Non-Traditional Harmonic Systems

Do you use non-traditional harmonic systems?

How do you go about creating them and applying them to your music?

What are to you the essential aspects of a harmonic system?

Composers Phil, thanks for the detailed answer and the book suggestion! Although i don't see how your first system is atonal compared to the second (don't you use "dominants"?)

I would like to know: Do you also have principles for employing non-harmonic tones? which ones? Do you use the same as in traditional harmony (resolution by step,etc..) or did you create your own ones? How do you employ your harmonic system in a contrapuntal context?Do concepts like scales and modulation exist in your non-traditional harmonic systems?

Well, I have devised a number of different 'systems', but I think the two I have recently come up with have potential to prevail over a number of works. One set of restrictions applies to atonal passages/ideas in my works: the other, tonal. The former is basically a catalog of 6 note chords (aka hexachords), built up of two 3 note chord that are identical in structure. With each hexachord: the other remaining 6 notes in the total chromatic form the exact same harmony at a transposition. These hexachords (16 in total: each having the potential to be formed in a number of different ways for a different characteristic color) are ranked precisely by their interval content (for example: the hexachord with the most tension and which is treated as a 'dominant', has 3 tritones and 4 semi tones; the least dissonant having no tritones and only one semitone).

My tonal system is based on the overtone series and the controlled resolution of tri tones. I partitioned the full chromatic into 4 augmented triads: each having a particular function to one another (for example: for any triad, there is one other which consists entirely of overtones for every pitch in the first group. For the C/Ab/E triad, the Eb/G/B group can function as supporting tones for any tone in the first triad which would function as the root). The two other triads form tri tones: one to the 'roots', and the other to the 'supporting tones'. I use this system in the following manner: for a single tonality, there are two tri tonic dyads which can resolve by step in contrary motion to it (for example: if C is the tonal center, these dyads would be B/F and Bb/E). These dyads can resolve to several other places as well, but when they both appear together, they only resolve to C or it's counter pole F#. I 'pick and choose' which notes will be used in a chord depending on what the context calls for: only a few notes are absolutely necessary, though the addition of others serves to strengthen the root.

This all being said (and I do hope that I presented this in a language that is easy enough to follow): it is a good idea to consider how you might create a sense of direction (although this is just my opinion: many composers have put restrictions for themselves with different purposes than conveying a sense of tension, release and or harmonic direction). I am personally grounded in the idea of tonality: whether I am being direct with root progressions and carefully resolving tri tones, or I am destroying any emphasis on a single pitch while still manipulating the amount of tension.

I don't expect anyone to use my systems (and they are far from perfect), but I hope that people reading this might be inspired to go in their own direction which is why I took the time to attempt to explain them. It is important to understand that these type of restrictions are best viewed as methods to achieve coherence and consistency: not those to generate music on their own. For those in the same boat as the OP: I'd highly recommend checking out Hindemith's "Craft of Composition". He covers some really important things that are a good place to depart from (though I may not necessarily agree with everything he says).

That's interesting, as I also devised a system around the notion of manipulating the 4 augmented triads. This can be seen in my Nocturne No.1 for Violin and piano. Mine doesn't seem nearly as complicated though, and I use nonchord tones pretty freely as long as they resolve towards a pitch in the harmonic field.

Uh

I guess by "activation of the harmony" you mean arpeggiation?

Also,how do you "manipulate" the augmented triads? Frankly I couldn't spot it in the score of your piece

This is what I wrote, explaining what I did in the piece, to my professor. I typed it up in like 10 minutes so it's not that in depth or well written, but it should give a basic idea of what I was trying to do.

Although the project was aimed at using twelve tone as a method of tone organization, I decided against it, to instead use my own system that I used on a few of my pieces last semester. This system is based on augmented triads and the intervals they create from the bass to the soprano line. Most of what I have is based on experimentation. I would construct chords and judge them. If I liked how they sounded and progressed I would ask myself, why? Then analyze the properties of the chords. One of the easiest ways to explain what I have done, is to look at my piece, especially the first phrase, which is ideally what the system is about. Similar to a triad in tonal western harmonies, the piece uses chords of a different kind. They are essentially augmented chords, such as C, E, G#. However, I also mix them with another augmented chord to make a larger and more robust chord. Since technically, based on pitch content, there are only 4 possible augmented chords, and there really aren’t that many combinations of the augmented chords. Although a significant factor I thought was important, is the relationship from the soprano to the bass line, often a major third. Of course, this is definitely not always the case, as using different inversions can provide a slightly different sounding chord altogether, despite the unchanging pitch content. Let’s look at measure 1 of Nocturne No.1. One could look at it as an F major chord with an added C#. This is still true, however that is not what I was thinking when I constructed that first measure. Instead, it can be looked at as, a C augmented chord, where the E and G# are missing, combined with an F augmented chord (all the pitches present, F, C#, A). It is still hard to for me to explain why I put the chords in such an order besides saying, I like the way it sounds. Generally, I aim to make the major third relationship, which is seen in measure 3 when the violin comes in. It uses an E above C (in the bass) and creates the major third relationship. The inverse of that, a minor 6th is interesting to me, as it sounds quite a bit different. The first inversion, if you will, occurs at measure 4, when the overall harmonic structure remains the same, yet it has slightly changed inversion, instead with a E in the bass and the C# above, creating the minor 6th. I also found that the transition from measure 5 to 6 is very strong. I’m not quite sure why, but my best guess is because of the split from the major 2nd, F# and E to make another major 3rd relationship. This acts like a modulation, and the overall harmonic structure then is based on augmented D (D, F#, A#) and G chords (G, B, D#). A final interesting thing about this system is the easy creation and importance of a whole tone scale. If you take two augmented chords that are a whole tone apart, it makes a whole tone scale/harmonic field. This is almost like a final cadence, or ever perhaps like a tonic chord, and is useful for transitions. This is seen in the piece of measure 8 in which augmented chords F and G are used. As you can see, I do not strictly follow staying within the harmonic field created by the augmented chords. I use passing tones, and did use a fairly twelve tone-esque melody. The rest of the piece can be largely examined just based on these ideas presented in the program notes. There are a few moments of experimentation that I’m almost uncertain of what I did, but I do like what I have done overall. The form is a bit experimental for me as well. Opening with a theme, and giving small chunks of themes that reach mini climaxes, which was a goal to make a larger scale gesture within the piece. Although, making an entire piece a giant gesture was much more difficult than I anticipated, thus I made the gestures more like themes on a small scale.