Sunday, September 18, 2016

Post-Tonal Harmony Ideas (1)

1. Post-Tonal Harmony

"Post-Tonal" Harmony refers to harmonic practices not based on tonality that emerged since the end of the nineteenth century.

Basically, this includes any variety of atonality, such as free (i.e., non-serial) atonality and serialism, but, at least in my definition, it could also include music based on Messiaen's modes of limited transposition (or other constructed modes), quartal and quintal harmony, bitonality (provided it does not sound like tonality with chord extensions), and even the use of chords borrowed from tonality, but not used in a tonal context. A longer, but by no means comprehensive, list can be found in an earlier blog post I wrote (A Sampling of Post-Tonal Techniques and Ideas for Composition), and there are many on-line sites with information on this topic.

2. Atonal Harmony

"Atonality" which can be thought of as a sub-genre of post-tonality, tends to be defined more narrowly. Here is the opening paragraph of Wikipedia's article on Atonality:
Atonality in its broadest sense is music that lacks a tonal center, or key. Atonality, in this sense, usually describes compositions written from about 1908 to the present day where a hierarchy of pitches focusing on a single, central tone is not used, and the notes of the chromatic scale function independently of one another (Kennedy 1994). More narrowly, the term atonality describes music that does not conform to the system of tonal hierarchies that characterized classical European music between the seventeenth and nineteenth centuries (Lansky, Perle, and Headlam 2001). "The repertory of atonal music is characterized by the occurrence of pitches in novel combinations, as well as by the occurrence of familiar pitch combinations in unfamiliar environments" (Forte 1977).
To be clear, my definition of post-tonality is considerably less restrictive than the opening sentences of the Wikipedia article above, which appear to preclude the possibility of pitch-centres in atonal music.

3. Pitch Centricity

The idea of "pitch centricity" – music that is based in some way on a pitch centre – is inherent to tonal and modal music, but many (click this link, and/or Google the term) argue that it is also relatively common in atonal/post-tonal music.

I agree with this, which is why I often encourage students to write some variety of post-tonal music with pitch centres, and to move between different pitch centres within a composition, borrowing from tonality the concept of departure from, and return to, a "home" pitch centre, using various "modulations" along the way. A fellow composer and long-time friend of mine, Omar Daniel (who teaches at Western University), once told me something along the lines of, "one of the biggest problems I see in student compositions is an unwillingness to modulate," by which he meant change pitch centre, not change key. I think.

4. Can Post-Tonal Music use Triadic structures from Tonality?

Quick answer: Yes, it is fine to use harmonies borrowed from tonality (e.g., major, minor, diminished, dominant sevenths, etc.) in post-tonal music, as long as they are removed from their hierarchical/functional context within tonality. Indeed, that is the main topic of today's blog, and if you want to skip ahead for examples of how this can be done, scroll down to #8 below.

If part of our definition of post-tonal harmony is "harmonic practices not based on tonality," it would be useful to understand what we mean by tonality.

5. Tonal Harmony

Tonality refers to a systematic approach to musical composition using major and minor scales, based on:
  1. Hierarchical chord-progression practices involving chord functions (e.g. pre-dominant to dominant to tonic class; );
  2. Relationships between notes, such as contextual attractions or tendencies (e.g., leading-tone resolution in dominant harmony (^7-^8));
  3. Resolutions of perceived instabilities (e.g., chord 7ths, suspensions, and other non-chord tones).

6. Common Chord Progressions Found in Tonal Music; A Chord-Flow Chart

"Hierarchical chord-progression practices" in tonality refers most generally to the chords that establish a key, namely dominant – tonic harmony, and predominant – dominant – tonic harmony. This is the basis of the following chord-flow chart, as found in Tonal Harmony, by Stefan Kostka and Dorothy Payne (McGraw-Hill):

By the way, this is a diatonic version of the chart for major keys, but it is virtually identical in minor keys. Chromatic variants of the above chords usually function as their diatonic versions, so bIII functions as iii, bVII functions as vii°, bVI functions as vi, etc. Also, there are exceptions to this chart found in the music of many composers of tonal music; the chart is a pedagogical tool, meant to represent the chord-flow options that are usually found in tonal music.

7. Does this mean chord progressions that do not follow the above chart are post-tonal?

Not necessarily; V - IV - I is a relatively common pop and blues chord progression that is clearly tonal, and yet V to IV is not available in the chart, and there are other exceptions as well (another common one is bVII - IV - I).

The following progression, in which every chord after the third does not follow the above chart, is clearly tonal. It consists of a descending C-major scale with a first-inversion triad on every note. This is an example of "parallel-sixth chords," wherein passing sonorities are not considered to be functional; the underlying functional harmony would be I6 - V6 - I6:

8. Finally! Some Post-Tonal Options: Combining and Recontextualizing Chords to produce Post-Tonal Sonorities; You won't BELIEVE #3!

As stated previously, my definition of post-tonality is fairly open; harmonic practices that came after tonality and are not tonal can be considered to be post-tonal. This would include post-tonal music that combines triads (or seventh chords, or ninths, etc.) found in tonality in such as way as to produce sonorities that are clearly not tonal and are not used within a tonal context.

Here are some examples; play the audio file below each example to hear what they sound like:

1. This is based on the combined C major and F# major chords (i.e., two major chords whose roots are a tritone apart) found in Stravinsky's Petrushka (1911); I added a three-note figure with two additional pitches (Ab and D) at the end, because I like the sound:

2. This begins with a C7 chord, upon which four additional pitches based on a B° triad are added:

3. The next example starts with a D7 chord that becomes a D9 on the third beat of the bar; a G#m chord with a major seventh and major ninth is superimposed:

• Examples 2 and 3 above, which began with dominant seventh chords, could be used in a tonal context, if the dominants resolved to their expected tonics within tonal music. #2 could therefore resolve to an F chord, and #3 could resolve to a G chord. Try this yourself, if you can access a keyboard, to hear what this would sound like.
• Therefore, in order for the above examples to truly be post-tonal, they should not progress to any chords that could be interpreted as constituting a progression of functional harmony.   
 4. The next example uses quartal harmony, but, instead of stacking a series of perfect fourths on top of one another, which creates a pleasant-but-static quality, I stacked two perfect fourths, then went down by whole tone and stacked two more perfect fourths on that note, then repeated it a third time, finishing with three stacked fourths instead of two. The result is very different than just stacking fourths on top of one another until you run out of notes:

Try superimposing different chord combinations, notating any you like and/or find to be of potential use in your compositions. Feel free to borrow any of the examples above as well. You don't need to limit yourself to chords, either; you can start with a chord and then add to it different notes or scalar passages that happen to sound good, and help recontextualize the chord so that it no longer sounds like a traditional tonal sonority.

9. But Wait! There's More! Tonal Chords Progressing in a Non-Tonal Way

Another way to present tonal chords in a post-tonal context is to create progressions that consistently and deliberately do not follow the above chord-flow chart, and do so in a way that prevents any suggestion of a clear tonic chord and functional harmony. If you try this, you may find that it is a surprisingly difficult task to create a chord progression that doesn't sound "wrong" to your ears.

This may be due to the strongly tonal association each individual chord has, since each individual chord in such a progression is typically major or minor; when recognizable chord-types do not "behave" (i.e., progress) as we expect them to, it can be disconcerting. In the section 8 examples above, where different chords were superimposed, the resulting vertical structures were not traditional tonal chords, and thus created fewer expectations that they "ought" to progress in a tonal way.
– – – – –
Giant Steps is a John Coltrane jazz composition so seminal that its chord progression is known as the "Coltrane changes;" it is required learning for any gigging jazz musician. Although it is tonal, it uses some unexpected chord changes: BMaj7 to D7, GMaj7 to B, and EMaj7 to F#7; these are somewhat unusual progressions in tonal music, although they are common enough that there is a name for them: Each chord pair forms a chromatic-mediant relationship. Not only that, and this is probably what makes it sound so unusual, but the first chord of each of the chromatic-mediant pairs also forms a chromatic-mediant relationship with the first chord of the next pair, and the same is true for the second chord of each pair as well.

It also uses some very common progressions, notably, several V7-I tonicizations. However, each tonicized chord (GE, and B) is a major third from the next one, which means that together, they outline an augmented triad; this is highly-unusual! It is usually played very quickly, which helps make the augmented triad of tonicized roots even more evident:

Again, Giant Steps is tonal, but you can explore the possibility of using tonal triadic structures (i.e., major, minor, diminished, etc. chords, possibly with chord extensions like 7ths, 9ths, etc.) in a post-tonal context by writing chord progressions that do not follow our chord-flow chart above, taking particular care to avoid any hint of ii - V - I progressions, which are used to establish keys in tonal music. As mentioned above, You may find this a challenging task, but if you do come up with any you'd be willing to share, please do so in the comments section!

Here's one attempt; some of it uses double-chromatic-mediant relationships (two triads a third apart with no notes in common), some uses chromatic-mediant relationships (two triads a third apart with one note in common), and there are some non-tertian root movements as well. To my ears, it succeeds in avoiding being tonal (at least in any obvious way), but does it succeed as a musically-useful chord progression?

10. And That's Not All!

While this last approach above can produce useful results, I find that a much more satisfying and rewarding approach is to write a progression of non-tonal harmonies, each of which would be the result of sitting at a piano and just trying different harmonic sonorities until you find one you like or consider to be useful, and repeating this until you have perhaps 12-16 chords. If you'd like learn more about this approach, it is described in greater detail in this blog post: Project 1: Writing an Atonal Theme and Variations. In my experience as a teacher, it has produced some of the best work I have heard from early-stage composition students.

One of the keys to growth and improvement as a composer is to be willing to try new things; I encourage you to experiment with these approaches and many others.


Emery van de Wiel said...

Seeing all these different examples of non-tonal progressions is very helpful. As a student who has studied classical music my whole life if is hard to veer away from using the classic V-I and to keep away from the chord hierarchy even when not thinking about it. I've done a lot of thinking about it myself and have come to the conclusion that, for me at least, I enjoy listening to music for anticipation. I have an idea that there is a correlation between the excitement of a piece and anticipating what's coming next. Of course, surprises are welcome but most welcome when you expect something else. A sequence of surprises is not very surprising. This is not in any means a rebuttal to this blog post but an excuse/reasoning for why I personally have such trouble getting away from tonality. In fact, it is good that there is a certain amount of forcefulness going into getting away from it otherwise I never would even try. That being said it may still be difficult to write a piece I am truly happy with under such restrictions.

Clark Ross said...

Thanks for sharing your thoughts, and I'm glad you found this helpful. With regards to your last sentence about the difficulty in being happy with music you might write in the future that is restricted to post-tonality, my thoughts are:

1. It is fine to feel the way you do. I suspect many composition students have these trepidations as well. Heck, even I remember being very suspicious of all the modernist music we had to listen to when I was a student.

2. Many students over the years started out feeling this way but changed their minds after trying new things and discovering that they actually liked some of them. An aspect of post-tonality that I try to stress is that it encompasses a huge range of possible styles and techniques. Some of them, like serial music, can be a tough sell for many musicians, but (a) if you try hard enough, there is often a way of writing a piece that you like, using a technique you did not initially like (in yesterday's class, for example, we heard a 12-tone piece by Jack that had great rhythmic vitality, and I suspect that made the atonality less of an issue for many people), and (b) there are so many available approaches to post-tonality that I find it difficult to imagine that you would not eventually find at least one that you like, and that opens your eyes and ears to new possibilities. So, all I ask that you keep an open mind to this possibility, and actively seek out possible alternatives to tonality.

3. Please check out the third blog post in this series, and listen to the piece I wrote; I would be very interested to know your thoughts on that approach to harmony (it involves superimposing triadic-based chords that are not normally combined in tonal music, and the chords can include 7th and 9ths, etc.).

Kassandra-Anne Demers said...

Reading this post just before our final composition of the semester could not have been more perfectly timed.

Taking the Petrouska chord and adding your own spin to it was really neat and also a great tool in exploring post-tonal sonorities. My favourite was no. 4, the stacking fourths.

I often find my ears just always have old habits and tendencies to go places of what I WANT to hear. This is probably a result of studying and primarily being exposed to tonal music. So as a precaution I may not be thinking outside of the box much.

By looking at other compositional works and taking pre-existing post-tonal chords and messing with them is a great method to explore new harmonic possibilities. My last composition semester with Dr. Staniland I was given the assignment to compose in the style of selected composers (Scriabin, Ives, Shostakovich). This essentially opened my harmonic language to new possibilities because I had no choice but to try and capture the sound and style of the given composer. This forced me to move away from my own tendencies. Taking from other composers is a great way to explore and generate new ideas.

I also want to add that the recording examples are really helpful to get a sense of your topic.

-Robert Humber said...

I liked the examples you used for the different combinations of chords. One thing I have enjoyed in the past is balancing tonality and post-tonality in a way that accentuates the beauty of each. Two of my favorite newer composers, Rautavaara and Silvestrov (new meaning Rautavaara died this year and Silvestrov is probably 80+ years old), both share this philosophy it seems. The challenge I always find then is making it sound natural, which is sometimes not easy. I continue to work on this aesthetic, however, confident that my work will get more and more polished with practice.

Flutiano said...

Thanks for summarizing your definitions for post-tonal music in this post, Dr. Ross! It helps clarify what you're looking for in our compositions.

I found the cadence in your tonal-chords-progressing-in-a-non-tonal-way progression really interesting. The Dm, Fm7, Bm(maj 7) had a really interesting sound. I may steal that for a piece some day . . .

In terms of not believing number three. Well, okay, nothing to do with not believing number three. When I was listening to number three my ear wanted it to keep going up to the next D instead of stopping on the Bb. I wouldn't have expected that, given that there is an E sounding and the right hand was playing a G#mM7M9 chord. I tried experimenting with it in Finale, and even without any sustain of the initial D I really felt the pull to the next D. I wonder how much of that has to do with wanting the top triad to be a G minor chord and how much of that has to do with the bass note and the bottom chord?

Kristin Wills said...

Listening to these examples has made me want to experiment more with chords in atonal composition. Recently I have been trying to write atonal music that is not chord based, but I find it confusing, especially when I want to reuse harmonies and I realize that I don't really know how they worked in the first place. I think chords make everything much more structured and easy to understand. I find it helpful to just play random chords on a piano, not thinking about how they fit into a key. This is a way to come up with progressions that are not tonal, but do not sound "wrong" either. The examples of combined chords were very interesting to me. I did not really like the idea of combining chords until I heard Stravinsky's "Rite of Spring," which has simultaneous repeated Eb7 and EM chords. When I first heard this, I was surprised at how effective it was. I will certainly try writing these types of harmonies at some point.

Stephen Eckert said...

I especially enjoyed hearing Coltrane's progression of 7ths with mediant relationships and the double chromatic mediant chord example you created. I have found composing music which hints at tonality yet never affirms it especially tricky. I really liked the idea of superimposing quartal chords such as in the example. As a pianist, the majority of quartal chords are comfortable for the hand and thus I have been drawn to them when messing about the keyboard. A very good example, to my ears anyway, is Carl Vine's First piano sonata. He uses a lot of quartal sonorities and modal scales which create a very interesting sound world which is certainly post-tonal but definitely includes pitch centricity. The comment about being afraid to move pitch centers certainly rang true for me now that I have taken the time to think about my writing. I will definitely think more consciously about moving pitch centres in the future.

Alison Petten said...

I find that what I struggle the most with is finding post-tonal sonorities that I find pleasing to listen to. In general, I am a very big fan on 19th century romanticism, and so my ear tends to lean towards music that sounds more like some of that. In that kind of music, I love hearing the chords resolving the way that they do and being able to hear a repeating theme. I also find it difficult to communicate emotion using post-tonal music. I find it very easy to hear the mood of a piece that is tonal, and sometimes I feel like all post-tonal music is just a jumble of notes that don't really communicate anything clearly. Now I know that this is a very uneducated statement, I guess it just shows my preference towards more tonal music.

Josh McCarthy said...

I somewhat have to agree with Alison on this one. Throughout my four years in music school I have found that my preferred era of classical music, would have to be the romantic period because of it's lush, rich harmony, and the musicality it brings to the table by its extraordinary performers. But, for the most part this is as far as my ear will stretch in terms of how far into post tonality I am willing to go to find "good" music before I can't handle it anymore. Don't get me wrong, I respect post tonal music and it's composers for trying new things and being evolutionists, and some modern music is very cool. BUT. I do find that more modern music is meant more for scholars than the general public, in that, post tonal music is meant more to be analysed and not as much purely enjoyed.

Jack Etchegary said...

It is important to branch together and analyze the similarities between traditional tonal music and post-tonal music, as I believe it opens up more room for exploration for both forms of musical composition. What I find most of the time, in my discussions with people who do not have a formal classical music education/background, is that post-tonal music and atonal music are synonymous to them, and that both just sound bad/unpleasant. What should be noted however, is that post-tonal music has the exact same ability to lend itself to the collection of dissonances and consonances, or tensions and releases, that are found in traditional tonal contexts. This idea is present throughout many pieces of music spanning several eras and centuries, and I believe that this is an element of music that can help those who have no contemporary music knowledge begin to appreciate its existence a little more. I also find so incredibly interesting how triadic sonorities can become so strangely dissonant when placed on top of one another. The examples you have shown in your post from Rite of Spring show on a fundamental how a series of very common tonal chords can create a very dense and harsh sounding sonority. The the other examples you used which featured collections of tonal chords played in succession reminded me of Liszt's St. Stanislaus, which uses an E major chord and a C minor chord idea that modulates up a major second, resulting in the inclusion of all twelve pitches after all four chords have sounded. I have always found this very interesting, for it does not necessarily sound like a post-tonal composition, but indeed it is. To summarize, the bridges between tonal music and post-tonal music are sometimes rather short and easy to cross from both an analytical and compositional standpoint.