# QUESTION: Symmetrical Triads and Inversions



## Osorio (Feb 29, 2012)

I have been studying some musical theory and Im particularly intrigued by the subject of symmetry vs. asymmetry and the implications and applications, but Im kinda stuck. 
I know of the existence of the whole, whole-half and half-whole tone scales, and that they accommodate a variety of chords amongst diminished, augmented and sevenths, but to what effect can I use these scales and chords? What are their colors, how have they been used through-out the history of music? What could be called a common function for such chords and inversions? Build tension, release?

How is that knowing a scale as it being symmetrical can aid me in composing and interpreting? How can I use these less standard intervals to their maximum effect?

What are the implications (melodically and harmonically) of the Augmented Chord being a symmetrical inversion?

Hope this is not asking to much... I tried looking around on google for symmetrical on the forum, but I find more information of 12 tone row, for some reason. While interesting, now what Im looking for right now.
Thanks in advance for any info you can provide. Cheers!


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## Mr. Big Noodles (Feb 29, 2012)

There are two symmetrical tertian chords: the diminished seventh chord and the augmented triad. In functional harmony, these are vii°7 and V+, respectively. So, they have a leading tone function. They can, indeed, invert in this context. Though they are symmetrical, you'd still describe a first inversion vii°7 chord as vii°6/5, or a second inversion V+ as V+6/4. I'm at school right now, but I can expand upon this more later.

In atonal composition, you probably want to avoid tertian sonorities, so they're not much use there. The whole tone scale and diminished scales are, therefore, only coincidentally a source for these sonorities. In chord-scale theory, it's simple: match the scale with the chord. Otherwise, I don't relate the two.


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## Osorio (Feb 29, 2012)

Thanks a lot for the quick look into my questions! I don't understand atonal too much to be able to comment, but I thought the whole point of atonal was to have scales and notes that don't match traditionally.
As for their leading tone functionality and "harmonic spelling", thanks for clearing that up. Inversions of chords confuse me deeply...



SchecterWhore said:


> I'm at school right now, but I can expand upon this more later.



I would really appreciate that if it doesn't hamper your schedule too much!


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## Mr. Big Noodles (Mar 1, 2012)

venneer said:


> Thanks a lot for the quick look into my questions! I don't understand atonal too much to be able to comment, but I thought the whole point of atonal was to have scales and notes that don't match traditionally.



Atonalism has nothing to do with scales, really. It's all about the power of the motive. You're right that there is an element of avoiding traditional sonorities, since atonal pitch philosophy generally states that tonality is limited in what it can express and that the socio-musical ideas since the year 1900 are too complex for tonality to handle. After all, at the end of World War II, humanity possessed the ability to destroy our entire planet. How do you write about that with a pitch system that is built on resolution and a rhythmic language that uses a predictable, regular pulse? The fear of nuclear disaster is still a reality, and we're well aware of all of the other atrocities that humanity commits. Predictability and natural stopping points just aren't part of that equation.

Forgive me if that sounded preachy, but we have to talk about atonality on a philosophical and sociological level in order to grasp the thinking behind abandoning tonality. Besides, it's a lot easier and more intrinsic than pulling out the 12-tone matrices and doing set theory analysis.

Charles Ives - The Unanswered Question


Edit: By the way, there are many 'atonal' pieces that use the diatonic scale. Atonality is more of a concept than a process, although there are processes that ensure purity of the concept, like Schönberg's twelve-tone method, or composing with symmetrical scales, or soundmasses.



> I would really appreciate that if it doesn't hamper your schedule too much!


Gladly. This is proper voice leading for this kind of thing:







Basically, the fifth of the augmented chord acts as a "leading tone" to the third of a MAJOR tonic chord. When dealing with MINOR, though, the fifth of V+ and the third of i are the exact same note, and just having it carry over by common tone is kinda lame, so it leaps down to the tonic instead. This thread has a bit on augmented chords: http://www.sevenstring.org/forum/music-theory-lessons-techniques/114783-show-me-some-whole-tone.html
Let me know if you need further explanation.


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## Osorio (Mar 1, 2012)

That was all excellent! Thank you for the help  I think I get how to dissolve and more properly apply these concepts now... The linked thread was also extremely useful, thanks for it.
I really liked your explanation on atonality, makes a lot of sense. It was an interesting experience listening to that piece before and after reading your thoughts, I'm glad I did it. Changed my perspective on the whole piece. Also, the resolution of the V+ on Minor and Major with the proper voice leading were JUST what I was looking for, that one really helped.

I think I got what I needed, but I am inclined to ask for the further explanation just so I can keep learning  Don't worry though, I think I got it. Maybe after some more hours of play and read I can ask something more interesting to you and all of us. Thanks a lot


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## Mr. Big Noodles (Mar 1, 2012)

Oops, I screwed up. In the V+ i resolution, the B in the tenor voice should leap down to G. Otherwise, there's no third in the chord. Better yet, use a seventh chord. An updated version:






When you're using an +7 chord, you want to voice the augmented fifth above the seventh, or else the resolution will be weak.

As with all tertian chords, there is a functional element as well as a textural element to augmented and diminished chords. Here is a functional use of an augmented triad:

The Beatles - I Want You (She's So Heavy)


The first phrase ends with a half-cadence at 0:10. That chord is A+, or V+ in Roman numeral notation. A normal half cadence would just be A, but if you play it like that, you'll quickly realize why they didn't do that. Augmented triads are much more evocative than major or minor triads. Their strangeness prevents their widespread use, but when they are used, it is to great effect. Their dissonance is greater than any other triad, and they have to be handled more carefully when resolving, but they can have a very nice effect when used in the proper context. The same principle makes them ideal candidates for use as color chords.

Claude Debussy - Voiles


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## Osorio (Mar 1, 2012)

SchecterWhore said:


> The first phrase ends with a half-cadence at 0:10. That chord is A+, or V+ in Roman numeral notation. A normal half cadence would just be A, but if you play it like that, you'll quickly realize why they didn't do that. (...)
> 
> Augmented triads are much more evocative than major or minor triads. Their strangeness prevents their widespread use, but when they are used, it is to great effect. Their dissonance is greater than any other triad, and they have to be handled more carefully when resolving, *but they can have a very nice effect when used in the proper context.* The same principle makes them ideal candidates for use as color chords.



I don't know how the song actually goes (my hearing is still in training process to be able to analyze this sort of thing on the fly), but having the A as the Fifth, I played a progression from D to A, and a cadence from C down to A. Neither sounds jarring so as to say that I would rather place a V+ there. I don't know what I'm missing, maybe I just don't have experience enough in this kind of arrangement. I understand they sound different, the V+ is a much stronger chord, and if my understanding of "color chord" is correct, then yes. It is there because it places more emphasis on the turn around; but I can't really say I feel is obvious that the chord would go there, if I was composing it for that effect. (not sure if I'm making sense).

Also, I have no idea what the proper context would be. Why does that substitution work so well while others wouldn't? Maybe this is why I'm having some trouble getting the whole picture on this one. I mean, it makes all the logical sense it could, but I have no idea how I would apply this mechanism / concept.


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## Mr. Big Noodles (Mar 2, 2012)

V+ isn't a substitution, it's a chromatic alteration. A substitution is when a chord with a different root is used to fulfill the function of another function. So, vii° and V are substitutions for each other. So are IV and ii. However, if you use v instead of V, then you're dealing with an alteration.

The progression at the beginning is Dm Dm/F E7(b9) A+, i i6 V7b9/V V+. If it were Dm Dm/F E7(b9) A, then the harmonic functions would still be the same, but you lose some of the tension that comes with the augmented triad. V is still tense, but V+ is more tense. The effect is intensified because the phrase comes to rest on the V+.


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## Osorio (Mar 2, 2012)

I see, sorry for the improper wording and mix of concepts. 

So, as I understand, the alteration was made to accentuate "the phrasing" (having troubles with words here), and take advantage of the leading qualities of the V+ for a stronger "break" (sorry about the terminology). Since the half-cadence is considered weak in resolution, the intent was to give it an extra push with the augmented qualities... Correct?
In this manner, both harmonically and rhythmically, the phrase was constructed in order to have as much impact as it could, even having a rest on the V+ so the alteration could be more "visible". I think I get it.

I still sort of have trouble on identifying this sort of situation, but I think I realize now that it's not a right or wrong thing, but more of understanding when I want tension to build and to release and how do I control these voice leadings so that they become more effect to whatever purpose I have in mind.

Thanks a lot for your help, SW! Greatly appreciate it.


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## Mr. Big Noodles (Mar 2, 2012)

Yeah, you've got it. You're welcome, dude. The normal purpose of a cadence is to provide resolution to a phrase. However, the instance that I pointed out above is a half cadence. Half cadences crave resolution, they make you really want it, and that desire only becomes more apparent when the dominant chord has some ugly chromatic alteration. Notice how ending on the V makes the music linger, and that augmented fifth gives it a biting quality. We're dealing now not only with the dissonant function of the harmony (the dominant chord) but with the dissonant color of that chord quality (augmented) as well.


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