Chord tensions

Natural chord tensions form corresponding arpeggios on top of chords.

For example:

• A minor 7th has three tensions: 9, 11, 13. Together with the 7th they form a major 7 arpeggio a tone below.

This relationship results in the following table:

* (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:

Once you get hold of these possibilities, you realize you can play chord superimpositions that emphasize 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:

The idea:

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

The result is quite pedestrian: you build… the chords of the major scale (gasp!). 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. Most people also consider the b13 as an unavailable tension.

The concept also applies to the tensions of dominant and major 7th chords, with an explosion of possibilities in the first case.

And how the hell am I supposed to practice this?

Now, imagine you have a ii-V-I to play over, and you want to try some of these combinations. If you follow this page, you’ll quickly notice that with all the possibilities of dominant alterations, you can get 702 combinations of chord superimpositions, specially if you consider each diminished chord as distinct (though we know in practice that’s not the case). It’s hard to navigate this space of possibilities.

The good news is that this is one of those problems a computer can quickly solve, so I wrote a small program that, given a ii-V-I chord, gives you a random combination of chord superimpositions for those. Similar to repeatition learning, the purpose of this program is to give you:

1. Chord possibilities that you wouldn’t have considered otherwise.
2. A way to get used to the sound of these subtitutions
3. Spaced repetition is necessary for long-term memory. Interleaved repetition is then the best approach to practice this

God bless Python:

import sys
import numpy as np
import random
np.set_printoptions(threshold=sys.maxsize)


# creating various numpy arrays for each of the chord qualities
minors = np.array(["1: Min7", "2: Min7","b3: Maj7", "4: Dom7", "5: Min7", "b7:Maj7"])
dom = np.array(["1: Dom7", "1: Min7 (b5)", "1: Dim7", 
                "b2: Dim7", "b2: MinMaj7",
                "2: Dom7", "2: Maj7",
                "b3: Min7", "b3: Dom7", "b3: Maj7", "b3: Min7(b5)", "b3: Dim7",
                "3: Min7(b5)", "3: Dim7",
                "#4: Min7", "#4: Dom7", "#4: Min7(b5)","#4: Dim7",
                "5: Dim7", "5: MinMaj7",
                "b6: Maj7","b6: Dim7",
                "6: Min7", "6: Dom7", "6: Maj7", "6: Min7(b5)", "6: Dim7",
                "b7: Dim7",
                ])
majors = np.array(["1: Maj7", "1: Maj6", "2: Dom7", "3: Min7", "5: Maj7", "6: Min7", "7: Min7"])

# Arranging them to get all possible II-V-I possibilities
combinations = np.array(np.meshgrid(minors, dom, majors)).T.reshape(-1, 3)
# just get combinations out to a file to see all possible combinations

# if you just want a random one, do something like this:          
allchords = {"I" : majors,
            "II" : minors,
            "V" : dom}

for key, val in allchords.items():
    print(key, "from",  random.choice(val))
# plus, if you want any other combination of chords,
# like minor, minor and major,
# just change the dictionary

This is a very easy, kind of brute force implementation of a II-V-I superimposition randomiser. Each time you call this program it’ll give you a randomized superimposition option - in a certain sense, very similar to the anki approach to learning, if a bit more modular. The output is composed of the degree of the chord from which you build a chord quality. For example, consider this output:

II from 2: Min7
V from 3: Dim7
I from 1: Maj7

What this output is telling you, is that over a minor chord of a II-V-I you could try to play a minor 7th arpeggio from the second degree (, a diminished arpeggio from the third degree of the dominant (so, a V(b9) after all) and finish with a regular major chord over the I. In C, that would mean that over D-7 / G7 / CMaj7 you could try playing E-7 / Bdim7 / C-Maj7. Maybe not the best combination, but interesting still.

Further developments I’d like to implement:

• Imagine the possibility of adding fragments of a jazz standard here, or common progression movements (like movements in fourths) - it’d be fairly easy with the current implementation of the code, actually.
• Creat an historic log, so that those combinations that have appeared already don’t reapear until x iterations of the program (in order to maximize spaced learning)
• And, of course, expand to minor harmonies and other kinds of chord types.

Exploring II-V-Is superimposed lines

This way, I’ve found some otherwise unlikely combinations that I particularly like:

• b7:Maj7 / b3:Dom7 / 7:Min7 sounds great - I love the sound of the dominant 7th over the minor third, but it’s feels quite out. I find the maj7th at the start makes the tonality clearer, while the minor over the seventh is conveniently just a half-step over the dominant 7th’s outside range, making it a fairly positional movement. Note that the root movement actually happens over a degree interval, so you can easily voice lead you way over these.
• 5:Min7 / 6:Dim / 6: Min7 is interesting in that both the first and the third superimpositions are the same chord (in C, that’d be A-7), with some spicy diminished in between, conveninently located a fifth away.
• b3:Maj7 / 2:Dom7 / 6:Min7: a fairly positional possibility that just rings nice by virtue of not being too dense. Both the start and the end are fairly relaxed, as they emphasize tonic functions, while the dominant chord adds a bit of tension through the #4.
• 4:Dom7 / 6:Dim / 3:Min7: another “diminished-in-the-middle” kind of sound.
• b7Maj7 / b3Min7 / 2:Dom7: Similar to the first version, but finishing in a dominant sound. I wonder if you could sneak-modulate like this easily to all the common places, such as the V (V/V), III (as a b7), II, or even bI if you are feeling bold (as a tritone substitution of a V/bI).