Chord tensions

Natural chord tensions form corresponding arpeggios on top of chords.

For example:

This relationship results in the following table:

chord From 7th From 9th
Minor 7th 7b+9+11+13 = Maj7 9+11+13+R = Min 7th
Min 7th b5 7b+9+11+b13 = Full diminished 9+11+b13+R = Min 7th b5
Dom 7th 7b+9+#11+13 = 5# 7th 9+11#+13+R = Dom 7th
Maj 7th 7+9+#11+13 = Min 7th 9+11#+13+R = Dom 7th

* (R = Root, 8va) Patterns start to emerge, as some tensions produce the same kind of chords (but a tone away).
Extremely fun stuff.

As for altered tensions in dominant 7ths, the possibilities explode:

For example:

Dom 7th tensions From 7th From 9th
#9 #11 7+#9+#11 = 2nd inv Min/sus4? #9+#11(+b13!)+R = Full diminished

Once you get ahold of these possibilitys, you realize you can play chord superimpositions that emphatize tensions. A good practice routine should build up the memory of these relationships between chord types and what kind of upper structure harmonic structures one can create.

So let’s do that, and take a systematic approach to this information, by chord quality:

Minor 7th chords

How many upper structure arpeggios can we build from minor 7th chords and tensions?

Interval Tensions and chord tones Resulting chord
R - -
9 9+11+13+R Min 7
9 9+11+13b+R Min 7 (5b)
3b 3b+5+7+9 Maj 7
11 11+13+R+b3rd Dom 7
11 11+b13+R+b3rd Min 7
5 5+7+9+11 Min 7
13b 13b+R+3rd+5 Maj7
13 13+3+3rd Min 7 (5b)
7th 7b+9+11+13 Maj 7
7th 7b+9+11+13b Dom 7

The result is quite pedestrian: you build… the chords of the majord scale (gasp!), with a bit of wiggle room in those spots where you can treat the minor base chord as dorian or phrygian (meaning, considering the 13 or the b13 tension). Note that I’ve not included 9b, even if it’s in there in the phrygian mode, since it’s usually considered pretty disonant over minor 7ths.

Some interesting notes here and there: