Interval Reharmonization Chart

“Every single melody note works with every single bass note”

This is a line from a WIRED video featuring Jacob Collier and Herbie Hancock, but I’ve seen similar ideas espoused in various places. The concept is that for any given pair of bass and melody note, there exists a way to harmonize them. Put another way, there are 12 possible intervals that can exist between a bass and melody note, and each of those intervals fits with at least one chord.

This is a chart of the 12 intervals and all their possible harmonizations that composers can reference when looking to change up their harmony.

A note on methodology

Doing something like this involves making some decisions about what constitutes a chord. For the most part, I decided to limit this to common jazz chord qualities (excluding inversions and polychords).

Another issue lies in deciding what makes two chords meaningfully different from each other. I solved this by grouping chords that belong to the same chord-scale (maj7/maj9/maj7#11/maj13#11, etc) and only explicitly labeling extensions when they appear as the melody note.

For altered dominants I considered each additional alteration to be a new chord, but grouped unaltered extensions the same as the extensions of simple 7ths. As an example, 7b13b9, 7b13#11#9, and 7b13#9b9 all imply an altered chord-scale. I’ve grouped 7b13b9 and 7b13#11b9 because #11 appears in the unaltered lydian dominant chord-scale, but I’m considering 7b13#9b9 to be different because it introduces a new alteration.

For simplification of the added note chords, I grouped sus2 and sus4 into a single sus quality. The defining element of ‘sus-ness’ is the lack of a third; it doesn’t significantly change the sound whether the sus chord is voiced with 2, 4, or both. Also, it turned out that sus2 and sus4 were interchangable in most places that a sus chord could be used.

With the “Other Chords” sections, I included chords some chords that aren’t necessarily common to jazz but are still interesting and possibly useful. I decided to only include each chord in intervals where I’d actually seen it used or found voicings that sounded good. For example, maj13#15#11 could technically be used anywhere that a regular maj7/maj9/maj7#11/maj13 is used, but I only listed it under Minor 9th and Tritone because I’ve only seen it voiced with the #11 or #15 in the melody. This decision was mainly to keep the size of the list down and make sure everything included is useful.

With these restrictions in place, the numbers add up so that any given melody note has 244 harmonization possibilities.

Octave

I’m listing Maj7, +Maj7, and mM7 under Other Chords here because it’s not standard practice to use them to harmonize the root, but it can sound nice when the chord is voiced in a low register and the melody is higher.

Minor 9th

Triads

None

Simple 7ths

Altered Dominants

Added Note and Suspended Chords

B susb9

B 7b9sus

B 7b13b9sus

Other Chords

(chromatic dominant stolen from Jacob Collier)