For example an F13. How do you find the 13th note?
You play it. For an F13, that would be a D above the octave. But it is more than that. A 9 assumes a dominant 7. An 11 assumes a 9. Thus, a 13 assumes the 11. For F, we're at F A C Eb G Bb D. An easy way to remember is that a 13 is a 7th chord with a minor triad started on the second scale degree.
That looks more like a scale than a chord, doesn't it?
In reality, you would likely play with much less of that. The root and fifth, as I understand it, are two that jazz players routinely drop off. You probably want to drop or sharpen the 11, or else you get a dissonant b9 interval with the 3rd.
You need to look at the theory behind it. In a scale each note is represented by a number.
In a C major scale you have the notes
C D E F G A B (C)
This will be in numbers:
1 2 3 4 5 6 7 (8)
8 represents one octave. To find
13, you just have to continue up above in the next octave:
C D E F G A B C D E F G A
1 2 3 4 5 6 7 8 9 10 11 12 13
So here you have 13 as
In F13 you have
F G A B♭ C D E F G A B♭ C D, and there you have D at number 13.
The 13 note in the F13 chord is
A 13th chord is a dominant chord, such as a 7th chord, but with some extra notes.
When creating a chord you generally¹ stack thirds on top of each other and name the chord after the number of steps from the root note to the highest added note.
So the regular F chord is the triad
(F A C).
Adding a third gives you F7²
(F A C Eb).
Adding yet a third gives you F9
(F A C Eb G).
Another third gets you F11³
(F A C Eb G Bb).
A last third on top of that gives you the F13 chord
(F A C Eb G Bb D).
However in this stack of notes (the 13th chord), the interval A-Bb (3-11) is considered very dissonant so you generally omit the Bb (the 11) to avoid the dissonance. You shouldn't skip A (the 3), nor Eb (the 7), since this would ruin the dominant character of the 13th chord. The C (the 5) can be skipped since it is so consonant that it adds almost no character in this chord. Further the root F (the 1) is likely played by the bass and can be omitted. So to play the F13 on, for instance, the piano a normal voicing would be
Eb G A D.
¹ Chords like F6
(F A C D) or Fadd9
(F A C G) obviously don't follow the stacked third rule.
² A plain 7 implies the minor 7 note. Chords with "Maj" or △ would instead have the major 7: F△13 gives you the notes
(F A C E G Bb D) and might be voiced
(E G A D).
³ In an 11th chord the interval 3-11 is considered very dissonant. Since the 11 is the main feature of this chord you generally omit the 3 (the A in F11). F11 could then be voiced as
C Eb G Bb.
As the others have pointed out a F13 chord would contain 1/3/5/7/9/11/13, i.e. F, A, C, Eb, G, Bb, D. That's impractical to play and has way too many notes to make a decent sounding chord. As with most of these, it's important to figure out which notes to play and which ones to skip.
The primary feature of the 13 chord is the tension (major 7) between the dominant seven and the 13. In this case Eb and D. These are keepers. You also need to have a 3 (to make sure it's major and not a minor). On the guitar it's often played as F Eb A D (adding the root on the bottom). This is has the nice side effect that it's relatively easy to fret.
F13. F-A-C-D ... is a 6th, not a 13. (Actually, it could also be a dmin7 in 1st inversion depending on what's being played in the bass). It doesnt matter what inversion or where you place it. F-A-C-D-Eb ... IS in fact a 13th (though I wouldnt voice it quite like that). A 6th scale degree without a dominant 7th scale degree is merely a 6th scale degree. The magic "13th" requires the dominant 7th.
The simple answer is, count as if the "8" is "1" (because they are the same, an octave apart). Thus, the 13th is actually a 6th. The high number basically infers it's a melody note overtop a simpler chord. That isn't a hard and fast rule, it merely means that the 13th note is included. It could be the lowest note in the chord... or somewhere in the middle of other notes being played - where it 'should' be is purely a matter of how you are playing the overarching melody.
The simple answer is to play 9th, 11th, or 13th "CHORDS", you need the base chord, PLUS the b7, PLUS the 9th, 11th, or 13th note. If you DON'T play the b7 and add the 9th, 11th, or 13th note, it is an "add chord" (Example: a "Cadd9" is C-E-G-D (1-3-5-9), whereas a "C9" is C-E-G-Bb-D (1-3-5-b7-9). Again, the 9th chord MUST have the b7. The same rule applies to 11th, 13th chords... hence, 11th chord: 1-(3)-5-b7-11, 13th chord: 1-3-5-b7-13. Yes, in the 11th chord, the third will clash. (just try a C11 chord to see for yourself: play a open C7 chord (C with adding the Bb on the 3rd string) and then barre the F on the first string, now test with playing with the 4th string "E" played and then muted and you will hear the difference from a true 11th to an omitted third 11th). As far as variations, you can do whatever to divide the note duties among musicians but you generally need all but the 5th to do the chord justice or you might as well call it another chord name.