Monday, October 17, 2016

Ars Longa, Vita Brevis

The expression, "ars longa, vita brevis," is a Latin translation of the first two lines of the Aphorismi (Aphorisms) by the ancient Greek physician Hippocrates, who is perhaps most famous for the Hippocratic Oath. It translates as, "art is long, life is short."

Interestingly, the order of those two lines was reversed in the originally-published aphorism (I am using the Latin translation, because I know no Greek, except "papoútsia" which means "shoes;" I had to look this up when my shoes were stolen on an overnight train in Greece 40 years ago… end of digression):

Aphorism 1, Section 1, Hippocrates
Vita brevis,
ars longa,
occasio praeceps,
experimentum periculosum,
iudicium difficile.
Life is short,
Art is long,
Opportunity is fleeting,
Experimentation is perilous,
(good) Judgement is difficult.

What does it mean?

  1. Well, to paraphrase Inigo Montoya from The Princess Bride, it apparently does not mean what most of us think it means. According to one source, it means that "it takes a long time to acquire and perfect one's expertise (in, say, medicine) and one has but a short time in which to do it". The Wikipedia entry suggests that it "most commonly it refers to how time limits our accomplishments in life."
  2. The meaning that I suspect most people take from this aphorism is, "life is short, art eternal." •Today's post will explore both meanings, as they apply to music.

1. The clock is ticking.

We tend to have sporadic awareness of our impending demise; we know it's going to happen, but we just don't usually know when. The clock is indeed ticking for us all, which can be a little unsettling if you think about it too much. This is presumably why most of us do not think about it very much, even if we have experienced the death of a loved one. The first meaning above is not a suggestion that we obsess over our impending demise; quite the opposite, in fact!

Here is my composer-specific take-away from meaning #1: It takes a long time for a composer to develop a mastery of our craft, and, given that life has a finite time limit, it would be good to put whatever time we have to good use mastering these skills. Compose lots of music! Try to make each piece better than the previous one!

If Schubert (dead at 31) and Mozart (dead at 35) had been more casual about their desire to be great composers, they would not have achieved greatness. Ditto for Bizet (age 37), Gershwin (age 38), Chopin (age 39), and Mussorgsky (age 41).

The clock is ticking… Get busy!

2. Art is eternal. Or is it?

Some art has had impressive lasting power, sustained over hundreds or oven thousands of years. That's very cool!

Then there's music…

Unlike visual art or architecture, which produced works capable of lasting a long time, music was not notated for most of human history. The Seikilos epitaph is the oldest surviving complete, notated musical composition from anywhere in the world. It is thought to date from the first century AD, making it about 2,000 years old. That means there is no record of notated music for the previous 198,000 years of human existence on this planet.

For how many of the roughly 200,000 years of human existence have our ancestors been making music? To borrow a common "click-bait" phrase, the answer may surprise you! Archeologists have discovered ancient flutes from approximately 43,000 years ago, which suggests that (a) music was being made 43,000 years ago, and (b) it was probably being made before that as well, since the first forms of musical expression probably involved the human voice and percussion instruments.

There is no record of the actual music made for most of human history, for at least one very simple reason: Then, as now in most cases, music was ephemeral; it was there when people played it, and not there when they didn't; there appears to have been no desire to make it "eternal" (or at least, "long lasting") by writing it down, until the Seikilos epitaph.

Not only that, but, to my knowledge, the Seikilos epitaph did not signal a vanguard in the new practice of notating music; the following 1,000 years or so produced very little notated music. According to Wikipedia, the founder of what is now considered the standard music stave was Guido d'Arezzo, an Italian Benedictine monk who lived from about 991 until after 1033.

In the centuries following Guido d'Arezzo's life, notation became more commonplace, especially so when music became more complex, because the increasing complexity required a system of notation in order to be performed accurately.

Nowadays, despite the1,000+ year history of notated music, most of the "old" music that is performed or recorded was written since the late renaissance, meaning it comes from the past 500 (or so) years.

So, while it is entirely possible that some of the musical art from the recent past will be long-lasting, the inherently-ephemeral nature of music is such that most music, even in this day of easy digital recording, will only last for as long as we retain its memory in our minds, because most music is not recorded. I play guitar practically every day, but I doubt that I have recorded more than about 100 minutes of guitar music over 45 years of playing guitar.

Despite its essentially-temporary nature, however, it is undeniable that some music has lasted an impressively-long time, possibly because it is thought to represent the pinnacle of musical artistic expression,  or possibly because a lot of people just like it (Vivaldi: 4 Seasons; Pachelbel: Canon in D); that gives all composers something to aspire to, should they wish to do so.

And even if our music does not make it into the pantheon of musical greatness, there is a realistic chance that at least some of it will last longer than we will, provided we unceasingly strive to write better music.

Anyway, tempus fugit! I need to get back to the piece I'm working on…

Postscript: Experimentation is Perilous?

Hippocrates was a doctor, so when he called experimentation "dangerous," he probably meant that experimenting on a patient could harm that patient. If you are an air-traffic controller, experimenting on the job could have disastrous results; ditto for a military strategist, or an operator of a nuclear power plant.

If you are a composer, however, there is no equivalent worst-case scenario that results from a failed musical experiment. Some may not like your experiment, or performers may call it unplayable, but, generally speaking, people are not physically harmed by compositional experimentation. I would suggest that some experimentation, as in trying new things, is essential for an artist.

Wednesday, October 5, 2016

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; there is an audio player beneath the score below so you can hear it as well:

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.

Monday, October 3, 2016

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. 

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. 

-  -  -  -  -  -  -  - -  -  -  -

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)?


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.

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 ←