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Elements of non-functional harmony is ubiquitous among contemporary music creations. In most cases, it materializes in the way of non-functional chord progressions, which are characterized by its "successive" feel and lack of diatonic association, in contrast to the "progressive" feel functional harmony emits, which is the natural result of attempting to establish a tonal center via resolutions, often accompanied by a bass movement of perfect fifths.

A majority of music theory books pertains to Western music during the Common Practice Period refrain from discussing the topic of non-functional harmony (though some do talk about atonal theory and the like), and those do often focus on enharmonic chords, (tritone) substitutions and deceptive cadences, or are sometimes presented only through short excerpts, which do not give much insights in the matter.

However, some successive chord progressions can still be analyzed in the traditional and functional way. For example, the chord progression FM7 - Fm7 - Fm6 - C in the key of C Major can be thought as a Plagal Cadence extended via mode mixture, and has two voice leading lines: 6 - b6 - 5 and 3 - b3 - 2 - 1 that contributes to a strong cadence. The ii - V progression can be enhanced by throwing in a secondary dominant chord: ii - V/V - V, creating a smooth voice leading of 4 - #4 - 5.

In fact, some functional chord progressions, especially cadences, can be regarded as successive, because they contain (sometimes chromatic) leading tones that naturally resolve to a diatonic note. However, more often than not are successive motions in modern music - like ascending or descending bass lines - non-functional.

To give a few examples:

The first few chords of the intro to Led Zeppelin's Stairway to Heaven form a chord progression of Am - E/G# - C/G - D/F# - Fmaj7, which has a chromatic descending bass line of 6 - #5 - 5 - #4 - 4. If you try to analyze it the functional way, then maybe the first two chords can be thought as a retrogression i - V6/i, and maybe the next C/G can be regarded as a deceptive cadence, but then it stops there.

This electronic music track of Art Of Trance - Blue Owl has a progression of Cm7 - F7 - AbMaj6 - Cm7/G starting from 5:24, which in Common Practice Roman Numerals is i7 - IV7 - iv56 - i46, producing a voice leading of 5 - #4 - 4 and a nice chromatic feeling.

The above two pieces both have their distinct tonal centers, but sometimes even those are derived from non-functional harmony. The intro to the Glitch Hop piece Haywyre - Doppelgänger features a progression of Fm7 - Gm7 - GbMaj7 - Bbm7 - F/A - Fm/Ab - DbMaj7 - GbMaj9, which already doesn't make much sense when written in Roman Numerals: i7 - ii7 - bII7 - iv7 - I6 - i6 - VI7 - bII9, but one can identify the three chromatic voice leading successions: 5 - #4 - 4 - 3 (starting from Fm7), 1 - 7 - b7 - 6 (starting from Fm7) and 2 - #1 - 1 (starting from Bbm7). Also, the ambiguity with regard to its tonal center certainly contributes to its good vibe.

From all the examples above we can find out that chromaticism and smooth voice leading plays a big role in successive, non-functional harmony, but simply throwing a bunch of chords that share chromatic passing notes together just won't work. Some books discussing voice-leading introduced a technique of judging how far two temporally adjacent chords are away in a voice-leading sense by counting the semitones needed to change a chord into the other (sort of like earth mover's distance), which made me think that the same technique could be used in writing successive chord progressions, but apparently it isn't that simple, as some chord notes can still come as unprepared when the chord plays.

Which brings me to my question, how DO you write successive, non-functional chord progressions like chromatic ascending/descending bass? Do you play on the keyboard and hope something good will arise through trial and error? Are there any rules or advanced music theory topics regarding how to write it? Does it just come by naturally during the process of improvisation? Or is it a talent that someone is just good at without reason?

P.S. I really tried to keep the question from being overly subjective, but I don't know if that's possible.

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    First, I only read the last two paragraphs of your "question", and I'm not sure that a short essay on non-functional harmony is really necessary as a preface for your question. Second, writing is probably very personal and you may get as many answers as there are writers. I try to forget all about music theory and look for good sounds, go with my gut, and use trial and error. It's an instrument-centric approach which seems to be used by many in the pop, rock, and related genres. – Todd Wilcox Mar 22 '15 at 7:00
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    @ToddWilcox Some people may find the extra context useful - and there is a question there, no need for the quotes! – topo Reinstate Monica Mar 22 '15 at 9:33
  • It seems to me that "non-functional" my be a misnomer. If it works it's functional in my book. – Rockin Cowboy Mar 22 '15 at 17:29
  • @RockinCowboy Agreed. These chords certainly have an individual pull and a tonal center. But, particularly with Doppelgänger piece, sorting them into the common practice Tonic, Predominant, and Dominant categories is less than satisfying. – Dan D Mar 22 '15 at 19:23
  • To me, your Am - E/G# - C/G - D/F# - Fmaj7 chord progression looks like i - V6 - (b)III6/4 - IV6 - (b)VI7, which looks functional to me. The hardest to explain is V6 - (b)III6/4, which can be interpreted as V6 - V6/4/(b)VI, but it's a stretch. – Dekkadeci Oct 10 '17 at 15:42
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Which brings me to my question, how DO you write successive, non-functional chord progressions like chromatic ascending/descending bass?

You write them using pencil and paper, sometimes a computer, sometimes just in your head, sometimes as you play an instrument. I believe your real question is how do you create successive non-functional [sequences]? Keep in mind that the use of the word "progression" implies a certain functionality to your chord choices. Also keep in mind the word "functional" as you are using it describes typical tertian voices, smooth voice-leading, and the anticipation and resolution of harmonic cadences.

Here is one exercise: pick a note on a piano, and reharmonize the note as many times as possible - say we choose the note "E". Here are some possible chords that may be harmonized with E:

  • Emaj, Emin, E+, Edim, Cmaj, C+, C#m7, Fmaj7, Ab+, Bbm7#11, etc etc

As you can see, through simple reharmonization we can recontextualize any not to any desired result / effect. Therefore, to write a sequence including a downward / upward chromatic bass line (or any line for that matter), the bass notes may simply be reharmonized to be contextual with different chords; how different or similar the chords are to one another in tonal region is a matter of the composer's whims. The added dimension of bass lines is that you can also reharmonize with inversions as well. For example, the Bbm7#11 chord from above could have an E in the bass, thus putting the chord in 5th inversion.

For related reading, check out my answer to this question about chromatically moving bass lines.

Do you play on the keyboard and hope something good will arise through trial and error?

Sometimes, it depends on how the composer writes. Sometimes you stumble across something unknown to you, and sometimes you need it work out an idea that came to you in abstraction. Composers are obsessed with working out puzzles.

Are there any rules or advanced music theory topics regarding how to write it?

It really depends on your definition of function. For example, in Set Theory, you would use your sets (usually hexachords) and intervals to derive your chord-language. In Serialism, you use the order of the tone row for your pitch-language. In either of these scenarios, aural connections defined as "progressions" may not be readily heard / perceived, but they do succeed in unifying a work.

If the function of chords in your music is to creating a terrifying sound wall or a barely audible whisper, then your method of composition should reflect your larger goals.

Music is unified through repetition. If nothing in your music repeats (no chords repeated), then a particular, un-unifying effect is created, and therefore the chords truly have no function (unless it was your goal, then of course that would be their function).

Does it just come by naturally during the process of improvisation? Or is it a talent that someone is just good at without reason?

These questions relate more to how you think other people create "non-functional" progressions. Yes, some people may hear chords a certain way, as others have put it, if it sounds good to you, it probably is. However, as I've shown above, you can use simple theoretical knowledge to greatly diversify your chord-vocabulary.

I feel it is important to point out that many contemporary bands / artists that are not trained stumble into certain sequences through ignorance. They are unaware of how the chords are supposed to be put together, and so therefore many songs result from a lack of foundational knowledge - progressions using "beginner" chords run rampant: Am, E, G, D, C, F all just sort of thrown together in any four-chord order.

I would not posit that someone who comes up with a "non-functional" progression is "talented" as anyone through ignorance can play cluster chords on a piano (much like any non-painter can throw paint at a canvas). Rather, it is how the chords are used that makes the difference. If someone is stringing chords together because they don't know any better, it will create a certain type of music. If someone is carefully planning how their chords interact, then again, it will create a certain type of music.

  • I like your one exercise. Reharmonisation is a great way to move around. Especially for those who throw off the diatonic mantle and realise that 'foreign' harmonies can and do work well in interesting ways.+1. – Tim Mar 22 '15 at 17:26
  • @Tim, I'd say that reharmonisation is often great for people working within diatonic constraints as well. I did an arrangement of "Uppon La Mi Re", an old Tudor keyboard work, last year as an exercise to keep my hand in: the bass was an ostinato on A-E-D in semibreves, with the tenor following a minim behind in parallel fifths. That throws a distinct "crimp" in things, and the original composer had reharmonised like Billy-be-damned (and I, certainly no less). Even diatonic lines can profit from reharmonisation - it's a "chromaticism-agnostic" procedure. ;) – user16935 Mar 22 '15 at 19:53
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You obviously know a lot about theory, but always be aware that theory is someone's attempt to explain what has happened. None of this theory has passed into 'law', so it's still 'theoretical'. Before the theories, folks were writing and playing music. It stood or fell on its own merits. O.k. some of it was way before its time, so was not accepted when it was first around. Imagine a Blues being played during Beethoven's era. Thrown out immediately!

Instead of trying to follow the 'rules', you're better off messing about until something palatable occurs. It may be sooner, or later, but as it emerges, you'll recognise something good is happening. Trying to explain it may be fun, but surely it's the piece that's the important thing. Sometimes, playing ad hoc, without referring to the stuff you know is 'correct' will produce what you wanted - serendipity, they call it...

How often do we see and hear "If it sounds good, it probably is."

  • So are back to a 'before the theories' era - except now, it's 'after the theories'? – topo Reinstate Monica Mar 22 '15 at 9:34
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    @topomorto = could be put that way. I don't think the folks who made music before it was written down, and categorized, thought much about it. But when was the change - not sure! Somewhat like there were words being used before Dr. Johnson compiled a dictionary. – Tim Mar 22 '15 at 9:41
  • Well, it's been written down for a very long time. I seem to recall discussion here about a Sumerian tablet... – user16935 Mar 22 '15 at 15:48
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    I see theory as an attempt to EXPLAIN or understand why something sounds good and perhaps derive a formula to arrive at something else that sounds good by applying the same formula (using theory). I am sure that the first musicians composed by playing what sounded good. – Rockin Cowboy Mar 22 '15 at 17:27
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Use a method called harmonic relativity (here is a video from the 'creator'

).

In essence you look at the intervals between successful chord progressions and in what genre they stem from. For example, a common chord progression used by JW in Star Wars is the I - majbVI (eg. C-Ab). You would class this as a spacey sounding progression. Next time you write some 'spacey' epic music, by combining a variety of these intervals (that you've categorised as 'spacey') you end up with a very space themed chord progression.

Another example of a harmonic relativity progression would be minor i - minor major 3 (eg. Cm - Em). This interval I would class as 'evil' and therefore I could refer back should I feel the need to write a motif for an evil character (just as an example).

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The whole purpose of a progression is to move from one harmonic entity to another. If you want to approach this by the non-functioning-harmony-way you would have to look at the building pieces of chords which are the intervals.

Every chord you build, even the most wild one, consists of some intervals built upon a fundamental tone. (For example a C major chord consists of the intervals of a major 3rd and a perfect fifth upon the fundamental tone c.)

Now, some intervals are more consonant and others more dissonant and that could be explained with science but a phycisist could bother more. Naturally, the consonant intervals provide you with the opportunity to make them dissonant and vice verse. (The traditional theory speaks only of dissonances who must become consonances but if you don't care for harmonic functions or tonality in general there is no rule that you shouldn't treat consonances as yet-to-become dissonances.)

Consonances & dissonances are the drive of your progressions. As long as there are dissonant intervals that wait to become consonant or consonant intervals waiting to be disturbed by some alteration, you will find that there are many chord changes to explore.

Now, your progression should have an ultimate goal (or not :P) to justify all these freedoms. A pedal tone, a chromatic passage, a movement in the bass, an ultimate chord to arrive, you name it.

The fact about theory is that is our way to understand truth, it is not truth itself. As art progresses, theory has yet to catch up and provide as with a logical context. What a fascinating subject!

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