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.

Tuesday, September 6, 2016

Blog Index — Organized by Topic (®Sept/2016)

Welcome to another year of composition studies! I wish you much growth and success on your journey to becoming a better composer.

My primary motivation in creating this blog was to provide a forum in which a variety of composition-related topics could be explored and discussed in greater depth than is feasible in the classes I teach at Memorial University. While this was created for my students, comments may be left by anyone. Periodically, spam-bots leave comments, usually characterized by their enthusiastic brevity, followed by a link of some sort, kind of like this: "Great post! It really made me think. Check out DezynerSunGlassez.con for fantastic deals!"

Other times the spam-bot leaves some incredibly long-winded word collection, possibly copied from some obscure technical manual. I have no idea what the point of any of these spam posts is, but, if you see a comment that even vaguely resembles spam, do not click on any links, and let me know about it asap.

I get an automatic notification anytime someone leaves a comment, no matter how old the post, so, feel free to comment on very old posts if the topic interests you.

Below is an index of most blogs posted thus far. Entries relating to class business – reminders of deadlines, concert congratulations, order of class presentation, etc. – are omitted.

Links are loosely organized by topic to facilitate browsing.


→ Exploring the Creative Process; Struggles and Solutions ←
Strike While the Iron is Hot! (includes section on "writer's block")

→ Planning ←

→ Playing With Expectations; Musical Dichotomies ←

→ Composition Techniques 

→ Form in Post-Tonal Music ←

→ Atonality; What's in a Name? ←


→ Winning and Losing; Judging and Being Judged ←

→ Audience Response to Contemporary Classical Music and Marketing ←

→ Composition Issues (10-part series that started this blog) ←
1.1. The quality of ideas may not matter very much in assessing compositions that emerge from them; and
1.2. The degree to which these ideas are original may not matter very much.
2.1. Study the music of others.
2.2. Compose as much as you can.
2.3. Invite criticism from others.
3.1. Live with it for a while.
3.2. What is it about?
3.3. Does it change character?
3.4. What is its function within the context of the piece?
3.5. Structural Analysis.
3.6. Harmonic (or Pitch, Scale, etc.) Analysis.
7.1. Less is more / More is more
7.2. Always leave them wanting more / Give them what they want
7.3. Don't treat the listener like an idiot / There's a sucker born every minute
7.4. There can be too much of a good thing / If you have a good idea, then stick with it!
7.5. The George Costanza approach.
8.1. Three models for the role of a composer
8.2. Mastery or Mystery?
8.3. The value of a plan
8.4. Getting stuck, and possible workarounds
8.5. Don't obsess
8.6. Challenges = Opportunities

→ Composition Projects ←