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Functional Harmony in contrapuntal Music

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#1
DAI

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Hi,

is there any guide that describes how to imply functional harmony progressions in contrapuntal music? Most articles on counterpoint seem to be mostly concerned with which intervals are allowed and how dissonances have to be resolved but none explains properly how to combine this approach to composition with functional harmony.

#2
composerorganist

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All I can do is recommend a book by Kendall Briggs - Counterpoint. He does a nice job linking harmony with counterpoint by discussing the harmonic implications of scale degrees in common practice music and then takes it from there.
Chris S

#3
calebhines

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Syntactic Structures in Music by Tom Sutcliffe
http://www.harmony.o...tonal_music.htm

In the first paragraph of the Introduction, he makes the following claim:

Conventional theories of structure in tonal music concentrate either totally on root progression patterns (Rameau. Schoenberg, etc) or totally on voice leading. (Schenker etc) This book is the first to explain how root progression patterns and voice leading work together.

Although the site refers to a forthcoming book, I'm not sure it has actually been published (yet). Nevertheless, I've found the contents of the website to be extremely helpful. Especially his distinction between static and dynamic harmony, his labeling of chord progressions as alpha, beta, and gamma progressions, and his formulation of musical phrases in terms of linguistic phrase structure trees.

Granted, it's more focused on the structure of musical phrases, rather than the intimate details of species counterpoint, but in focusing on this structure, he demonstrates the interactions between contrapuntal voice leading and functional harmony. Appendix A does contain an overview of voice leading principles in terms of species counterpoint, though.

#4
DAI

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I still didnt find a precise rule for determining which notes belong to the currently implied harmony and which dont.

Look at this: http://www.harmony.o...ples/ex_7p6.gif

in the third bar: why are only c and G considered in the harmonic analysis?many different chords appear afterwards. By which principle do you identify that they are nonharmonic (and are they really?)

#5
composerorganist

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Well, you need to understand non-harmonic tones, and what inversions are suggested. In the analysis presented you would understand it better (and I fault the analysis too) if you see the first three eighth note beats in bar 3 as two first inversion (6-3 chords) chords going to G , eg Eflat-C, B natural-G, G-G . Bach's figuration avoids many contrapuntal problems with the figuration in the left hand. Yet as the G-G octave falls on a weaker beat of the bar and the quality of the chord hinted at - G major chord, (to serve as a V of C minor) fails to do something which Bach's statement of the fugal subject in the dominant is pushing to do - move the harmony into the dominant to create a contrasting section and expand the form of the piece. So he has to figure a way to reinforce the B flat to get to G minor and convincing chords to lead to G minor. IN this instance the I in Cminor becomes a iv in G minor leading to a i6- viidim- i. The diminished chord supports the fugal subject and reinforces the move to the root position G minor chord.

Another way to understand it is to reduce it to the chords suggested - starting on bar 3 - Eflat-G-C to D-G-Bnatural to C-Eflat-G to Bflat-D-G to A natural-c-F# to G-Bflat -D. The implied roots to the subject then are E flat- D-C-Bflat- A natural- G, the first six degrees of the G minor scale!

In fact, here is one dirty little secret, you can with practice improvise in a Bach style by taking fugues reduce it to the chordal skeleton and then add figuration of your own! A rather advanced technique of improv organists learn and employ to gussy a hymn when they are up to the 7th stanza.

In addition to the text I gave and the other one listed, Aldwell and Schachter do a nice job of linking Harmony and elements of counterpoint in their Harmony and Voice leading book. They offer the best exercises - realization of figured bass, harmonization of melodies and basses. They are hard but you really learn harmony and key concepts of counterpoint. You won't learn counterpoint thoroughly per se - that requires specialized study. But such texts will help you very much when you do get to that topic.
Chris S

#6
DAI

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Another way to understand it is to reduce it to the chords suggested - starting on bar 3 - Eflat-G-C to D-G-Bnatural to C-Eflat-G to Bflat-D-G to A natural-c-F# to G-Bflat -D. The implied roots to the subject then are E flat- D-C-Bflat- A natural- G, the first six degrees of the G minor scale!


My question was actually HOW you determine, which tones/chords belong to the chordal skeleton.

For example in bar3: why aren't the last two chords D-G and C-A considered in as "harmonic"? They don't even resolve to the supposedly implied harmony c-minor.

Or in bar4: why isnt A-G considered as harmonic?. It's metrical position isn't even any weaker than that of the G major chord in bar 3.

#7
DAI

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Of course i already know harmonic functions and all that stuff , i don't really see how it relates to my question?
By which principle did you identify the A as an auxillary tone, whereas the lower B in the same metrical position in bar 3 isn't auxillary?

#8
wayne-scales

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When you're analysing the above, why don't you analyse the whole thing as just one big C minor chord? Or why don't you just analyse every single note as a chord (that'd be fun to do for ornaments)? Why don't you analyse the first beat of bar 3 as an A dim 7 with an appogiatura? Why wouldn't you analyze the first half of the first bar as a C major chord?

I don't think any of the stuff on its own has any sort of function, it's only in the context and in how it's used that it does.

Looking at the first beat of bar 4, I can say to myself, 'Bb and D... Well, G has a B, so it could be a VII without the fifth'; I look at the next half and go, 'Oh right... G and A... What the hell is that? Oh, maybe the G's an apppogiatura and it's a diminished chord' and I could reason the same way for the next beat.

On the other hand, I could look and say to myself, 'D jumping to G in the top with a Bb on the first beat; that's a v... But what about that A on the next beat? Oh look, he's going back to a Bb, so I'll stick with this G business'.

Or (and I don't know if this is a thing), I could analyse the whole first half of the bar as revolving around Gm (by the second method above) and still take into account that actual spellings of chords occur because of non-chord tones; however, I would be wary and would rely on my ear if I wanted to give these 'auxiliary' chords functions, since they happen so quickly/incidentally when Gm is so prominent.

If I look at how the whole thing moves, I could notice that the first half of the bar is very G minorish, and the second half emphasizes a diminished 7th on an F#, which would be the vii7 chord in the key of G minor and analyse it: i - vii7 in the G minor context or i/v - vii7/v in the context of the key of the C minor key of the piece. Of course, there's nothing incorrect about analysing it iii/#III/i/i - I/v/I/i, or something; but why the hell would you? The tonic chord, for instance, could be analysed as I/I/I/I/I...; but people don't think about that when they write their V/V's &c., just like they don't think about the infinite amount of zeros afters an integer's decimal point, though they consider things like that when it comes to the irrationality of a number like pi.

It's all about which is simplest and about how it's all used, I think. There are a million ways to analyse it that could be hella complicated, but make just as much sense (i.e., be equivalent); for example, analysing F#-A-C as a dim chord on the 7th degree or as a V without the root: what's the difference and who cares? They're the same thing, as far as function is concerned.

Basically, I think most analyses just try to strip it down to be as simple as possible: if you can analyse 180 bars coherently in the context of one single chord, go for it; if, as above in the third bar, you can't make sense of even half a bar with a single chord, that's when you change. It's just like in physics when some people will tell you that the earth revolves around the sun and some will tell you that the sun revolves around the earth: both and neither are true; it's just a combination of perspective and simplicity; and that could relate exactly to whether the fourth bar above contains a change to a dominant function on the second half-beat or not.

In short: whatevs.

Also: beats and speed and stuff.

#9
DAI

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You could analyse the A as an auxillary tone if you suppose that g is still the implied harmony. But how do you determine that it really is? Maybe the harmony changed to f#-dim (with the nonharmonic g in the upper voice resolving to the chord-tone f#)

#10
wayne-scales

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How do you know one tree is taller than the other? How do you know what time it is? How do you know any of the chords' functions at all, if they could have others? How do you know the piece isn't in F# major with a different key signature and accidentals?

Just 'cause.

If you want to think about it differently, think about it as analysing what was going through the composer's head at the time, and not analysing the music in the one true objective way to do it.





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