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Diatonic Music

Much of Early Western harmony is based on Diatonic chord patterns. A typical song has at least two levels of structure. In addition to the melody, there is also a chordal structure. This means that the melody tends to "linger" in the vicinity of certain particular notes for a period of time. For instance, a section of melody that tends to emphasize the notes (1,3,5) will often be harmonized by a chord containing these same notes. Since such a chord is composed of the overtones of the note (1), then it is also common for 1 to be emphasized in the bass line for that portion of the melody.

The simple diatonic triads (three note chords) in the key of D are as follows:

*Name* *Symbol* *Notes*
D major I [1 3 5]
E minor ii [2 4 6]
F# minor iii [3 5 7]
G major IV [4 6 1']
A major V [5 7 2']
B minor vi [6 1' 3']
C# dim vii-dim [7 2' 4']

Each chord is created by skipping notes in the major scale. For the V (five) chord, start with 5, skip 6 and include 7, then skip 1' and include 2'. The name of the chord is the first note of the triplet. It is called major if the interval between the first and second note of the chord is a major third (4 half-steps), or minor if the interval is 3 half-steps (a minor third). For all of the chords except the vii-dim, the interval between the first and third notes is a perfect fifth (seven half -steps). For the vii-dim chord, the distance between the first two notes is a minor third, and the distance between the first and third note is a flat-fifth (6 half steps).

In early western music, this flat-fifth interval was called the "sound of the devil", diabolos, and was considered extremely discordant. This interval is now called the "tritone" because when it occurs in a melody, it sets up a strong "fork" in the possibilities of the future harmonic development. You can either resolve the dissonance by going up a half-step to a perfect fifth, or by going down a half-step to a perfect fourth. Both these possibilities are nearly equally compelling and, for the early musical mind, created an unacceptable "dilemma" (eg: two-horns). The roman-catholic church actually banned this interval from all church music for a time.

Here's a question for the advanced thinker. Can you craft a chord progression using the tritone that can resolve into multiple places equally plausibly in any context? In other words, much modern harmony tries to "control" the tritone to trim the mind into one course, the desired harmony. What if we were less controlling? Could we make a phrase that is as equally probably continued to two different possible phrases? How balanced could it possibly be made assuming the 12 tone scale?

This is similiar to the problem of parallel fifths. THis is normally dissallowed as all chords except the vii-dim have fifths between their outer two notes. If the harmony creates other parallel fifths then the harmony becomes ambiguous. This was to be avoided at all costs unless both harmonizations were reasonable. Then you have good art.

Typically, the vii-dim chord doesn't usually show up by itself. It is usually disguised by adding one more note to the chord: changing from [7 2' 4'] to [5 7 2' 4']. You can see that this makes it into a V chord with an added note, the [4']. So you can think of this new chord as a kind of V chord. The extra note is actually the b7 in the V key, so the chord is called a V7 chord. Transposed to its fundamental position, this chord is [1 3 5 b7]. The tritone is hidden in the interval between [3 b7]. The presence of the new 5 note in the V7 chord helps the ear to anticipate a strong resolution back to the I chord. In other words, the tritone is used to add tension to the V chord which is then released by playing the 1 chord. The ambiguous possibilities of the tritone are tamed by making one of the "forks" very strongly preferred. So [5 7 2' 4'] is resolved to [1 3 5].

OK. So what can we do with this?

Most popular western music: blues, folk, jazz, pop, and rock is written as a melody with chords. Usually the right hand of the piano plays melody, and the left hand plays a skeletal chord structure which tries to keep a rhythmic pulse, and to spell out the changes of the chords.

On the erhu, it is possible to improvise by knowing (or hearing) the implied chord structure and playing phrases which emphasise these chord tones, and lead the listening ear from one chord to another in a plausible way. To be able to do this, one needs to be completely fluent in producing arpeggios of any possible diatonic chord, and to be facile in moving from one chord to another without difficulty.

Here are a few exercises that make a start in that direction:

All possible diatonic triads:

First, lets arrange them in a order in which all the notes change from chord to chord:

  1 3 5
  2 4 6
  3 5 7
  4 6 1
  5 7 2
  6 1 3
  7 2 4

Unique Progression by changing three at a time:
(moves scalewise: seconds/sevenths)

I        ii      iii     I       V       vi      vii(dim)      I
135      246     357     461     572     613     724           135

Notice that every triad shares *no* notes with either the chord before it, or the chord following. This is a progression through the diatonic chords by major/minor seconds or sevenths. You can practice these chords in the forward direction:

D(15) 4/4:

 1 3 5  1  |  2 4 6 4   |  3 5 7 5  | 4 6  1' 6 |

 5 7 2' 7  |  6  1' 3 1 |  7 2' 4  2 | 1 3 5  1 |

For completeness, learn them also in the reverse order:

 1 3 5 1        |  7 2 4 2  |  6 1 3 1  |  5 7 2 7  |
 4 6 1 6        |  3 5 7 5  |  2 4 6 4  |  1 3 5 1  |

Make sure and practice other arrangements of the notes (and different octaves) as well:

  5 3 5 1'  |  2' 2 5 7 | 1' 1 3 6 |  7 5 2  5 |
  6 4 6 1'  |  7 3 5  7 | 6 2 4  6 |  1' 5 3 5 | 1 - - -

In similiar manner, you can make up exercises to study the other two arrangements of diatonic triads.

The second ordering is where exactly one note changes at a time:

  6 1 3
  1 3 5
  3 5 7
  5 7 2
  7 2 4
  2 4 6
  4 6 1

Unique Progression by changing one at a time:
(moves by sixths/thirds)

I         vi     IV      ii      vii(dim)    V       iii     I
135      136     146     246     247         257     357     135

This is a progression by major/minor thirds or sixths. Practice these triads in both ascending and descending order.

The final ordering is where exactly two notes change from chord to chord:

  6 1 3
  2 4 6
  5 7 2
  1 3 5
  4 6 1
  7 2 4
  3 5 7

Unique Progression by changing two at a time:
(moves by fourths/fifths)

I        IV      vii(dim)     iii     vi      ii      V       I
135      146     247          357     613     624     257     135

This is a progression by major/minor fifths/fourths.

Here is a midi file that goes through the above progression, one 4/4 measure per chord:

[MIDI]

And here's the same thing as an mp3 file with the pattern repeated 8 times:

[(key of D) MP3]

Improvisation ideas:

 I                  IV                vii(dim)
 1 2 3 4 5 6 7 1  | 4 5 6 7 1 2 3 4 | 7 1 2 3 4 5 6 7 | ...

In other words, play scale fragments starting on the note of each chord. Notice how the dominant beats of the scale spell out chord tones. You can use this technique for creating very intricate melodic passages based totally on scale fragments.

---

The three exercises of chord changes by seconds.sevenths, thirds/sixths, and fourths/fifths, *completely* cover all possible transitions from every diatonic chord to every other chord. If you learn these fluently, you'll be much closer to sight-reading the chord charts for most "simple" western music.

Jazz expands on this concept by moving in and out of other keys. For jazz, you'll also need to be comfortable playing non-diatonic chords such as bV, III, II, i, etc. This is a more sophisticated stage, and is most easily approached after a thorough mastery of diatonic harmony. (phylogeny recapitulates ontogeny).


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Last edited January 23, 2007 5:59 pm by h-66-167-204-147.snvacaid.dynamic.covad.net (diff)
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