12 TET Interval Ranking

Question

Is it correct that composers of most popular genres use 12 TET based interval consonance and dissonance when building chord progressions and a composition as a whole?

Could you provide me with the interval ranking (intervals from most consonant to most dissonant, in that actual order) of the 12 TET tuning system please as this will allow me to finalize this topic and move forward.

What i am solely and absolutely trying to achieve here is acquiring the notes of an octave or intervals of our standard tuning system 12 TET from most consonant to most dissonant so i can utilize them in composing and have complete control over the composition. I don't require explanations as to why or how the process works with all due respect. I am solely seeking 12 TET intervals from most consonant to most dissonant.

I was under the impression that the ratios from just intonation was my answer but I've found out recently that I'm wasting my time speaking on just intonation as we compose in 12 TET.

Kind regards.

Answer 1

Is it correct that composers of most popular genres use 12 TET based interval consonance and dissonance when building chord progressions and a composition as a whole?

No, not really. I mean, it's true that popular songs use mostly 12 TET for their framework (although not strictly, since singers don't stick to religiously to 12TET, not do lead guitarists or many other instruments), but "interval consonant and dissonance" is only 1 part of composition, and isn't enough to define how and why chord progressions work. It is one part of the equation, but still only paints about 10% of the picture (to be completely unscientific for a second)

If you're talking about melody (i.e., horizontally), then the "consonance" of an interval used in a melodic step is not really relevant to making a good melody; melodies may move in half steps, whole steps, thirds, fourths, fifths; the consonance or dissonance of those stepwise movements when expressed as intervals is rarely a factor at all (unless outlining some implied harmony).

When talking vertically, unless you're talking about a melody played against a drone (like in Indian classical music, which doesn't use 12TET), then "interval consonance" is not going to tell you all that much, since music uses way more than 2 tones simultaneously.

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So let's dispense with intervals and talk about chords (as you said in the opening to your question). The consonance and dissonance of specific chords is of course one of the factors in composition of a song, but it's by no means the only factor. Why some harmonic movements work isn't just a factor of consonance vs. dissonance, there are many, many other factors (otherwise C major to G major would sound the same as C major to Eb major; they're both a movement between 2 equally consonant chords).

If what you're looking to do is obtain a scientific measure of consonance vs dissonance then I believe that there are some equations that psychoacousticians have written to try and scientifically describe this human perception of frequency (links at the bottom). But measuring consonance and dissonance doesn't in itself explain either melody or harmony very well at all.

Let's be scientific, and take a premise (the one more or less implicit in your question): "consonance (as defined scientifically by frequency relationships, sometimes called "acoustic roughness") is the primary determiner of how chord progressions are determined in western music."

With that premise in mind, let's think scientifically. What would this model predict?

Well, take the following 3 chord progressions for example:

(1) | C | D | F | G | C

(2) | C6/9 | D9 | Dm11 | G13>G♭13 | CΔ9

(3) | CΔ | Am6 | FΔ7/A | Ab6/9 | C

You should expect them to sound radically different.

Why? In terms of consonant/dissonance relationships they're all over the shop, almost as far apart as you can guess. And to add to that, the movement of the roots is in different intervals too (if you want to look at it in a stepwise approach).

How do they actually behave though. Well, they're very close to each other; in fact they could all be used completely interchangeably in certain musical contexts (I've deliberately given extreme examples to stretch the point as far as possible, but it's still the case).

Now, for a converse example, let's look at the following chord progressions:

| C | D | F | G | C

| C | B♭ | G | F | C

| C | A | B | F♯ | C

You would expect them to sound and behave similarly according to the "consonance/dissonance is what's important". They're all combinations of major chords, and so with exactly the same "consonance". But 1 sounds like a basic chord progression, and 3 is almost completely unusable.

1 and 2 have the same interval steps between each chord, and yet they're still completely different beasts (way less similar than the chord progressions above for example).

So I think we can see from this that a model of harmony based only on "chordal consonance" is insufficient (in fact; useless) to explain (and therefore, conversely, to build) chord progressions and compositions as a whole. Chordal consonance is 1 ingredient in a vast array of (sometimes complimentary, sometimes competing) elements that make up melody and harmony. A significant one for sure, but not by any means a standalone "explainer". And, of course, melody and harmony are themselves only 2 elements that make up "music" as a whole.

Basically, consonance and dissonance exists, and is important, but is just one piece of a large large puzzle.

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Now, that said, if you want the list of intervals by consonance as plain intervals (without musical context) it's conventionally (from memory):

Octave P5 P4 M6 M3 m3 m6 m7 M2 M7 m2 b5

That's in 12TET, and pretty much all other meantone temperaments too (of which 12TET can be considered a "special case".

In just intonation it's the same, so long as you're not using the 7:4 harmonic seventh, in which case m7 jumps up the pecking order a little. But conventionally the m7 in just intonation is represented by 16:9 (2 fourths) or 9:5 (p5 + m3). The same with tritones, if you consider just tritones then they can become a little more consonant, but that's quite a complex problem, so it's best to leave it out.

Of course, musical context changes this. A M7 can sound much more stable in a major 7th chord or a minor 9th chord for example than it does in a minor major 7th chord. Even a tritone can sound consonant in a spacious, airy voicing of some sort of lydian-y chord, like a good voicing of a Δ♯11

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links for places to start looking about mathematical descriptions of consonance and dissonance.

https://en.wikipedia.org/wiki/Consonance_and_dissonance#Physiological_basis
https://courses.physics.illinois.edu/phys406/sp2017/Lecture_Notes/P406POM_Lecture_Notes/P406POM_Lect8.pdf
http://upcommons.upc.edu/revistes/bitstream/2099/8052/1/article2.pdf http://sethares.engr.wisc.edu/consemi.html
https://en.xen.wiki/w/Harmonic_Entropy

a stack question about it: Is there a way to measure the consonance or dissonance of a chord?

Answer 2

The ranking of consonance and dissonance of intervals is essentially the same in 12-tet as in "just" tuning. Same for the "mean-tone" tuning. That's why the tempered tunings work well.

Answer 3

Is it correct that composers of most popular genres use 12 TET based interval consonance and dissonance when building chord progressions and a composition as a whole?

Yes, but this just begs the question: how are consonance and dissonance used?

Could you provide me with the interval ranking (intervals from most consonant to most dissonant, in that actual order) of the 12 TET tuning system please

A slight alteration to the beginning of @Some_Guy's list...

P1 P8 P5 P4 M6 M3 m3 m6 m7 M2 M7 m2 b5

...as this will allow me to finalize this topic and move forward.

Finalize what topic: 12 TET Interval Ranking, building chord progressions, complete control over the composition?

...I don't require explanations as to why or how the [composition] process works with all due respect.

I think you mean you don't need an explanation of how consonance and dissonance are used in composition but rather you intend to use an interval ranking to guide composition.

Compose in what style?

Perhaps you can use an interval ranking to compose in your own eclectic style, but I've never seen any composition method like this in common styles like classical, rock, blues, etc.

Answer 4

I don't know if this is the true dissonance ranking but here is my personal ranking:

Rank -1

Unison

This I don't really consider to be an interval because the 2 notes are exactly identical. So, that is why I gave it the negative rank.

Rank 0

Octave and Perfect fifth

These are the 2 most open intervals and so it isn't surprising that these intervals would be the most consonant. I don't consider the seventh to be open because when you invert it, it becomes a second. Octaves technically invert to a unison but practically speaking, they self-invert, meaning that an octave becomes another octave. Fifths invert to fourths so there isn't much difference. Also, these intervals are fundamental to any tuning system. Without them, the entire field of music theory would fall apart.

Rank 1

Perfect fourth, Major third, and Major sixth

Unlike some people who view the perfect fourth as dissonant, I don't, at least outside of contrapuntal contexts. It isn't as consonant as the perfect fifth but it isn't all that dissonant either. Some might argue If it doesn't appear in the harmonic series, than it is dissonant but then that would lead to the tritone being more consonant than the perfect fourth which is just wrong.Thirds and sixths tend to be consonant but the major ones are understandably more consonant than their minor counterparts.

Rank 2

Minor third and Minor seventh

This again isn't agreed upon but I view these 2 intervals as being consonant but not as consonant. This is partly because, when you combine the two intervals, you get a very peaceful sounding minor seventh chord.

Rank 3

Major seventh and Major second

These 2 intervals are both quite dissonant, the second especially. But they still have a lower ranking than the last few intervals.

Rank 4

Minor second and Minor sixth

Now this might seem odd, after all the minor sixth shows up everywhere. But here's the thing. When it shows up as part of a chord, I rank it based on how consonant the chord is in root position. When it is all by itself with no harmonic context, at least to me, it sounds augmented, more specifically like an augmented fifth. And augmented fifths are dissonant.

Rank 5

Tritone

This is the only rank besides the negative rank that has a single interval. To put it simply, the tritone is the most dissonant interval, not just a very dissonant interval. Part of the reason is that it divides the octave cleanly in half. Now you might think that octave symmetry should make it very consonant. But in fact, this usually turns out not to be the case. For example, the whole tone scale, as a scale is relatively consonant. But harmonically, it is extremely dissonant. All the fifths are either diminished or augmented. This makes for some weird harmonic progressions. So actually, symmetry is kind of a guarantee for extreme dissonance. That is, unless you consider Dorian to be symmetric(which most don't, when most people say symmetry in music theory, they mean octave symmetry, not palindrome symmetry).

But like I said, this is my own personal ranking of the intervals. The objective ranking in 12TET may very well be different. But this personal ranking does all have to do with 12TET since it is the only tuning system I use.