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For example an F13. How do you find the 13th note?

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What instrument are you playing? – user1044 Aug 10 '12 at 3:58
Does it matter? This a matter of theory, not play-ability. This is applicable to any chordophone or group of instruments playing together. – American Luke Aug 10 '12 at 16:54
It matters because on piano, you can cover most of the 7 notes in a 13th chord using two hands. On guitar, you have to abbreviate it to about 4 notes, for instance, root, 3rd, 7th and 13th. – user1044 Aug 10 '12 at 19:01
So this about playability? It's not tagged for any specific instruments. It's tagged theory. – American Luke Aug 11 '12 at 15:25

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.

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+1, but "hax players"? Haven't heard that expression before. Like "crack shot"? – NReilingh Aug 10 '12 at 3:53
1. Don't drop the 3rd on a dominant 7th chord, otherwise you loose the dominant characteristic of the chord which comes from the tritone between the 3rd and 7th. Drop the 5th, then drop the root (and leave it to the bass player). 2 on a dom 7 chord, you want a #11, otherwise the 11 conflicts with the 3rd (awfully sounding b9 interval) – gurney alex Aug 10 '12 at 9:00
Written on my phone. "jazz players" was the intended line. – Dave Jacoby Aug 10 '12 at 18:13
gurney alex, you are right about what notes to drop. Thanks. – Dave Jacoby Aug 13 '12 at 19:13
The #11 is also very often dropped in the 13 chord, I believe. A typical one-handed voicing for F13 on the piano is Eb-G-A-D (which assumes a bassist, but not necessarily). – Gauthier Aug 14 '12 at 19:06

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)

Where 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 A

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.

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The 13 note in the F13 chord is D.

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.

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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.

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A F13 chord has a #11, not a 11 (ie e B not a Bb) – gurney alex Aug 14 '12 at 7:38
@gurneyalex: I don't think this is a 100% truth. First, the 11th is often omitted anyway (the 11th either raised or not, changes the color so much...). Then, wikipedia (I know, wikipedia is not always right, but still) does not agree: "A thirteenth chord does not imply the quality of the ninth or eleventh scale degrees." The same article says also: "The underlying harmony during a thirteenth chord is usually Mixolydian or Lydian dominant", which differ only in their natural/raised fourth. – Gauthier Aug 14 '12 at 19:16
@Gauthier well, if you want to play a 11 on a 13 chord with the 3rd, you're going to have problems making it sound correct. Either you have a sus4, in when case I agree you won't have a #11, or you're playing the 3rd, in which case you either omit the 11, or play a #11. The 4th is very tricky in a Mixolydian mode because the 3rd is such a strong note, and the potential for a b9 is very high. Better be on the safe side and omit the 11 or raise it IMO (at least in a jazz context). Maybe not 100% true, but certainly 98%. – gurney alex Aug 16 '12 at 8:45
I do agree that the natural 11 is more awkward than the #11. But the #11 changes the sonority of the 13 chord very much, so I'd say that the #11 is omitted in most cases (more often than played). Maybe not the case whe you play the chords, and it's just fine. As a soloist I often play the fourth of a dominant chord as a passing note. If the chord instrument plays a #11 that would sound kind of strange, wouldn't it? – Gauthier Aug 17 '12 at 9:29
(i.e. the soloist assumes mixolydian while the chord instrument assumes lydian dominant. Plus that if F13 is the dominant chord, the soloist is likely to play in Bb major, thus Bb. If the tonality is C minor (with major 6th and 7th), then B is better.) – Gauthier Aug 17 '12 at 9:34

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.

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