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Music theory states

b_elliott

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That the strongest rest points outline the basic triad over the tonic (scale tones 1, 3 or -3 and 5).

To demonstrate this point I selected a random song (Bob Marley's Exodus) and created two short versions:
1. shows a Piano and mallets playing all the tones in phrase from Exodus.
2. now with only tones 1, 3, -3 and 5.

I felt I learned some theory by doing this demo.

I thought I would post this in case someone else chose to post a different example song that mutes all tones except for 1, 3s and 5. Different examples may show some intriguing results.
 

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b_elliott

b_elliott

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Just discovered a side benefit to stripping a song down to its 1, 3s, 5 as something which is useful for arrangement purposes.
It's not likely to knock a David Campbell off his throne; but, it was easy-peasy to have this string arrangement fall out of the hamper effortlessly.
Thought I'd share this in case it helps another.
 

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pmcrockett

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This actually sort of resembles the spirit of Schenkerian analysis, which is all about reducing a piece of music to its essential motion through a tonic triad. The idea is that a piece starts and ends with the tonic triad and all tonal motion within the piece can be viewed as a fleshing out of motion between the first, third, and fifth scale degrees. I wish I could recommend an intro text on it, but I'm not really aware of any, and even the Wikipedia entry is fairly dense. There's a decent bird's eye view of it here, though, for anyone who's interested in exploring it.
 
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b_elliott

b_elliott

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This actually sort of resembles the spirit of Schenkerian analysis, which is all about reducing a piece of music to its essential motion through a tonic triad....
Thanks for the link. I was unaware of Mr Schenker or his analytic method; Tom Pankhurst a worthy educator to plumb those wild analytic depths....
 

anjwilson

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This actually sort of resembles the spirit of Schenkerian analysis, which is all about reducing a piece of music to its essential motion through a tonic triad. The idea is that a piece starts and ends with the tonic triad and all tonal motion within the piece can be viewed as a fleshing out of motion between the first, third, and fifth scale degrees. I wish I could recommend an intro text on it, but I'm not really aware of any, and even the Wikipedia entry is fairly dense. There's a decent bird's eye view of it here, though, for anyone who's interested in exploring it.
Piggybacking on that, one of the first principles of David Temperley's and Drew Nobile's "Melodic-Harmonic Divorce" (although they both mention "rock" music in their titles, the theory is widely applicable to most modern pop musics, because of rock's enormous influence) is that, in this music the notes of the tonic triad tend to remain stable regardless of the harmonic context. So scale degree 3 remains a viable consonant ending even if the harmony is on the supertonic there (as in the line "Baby you're a firework" in Katy Perry's "Firework," for example).

Using this idea can bring a little of the sound and expressive world of popular musics, which can be very appropriate for certain pieces and moments.
 

youngpokie

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This actually sort of resembles the spirit of Schenkerian analysis, which is all about reducing a piece of music to its essential motion through a tonic triad.
Not sure I agree with this.

The Schenkerian position is that triads (and any chords) are created as a result of voice leading. The triads are the byproduct, in other words.

I think what the OP is discovering here is more in line with Riemann view of music - that 2 or 3 basic chord functions are the building blocks of music and voice leading is something that happens when triads are connected to each other.

Might seem like a trivial chicken or the egg argument, but the consquences are quite far reaching.
 

anjwilson

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Not sure I agree with this.

The Schenkerian position is that triads (and any chords) are created as a result of voice leading. The triads are the byproduct, in other words.

I think what the OP is discovering here is more in line with Riemann view of music - that 2 or 3 basic chord functions are the building blocks of music and voice leading is something that happens when triads are connected to each other.

Might seem like a trivial chicken or the egg argument, but the consquences are quite far reaching.
Schenker would definitely not agree that the stable tonic that is prolonged arises from voice leading. Voice leading is what is done to expand the pre-existing chord. The prolongational chords arise from voice leading. Since the OP is discovering an inherent stability of certain scale degrees, Schenker is quite apt here.
 

youngpokie

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Schenker would definitely not agree that the stable tonic that is prolonged arises from voice leading. Voice leading is what is done to expand the pre-existing chord.

I'm pretty sure he would. Schenker's entire theory has come out of counterpoint and it's basic premise is that music is essentially a contrapuntal unfolding of individual voices. Prolongation is one technique of such unfolding and it starts with individual voices not chords, at least in the meaning given to it by Schenker himself. This view puts all scale degrees on equal footing and makes all chords secondary to voice leading.

Riemann's view of the mechanics of how music works is explained by the specific function a chord is performing in a given progression and that there are 3 "anchor" chords underlying all tonal music. The way these chords are linked is what gives rise to voice leading (and melody).

It's a fine line, as I said - not to mention the confusion created by names like "Schenkerian" or "Neo-Riemann" given to derived and modified theories.

Meanwhile, to come back to my point - the OP has shown that you can harmonize most songs simply by figuring out where the underlying functions (I, IV or V) are located. No voice leading or counterpoint of any kind is necessary, it would still work.
 

pmcrockett

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I think whether the counterpoint or the tonic triad is more basic to Schenker is a matter of interpretation. I could be misremembering Schenker here, but I think his take on the overarching harmonic reduction was that the third and fifth exist on a basic structural level because they're implied by the overtones in the tonic pitch, not because they arise out of counterpoint per se. I would call Schenkerian analysis an attempt to explain why and how counterpoint works on a large scale, though, so in that sense, it is presupposed that counterpoint does in fact work -- in that sense, the counterpoint is more basic than the tonic triad. And we can see this by how Schenkerian theory tends to fall apart when we try to apply it to stuff outside Western common practice that isn't based on counterpoint.
 

youngpokie

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..the third and fifth exist on a basic structural level ...
I agree with this, of course. The shift from the monody based only on 5ths to a combination of 5ths and 3rds happened as polyphony and counterpoint were developing in Europe, so it makes complete sense that Schenker would point it out. It's the birth of tonal music as we know it today. My caveat is that the 5th and the 3rd are the foundational intervals of tonality as such. So these intervals, along with their resulting tonic triad, are inherent in both systems.

And we can see this by how Schenkerian theory tends to fall apart when we try to apply it to stuff outside Western common practice that isn't based on counterpoint.
Yes, it actually starts falling apart immediately outside of the works written by the Viennese school. I think he made some important observations (the macro development of the line away and back to the tonic, for example). But my strictly personal opinion is Schenker is a bit like Freud - pointing at something valid and true but not necessarily providing the best explanation for it. Both became the celebrated theories in the US around the time of WWII. Freud has already faded away. Schenker finally started fading, since Lewin and especially Cohn's Neo-Riemann work...
 

anjwilson

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The shift from the monody based only on 5ths to a combination of 5ths and 3rds happened as polyphony and counterpoint were developing in Europe, so it makes complete sense that Schenker would point it out. It's the birth of tonal music as we know it today. My caveat is that the 5th and the 3rd are the foundational intervals of tonality as such. So these intervals, along with their resulting tonic triad, are inherent in both systems.
Ah, you're speaking about the historical rise of the tonic vs counterpoint. Yes, of course counterpoint predated the tonic triad.

I was speaking about the ontological significance of the triad vs counterpoint in a musical work itself. In his mature theories, Schenker always spoke about the surface of the music arising as an elaboration of [ontologically prior] deeper layers; naturally, the tonic triad would arise before any contrapuntal elaboration of it. I don't have "Der Meisterwerk" or "Der Freie Satz" in front of me now, but I could add some quotes later if necessary. Based on the clarification of the apples-to-oranges disagreement earlier, though, I expect this is unnecessary.

Yes, it actually starts falling apart immediately outside of the works written by the Viennese school. I think he made some important observations (the macro development of the line away and back to the tonic, for example). But my strictly personal opinion is Schenker is a bit like Freud - pointing at something valid and true but not necessarily providing the best explanation for it. Both became the celebrated theories in the US around the time of WWII. Freud has already faded away. Schenker finally started fading, since Lewin and especially Cohn's Neo-Riemann work...
I would encourage you to look at Drew Nobile's work to see promising ways of applying Schenker's insights outside of the Viennese school. It's the first I've seen that tries to build from the ground up a Schenker-like analytical system for "rock" music (far more satisfying to me than Walter Everett's earlier work). His dissertation (link here) is open access, and a shorter journal article of his regarding Schenker-like prolongational analysis is available free here.

[This is the second time I've plugged Nobile's work here, so -- full disclosure -- he is a personal friend. That biases me, of course, but I do think this is very significant scholarship.]
 

sinkd

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Not sure I agree with this.

The Schenkerian position is that triads (and any chords) are created as a result of voice leading. The triads are the byproduct, in other words.

I think what the OP is discovering here is more in line with Riemann view of music - that 2 or 3 basic chord functions are the building blocks of music and voice leading is something that happens when triads are connected to each other.

Might seem like a trivial chicken or the egg argument, but the consquences are quite far reaching.
The Schenkerian analogy is stronger than any reference Riemann's transformational theories. The OP's examples show the song working it's way through and consistently (and in Schenker's view inevitably) "composing out" a prolonged version of tonic throughout. A Riemannian "L" transform might change minor tonic into first inversion submediant (bVI6) but what we hear is the ineluctable pull of the minor tonic scale degrees coming back over and over. The scale degrees ("Stufen") and the tonic triad (Dreiklang).
 

Gene Pool

Active Member
I would encourage you to look at Drew Nobile's work to see promising ways of applying Schenker's insights outside of the Viennese school.
Salzer's Structural Hearing (1962) does this very well, though the book is not formatted well in its page size, which makes it annoyingly and unnecessarily thick, almost as small of a page size as one of those cheap paperback novels, with similarly shitty printing quality. Too bad; the content is great.

<EDIT> Last paragraph deleted by moderator. Please discuss politics on some other forum, not this one. Thanks.
____________________

EDITED BY GP:

I wasn't discussing politics. I was warning that if you're interested in studying Schenkerian analysis, you'd better acquire your resources soon, and I wildly imagined that I should give a reason for that. It's someone else who decided to "Well akshually..." me. So instead I'll just put it like this:

If anyone is interested in studying Schenkerian analysis you'd better acquire your resources soon cuz reasons I can't mention.

Can I say that at least?
 
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rrichard63

Perpetual Novice
This is a digression here, but I'm curious. I've never seen the notation "-3". A (major) third below the tonic would be either a flat sixth or sharp fifth. I doubt that's what is meant but I don't know what is meant.
 
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b_elliott

b_elliott

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This is a digression here, but I'm curious. I've never seen the notation "-3". A (major) third below the tonic would be either a flat sixth or sharp fifth. I doubt that's what is meant but I don't know what is meant.
Good question. TBH I had not considered it referring to a flat six, sharp fifth nor using interval counting down 3 semitones. But,

Short answer: -3 = flat/minor third.

Longer answer: It comes from an article "Tonal Centers" by Music Interval Theory Academy out of Europe. I am currently studying one of its free courses "Composition from Scratch". Link to article:

Cheers, a fellow novice.
 

Leon Willett

Active Member
Salzer's Structural Hearing (1962) does this very well, though the book is not formatted well in its page size, which makes it annoyingly and unnecessarily thick, almost as small of a page size as one of those cheap paperback novels, with similarly shitty printing quality. Too bad; the content is great.

<EDIT> Last paragraph deleted by moderator. Please discuss politics on some other forum, not this one. Thanks.
____________________

EDITED BY GP:

I wasn't discussing goddamn politics. I was warning that if you're interested in studying Schenkerian analysis, you'd better acquire your resources soon, and I wildly imagined that I should give a reason for that. It's someone else who decided to "Well akshually..." me. So instead I'll just put it like this:

If anyone is interested in studying Schenkerian analysis you'd better acquire your resources soon cuz reasons I can't mention.

Can I say that at least?
I'm curious about the reason you're saying this and find it to be a shame it was deleted, so would you mind PMing me your original post? I googled around and can't piece it together.
 
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