Post-Tonal Harmony Ideas (3)

I wrote a short piece for today's post, based on the arpeggiated chords presented in section 8 of my Post-Tonal Harmony Ideas (1) post. You may wish to listen to those chords again before listening to today's composition , but it's fine to skip this and just listen to the piece below.

The chords in section 8 of Post-Tonal Harmony Ideas (1) were constructed by superimposing different harmonic structures found in tonal music, such as an F# major triad and C major triad, a combination used by Stravinsky in Petroushka, in order to create post-tonal sonorities.

There are no particular "rules" to follow in combining chords in this way, but I would suggest that the resulting sonority should not sound overtly tonal; if you start with a G chord and superimpose an F chord, for example, it would result in a G¹¹ chord, which is overtly tonal.

That said, however, it is really the context in which such chords are used that determines whether they are tonal or post-tonal. If you play the chord in bar 3 below, for example, and resolve it to an Eb chord, it will sound like an altered V⁷ resolving to I in Eb major, because bar 3 starts with a Bb⁷ chord. If you play the same chord (bar 3) but move to a different sonority that in no way suggests an Eb chord, then you've placed it in a post-tonal context.

Another suggestion, if you try this approach, is to use chord combinations in which the two triad-based chords have no notes in common with each other, although that is by no means an essential condition.

The approach I find that works best is to work these out at a piano, exploring the possibilities by playing different chords in each hand until you find combinations you like, and then immediately write them down. Frequently, the experimentation may involve just altering one note at a time until you find a sonority that you'd like to keep.

Once you have a collection of chord combinations that you like, you can use them however you wish in a composition; you can transpose them, add further notes to them or otherwise modify them, invert them, re-use them, etc.

Here is the piece; you can hear it with the audio player below the score:

 

More Details on this Composition:

• I began with the first three arpeggiated post-tonal chords presented in my Post-Tonal Harmony Ideas (1) post (they are in section 8, numbers 1, 2, and 3). 
• I transposed the second arpeggio, and subsequently re-used and transposed the other arpeggios as well. 
• In bar 7, I introduced a new chord (i.e., one that wasn't in the original blog post), which consisted of a Db Maj.7th chord plus an Eb Maj.7th with augmented fifth. I also reused transpositions of this chord.
• One way to vary these chords, aside from changing notes within them, is to add notes on top of them that are not part of the original sonority; I did this a few times in this piece, especially in my choice of flute notes.
• As you can hear, I took time in the score to move from one sonority to another, because the harmonic complexity of these chords is, to me, inherently captivating, and it takes time for the ear (well, the brain, actually) to absorb them. 
• Harmonic progressions using these chords can proceed as quickly as you want, however.
• This is "colour-based" composition; each chord has its own colour. The process is something like an artist creating an abstract painting using only splashes of colour here and there, with the result being pleasing to the eye (well, the brain, actually).
• "Mystery" and "Wonder" were the names of two of our cats that passed away several years ago.

Final Thought: Practicality

• One very practical advantage of this approach to composition is that the chords should fit naturally into the pianist's hands, provided you started by experimenting at the piano with chords that fit your hands. A skilled pianist has spent years training their hands to instantly form the correct shape in playing tonal chord structures, like triads and 7th chords, so if you use those same chord shapes, but combine them in untraditional ways, the pianist is likely to find the music easier to play than a lot of contemporary music.

Post-Tonal Harmony Ideas (2)

In Post-Tonal Harmony Ideas (1), we examined tonality, atonality, and post-tonality, and explored two possibile ways of using tonal chords in a post-tonal context. 

One way is to superimpose triadic structures in order to create sonorities that would not normally be found in tonal music; perhaps the most famous example of this is Stravinsky's "Petroushka" chord: A combination of F# major and C major chords. Another Stravinsky example comes from the Rite of Spring, in the section called "Augurs of Spring/Dances of the Young Girls," which features a strongly-rhythmic repeated chord and irregular accents; the chord is E major in the lower strings (spelled enharmonically as Fb), and Eb7 in the upper strings.

A second way uses triadic-based, tonal chords in progressions that do not follow the chord-flow practices of tonal harmony (e.g., avoiding descending fifth root movements). 

I will explore the first idea (e.g., Petrushka chord, and other combined sonorites) at greater length in my next post, but  the objective today is to expand on the second idea, using the last musical example from Post-Tonal Harmony Ideas (1) as a starting point. 

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The example below is a very short composition written specifically for today blog post, beginning with the piano chord progression from the end of my previous post. The first five bars are virtually identical (dynamics and octave doublings have been added), but a trumpet enters at the end of m. 5. The piano chord progression is repeated in the second system while the trumpet plays a new melodic line, and the last two systems are an expansion of this chord progression, while the trumpet continues to play its melody.

For the trumpet notes, I picked pitches that, at the point they begin, are not part of the accompanying piano chord, although several subsequent piano chords include the pitch being held by the trumpet. My rationale for doing this was to increase the sense that this was not intended to be heard as an example of tonal harmony.

Have a listen; discussion to follow:

Dreary, isn't it? ;-)

As a reminder, the objective was to (a) create a succession of tonal chords that do not follow the typical chord progression patterns in tonal harmony, and (b) expand this into a short composition.

You might well ask, why would anyone want do such a thing? Isn't this like putting old wine in new bottles (i.e, repackaging something old and calling it new)?

Why:

This was an experiment. Whether it produced anything useful or not is up for debate, but there would have been no way of knowing if this approach (and yes, it is rather like putting old wine into new bottles) had any useful compositional possibilities to offer had we not tried it. FWIW, I don't know of any music that actually does this, although I would not be surprised to find that others have explored this approach as well.

Exploring new ways of using old harmonic structures completely violates the spirit and practice of modernism, and I therefore suspect many contemporary composers would reject this approach. We live in what some have called a "post-modern" period, however, within which this sort of exploration is completely appropriate.

Whether it is appropriate or not, the main thing most composers would want to know is this: Is there any situation in which this approach could be compositionally useful to me? I suggest that you ask yourself this question while playing the audio clip above at least three times, and, if you haven't run screaming from the room by the end of the third play-through, please share your thoughts in the "comments" section below. It's fine to decide that you do not find it worth exploring, but, whether you find it potentially useful or useless, I'd be interested in your thoughts.

Also, if you would be willing to share a chord progression that you came up with, and that fits this approach (tonal-based sonorities that do not follow the harmonic progressions associated with tonality), please do so in the "comments" section.

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 E♭Maj7 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 (G, E♭, 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.