Compound Intervals · Jazz Wiki

A compound interval is just a simple interval that’s been stretched past the octave — a 2nd pushed up twelve half steps becomes a 9th, a 4th becomes an 11th, a 6th becomes a 13th. Jazz names its extensions this way for a reason: the number tells a player exactly where to put a note and what it implies is stacked underneath it. Without compound naming, “add a 9th” and “add a 2nd” would look identical on paper but mean completely different chords.

The arithmetic is just octave displacement

Every compound interval equals its simple counterpart plus 7 (because the octave itself absorbs one scale-degree count). This is pure scale-degree bookkeeping, not new material.

2nd + octave = 9th
4th + octave = 11th
6th + octave = 13th
3rd + octave = 10th (rarely notated — it’s the same pitch class as the 3rd)
5th + octave = 12th (rarely notated — same pitch class as the 5th)

This is exactly Interval Inversion’s cousin idea, except here we’re adding an octave rather than flipping one — the quality (major, minor, perfect) never changes when you displace by an octave, only the register does.

Same pitch class, different job

Here’s the honest simplification to flag: a D above middle C and a D an octave higher are the same pitch class — octave equivalence, a separate idea from Enharmonic Equivalence — but they do not function the same way in a chord. A bare 2nd sitting a half step or whole step next to the root or 3rd creates a tight, grinding dissonance — it beats audibly against its neighbor. Move that same D up an octave and it becomes a 9th, floating above the 7th with enough space that the ear reads it as color, not clash.

Cmaj9 = C–E–G–B–D (spelled 1–3–5–7–9)
The D is a major 9th above C, identical in pitch class to a major 2nd, but voiced an octave higher

That registral separation is the whole reason extensions exist as a category. This is also why chord symbols write “C9” rather than “C(add2)” — the “9” tells the player both the register and that a 7th is implied underneath it, while “add2” specifically means the 2nd sits close to the root with no 7th at all. That single digit is doing real work in Chord Symbols.

Mapping the extensions

Simple interval	Compound interval	From C
2nd	9th	D
4th	11th	F
6th	13th	A

Cmaj9 = C–E–G–B–D (1–3–5–7–9)
Cm11 = C–E♭–G–B♭–F (1–♭3–5–♭7–11)
Cmaj13 = C–E–G–B–D–A (1–3–5–7–9–13)
B♭maj9 = B♭–D–F–A–C
E♭m11 = E♭–G♭–B♭–D♭–A♭

Stacked as chords, each extension sits clearly above the triad and 7th:

The same relationships transpose to any key:

Why the 11th is the awkward one

Not every extension behaves the same over every chord quality, which is the domain of Available Tensions. Over a major chord, the natural (unaltered) 11th sits a half step above the major 3rd and clashes badly — the standard fix is to sharpen it to a #11 or drop it entirely, which is exactly how altered upper structures get built. Over a minor chord, that same 11th sits a whole step above the ♭3rd and is perfectly consonant, which is why Cm11 voicings are common and Cmaj11 (unaltered) almost never appears in real charts.

Pianists like Bill Evans and McCoy Tyner built their signature sound by leaving the root to the bassist and stacking extensions in the right hand — a technique formalized as Rootless Voicings. Tyner in particular favored stacking 4ths rather than 3rds, a related but distinct approach called quartal voicing that implies 11ths without spelling a full tertian stack, and which relates closely to Upper Structure Triads and Cluster Voicings as ways of coloring a chord’s top.

♫ Listen

Bill Evans — “Waltz for Debby” (Waltz for Debby, 1961): Evans’ rootless left-hand voicings stack 9ths and 11ths with no root at all — listen in the theme statements for how open and unresolved the chords feel compared to a plain triad.
John Coltrane & McCoy Tyner — “Acknowledgement” (A Love Supreme, 1964): Tyner’s stacked-4ths comping under the modal vamp implies 11ths throughout — listen to the left hand for the wide, muscular quartal sound rather than tertian stacking.