Dissonance and the Modes

The more and more I go into studying AH scales (intro), the more I feel the need to categorize them…almost like a taxonomist. It’s not really necessary for composing, and I told myself that I’d keep most of this study oriented away from the abstract and theoretical, but I’m always curious why things sound the way that they do. There’s such a rich pallate of colors to chose from when you take into account all 28 AH modes, and so it’s nice to have a starting point. Gradational Modulation sought to give a framework for the 28 modes with regards to controlling the difference of sharps/flats between different chord/modes, as well as controlling root motion and brightness/darkness, but I still didn’t have a way to understand and quantify something I could intuit very easily – “modal dissonance.”

Dissonance can be subjective, of course, but it basically is why Dorian voicings are “stable” and Locrian bb7 voicings are “unstable.” This is something that everybody can understand and “feel,” but becomes hard to quantify when trying to create a ranking of modes for the purpose of a mechanical technique like Gradational Modulation. Now, mechanical techniques aren’t why I compose or how I compose at all, but they’re great for getting the material in your ear in a way that you can understand how the harmony “moves.”

I set about creating a ranking for every one of the 28 modes for stability based upon measuring the intervallic relationships of every note within the mode to the tonic. I created four categories to describe these relationships – “Perfect Consonance” (Perfect 4ths and 5ths), “Imperfect Consonance” (Major/Minor 3rds and 6ths), “Mild Dissonance” (Major 2nd, Minor 7th, Major 7th, Diminished/Augmented 4ths and 5ths) and “Harsh Dissonance” (Minor 2nd). The reason why the minor 2nd gets a category of its own is because when arranged in a voicing, it forms a minor 9 dissonance with the root – a traditionally “unacceptable” interval for arranging. All 28 modes have two imperfect consonances – the 3rd and 6th of the mode – so its the other three categories that we are interested in. Here’s a table with all of the data. Augmented and diminished mild dissonances such as augmented 2nds or diminished 7ths are notated with a plus sign.

Major Scale

Mode Perfect Consonance Mild Dissonance Harsh Dissonance
Ionian 2 2
Dorian 2 2
Phrygian 2 1 1
Lydian 1 3
Mixolydian 2 2
Aeolian 2 2
Locrian 1 2 1

Melodic Minor

Mode Perfect Consonance Mild Dissonance Harsh Dissonance
Ionian b3 2 2
Dorian b2 2 1 1
Lydian #5 4
Lydian b7 1 3
Mixolydian b6 2 2
Locrian nat. 2 1 3
Locrian b4 3 1

Harmonic Minor

Mode Perfect Consonance Mild Dissonance Harsh Dissonance
Aeolian nat. 7 2 2
Locrian nat. 6 1 2 1
Ionian #5 1 3
Dorian #4 1 3
Phrygian nat. 3 2 1 1
Lydian #2 1 3+
Locrian b4 bb7 3+ 1

Harmonic Major

Mode Perfect Consonance Mild Dissonance Harsh Dissonance
Ionian b6 2 2
Dorian b5 1 3
Phrygian b4 1 2 1
Lydian b3 1 3
Mixolydian b2 2 1 1
Lydian #2 #5 4+
Locrian bb7 1 2+ 1

The next step is to group modes with similar intervallic characteristics together. These are the six “grades of dissonance,” that relate the modes by degree of stability. Pardon the invented jargon, but I felt that it was more descriptive to tie a Greek mode to each grade of dissonance versus a number. The numbers next to the names refer to the number of perfect consonances, mild dissonances and harsh dissonances respectively.

I. Neutral Grade Dissonance (2,2,0)

Major Mode Ionian, Dorian, Mixolydian, Aeolian
Melodic Minor Mode Ionian b3, Mixolydian b6
Harmonic Minor Mode Aeolian nat. 7
Harmonic Major Mode Ionian b6

II. Lydian Grade Dissonance (1,3,0)

Major Mode Lydian
Melodic Minor Mode Lydian b7, Locrian nat. 2
Harmonic Minor Mode Ionian #5, Dorian #4, Lydian #2 (+)
Harmonic Major Mode Dorian b5, Lydian b3

III. Phrygian Grade Dissonance (2,1,1)

Major Mode Phrygian
Melodic Minor Mode Dorian b2
Harmonic Minor Mode Phrygian nat. 3
Harmonic Major Mode Mixolydian b2

IV. Locrian Grade Dissonance (1,2,1)

Major Mode Locrian
Melodic Minor Mode
Harmonic Minor Mode Locrian nat. 6
Harmonic Major Mode Phrygian b4, Locrian bb7 (+)

V. Super-Lydian Grade Dissonance (0,4,0)

Major Mode
Melodic Minor Mode Lydian #5
Harmonic Minor Mode
Harmonic Major Mode Lydian #2, #5 (+)

VI. Super-Locrian Grade Dissonance (0,3,1)

Major Mode
Melodic Minor Mode Locrian b4
Harmonic Minor Mode Locrian b4, bb7 (+)
Harmonic Major Mode

Now, these six grades of dissonance seem to explain rather clearly what my ear already tells me – Locrian b4 is less stable than Lydian, for example. However, what’s a little confusing is, for example, why Aeolian nat. 7 ends up ranked as stable as Aeolian, or why Dorian b5 is ranked as stable as Lydian. To me, modal voicings in the former cases sound definitively less stable.

The reason for this lies in their parent scales. If we measure the intervallic relationships between ALL notes to ALL other notes instead of just the root for each scale system, we end up with these numbers.

Scale Perfect Consonance Mild Dissonance Harsh Dissonance
Major 12 14 2
Melodic Minor 8 18 2
Harmonic Minor 8 17 (++) 3
Harmonic Major 8 17 (++) 3

We can see what we already probably knew. Modes of the major scale are the most stable since they have the ratio of perfect consonant relationships to harsh dissonant ones, followed by modes of the melodic minor scale, and followed then by the harmonic major and minor, which are equally stable/unstable. So, within each grade of dissonance there is another breakdown of intervallic relationships to explain why Ionian/Dorian/Mixolydian and Aeolian are more stable than Ionian b6, for example.

There’s a problem here, of course. All of this is supposed to explain the relative stability and instability of the modes specifically how they relate to modal voicings. It can only go so far. Ionian modal voicings can be extremely unstable, for example, when both the major 7th and perfect 4th (the diatonic tritone) are voiced, and selective use of notes from modes like Locrian b4 bb7 can make them seem relatively stable within context. These grades of dissonance are instead meant as a general guide for understanding what you probably already know by ear if you’ve tinkered with the sounds of the modes before. They’re not particularly useful with specific techniques like understanding Brightness was, but they’re still a nice conceptualization.

Anyway, by now I’ve hacked these modes to death in terms of theoretical categorization, I think its nigh time I write some more music. Expect some in the next blog.




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