Chord Extension - the "add" chords

The 6th chords are the most notable exception. A note about compound intervals is in order.
A 9th, for example, is a 2nd in the octave above the root of the scale. As a rule of thumb subtract 7 from the compound name to find the equivalent scale degree. Following the 3rd rule you get the following types of chords: 7th 9th 11th 13th. Note that any of these types of chords imply that there are also each of the types of notes to the left of it. For example a 9th chord implies that there is also a 7th, an 11th chord implies that there is also a 7th and a 9th. I don’t believe that there are any others of these types of chords because a 15th would be the root note two octaves up and that would be considered doubling the root note. It is possible to build a chord with a 9th but without a 7th. This would be called add9. Similarly for other intervals.
In the case that you need to spell an extended chord, I would suggest that you write out the scale of the root of the chord. Make it a minor scale if the triad is minor, and a major scale if the triad is major. Then you add each extended note to the triad. Diminished triads must be treated more carefully. You’ll have to build a scale that contains the proper type of diminished 7th on the seventh note of the scale.
As an example lets built a C11.
What is a chord extension?
A chord extension is a basic chord with extra notes added on to give the chord a more complex sound. Think of it like a painting: A painting of a tree may look nice. But if the artist adds in other details like birds on the branches, drops of rain dripping off leaves, and flowers at the base of the trunk, then the painting starts to come alive with color and reality. Chord extensions are like the colorful details in a painting that will give your chords extra life and texture.
How to create a chord extension
There are many different chord extensions. But knowing some basic principals of chord extensions will allow you to learn them much quicker and build them on your own.

Just as a refresher: the notes of a basic major chord the notes of a major 7th chord are 1-3-5-7. So there are still some notes of the major scale that are not used in those chords, namely the 2, 4,and 6. So we can add those notes to our chords to make chord extensions.
But it is important to note that these notes are almost never called by 2, 4, and 6 in chord extensions. They are almost always called the 9, 11, and 13. Why? Well because when you ad these notes to your chord you play them in the next octave. Here is what I mean:

So once the major scale gets to the second octave the note numbers are still being counted from the first octave. So even though the D note is a 2 in the 1st octave, it is called the 9 if you are playing it in the second octave. And when you play chord extensions you add the extensions to the second octave so it goes by 9, not 2. So let’s take a look at a Cadd9 chord:

See how the D note is played in the next octave above the root C note. If it were in the same octave than the D not would be on the 5th fret of the A string (or just an open D string). This is also known as a Drop 2 Chord voicing.
The difference between Cadd9 and C9
Also note that when you see a chord and then “add’ and then the extension number, like Cadd9, it just means play the regular C major chord and then add the 9th to it. So Cadd9 would have the notes 1, 3, 5, 9. But if you just see a chord and an extension number it means add all the chord tones all the way up until that extension. So a C9 would be the notes 1, 3, 5, b7, 9. (There is a flat 7 b/c if there is a chord name with a number directly next to it than it means it is a dominant chord and there is a flat 7. If the 7 was natural, the chord would be called Cmaj9, which would be 1, 3, 5, 7, 9).
Altering notes to relieve dissonance
There are certain cases where chord extension notes create dissonance. For example in a major chord with an 11th extension the 3rd of the major scale sounds dissonant against the 11 (because the 11 is the same as the 4 and there is only a half step between the 3rd and 4th note of the major scale. And notes ½ step apart played at the same time sound dissonant). So relieve this unwanted tension we will always make the 11 sharp of any 11th chord extension. So a Cmaj11 is 1, 3, 5, 7, 9, #11 even though the chord name is just Cmaj11, not Cmaj#11. You do not need to play the #11 in minor chords with an 11th extension because the 3rd is flat in the minor chord so there is a whole step distance between the 3rd and 4th note, not a half.
How To Play a Chord Extension on guitar
So now lets apply some of this knowledge to playing chord extensions on guitar. We first have to realize that since we keep adding notes as our extensions get higher that some extensions will have too many notes to humanly fret on guitar. But there is a solution. We can drop some of the notes and keep just the notes that will bring out the essence of the chord.
So here’s what we do: We keep the root note, because it will define what the name of the chord is. We keep the 3rd note, because it will define if the chord is major or minor. We keep the 7th note, because that tells if the chord is dominant, major, or minor, and we keep the highest extension we want to play, because that defines what chord extension it is. We drop the 5th note and all the extensions besides the highest one.
So for example a C13 would be played with a 1, 3, 5, b7, 9, #11, and 13. But on guitar we just play the 1, 3, b7, and 13:

So now you have the ability to create chord extensions on your own. But be sure to use drop 2 voicings when you play them!

C Major scale: C D E F G A B
C triad: C E G
Note that the 11 implies a 7th and a 9th
C7: C E G B
C9: C E G B D
C11:C E G B D F
Another example Am6
A Minor scale: A B C D E F G
Am triad: A C E
Am6 : A C E F
The highest number/note in the chord is the number you use in the chord symbol - AS LONG AS - the notes/numbers preceding it are also included!
In add chords we don’t need to include lower notes.
Eg. C add9 means add 9 to C.
Cadd9 : 1 3 5 9
So 7 is missing and you have not to play 7 at all.
Eg. Consider G add9, where we don’t play 7.