result is the following:
This means that you no longer have to rote learn the major scale in all keys and in all positions. You just have to remember three things and you can work it out !
  • 2212221, the intervals of the major scale
  • 4 9 2 7 11 4, the standard tuning of the guitar
  • When you speak with other musicians or read partitions, you need to know the correspondence between note letters and note integers: C D E F   G A B C => 0 2 4 5   7 9 11 0
As an exercise, try to use this trick to play a 8 (G#) major scale, starting on the 4th string.

In my next post I will explain how to find and play chords using the clock notation.