Reciprocal notes

If you take any note it can be paired with another note to 'add up' to an octave.

For example if you play a G note, then a fifth above that is D and a fourth above that is G again.

Here are the pairs:

b2   7
 2  b7
b3   6
 3  b6
 4   5
b5  b5
 5   4
b6   3
 6  b3
b7   2
 7  b2

In fact you only need to learn this up to the flat 5, because above that it's the same pairs of notes—the notes are just switched.

It's also interesting that there is a symmetry to the pattern, which may help you to remember it more easily.

The Circle of Fifths 4

So what happens with the key of F# or Gb then? These key signatures are a special case because they are written with 6 sharps or flats, but there are only 5 sharps or flats available. There are some very good related reasons why this happens:

1. Firstly in written music each letter is used exactly once in a key signature—the thing that varies is whether a note is natural, sharp or flat.


2. So, in the F# key signature the leading tone (i.e. maj7) of F# is F, but we use E# instead of F to avoid having both F# and F natural notes present which would make the written notation more confusing than it needs to be.


3. Likewise in the key of Gb we avoid having to name the 3rd and 4th degrees as Bb and B by using Cb instead of B.

This is how they look on the staff, F# first:

And the Gb key signature:

The Circle of Fifths 3

To use the circle of fifths to show how the flat key signatures relate to one another, you need to move one step around backwards around the circle from C to F, the relationship between these two as modes of C major is this:
C: 1 2 3 4 5 6 7
F: 1 2 3 #4 5 6 7
So the difference between Ionian mode and Lydian mode is one note: the fourth which is a perfect 4 in Ionian and a sharp 4 in Lydian. If we decide to play in the key of C there are no sharps or flats, and in the key of F there is one flat which is produced by taking the sharp 4 of F Lydian (a B natural note) and lowering it a semitone to become the perfect 4 of F Ionian which is a Bb note.

The key signature for F major has one flat and that is indicated on the B bar of the staff (image to come) to show that the key of F major has one flat (Bb) and all the other notes are natural. This works the same way as the keys progress around the circle of fifths: each successive key signature adds a flat note as the perfect 4 note of the new key. So going another step backwards around from F to Bb adds the Eb note to the key signature—we keep the Bb from the previous key (obviously because it becomes the tonic in the new key). The further back around you proceed in steps of a fourth, the more flats get added:

C: no sharp
F: 1 flat  (Bb)
Bb: 2 flats (Bb - Eb)
Eb: 3 flats (Bb - Eb - Ab)
Ab: 4 flats (Bb - Eb - Ab - Db)
Db: 5 flats (Bb - Eb - Ab - Db - Gb)

You'll note that the flats shown above in the order they appear on the staff in a key signature are all mapped out in the same order in the circle of fifths (image to come).

So what happens with the key of Gb? Well that is a special case which I'll cover in another post.

The Circle of Fifths 2

One of the many interesting things about the circle of fifths is that it can be used to show how all the key signatures relate to one another. If you move one step around the circle from C to G, the relationship between these two as modes of C major, the Ionian mode (with a root of C in C major) and the Mixolydian mode (with a root of G in C major) is this:
C: 1 2 3 4 5 6 7
G: 1 2 3 4 5 6 b7
Looking at just the intervals in these two modes the difference is one note: the seventh which is a major 7 in the Ionian mode and a flat 7 in the Mixolydian mode. If we decide to play in the key of C major there are no sharps or flats, and in the key of G major there is one sharp which is produced by taking the flat 7 of G Mixolydian (an F natural note) and raising it a semitone to become the natural 7 of G major (Ionian) which is a F# note.

The key signature for G major has one sharp and that is indicated on the F bar of the staff (image to come) to show that the key of G major has one sharp (F#) and all the other notes are natural. This works the same way as the keys progress around the circle of fifths: each successive key signature adds a sharp note as the major 7 note of the new key. So going another step around from G to D adds the C# note to the key signature—we keep the F# from the previous key because it becomes the major 3rd note in the new key. The further around we go in steps of a fifth, the more sharps get added:

C: no sharp
G: 1 sharp  (F#)
D: 2 sharps (F# - C#)
A: 3 sharps (F# - C# - G#)
E: 4 sharps (F# - C# - G# - D#)
B: 5 sharps (F# - C# - G# - D# - A#)

You'll note that the sharps shown above in the order they appear on the staff in a key signature are all mapped out in the same order in the circle of fifths (image to come).

So what happens with the key of F#? Well that is a special case which I'll cover in another post. But for the very next post I'll show how the above process works to produce the key signatures that contain flats by going the other way around the circle in fourth intervals.

The Circle of Fifths 1

It will take a couple of posts to cover this I guess—not that it's that complex, but for me the explanation is a work in progress so I'll take my time with it. I also need to develop some images to show what it's all about, and it will take a bit of time to do that. So, what is the Circle of Fifths?

If you start on a given note then go to the next note a fifth interval away, and keep repeating that you will eventually play all twelve notes and end up back at the note you started with, hence the circle of fifths. You can use fourths too seeing as they're related intervals as a kind of reciprocal—but that's a topic for another post.



So usually the circle of fifths is taught starting from C, which is important when covering key signatures, but here's a tip: it's a tiny bit easier to remember if you start a fourth away from C on F:

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

Rearranging this into two rows, you will observe that once we get to B the sequence of notes repeats as sharps:

F  C  G  D  A  E  B
F# C# G# D# A#

Starting on F gives us all the natural notes, then the first 5 repeated as sharps covering all 12 notes quite neatly and in a way that is easier to remember.

Back-cycling is the term that is often used to describe traversing the circle of fifths in the other direction, which is in fourths. For reasons that will be made clear in a future post on the circle of fifths, the accidentals are described using flats rather than sharps when back-cycling.


Again when taken from C it is used for describing a logical progression of key signatures, but it is a bit easier to remember the sequence starting two fourth intervals around on B flat:

Bb Eb Ab Db Gb B E A D G C F Bb

Again the reason this is easier to remember is that once we've covered the 5 flats we get the same sequence of notes as natural notes:

Bb Eb Ab Db Gb
B  E  A  D  G  C  F

You will find it very valuable to be familiar with the Circle of Fifths no matter what the starting note is, proceeding in fifths or fourths, and using both sharps and flats.

E flat pentatonic

You may be familiar with the pentatonic scale - a lot of guitarists learn this early on. Here's a typical fingering of the minor pentatonic pattern in E flat:

Why E flat though? Well this scale in this 'key' uses all the accidentals—the sharps or flats—and no natural notes. Here it is with all the notes:

Its a handy thing to keep in mind when learning the notes on the fretboard.

Learning all the notes on the fretboard

OK, it's been a while since I posted anything on this. To summarise what I covered previously:

1. Learn where D is everywhere on the fretboard
2. Use that to see where B, C, E and F are (hint: they have symmetry around D)
3. Learn G#/Ab, as this is the flipside to D—the same sort of axis of symmetry applies to G#, and this also establishes the tritone relationship

So where to from here? I would suggest the following:

1. Use your knowledge of the location of G#/Ab to learn G and A seeing as they are only a semitone below and above. You should now know all the natural note locations.
   
2. You can learn the sharps/flats by their relationships to the natural notes, and I recommend the following:
   
   • that you learn the notes immediately either side of D, so that covers C#/Db and D#/Eb
   • then you should learn the sharp/flat notes either side of G#/Ab, which are a tone above and below at A#/Bb and F#/Gb respectively

Remember that becoming aware of the symmetry is that exists alongside the note names can really help to remember the note relationships and locations.

There are a couple of other helpful things to investigate including becoming familiar with the distinctive tritone pattern occurs on the 4th and 7th degrees of any major scale—so in C major that's F and B. There is also an interesting relationship with the Pentatonic scale which I'll cover next time.

2 string modes: Locrian

Lucky last locrian:

2 string modes: Aeolian

Same deal as last time—the fourth degree is marked in blue as you would usually choose to play one or the other.



Note the nice symmetry in the Aeolian mode when it is shown this way.

2 string modes: Mixolydian

The Mixolydian mode as a pattern that repeats every 2 strings:




And here both of the above patterns are combined. The blue coloured notes are the 4th degrees of the scale, so typically you would play only one of each in a scale or arpeggio because they are the same notes (they're enharmonic):

As I stated a while ago, this is actually a feature of these 2 string modes—the 4th degree is immediately before/after the string crossing so you have the option to play it wherever it suits you.

2 string modes: Lydian

The next mode is Lydian. With all 7 notes on 2 adjacent strings the pattern repeats identically in each octave:




Personally I prefer the 2nd pattern which places the semitone steps at the string crossings. Note that with the scale of F Lydian all the notes are natural (i.e. from C major).

2 string modes: Phrygian

Two patterns for the Phrygian mode:





Note that the pattern repeats over pairs of adjacent strings.

2 string modes: Dorian

A while ago I posted a major scale pattern that covered an octave on 2 strings. A big advantage of this is that the pattern can be repeated across the fretboard without alteration to cover 3 octaves in total.

This can be applied to other scales or modes of course, so here's the first which is for the Dorian mode:





You can see that it's possible to finger this 2 ways depending on which of the two strings you choose to play the 4th degree of the mode. There are a number of places to make the position shifts, and you may choose to alter these depending on if the notes are ascending or descending.

The other cool thing about learning these 2 string groupings is that it's really easy to just locate the root of the mode wherever you like on the neck and play with the 2 string pattern from there— the only one that's different is when the root is on the G string (just shift the 2nd string notes up a semitone).

That pesky B string

This is just a short post to explain how I think of intervals that cross the G and B strings on the guitar. You can apply this to intervals in chords, scales, arpeggios or just for intervals themselves (aka: diads).

As you probably know the standard guitar tuning uses 4 semitones between the open G and B strings which is different to the usual 5 semitone interval that exists between all the other adjacent open strings. This gives a major third interval between the G and B strings as opposed to the usual fourths based tuning between the other adjacent strings.

You apply these rules where the lowest note of an interval is on the G string or lower, and the high note is on the B string or higher:

• if the target note is higher, then the note on the higher string is 1 fret higher than usual


• if the target note is lower, then the note on the lower string is one fret lower than usual

Simple isn't it?

Putting the patterns together

Here's a picture showing relationship between the two major scale patterns discussed previously:



These are in C major, so the notes are all the natural notes. The pattern with the green background has root notes on the 1st and 6th strings—I'll refer to this as pattern 1. The pattern with the blue background has root notes on the 2nd and 5th strings—I'll refer to this as pattern 2.

More major scale patterns

The last post about showed an F major scale and highlighted the use of an easy major scale pattern and how that pattern sits between what I have called the tritone pattern. F major differs from C major by 1 note—the B which is flattened in F major and obviously is natural in the C major scale which uses only the natural notes. In the following picture the difference between the pattern for F major (from the previous post) and the pattern for C major can be seen where I've raised all the green notes up a semitone:



Learning the C major scale would be valuable step in learning all the notes on the guitar fretboard. Here's a version of the above pattern with a few tweaks to clean it up a bit:



This pattern is also framed by the tritone pattern at each end, and because of that there are duplicate notes present. Typically if you were playing this as a scale you would choose to play only one of the duplicates in each octave. So it could be played in two obvious ways:





This pattern and the one from the previous post can cover the entire fretboard. They can just be stacked up using the common notes from the tritone pattern at each end. Hopefully I'll get around to showing this in the next post.

And for my next trick...

You can see that the major scale pattern I described in the last post can be combined with the tritone pattern from the post before that to get this:



The green notes are the 4th degree, while the blue coloured notes are the 7th degree of the major scale. A thicker border around one of these coloured notes indicates that it's part of the major scale pattern.

The easiest major scale pattern ever

I was checking out an instructional DVD from Paul Gilbert and in it he shows this great way of playing the minor blues scale which is a pentatonic minor with the flat 5 added to get 1, b3, 4, b5, 5, 7. Here's a picture of the pattern over one octave on two strings:



You can see that this contains some stretches, but I like the way it's easily repeated over groups of 2 strings:



So we have one 6 note pattern which is identical on pairs of strings 6-5, 4-3, and 2-1. It's so easy to remember, and the concept can be applied to other scales too such as the major scale:



Here's the entire pattern covering 3 octaves:



Also note how this pattern has a bonus characteristic that all notes on the same string are a tone apart. The semitone intervals occur where the pattern goes to the next adjacent string. This makes it super easy to remember.

More on the tritone

So, following on from the last post, if you string together the tritone across the fretboard you get the following pattern:



And the other cool thing is that it occurs twice in any given 12 fret span:



You may also note that this contains the octave patterns that I posted on previously. But the absolute best thing about this pattern is that it directly relates to a number of chords and modes:

• the major third and flattened seventh tones in a Dominant 7 chord, which also directly relates to the Mixolydian mode (the chord is built from the root of the mode and is unique to the mode)
• the root and sharpened fourth tones in a Major (#11) chord and any related chord variations—directly relates to the Lydian mode (chord is built from the root of the mode and is unique to the mode)
• the root and flattened fifth tones in a Diminished chord where the related mode is Locrian (same same)

There are other relationships, as this pattern must occur in all modes, although some of the related chords are quite dissonant or uncommon. Still, I'll map these out in a future posting once I get my head around this.

The other, other magic note

Some readers may have realised that the symmetry associated with the D note* must have a counterpart. That note is G# or Ab, which is the place where the musical alphabet wraps around. It has a special relationship to D which is a flat 5 (or sharp 4), which places it exactly half way between an octave span from one D to another. Here's an image of the piano keyboard showing the symmetry around G#/Ab:


* see the original 'magic note' post

Here are a couple of images showing the physical relationship between D and G#/Ab on the fretboard (note that the nut and 1st fret are not shown):





That relationship should make it easier to learn where all the G#/Ab notes are in relationship to D as it is almost always either 1 string and fret higher or 1 string and fret lower. The only catch is when going between strings 2 and 3 (the G and B strings) where the guitar tuning makes the span 2 frets rather than one:

The easiest octave pattern ever

When learning where each instance of a note, such as D, is on the fretboard its handy to know the relationship of that note on any string to the all the other occurrences of the note, either the same note or the note in other octaves.

There's an easy to remember pattern that covers the same note over two octaves. The same pattern can be used to cover strings 5-3-1 (A-G-high E) as a group and 6, 4 and 2 as the second group (low E-D-B). Here it is with its lowest note (A#) on the A string:



And here it is with its lowest note (A#) on the low E string:



You can see that the notes (and your fingers) maintain the same relationship in each pattern so it's easy to remember. I list the 5-3-1 version first because the note on the 1st string will set you up for the 6-4-2 version which starts on the same fret. Here's the whole pattern with the notes on strings 1 and 6 highlighted:



Next, to get between the notes on strings 2 and 5 (the B and A strings), the note on the 5th string is two frets higher. Here's the pattern (using F this time) with that relationship highlighted:



Best of all this covers every string and every instance of the note within a 12 fret span. The only catch is where the nut lies in relationship to the notes you're looking at, so you need to be familiar with using this pattern from any note within it.

The 'magic' note

I've been playing guitar for quite some time—in the order of decades now—and the amazing thing is I still keep discovering things about music and the guitar. Recently I've been trying to sharpen up my knowledge of the fretboard using the Guitar Fretboard Workbook by Barrett Tagliarino. It's a good resource, from the Musician's Institute Press so you know it's from a respected source etc. But, you won't find this tip about the 'magic' note in there.

Now I've been wondering why it is that this idea which is quite obvious when you finally realise it's there, seems to be elusive for guitarists to see. I think there are two reasons:

• firstly the musical alphabet tends to be taught with C at the centre of it's universe


• secondly, the alphabet we learn in English at school starts with the letter A

These ways of thinking about the note names can tend to obscure the idea of symmetry and the musical notes. Now I'm assuming you already know the names of all 12 notes commonly used in the Western musical system. If you don't it would be beneficial to find that out ASAP if you are serious about learning more about playing music.

Eventually you will want to learn the names and positions of every note on the guitar, but you have to start somewhere. And I think that particular somewhere is D. That's the 'magic' note. So the note you should really learn in every position on the neck is D, and the reason why is the symmetry that shows up when you look at it in relationship to the other notes, particularly the pairs B-C and E-F which sit below and above D in pitch. Lets look at a diagram of one octave on the piano keyboard:


I made this up to show the symmetry around D, and to emphasise that the tricky notes B, C, E and F straddle the note D in a symmetrical relationship. Here's how those five notes look on the guitar just focussing on one string only:


Those notes are tricky because between B and C there is no B#/Cb, and between E and F there is no E#/Fb (see note below), so learning D will essentially help you to learn four more notes on the fretboard more easily. That is why I consider it's an advantage to learn D: because it helps to learn about these other quirks of the musical alphabet more easily.

This idea leads on to a few others which I will cover in the next couple of posts, so stay tuned in.

Note: B/C and E/F are separated by a semitone (one fret apart on the guitar) whereas every other natural note is separated from it's neighbouring natural notes by a whole tone. All the accidentals (the sharps/flats) are also separated from their neighbouring accidentals by at least a whole tone.