Alistair S, on 26 August 2011 - 12:54 PM, said:
OK. Let ma ask the dumb question (apart from, "Shouldn't it be "have" instead of "has".. "..

)
My dear sir, I fully understand you are far more an expert in
English than I (coming from Long Island!)...
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If you don't play all the notes in a chord, why is it considered to be that chord? Sometimes it could be one of a number of chords, surely?
I'll answer the second question first.
Yes, it could be one of a number of chords, however it depends on context. The same way the words "there", "their", and "they're" all sound the same, they are actually different words depending on context within the sentence.
The context we are generally speaking of here is the "circle of fifths chord progression" (not to be confused with just the "circle of fifths). (The name, "circle of fifths chord progression" is actually pretty confusing and, IMO, a very BAD name, because this progression is actually moving by fourths, but we're stuck with calling it the "circle of fifths chord progression" for reasons I'd rather not go into...).
Anyway, this is the circle of fifths chord progression in a Major scale:
I IV vii° iii vi ii V I
As others have stated, all Western music, Pop or otherwise, is related to this progression (and its variations, and ways to move around in). The roman numerals in Upper Case are Major Chords. Notice, if you focus only on those, you have the I IV V I progression, which appears over and over in Pop music. This is probably the most used variation of the cycle of fifths chord progression.
So, in the context of the cycle of fifths chord progression, in the key of C, the IV chord would be an F major chord: FAC. If you were using the cycle of fifths progression in the key of F, that same set of notes, FAC, now becomes the I chord.
Now for the first question regarding *not* playing all the notes in a chord:
The example chords I used so far only consisted of three notes: the root note, (which names the chord), third above the root (aka: the third in that chord), and a third above the middle note (which is five notes above the root, aka: the fifth in that chord). These three pitches stacked in thirds on top of each other is the basis for "triadic" harmony.
By continuing to stack additional notes in thirds, we alter the original chord. If we stack another note on top of our F Major chord, one third above the last pitch, the notes become in that chord become F A C E. The newest pitch, "E" is an interval of a 7th from the original pitch, "F". This chord is thus named "F Major 7". By flattening the 7 degree (E) a half step (to Eb), so the notes are F A C Eb, the chord is now known as a Dominant Chord, in this case F7.
When we hear a Dominant chord, say F7 played with all the notes, F A C Eb, and one missing the Fifth of that chord, F A _ Eb, they sound the same to our ears. The reason for this has to do with acoustical physics, and the overtones generated, which I won't discuss further here. Suffice it to say, they sound the same. If it's easier to leave the fifth out when we play or compose music, we do. It is still called an F7 (or F Dominant) chord.
We could rearrange the chord, F A
C Eb, stacking it in thirds, assuming other missing pitches, and name it a different chord: A
C Eb
G B D F. This might be called an A diminished 13 chord. The pitches wouldn't exactly be the same, as the "F" is actually tow octaves higher than the original "F". This "A diminished 13 chord" however, is cumbersome, and might not fit within the key signature being used within the music following the circle of fifths chord progression variation. (Other music theorists might come up with other chord names besides my example.)
Have I confused you further? Or does any of this make sense?
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What if I play a note that isn't in that chord as part of the arpeggio? Maybe that doesn't matter.
That note is usually called a "passing tone", or sometimes it's part of the melody (which doesn't have to be part of the chord, but usually is.)
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Sorry, I know this is OT.
I think your questions are spot on topic!
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By the way, I like "broken chord" .. it sounds lyrical

Me too.