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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.

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    Our old friend sethares.engr.wisc.edu/images/image1.gif shows 12-tet steps along the top - is that high enough resolution to work out a ranking?
    – topo morto
    Jul 16 '19 at 23:20
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    I don't understand why you say "This statement doesn't match the ratios presented in the image you provided" ? From the image, it seems that the 12-tet fifth (marked at the top) is a little lower in frequency than the just fifth, the 12-tet major third is a bit higher, and so on…just as phoog said? The image might not be high-enough resolution to clearly see what you want, but it gives you an idea. I've asked endolith if he can share how he made the graph here.
    – topo morto
    Jul 16 '19 at 23:34
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    At the moment, all I could do would be to visually correlate the 12-TET steps at the top of the graph with the horizontal positions on the curve, but of course you could do that just as easily as I could. It's because the graph is low resolution that I've asked Endolith how he made his - if we can make a higher resolution one we can answer this question.
    – topo morto
    Jul 16 '19 at 23:52
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    Isn't this going to be close to 'painting by numbers'? I don't believe any composer consults a list such as this - real or imaginary. Mainly because two notes which obviously produce an interval together will be only a very small part of any piece, and even if they themselves are construed to be dissonant/ consonant, the bigger picture (get the analogy?) needs far more than picking two notes because of their interaction together. What am I missing?
    – Tim
    Jul 17 '19 at 9:50
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    This seems like a repeat of one of your earlier questions music.stackexchange.com/questions/84269 trying to get a pure physics answer to a musical (art) question about consonance and harmony (style) Jul 17 '19 at 16:37
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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.


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.


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


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?

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  • guy you nailed my specific question. Like I have stated in the response before you, I'm going to sleep but I will reply to your much appreciated post in a few hours. Thank you for this guy!
    – Seery
    Jul 17 '19 at 6:11
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    No worries mr Seery, your appreciation is appreciated :)
    – Some_Guy
    Jul 17 '19 at 15:04
  • Yes, i understand consonance and dissonance is only one element to producing chord progressions.. My following research is on tension and resolution which this answer will be the basis off which i work off. Although music uses more than two tones simultaneously, having this interval ranking information will aid me in adding multiple intervals together to produce the desired tension or resolution. I understand consonance/dissonance is one piece of the puzzle and as that i take it. This concept is a building block and not a primary element. Thank you very much for all this, im documenting this!
    – Seery
    Jul 18 '19 at 4:54
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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.

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  • Comments are not for extended discussion; this conversation has been moved to chat.
    – Dom
    Jul 20 '19 at 2:04
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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.

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    @Seery - from your last comment - I believe you've hit the reason a lot of us are questioning this approach. We're humans, and look at (listen to) things subjectively. Music can be considered mechanically, scientifically, from a physics point of view, but an end product ( a piece) will never be perceived in anything like the same way by different people. You may well compose something and believe there's tension/release at certain points, but others will miss those completely, or translate what's heard in many different ways. So the 'absolute' parameters won't be 'absolute',Not even in a list.
    – Tim
    Jul 18 '19 at 5:46
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    I'm approaching this mostly from the aesthetic view and have to take the math from reference sources. To get an objective ranking we need to mathematic ratios. The tritone is the strangest in that regard. It get's all kinds of ratios depending on tuning system and A4 versus d5. This is then further complicated when regarding the tritone's dissonance which yanks the discussion back into aesthetics. Jul 18 '19 at 13:02
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    The tritone is at the end of the ranking, because its ratio is apparently least simple. Regardless of where exactly it falls in the ranking its treatment as a dissonance is an aesthetic matter that changes depending on style. Impressionism can treat a tritone as a soft, trembling vibration, blues can make it a aching moan, classical treats it like an instability that needs to regain balance. The various idiomatic treatments are what they are regardless of any mathematical ranking. Jul 18 '19 at 13:08
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    FWIW, I'm not questioning your approach - actually you haven't describe what you intend to do with the ranking - but if you want to compose in an established style, composition methods already exist. Jul 18 '19 at 13:21
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    @Seery -- I don't really understand what you mean by "intuitive means." Tension and release is not rule-bound, but sound-bound. Most of us don't guess what will sound good; we try things out, and keep the things we like; we develop a vocabulary of sounds, and build on and with that. Starting from some "first principles" may be helpful in establishing a vocabulary, but be careful not to get trapped by your own rules.
    – ex nihilo
    Jul 18 '19 at 16:28
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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.

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    Major seventh is very dissonant on its own (similar in quality to a flat 9). Don't let the fact that it sits happily in a maj7 chord fool you, without context it's a dissonant interval.
    – Some_Guy
    Jul 17 '19 at 3:24
  • @Caters thank you absolutely so much!! This is the style of answer I was searching for. I'm going to sleep now but will respond to your wonderful post in a couple of hours. Thank you for your insight!!
    – Seery
    Jul 17 '19 at 6:05
  • @Caters I admire your in depth theory on interval ranking, it really is a joy to read so thank you very much. I have written down your ranks and will compare them to others answers and see which intervals coincide the most with the different answers and utilize that ranking. This is not a question but more so a comment.. You say that the Tritone is the most dissonant interval of an octave but i examined the Major Seventh interval and it seems that its the most dissonant interval in an octave by far! Even the Minor Second intervals seems more dissonant but not as much as the Major Seventh.
    – Seery
    Jul 18 '19 at 4:01
  • @Some_Guy I had someone give me there perspective on this already but im curious for your take.. Do compound intervals such as the flat 9 hold the same level of consonance/dissonance than its lower octave interval minor second? I suspect the answer is yes based off that octaves of pitches are the same frequency just doubled.. What do you reckon?
    – Seery
    Jul 18 '19 at 4:04
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    If this answer isn't proof that interval dissonance rankings are subjective, it's strong supporting evidence.
    – Dekkadeci
    Jul 18 '19 at 16:37

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