Building intervals & chords

I am assuming that the reader has read the last article and is ready to embark on our project of understanding how to work with chord and scale structures and use the chord symbol system. Initially, I am endeavouring to explain, as clearly and simply as I can, some basic steps and would ask those of you with more advanced knowledge to be patient with me.

Please do write and play the notes and exercises, as indicated, as this really does help speed up the learning process.

We begin by saying that in traditional western music we use 12 different pitch sounds but employ only 7 names (A B C D E F & G) to describe those sounds. In order to encompass the 12 pitch sounds we modify the 7 names and produce Ab, D# etc. To clarify this point, make a circle

Ex.1

and divide it, like a clock face, into 12 equal segments.

Ex.2

Now distribute the 7 note names ABCDEF&G according to the following scheme

Ex.3

If we start with A (but we can start with any note) and move around the clock, in either direction, the 8th note is always the same as the first note giving rise to the term Octave, or 8th. If we move clockwise, we can consider ourselves going up in pitch; if we move anti-clockwise, down in pitch. We can now see that

between A&B there are 2 segments

between B&C there is 1 segment    

between C&D there are 2 segments    

between D&E there are 2 segments    

between E&F there is 1 segment    

between F&G there are 2 segments    

between G&A there are 2 segments

When there are 2 segments between one note and its neighbour we call that interval a tone; when there is only 1 segment, we call that interval a semitone, or halftone.

The semitone is, therefore the smallest step, or interval, that we can make. On the guitar this step is equal to a move of one fret. A move of one segment on the clock is equal to a move of one fret on the guitar; a move of 2 segments equals a move of 2 frets and so on round the clock or up and down the fingerboard.

In the scale which we call C Major there are no modifications to the 7 note names. Being thus simpler than other scales we shall use it for our first example. Start on C and write out the scale by moving clockwise round our circle.

Ex.4

Now number the notes 1234567.

Ex.5

Thinking in terms of the 7 note names, D is the second note from C. E is the next or second note from D etc. The scale can be said to be constructed in 2nds.

This time write out the same scale but over a span of 2 Octaves 

Ex.6

numbering the notes 1 to 15

Write it yet again, over 2 octaves but omitting each 2nd note and writing only every 3rd note.

Ex. 7

We can now say that we have constructed a scale in 3rds instead of 2nds. If we examine what we have, we see that there are the same notes in our final scale of 3rds as there are in our original one octave scale of 2nds. In effect the scale in 3rds can be considered as a scale of 2nds in an expanded form.

Ex.8

With this in mind we can state that in traditional western music the harmony has been constructed in 3rds and understand that chords have evolved from scales laid out in an expanded form. We can realise that a scale and a chord are not two separate things but one series of notes looked at in two different ways. Traditionally, if we play the notes serially we conceive them as scale, if we play the notes simultaneously, we conceive them as a chord structure.

Let us now write out again the scale of C in 3rds and number the notes 1 3 5 7 9 11 & 13.

Ex.9

The 7th is the 7th note from the starting point in our original scale; the 9th is the 9th and so on. We have here the principle on which the chord symbol system is based. The root note of each and every chord functions as 1 and the other notes are named in accordance with their distance from that root note. The complications arise because (if we now refer back to our clock face) some 2nds comprise of a 2 segment interval (A to B) and others of a 1 segment interval (B to C). Therefore B functions as a 7th from C and C functions as a 7th from D. If we count the segments from C to B, we find 11 of them, but from C to D, only 10.

The complications in the chord symbol system result from trying to define 12 different sounds with 7 note names. Rather than bury ourselves in theory and explanations I feel, at this point, that we would better turn back to the music and let the musical examples explain themselves.

The first chord in the piece Teardrops is described as D minor 7th Dm7 and comprises the notes D F A & C. To understand why we must now refer back to our clock and write out the 7 notes over 2 octaves and starting on D. Thus

Ex. 10

= D minor 7^th (Dm7)

Remembering that we build chords in 3rds we find that we have D F A C E G B numbered as 1 3 5 7 9 11 & 13. Reading the first 4 notes in the series we have D F A & C. These are the notes of the first chord of the tune and that is why we defined the harmony as Dm7. We shall now analyse the symbol Dm7 after which you will be able to construct your own minor 7ths on any root note. Let us go back to the clock.

Ex.11

We start on D and describe the interval between that note and F. We know that the step from D to F is a 3rd, but we now ask what kind of 3rd. If we count the segments from D to F we see that there are 3. We now state that an interval of 3 segments is known as a Minor 3rd. From F to A makes the next 3rd, but when we count the segments between F and A we count a distance of 4 segments. To distinguish this 3rd of 4 segments from the 3rd of 3 segments we call the interval a Major 3rd. Minor equals lesser and Major equals greater, therefore the smaller interval is the Minor 3rd and the greater one the Major 3rd.

We now have a triad (3 notes) consisting of D F & A looking at the notes and consisting of a minor 3rd plus a major 3rd looking at the intervals between those notes. This pattern of a minor 3rd plus a major is the pattern for all triads described as minor triads. Using our clock as an aid, we should now construct minor triads on all of the 7 note names. Copy the D minor triad to use as a model and then build 6 other triads structured 3 segments plus 4. First of all build triads on each note of the scale

Ex. 12

Comparing the musical notation with our clock we read DFA as described in Ex. 13 (a) EGB follows the same scheme (b) the next one FAC (c) poses a problem as the distance from F to A is 4 segments not 3 and the distance from A to C is 3 segments not 4. In this instance we modify the note name and lessen the interval to make it 3 segments. We add a b sign to the A to make it Ab and which brings it down one segment and therefore 3 segments from F, producing a minor 3rd from that note. Because we are working with a closed circle the second interval from A to C, a minor 3rd, is now Ab to C, 4 segments, a major 3rd, and is automatically corrected.

Ex.13  (a) & (b)

   Ex.13 (c) & (d)

Ex.13 (e) & (f)

 Ex.13 (g)

GBD follow the same modification as FAC (d) ACE runs like D minor and E minor and needs no modification (e) BDF consists of 3 segments plus 3 segments. We therefore increase the second interval by adding a # sign to the note and moving on one segment, producing BD&F# .(f)

CEG needs the same process as FAC & GBD, that is lessen the first interval to produce C Eb G. (g)

We now know 7 minor chords and we must start to use them. The practical work now is to learn to play them anywhere on the guitar. I would suggest working each chord separately, treating it as a block chord of 3 notes and then as an arpeggio. Start on the 6th string and find the chord notes on that string, then find one of the notes on the 6th string and look for the other notes on other strings. Then start on the 5th string and repeat the process, then continue across all strings.

As you work this way you will find that some of the patterns will attract your interest more than others. When this happens you are beginning to tune yourself into your own biases and preparing the way for your own improvisations and inventions.

Next time we shall continue our examination of the minor chord and add on the 7th.