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"The Craft of musical composition" root movement confusion


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Hello

 

Just in case of the slim chance that someone who visits here owns Paul Hindemith's book "The Craft of musical composition, Book 1: Theory" I have a question to ask about "degree-progression" that is confusing the hell out of me and if someone here understands it better and could explain it to me it would be greatly appreciated.

 

Hindemith lists the harmonic value of a chord movement first by a fifth: "A progression based on the interval of a fifth between it's roots naturally has a surer foundation than one based on a minor sixth; this is the strongest of all chord progressions" and shows an example of a CMaj chord moving to a GMaj chord.

 

The next strongest chord movement is by a 4th: "the next best chord progression after that based on a fifth is that based on a fourth" and shows an example of a CMaj chord moving to a FMaj chord. So obviously this book differentiates the different chord movements of a fourth and a fifth of having different strength.

 

My confusion is how do you know when the chord progression is a fifth or a fourth? In the example shown a Cmaj chord moving to a Gmaj chord is considered a "fifth". Yet another example in the book shows a G chord moving to a C chord and calls this the movement of a fifth, but the movement "G-C" is exactly the same as "C-F" which was previously said to be a fourth. Hindemith sometimes calls a progression a fifth and then the exact same movement at other points in the book a fourth and vice versa, yet it's not like these are interchangeable as he has already established the difference in strength between a a root movement of a fourth and one of a fifth. I've read it all as carefully as I can but I can't figure out when a chord movement is considered a fifth up or a fourth down/ fourth up or a fifth down.

 

If any understands this could you please give me some pointers?

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It's pretty much as Rev. states.

A fourth down from C is a G. A fifth up from C is also a G...

 

Yes, but this specific book states a difference in harmonic strength between chord progressions of a fifth and one of a fourth and has examples of C going to G as a fifth and C going to G as a fourth. Whether it's a fourth down or fifth up does have significance they're not interchangeable. So how do you determine if the root movement of C to G is a harmonic fifth up or a harmonic fourth down?

 

I'm no expert, so hopefully someone who is will confirm...

 

It entirely depends on the key. Without any context, you're correct that they are exactly the same. The circle of 5ths is the circle of 4ths in reverse, and vice-versa.

 

It all depends on what else is going on, and where it goes from there.

 

Yeah it sounds logical that it's context within the key decides if it's a fourth or fifth, I'll study the book again keeping that in mind see if something clicks in my brain haha.

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Yes, but this specific book states a difference in harmonic strength between chord progressions of a fifth and one of a fourth and has examples of C going to G as a fifth and C going to G as a fourth. Whether it's a fourth down or fifth up does have significance they're not interchangeable. So how do you determine if the root movement of C to G is a harmonic fifth up or a harmonic fourth down?

 

Strictly speaking, you're right, but not in the way I think you think you are. Chord progressions are evaluated based entirely on the key, so while your arrangement may move down four degrees to G from C, it's still considered a fifth, because G is the fifth degree of C. Where the literal movement of notes becomes significant is in more holistic, emotive aspects of the piece—the mood/s you're trying to convey—though that's less to do with the chord progression, and more to do with melodies, counterpoints, and voicings.

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Harmonically G is V of C.

F is I where C is V.

G is to C as C is to F.

F is effectively a subharmonic.

A string whose fundamental is C will have G as its 2nd harmonic,suggesting that a string which is 1.5 times longer would have C as its 2nd.

That's why the movement down a fifth (or up a 4th) is the strongest harmonic movement.

Pile fifths on top of each other and the first 6 give all the notes of the diatonic scale bar the 4th.

Experiment and do some sums. :)

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Yes, but this specific book states a difference in harmonic strength between chord progressions of a fifth and one of a fourth and has examples of C going to G as a fifth and C going to G as a fourth. Whether it's a fourth down or fifth up does have significance they're not interchangeable. So how do you determine if the root movement of C to G is a harmonic fifth up or a harmonic fourth down?

 

Strictly speaking, you're right, but not in the way I think you think you are. Chord progressions are evaluated based entirely on the key, so while your arrangement may move down four degrees to G from C, it's still considered a fifth, because G is the fifth degree of C. Where the literal movement of notes becomes significant is in more holistic, emotive aspects of the piece—the mood/s you're trying to convey—though that's less to do with the chord progression, and more to do with melodies, counterpoints, and voicings.

 

Ok I'm still a tad confused. I get that in the Key of CMaj the movement GMaj to CMaj would always be regard as down a 5th and never up a 4th. But what about, in the key of CMaj, the movement of Em to Am for example? Would that be a 4th because A is the 4th of E, or a 5th because E is the 5th of A?

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When I first learned this 50 years ago, the Gmaj could be referred with either way a 5th up, or a 4th down.. I notice theory books now refer to it as a 4th down.. When I first started chords were notated a few different ways.. I think Berklee music's version eventually won out.

 

It's good to have one meaning,cause then we all understand what it means. I took a course in 18th century harmony.. The teacher there, said something about the theory.. That it would be interpreted differently by different authors, and the point in time when the piece was made.. That's what theory is..

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Ok I'm still a tad confused. I get that in the Key of CMaj the movement GMaj to CMaj would always be regard as down a 5th and never up a 4th. But what about, in the key of CMaj, the movement of Em to Am for example? Would that be a 4th because A is the 4th of E, or a 5th because E is the 5th of A?

 

First of all, it's not that it's moving down a fifth from G to C, but rather that it's moving down from the Fifth (in this case, capitalized to add emphasis). If the notes move up a fourth, then the notes move up a fourth. But that's not how you analyze chords, unless, again, you're specifically talking about the arrangement, even in which case, you still are talking about the notes.

 

In terms of key and harmony, you don't look at things in terms of direction. You look at it in terms of relation to the tonic. So in C, going from E- to A- is simply looked at as a movement from the iii chord—the third degree of C—to the vi chord—the sixth degree of C. Of course—and this is where theory gets fun—that's all dependent on what else is going on harmonically and melodically around that point in the music, and how the person analyzing the piece interprets the function of a chord. (For instance, it could be the start of a trip around the circle of fifths, Em – Am – Dm – G – C, iii–vi–ii–V–I, or it could be a temporary dip into a different key, a v/vi–vi, before heading off somewhere else.)

 

It looks like this all stems from some ambiguous wording in your Hindemith book.

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