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

Triads

Interval Harmonization v1.5 - Piano_0002

Simple 7ths

Interval Harmonization v1.5 - Piano_0003

Altered Dominants

Interval Harmonization v1.5 - Piano_0004

Interval Harmonization v1.5 - Piano_0005

Added Note and Suspended Chords

Interval Harmonization v1.5 - Piano_0006

Interval Harmonization v1.5 - Piano_0007

Other Chords

Interval Harmonization v1.5 - Piano_0008

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

Interval Harmonization v1.5 - Piano_0010

Altered Dominants

Interval Harmonization v1.5 - Piano_0011

Added Note and Suspended Chords

Interval Harmonization v1.5 - Piano_0012

Other Chords

Interval Harmonization v1.5 - Piano_0013

(chromatic dominant stolen from Jacob Collier)


Major 9th

Triads

None

Simple 7ths

Interval Harmonization v1.5 - Piano_0015

Altered Dominants

Interval Harmonization v1.5 - Piano_0016

Added Note and Suspended Chords

Interval Harmonization v1.5 - Piano_0017

Other Chords

Interval Harmonization v1.5 - Piano_0018

The m9b5 chord is just a halfdim7 with a major 9th in the melody. I wasn’t entirely sure what to call this. A half diminished chord is built on the locrian chord-scale, while a minor 7th chord is built on the dorian chord-scale. If you take m7b5 to mean that it’s a dorian chord-scale with an altered fifth degree, then the upper extensions of the m7b5 should be natural 9 and natural 13, versus the b9 and b13 of the halfdim7. I’ve also heard of m7b5 interpreted as the aeolian chord-scale with a flattened fifth (more commonly known as locrian #2, mode six of the melodic minor scale), which would give it a natural 9 and b13. In practice, the two chord symbols are used interchangeably and interpretation is left up to the players, but this is something to think about when using them to harmonize a 9 or b9 in the melody.


Minor 3rd

Triads

Interval Harmonization v1.5 - Piano_0019

Simple 7ths

Interval Harmonization v1.5 - Piano_0020

Altered Dominants

Interval Harmonization v1.5 - Piano_0021

Added Note and Suspended Chords

Interval Harmonization v1.5 - Piano_0022

Other Chords

None


Major 3rd

Triads

Interval Harmonization v1.5 - Piano_0024

Simple 7ths

Interval Harmonization v1.5 - Piano_0025

Altered Dominants

Interval Harmonization v1.5 - Piano_0026

Interval Harmonization v1.5 - Piano_0027

Added Note and Suspended Chords

Interval Harmonization v1.5 - Piano_0028

Other Chords

Interval Harmonization v1.5 - Piano_0029


Perfect 4th

Triads

None

Simple 7ths

Interval Harmonization v1.5 - Piano_0031

Altered Dominants

None

Added Note and Suspended Chords

Interval Harmonization v1.5 - Piano_0033

Other Chords

Interval Harmonization v1.5 - Piano_0034


Tritone

Triads

Interval Harmonization v1.5 - Piano_0035

Simple 7ths

Interval Harmonization v1.5 - Piano_0036

Altered Dominants

Interval Harmonization v1.5 - Piano_0037

Added Note and Suspended Chords

None

Other Chords

Interval Harmonization v1.5 - Piano_0039


Perfect 5th

Triads

Simple 7ths

Altered Dominants

 

Interval Harmonization v1.5 - Piano_0042

Added Note and Suspended Chords

Interval Harmonization v1.5 - Piano_0043

Interval Harmonization v1.5 - Piano_0044

Other Chords

Interval Harmonization v1.5 - Piano_0045


Minor 6th

Triads

Interval Harmonization v1.5 - Piano_0046

Simple 7ths

Interval Harmonization v1.5 - Piano_0047

Altered Dominants

Interval Harmonization v1.5 - Piano_0048

Added Note and Suspended Chords

Interval Harmonization v1.5 - Piano_0049

Other Chords

None


Major 6th

Triads

None

Simple 7ths

Interval Harmonization v1.5 - Piano_0052

Altered Dominants

Interval Harmonization v1.5 - Piano_0053

Added Note and Suspended Chords

Interval Harmonization v1.5 - Piano_0054

Other Chords

Interval Harmonization v1.5 - Piano_0055


Minor 7th

Triads

None

Simple 7ths

Interval Harmonization v1.5 - Piano_0057

Altered Dominants

Interval Harmonization v1.5 - Piano_0058

Interval Harmonization v1.5 - Piano_0059

Added Note and Suspended Chords

Interval Harmonization v1.5 - Piano_0060

Other Chords

Interval Harmonization v1.5 - Piano_0061


Major 7th

Triads

None

Simple 7ths

Interval Harmonization v1.5 - Piano_0063

Altered Dominants

None

Added Note and Suspended Chords

Interval Harmonization v1.5 - Piano_0065

Other Chords

Interval Harmonization v1.5 - Piano_0066

You could also  call the last one a Dbm7b15. I plan on doing a separate post for that at some point because it’s an interesting chord alteration that tends to sound good and not feel too out when used in context.

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