One of those canards beloved by lazy music students who don't want to learn theory is to ask, "When will I ever use this stuff?" The canard is predicated on an understandable but ultimately silly idea that may be described as a cognitive bias and this cognitive bias could be summed up by Daniel Kahneman as "What You See is All There Is". Because beginning instrumentalists and theory students don't realize they are already making use of applied harmony any time they strum a guitar or tickle the ivories they assume (wrongly) that they're never going to use certain abstruse concepts about manipulating physical objects so that the air vibrates in such a way as to transmit certain sounds.
But let's break it down for you folks, harmony is a part of music that you can use to your advantage. Let's say that you're a slightly better rhythm guitarist than you are a singer and you want some momentum in your song but won't be able to do a Mariah Carey thing like exploiting your multi-octave voice. Let's say you're Bob Dylan and you want the song to move forward with some energy but you're vocal range is "maybe" useful within an octave or a perfect fifth.
Harmony is your friend and a particular approach to harmonic movement known as "oblique motion" can save the day.
Let's take Dylan's classic tune "Like a Rolling Stone". Ignore some of those fake books that give you just three chords and go back and listen to the recording. Listen to the guitar part coupled with the organ. You're going to hear Bob and company stroll through the first five chords of C major.
We get Bob wailing away on that one note with "Once upon a time you dressed so fine, threw the bums a dime in your prime ... ". Now what's going on as Bob hammers on that one note? He's strumming the chords C major, D minor, E minor, F major and by the time he gets to G major he jumps up from his one note to a tone a major third above the tonic pedal tone (i.e. that note he keeps singing as the chords change underneath his voice).
You know what Bob just did there? It's called oblique motion. His voice sits at the top and the harmonic forces in play keep shifting upward beneath his singing. In music theory terms we're given a simple upward transition from the tonic (C major) through the supertonic (D minor), the mediant (E minor), the subdominant (F major) and finally reach the dominant (G major). In Roman numeral paralance that's I, ii, iii, IV and V. What happens after V? The cycle starts all over again.
Now I happen to be a Dylan fan so don't take this the wrong way but when you're possessed of Dylan's voice oblique motion is a harmonic approach where you can exploit you're being a better guitarist than a singer to add momentum in the rhythm section when you know you don't have the greatest singing range.
Oblique motion doesn't have to be restricted within a major or minor key. In blues you could be in C major and jump to an E flat major chord or a B flat major chord while still singing your ditty in C major. If you were a composer in a Tin Pan Alley or vaudeville setting and a capable pianist working with a lot of singers without formal training or a limited range then you could compose a simple diatonic melody and have all sorts of killer chromatic alterations to the harmony that give depth and musical drama to a vocal line that might be rudimentary. If you have a hard time imagining how that might actually sound go digging through Gershwin's song book. I assure you that a variety of examples will present themselves to you before long.
People already possessed of fantastic singing voices might be tempted to say that manipulating harmonic movement in this way could be the shortcut of less capable singers. Well, yeah, that would be true but by the same polemical token it could be pointed out that singers who could be described as multi-octave divas have often succumbed to the temptation of the same old three chords and presuming that their perorations of melody will somehow carry the day and make people want to listen to them squeal with amorous joy or whatever a la Mariah Carey (and, to be fair, there's been a market for that sort of music for decades, it's just not stuff I like to listen to).
There's other stuff about applied harmony I've been thinking of blogging about but I'll leave oblique motion at this case study for now. If you're a musician working with a singer who has trouble going behind his or her narrow singing range and just can't make it then what you can do as a performer or arranger is accept this fact and find ways to add harmonic momentum to a song by providing a dramatic musical change in the supporting harmony the singer wouldn't be able to bring to the situation. How and why you do that would be up to you, of course, but we can broadly propose that, at the risk of gross simplification, most applied harmony in popular musical styles is about how you mess around with subdominant substitutes.