'intervallic density' (chord theory)

[pianomankris]

Hey guys

OK - some theory regarding chords, and why a certain amount of notes are required for the use of the word 'chord' to be valid.

First issue - why are three notes a chord, but two notes aren't? (PS as an aside, two notes are known as a 'double-stop', or a 'dyad').

It is all to do with the amount of harmonic intervals the ear hears. A harmonic interval is simply the technical term for what we hear when we hear sounds together.


Let's take the C major chord - the notes are C E G.

The ear hears three different combinations of sounds. It hears the C - E, the C - G, and the E - G (try playing the chord, then the separate intervals).

This chord therefore has three different harmonic intervals (all three note chords (triads) have three harmonic intervals).


The true definition of a chord is 'sound that contains more than one harmonic interval'.


Let's go back to just two notes (e.g. a double stop).

C - E, for example. Even though we have two notes, we only have one interval. This is why two notes aren't a chord.

But they aren't a single sound. They have a 'harmonic content' (as a harmonic interval is present). Hence two notes played together has its' own special name.





OK - harmonic density means how many intervals there are in a chord.


Let's take a 4-note chord.

C - E - G - B is a basic 4-note chord (C major 7). Play this chord, then play all the harmonic intervals separately. The harmonic intervals are:

C - E C - G C - B E - G E - B and G - B.

So, even though this chord only has one more note than the basic triad (3 note chord), it has 6 intervals. Therefore, it has twice the harmonic density.

This is why 4-note chords sound very 'warm' in comparison to basic 3-note chords.





There is a basic algorithm for working out the harmonic density of a chord (rather than the long way of counting each interval).

The algorithm is this:

multiply the number of notes in the chord by the number before it, then divide this answer by 2.


So, for a 3 note chord, we would multiply the number of notes (3) by the number before it (2), then divide by 2.

So, 3 x 2 = 6; divided by 2 = 3.


For the 4-note chord, this would give us 4 x 3, which is 12. Then divide this by 2 - hey presto - we have 6.

This basic function is handy for working out the amount of harmonic intervals in a chord.




So, without doing all the working, we could calculate the harmonic density of a 5-note chord.

5 x 4, which = 20. Then divide this by 2. Which = 10. A 5-note chord contains 10 different harmonic intervals.





OK - so how does this apply to 'real world' music? Well, jazz uses this a lot. The reason jazz chords sound so 'warm' is to do with the harmonic density of the chords used. The denser the chord, the more intervals the ear hears. The result of this is that the sound sounds 'thicker' in a more harmonically dense chord (usually referred to as 'warm' sounding).

Jazzers use this to highlight certain chords e.g. they could play a passage using 4-note chords, then play a 6-note chord. The 6-note chord would really stand out, as it is far more harmonically dense than the 4-note chords that are around it (e.g. the 4-note chords contain 6 intervals, whereas the 6-note chord would contain 15 intervals. It would obviously satand out when seen like this, as it has more than double the harmonic density, even though there are only two extra notes in the chord).


Some people were asking about jazz theory. Even without actually learning jazz at the piano, this alone should help in understanding the nature of jazz chords, for when we do come to learn them. Which won't be far away.


Any questions, fire away. I realise this may be a little complex at first.

Cheers

Kris

 

[pianomankris]

PS harmonic density and intervallic density are more often than not used to mean the same thing.

Just assume they mean the same thing, and don't be confused by the interchange of these terms.

 

[pf]

Hey pianomankris, wow...I didn't know all those terminology before.

But that makes me understand how important are my voicings. I suppose you would explain about voicings next?

 

[pianomankris]

Forgot to add the mathematical formula for calculating intervallic density.

Here it is:

(n X (n - 1)) ÷ 2

With 'n' being the no. of notes present in the chord.


Kris

 

[kongwee]

For me quite confusing, but it is other way to look at chords. I don't play jazz of cos. Normally, I treat 5 or 6 note chord as double 3-note chord. Most of time I'm play 1-5-8 or 1-7 on left and run some scale note to do some fill in. Right hand will comp with a full chord with first note of the melody line, if the melody is fast, I will harmonize with 3rd or 4 interval. Too fast have to have be single note.

However, my new technique of left hand is to try to jump 1-10 or 1-12. It will force my hand to take new position and allow other combined of note to run. Next chord my 5 finger will finger the nearest root and will not jump. In a 4 bar phase, I have mixture of "heavy" root and "light" root.

 

[pianomankris]

Kongwee - compound intervals in the LH (e.g. root and tenth) is very common is jazz (as i'm sure you'll know) - especially in early jazz.

In jazz they usually also think of 6 note chords as two different chords.

My point isn't that jazzers don't think that way (as most of them do), but rather, to show why jazz chords sound 'thicker' than 'standard' chords, rather than discussing the actual intricacies involved in creating jazz voicings.

Once the theory of this is understood, it helps in understanding how certain chords can be emphasised purely through harmonic content.


PS the 1 - 10 you refer to would generally be known as an 'open' voicing, as it is a stretched-out shape in the LH. Open voicings are usually large voicings, and the hands can be far apart, whereas 'closed' voicings are chorde where the hands play the notes almost as a continuation of each other e.g. hands beside each other, and no large stretches (e.g. all notes in order, rather than inverting any voicing).

Hope that helps.

PS i'll start a jazz thread, since there seems to be an interest for it here.

 

[Unconscious]

Dear Kris,

This is cool, I never knew that harmonic density was a mathematical concept. Thanks for the information!

However, I cant help but think (and this is with all due respect) that your post is just a roundable way of saying, the more notes you play, the denser the sound. That would an intuitive statement, wouldnt you say?

I am sure there is more to the concept of intervallic density than just the simplistic conclusion I made here. Perhaps we could draw from this the principle that, in a performance, we can aim to vary the intervallic density of our voicings so as to keep things interesting throughout the song. Would that be a reasonable approach using this concept?

Write on dyad! I mean, dude! :-D

 

[pianomankris]

lol

Yes, it is a full explanation for why more notes sound denser.

But - and this is important - it has to be different notes. Octaves/unisons don't count I'll explain why in another thread. It is to do with the waveform.

So, a basic C major chord voiced as (LH) C G (RH) C E G would only be classed as three separate notes, even though there are 5 different pitches.

This is where things get more complex

 

[[vogue]angel]

havent heard this sort of thing before, this is really a good piece of advice.( no wonder jazz music sound so warm) But its kinda technical at times. mayb u can simplfy it further?

pianomankris, thus this apply to the blues and other genres for example ragtime?

 

[Unconscious]

pianomankris, thus this apply to the blues and other genres for example ragtime?

If my understanding of what pianomankris has said (kris pls correct me if I'm wrong) intervallic densities apply to any kind of music, jazz, rock, pop, even classical. While it explains (partially) why jazz chords sound they way they do, it would equally explain eg why Satie sounds so different from Debussy, or Ravel. The former's harmonies are simple and clear, whereas Debussy or Ravel tend towards lush and quite complicated chords. Even within jazz, one might be able to differentiate performers who play sparsely (Monk) from one who plays lots of thick warm chords (Shearing) based on the theory of intervallic density.