Perfect Chord Piano
Irmgard Rossie
Lastly, usually triads are played and accompanied by vocals (a 4th pitch) which is basically extended and added harmony. Meaning, the triads are definitely the harmonic foundation, leaving the voice to play around with consonance and dissonance on top of the triads. Do I have this correct also?
They certainly used to be. The modern theory of chords evolved gradually over several hundred years during which the primary theoretical framework was dyadic. Music in three or more parts that modern ears would recognize as chords had already existed for a few centuries before theorists started talking about chords as such.
The historical perspective is also helpful to consider here. Until maybe 100 years ago, it was highly irregular to end with anything more than three distinct pitch classes. Such chords were considered dissonant because they contained at least one second (or seventh). The dissonance was not only an acoustic property but a contrapuntal one: it had to be resolved, so it couldn't be present in the final chord. When Rameau developed his theory that equates the chord EGC with CEG, this led to a chordal theory based on the two possible triads that contain a perfect fifth, the major and minor triads.
Much later, people started regarding "extra" tones in chords as color. If you add a sixth or seventh to a major triad, you no longer need to hear it as tension requiring resolution; it could just be a different sonority that is still restful. In this context, however, the underlying harmonic relationships can still be described in terms of triads, which leads us to refer to the "extra" tones as "color."
Surely someone will think of an exception to the preceding paragraph, but to illustrate what I mean, consider the chord progression Em7-Am7-Dm7-G7-C7. Any song using this very tonal circle-of-fifths progression can also be played without any of the sevenths: Em-Am-Dm-G-C. The harmonic functions of the chords do not change, but the color is very different.
This is more or less it. The thing about "color" is, as I've said above, a change in the role of the acoustic dissonance: where before it provided from contrapuntal tension (also called "dissonance," which is sometimes confusing), it now serves to give the chord a different sonority.
Remember that the perfect fourth is frequently said to be consonant or dissonant depending on context. Also consider the diminished fifth/augmented fourth, which is always dissonant whether there is a third tone (or more) added to it.
In some styles, yes. But more generally, the solo melody (whether a voice or an instrument) will basically have one of the chord tones, too. In fact, you will often see songs where a chord symbol seems to have been chosen specifically to reflect the fact that the melody has a certain pitch. It's fairly rare that the melody's main pitch at any point is not reflected in the chords. For example, you're not likely to see a G7 with the melody on A; instead, the chord symbol would be some variety of G9.
The melody might have some figures that use non-chord tones ("play around with consonance and dissonance") but in an ensemble context any part can do that. For example, if the chord is C then the melody can have C-D-E without the chord having to change. But an inner part could also have E-F-G at the same time. If the passing tones (D and F) happen quickly enough then we would not analyze that as a change of chord.
Even with a lead sheet, depending on the degree of precision indicated by the given chords, a pianist or guitarist can play around with consonance and dissonance, for example seeing C and playing C-Csus4-C or adding a little scale or some other lick, such as the passing tones mentioned in the previous paragraph. Similarly, a good bassist can embellish the indicated bass notes with scales and neighbor tones. The chords just specify the harmonic framework. They aren't a precise indication of everything anyone should be playing. A composer or arranger who wants that degree of precision writes a score in staff notation, not a lead sheet.
If a tone intersects a given interval in an arithmetic way (at the arithmetic mean) it will support the base tone, if it intersects in an harmonic way (at the harmonic mean) it will weaken the base tone.
Take the most basic interval, the octave. The proportion of the frequencies of the two tones are 1:2. Now, add a third tone, which intersects this interval at the arithmentic mean (in other words: "halfways" in terms of frequency). This intersecting tone will be the fifth of the base tone, with a proportion of 2:3. This fifth will sound supporting to the base, e.g. when you play C-G-c-g-c'-... on a piano your impression will be that "c" is the base tone and that impression is reinforced by the g.
If you instead use a third tone which intersects the octave interval at the harmonic mean, which means the fourth (3:4, which is near the golden ratio), then the tone will weaken the impression of the base tone being the base and try to establish itself as the base. In the above example, playing C-F-c-f-c'-... instead of C-G-c-g-c'-... the "c" will not be heard as undisputed base tone any more, but the f will try to esablish itself as base tone with c as its fifth.
In light of this, what is a major triad? It is the base tone, the fifth (which, as we said above, is the arithmetic mean of the octave interval) and the major third - 4:5 - which itself is is the arithmetic mean of the base-fifth-interval. This is why the major triad sound so "in rest" - it only consists of intervals, which reinforce the base tone in its role.
Everything added to that will establish some sort of tension - "tension" here means no longer reinforcing the base tone in its role as base but in one way or the other poining away from it. Hear a C-triad major and c is undisputedly the base. Add a Bb to it you get a C7 and it points away from C, probably to F-major. Dyads are not considered to be basic in this sense, because they do not support the base to the maximum possible (by leaving out the major third).
The explanation I know as the usual explanation is Klang or the Chord of Nature. The harmonics of a string, the overtones of a fundamental pitch, outline a root position major triad for the strongest harmonics. This acoustic phenomena is thought to be the origin or many aesthetic preferences regarding harmony.
To some degree this is just a matter of terminology. When a textbook defines a chord as three tones, then that's your working definition. A broader view is that any number of simultaneous pitches is harmonic material, and that harmonic material can display harmonic function regardless of the exact number of simultaneous pitches. Those harmonic entities are functionally chords.
So, some consider two simultaneous tones to be chord, or partial/incomplete chords, because they can have recognizable harmonic function. In other words, when doing harmonic analysis, if you are able to, for example, label only two pitches as having function V, you have a dominant chord.
But, to be less abstract, the important thing that happens when adding a third chord tone is you can unambiguous know the chord root. Ex. with only tones C E you could have either a partial, root position C major chord, or a partial first inversion Am chord. Depending on the harmonic context one or the other is more strongly implied, but adding a third tone, either G or A will make the two cases clear.
One way of explaining this is a historic, contrapuntal approach. Assuming tertian harmony, the tetrad is a seventh chord, the seventh in the historic, contrapuntal context is a dissonance, not a chord tone, and part of some melodic voice movement.
V7 is an example, where some theory explains the origin of that chord being the melodic movement, the passing motion, of scale degrees ^5 of the V chord, through dissonant, non-chord tone, technically non-triadic tone, ^4, to ^3 of the I chord.
In other words the third and fifth above a root, or to be very historic above the bass, are consonant, and therefore actual chord tones, while the higher extension tones of seventh, ninth, and eleventh are dissonances. That leaves the thirteenth (or added sixth) the odd one out with additional history and theory discussing it, but let skip that for now. Historically, dissonances are not chord tones, therefore the fundamental chord ends with a third and fifth above a root/bass. Everything else will be either explained by chord inversions or non-chord tone motion.
I'm glossing over a lot of detail, because when taking a historic view of these topics you must remember that it goes back to a history before the concept of a chord root existed. It's hard to be complete and concise at the same time.
A dyad is ambiguous: the two notes in a dyad form an interval with both ends of the interval being equally important. The exception is a (straight) fourth or fifth that are harmonically so close that they define a root note and overtones. The lower note of a fifth or the higher note of a fourth is the root.
The most important color to fill in is major/minor: that creates a full chord entity in some inversion. Other colors are seventh/major seventh and suspensions. When those are missing major/minor, the result is not really satisfactory as a chord: with suspensions, that usually is the idea.
A diminished chord does not actually have the root-defining fourth or fifth. For that reason, it tends to work in the manner of a suspended chord as well, namely posing a question that only the context can answer. The difference here is that it does not even nail down a root note.
Jazz chords are more complicated since they tend to add significant more coloring and since the stacking is detailed enough that octave relations start making a significant contribution to the fingerprint of the chord.
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