For the past year or so, I have started to study music theory. I am an engineer by trade... I love math... As a result, I like proofs or a step by step explanation of how a concept arose based on the more fundamental concepts and how they interact. Applying this to my study of theory has been both incredibly enlightening and infuriating at the same time. I love that much of music boils down to patterns and their interactions. However, at the same time I have been frustrated because I typically have to dig pretty deep to find explanations or the logic behind basic concepts. So, to my current problem...

Why are harmonized scales/keys always built using 7th chords? Why not traditional I III V chords? It's driving me nuts. All of the resources I have (guitar teacher, workbooks, google) offer no explanation and just start covering keys with 7th chords. I'm sure it's simple it's just really bugging me.
A day without sunshine is like, you know, night.
- Steve Martin
Adding the 7th to the chord gives it more character. a V dominant 7 is functionally more important because the tritone between the 3rd and 7th strongly pulls towards the tonic. The other 7th chords mostly just add flavor and allows you to have more notes to play with if you're voice leading.

As to a more general why theory is the way it is, it's mostly to do with overtones and the harmonic series, these things kinda explain why consonant intervals are consonant, and most of music theory is based on consonance and dissonance.

http://en.wikipedia.org/wiki/Harmonic_series_%28music%29

edit: the reason the 3rd and 7th tritone resolves so strongly is because the 3rd of the V7 chord is a halfstep below the tonic (it acts as the leading tone) and the 7th of the V7 is a half step above the 3rd of the tonic chord.
Last edited by The4thHorsemen at Jun 23, 2014,
You don't have to harmonize your scales using 7th chords if you don't want to, there's no rule about that. If playing jazz you would be wise to do so, however.
Quote by The4thHorsemen
Adding the 7th to the chord gives it more character. a V dominant 7 is functionally more important because the tritone between the 3rd and 7th strongly pulls towards the tonic. The other 7th chords mostly just add flavor and allows you to have more notes to play with if you're voice leading.

As to a more general why theory is the way it is, it's mostly to do with overtones and the harmonic series, these things kinda explain why consonant intervals are consonant, and most of music theory is based on consonance and dissonance.

http://en.wikipedia.org/wiki/Harmonic_series_%28music%29

edit: the reason the 3rd and 7th tritone resolves so strongly is because the 3rd of the V7 chord is a halfstep below the tonic (it acts as the leading tone) and the 7th of the V7 is a half step above the 3rd of the tonic chord.

Clockwise...

Awesome, thanks for the explanation, that really helps! So it really just has to do with resolution and creating tension... interesting thank you for the explanation.
A day without sunshine is like, you know, night.
- Steve Martin
Quote by warningbomb
Why are harmonized scales/keys always built using 7th chords? Why not traditional I III V chords? It's driving me nuts. All of the resources I have (guitar teacher, workbooks, google) offer no explanation and just start covering keys with 7th chords. I'm sure it's simple it's just really bugging me.

I would say, if we're looking at genres like Blues, Jazz, Raggae, and some early rock...then you're correct. BUT there's a lot of times where we consider only I, IV, V chords (without a 7th). It all depends on what kind of tonic connections you're trying to make.

For example, in classical music, it was almost an unwritten rule that you didn't use a 7th -- except on the V. As others have said, this is because the 3rd and 7th (of a V7 chord) push heavily towards the tonic. But using a 7th in other chords was considered "bad form" or whatever.
Last edited by crazysam23_Atax at Jun 23, 2014,
Mathematician here. Are you trying to axiomize music? If so, you'll have supreme trouble doing it in any meaningful way.
i don't know why i feel so dry
Because you can remove the 7th if you want. It gives you more information. For example, it shows the difference between the V and other major chords (I and IV) in the same key - they have a different 7th in them.

In jazz almost every chord is a 7th chord. In classical music you would not usually harmonize the scale with 7th chords.
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

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Quote by Eastwinn
Mathematician here. Are you trying to axiomize music? If so, you'll have supreme trouble doing it in any meaningful way.

I can still try I am just trying to determine why all of my available theory resources go from talking about triads solely to talking about key progressions in sevenths.

If it is just a matter of preference or resolution vs tension I can deal with that. It just bugs me when things hop around with out explanation or logic. I was just trying to make sure I wasn't missing something fundamental.
A day without sunshine is like, you know, night.
- Steve Martin
Quote by MaggaraMarine
Because you can remove the 7th if you want. It gives you more information. For example, it shows the difference between the V and other major chords (I and IV) in the same key - they have a different 7th in them.

In jazz almost every chord is a 7th chord. In classical music you would not usually harmonize the scale with 7th chords.

That is kind of what I am gathering. It is just a preference thing. As well, I guess it is just how seventh chords get introduced. It just didn't logically flow for me...
A day without sunshine is like, you know, night.
- Steve Martin
Use of the 7th is genre dependent. In styles where you have accompaniment instruments, they are used as chord tones. Jazz, rock, pop... pretty much anything where you'd have a player sitting there with a chord chart. In styles where all the parts are composed, the 7th is incidental as part of a melody, and not really part of the harmony. You'll rarely hear old symponic music just laying on 7th chord (dominant/dim excepted).

Anyway, the point of Roman numeral labeling is to denote harmonic function, not just to name the chord. Non-dominant 7ths are rarely functional in "traditional" music, so there's little need to note the when they appear as passing tones.

edit: I and IV are both maj7.
Quote by Eastwinn
Mathematician here. Are you trying to axiomize music? If so, you'll have supreme trouble doing it in any meaningful way.

That implies you've tried.