Recall that chords are just a collection of notes played at once. Chords can be derived in a variety of different ways, the first way we'll discuss is a method of constructing chords from a scale.
Let's say we were given a 3* major scale. Let's create chords out of each note of the scale and also recall that 0 2 4 5 7 9 11 are the ai's involved in a major scale. We could choose notes in any way, but for the sake of this demonstration we'll do it in a way that creates chords known as triads, in order to do that we will skip every second ai.
|Starting ai||ai's in chord
|0||0 4 7 11|
|2||2 5 9 0|
||4 7 11 2|
|5||5 9 0 4|
|7||7 11 2 5
|9||9 0 4 7|
|11||11 2 5 9|
Chords created from a scale in this manner will be called the diatonic triads of the scale. The reason why these chords are called triads comes from the fact that the gaps between any two sequential ai's is 3 or 4, and in the standard system these types of gaps are called major or minor thirds, they are "stacked thirds".
If you were curious as to why they are always 3 or 4 steps between them, we just have to realize that the gaps between notes in a the major relative interval collection is o 2 o 2 o 1 o 2 o 2 o 2 o 1 (where an o represents a note), and so if we skip over one note the total distance will be either 3 or 4 since 2 + 1 = 3 and 2 + 2 = 4.
Additionally the way we constructed the chords here is not the only way we could have done it, for example another method could have been to start with one ai, take the next one and then skip one, and then skip one again. Using this method we could have produced the following chords.
|Starting ai||ai's in chord
|0||0 2 5 9|
|2||2 4 7 9|
||4 5 9 0|
|5||5 7 11 2|
|7||7 9 0 4|
|9||9 11 2 5|
|11||11 0 4 7|
Chords constructed in the above manner have no particular name.
Alternatively we don't have to define any set of predefined chords and when we're playing we can choose the ai's we'd like rather than a predetermined collection associated with each note of the scale.
The main thing we need to understand is that the most important information a chord has to offer are what ai's are involved in the chord and also what the quality of the chord is. Two chords with the same ai's are similar, two chords with the same quality sound similar, when both match they are the same. That is to say that the methods which we use to create chords is irrelevant, it's what the chords are made out of at the end that really matters.
Over time as we play chords we will be able to choose chords which we enjoy and be able to communicate by using chords.
There is notation that has been created which allows us to reference chords by the root tone and a quality, this information allows us to define a chord completely. An example of this could be "C maj 7" this is a chord that starts on C since that's the root and maj 7 is its quality, and then also has the notes which are a major 3rd (4 semitones), perfect 5th (7 semitones) and a major 7th (11 semitones) above the root. Which defines the notes C E G B, or 0* 4* 7* 11*.
Note: A quality is determined by a series of intervals above the root, as those produce notes which in turn produces a wave with a particular shape (that being its quality)
If we were playing a song in the key of 0* major, this 0* major 7th chord has some specific properties in that, it represents a resting place for the song, other chords we create from the 0* major scale have their own specific properties as well. One of the most important facts is that if we were playing in the key of 8* major, then the 8* major 7th chord would also have this same property, it's true for any starting note, so we can say that in the key of x* major, the x* major 7th chord has this resting place property.
We can start to see why this notation is useful, whenever we are in the 3* major scale we know that the 3* major 7th chord has the resting property or if we are in the 5* major scale, the 5* major 7th chord would also have that property. But something that we haven't talked about is that in order to play this chord on your instrument, the stardard method would be to figure out what notes are in the chord and then find them on your instrument.
If we utilitize this method of making chords on our instrument, then we'll find out that the 3* major 7th chord has the notes 3* 7* 10* 2* but the 5* major 7th chord has the notes 5* 9* 0* 4*. This seems fine, but since with respect to their own scales they have the same resting property, it would be nice if the way we construct it on the instrument could be the same and not have to use different notes.
In order to do that we'll have to find an in between notes and intervals, this is exactly what anchor intervals are designed for. If instead of describing our chords as notes, we instead describe them as distances from our scale root then our 3* major 7th chord with an anchor of 3* would be 0 4 7 11, and also our 5* major 7th chord with an anchor of 5*, would be 0 4 7 11. Since we also know how to play anchor intervals on our instrument, no other conversion is required, we can now simply play 0 4 7 11.
The benefits from the development we've just made is that the notation we use to denote chords and the way we make chords is identical, which allows us to memorize less information and see connections more readily.
In many chords you can find an interval of 7 steps (called a 5th in standard notation), this interval is one of the most simple sounding intervals (it has to do with the ratios involved between the root note and this one) and can usually be left out.
If you're playing this on an instrument which has difficulty playing many notes at once then you can also leave out other ai, mainly you want to leave in at least 2 of the notes which are not the root or the one which is 7 steps above the root.