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I know my question looks similar to many other questions. But, please be patient with me. I'm writing this question because I can't find any appropriate answer although I have searched for it for a long time. I read some books about music theory, got some private lessons, and searched Internet, but unfortunately, I was not able to find the answer.

I've learned and realized follows through my search, but they can't completely answer my question.

  1. Functions of chords are basically one of tonic, dominant, and subdominant. I've learned that tonal music is a kind of a journey that starts and ends with tonic.
  2. Diatonic chords and secondary dominant chords towards one of them consist a pool of basic available chords in tonal music(I know there are many exceptional cases when the tonality of a song changes, etc).
  3. I can confine a set of plausible chords for a specific measure by comparing notes of each chord of the pool with notes of a melody on strong beats except passing tones.
  4. I can find plausible chord progressions by trying each chord of the pool(diatonic chords first, others afterwards) on my instrument and judging by ear.

But it's very tedious to try every (diatonic) chord in every measure of a song to accompany it even though you can guess some of them with typical chord progressions like ii-V-I. And this approach is not applicable when you need to accompany a song immediately.

I know there's no one chord for a measure that we can all agree. You can use IIm7 - IIb7 - IM7 instead of IIm7 - V7 - IM7 if you want make different sensation. That depends on individual sense. But we can say IIb7 and V7 are members of a plausible chord set for the measure at least. In the other hand, there are chords which just make no sense. I'm wondering if there is a theory to decide a set of plausible chords for a measure where the whole melody of a song is given.

For example, let's assume that there is a song of C major and its melody is as follows. Every note is a quarter note.

C C E | E E D | C C A | G G G |

C C E | E E D | G G G | G G E |

It's impossible to decide chords for a measure when only the measure is given without context. The fourth measure of the above song has only note G and it belongs to I, iii, V. But we can't say all of them are plausible because iii doesn't sound good. So I suppose a theory to decide a set of chords should explain its rule based on not only notes on strong beats of a measure but also the context of the measure (i.e. melody or chord before and after the measure). But I've never seen a theory like that. If there is a theory like that, is it possible to show how to decide a set of plausible chords of the fourth measure of the above song based on the theory?

I'm not actually interested in theory itself. What I really want is the ability to accompany a song that I know very well without chord sheets. I saw some people can do that, and I tried in various ways, but I still can't. My teachers were not able to answer my question. So I feel desperate.

If such an algorithm exists and someone knows that, there should be a paper or a book about it. I'd really appreciate if you mention one of them. If no algorithm about it has been found, it must be a subject worth studying. But I need to start with figuring out whether such an algorithm exists.

Thank you for reading my long question. My question became long because I was desperate to explain it well.

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Should your iib7 read ii7, as in Cmaj. V7 =G7 and ii7 =Dm7? –  Tim Apr 29 at 7:27
    
@Tim I meant 'IIm7 - IIb7 - IM7' progression which can substitute 'IIm7 - V7 - IM7'. So I suggested IIb7 can be used in a place of V7. Probably I didn't describe it well enough. I realized that I made confusion by spell it with lowercase letters like iib7. I'll fix that. Thanks for your comment. –  Chanwoo Apr 29 at 8:17
    
I think iim7 is D-F-A-C. (in C). IIM7 is D-F#-A-C#. IIb7 could be construed as D-F#-A-C. Lower case Roman numerals usually denote min. and upper case, maj. I think you mean Dm7 can substitute G7, as in ii7 = V7. could maybe be written IIm7 = V7. –  Tim Apr 29 at 8:23
    
@Tim Maybe my writing of chord symbol was not correct. I meant to express as follows in C major scale. C-E-G-B = IM7 (I major 7), D-F-A-C = IIm7 (II minor 7), Db-F-Ab-B = IIb7 (IIb 7), G-B-D-F = V7 (V 7) –  Chanwoo Apr 29 at 8:28
    
I wasn't sure whether the 'b' belonged to the II or the 7 ! Maybe bII7 would work ( it is a dom.7th chord), and nice harmony. –  Tim Apr 29 at 8:35

6 Answers 6

up vote 8 down vote accepted

" can confine a set of plausible chords for a specific measure by comparing notes of each chord of the pool with notes of a melody on strong beats except passing tones."

Yes, but one thing you have to keep in mind is that the chord accompaniment itself suggests or at least adds to the overal rhythm. This, by adding chords, you exert active control over what are perceived as the weak and strong beats. Your note sample could be harmonized with one chord per three quarters, or one chord per quarter, or even two eights per quarter. Whether the melody notes need to be harmonized as chord tones is going to differ in these cases. In the "one chord per quarter" case, you probably need to treat each note as a chord tone, but the other two rhythms will offer more possibilities to treat the melody as non-chord tones.

"It's impossible to decide chords for a measure when only the measure is given without context"

On the contrary - it is possible to decide. But it is a conscious, creative decision. If it were determined we would't have to decide.

"But we can't say all of them are plausible because iii doesn't sound good."

You can't categorically say that. I bet it can be made to sound good. For example, if we harmonize it a s follows:

C C E | E E D | C C A | G G G |

I | iiib | vi | iii

...it sounds pretty decent IMO, although maybe it does not have the mood you had in mind.

"So I suppose a theory to decide a set of chords should explain its rule based on not only notes on strong beats of a measure but also the context of the measure (i.e. melody or chord before and after the measure)"

But there is. One the one hand, the notes that you want to harmonize imply a set of chords (and their derivatives) you can choose from. On the other hand, the harmony has its own drive - chord progression. However, there are no hard and fast rules. What you have is a set of popular chord progressions. You can make a matrix of how likely it is that, within one key, a particular chord is followed by another. Walter Piston's harmony book starts with such a matrix.

"What I really want is the ability to accompany a song that I know very well without chord sheets."

Practice a lot. Keep trying all possibilities - eventually you'll find what works and what not. Learn the chord progressions of popular songs - this will make it easier to find a combination of chords that resembles a popular progression, and this will make the song sound plausible. Better yet, when you stumble upon an "unlikey" chord progression, try to find examples where other composers used it, see how they solved it. And try to change the chords upstream to see what it takes to make that chord sound like it's a likely one.

You're feeling desperate because you feel all you have to do is to find that one rule that tells you how to do it. The trick is, accept that there is no silver bullet. Not only accept it, try to see this as a wonderful opportunity full of possibilities.

"If such an algorithm exists and someone knows that, there should be a paper or a book about it."

Sure, algorithms exist. There are books (well, research papers) about them. However, we still have to find the first composer that admits to favoring any such algorithm to their own creativity.

Just to humour you, here's an algorithm for barbershop harmonization:

http://www.cs.bath.ac.uk/~mdv/courses/CM30082/projects.bho/2004-5/StephenJeremyRoberts-2004-05.pdf

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I'd love to see that barbershop program in action. When I get a spare few hours I'll read that paper...(!) –  Bob Broadley Apr 29 at 8:35
1  
@BobBroadley same here! It even has source code (C/C++) –  Roland Bouman Apr 29 at 8:40
1  
@BobBroadley If I get around to it and extract the sources, I'll let you know. –  Roland Bouman Apr 29 at 8:51
1  
@Chanwoo, I have little to add to my answer, except that "the rules" simply still leave so much room that you have to creatively decide how to do it. I'm reluctant to accept your piano teacher example, since they might not have been pursuing the same goal as you are. As for why there aren't more books, I think the traditional harmony and counterpoint courses already provide what is considered enough to satisfy this need. I'd be curious to hear how far you get with that algorithm, keep us posted! –  Roland Bouman Apr 29 at 18:36
1  
Chanwoo, @BobBroadley I took some more time to read that algorithm article. You might be interested to review "6.3.2 Identifying the primary harmonies" - "the implementation of the identification of primary harmonies is the weak link in this program...It produces arrangements which follow the circle of fifths, but which are musically weak". –  Roland Bouman Apr 30 at 21:05

Here's a simple way to select chords but you need a little music theory. I use this for harmonizing melodies in live performance, especially when hearing the melody for the first time. This method is based on music theory but when playing all you have to use is your ear. Harmonizing by ear is much easier in live performance than harmonizing by theory.

For this example, assume that the time signature is 4/4 which means the accented beats are on 1 and 3. Also assume that the whole melody has only one key center (scale).

First, know the harmonized scale for the key center. A harmonized scale is each note of the scale with a chord whose root is the melody note and whose 3rds and 5ths are from the scale.

For example the harmonized for C major is:

C Dm Em F G7 Am Bdim

Now replace the note of the melody that is on an accented beat (1 or 3 in 4/4) with a chord from the harmonized scale that has that melody note as its root. If it doesn't sound right, then try other chords from the harmonized scale that have the same 3rd or 5th note as your melody note.

You now have many possibilities for chords for the melody. Now start picking chords that have the strongest sense of movement. Most of the time this means you'll lean on one to three chords. But with the palette of chords you now have to paint the harmony you can make the chords move up, move down or follow the melody, especially if you can play chords in many positions. You typically want to start neutrally, perhaps on the root, add some tension to the harmonization and then release the tension by returning to the root.

Let's say we have a tune that you figure out is a "two chord wonder", in this case, Em D. Chord movement up would be Em F#m G Am Bm C D. Down would the opposite. But when playing live I might make a decision to lean on the Am instead to create some tension which I then resolve with a turnaround like Am Bm C D Em. Or I might decide to use chords that have as their root the first accented beat and then fill in the third beat with some chord that links the chords on the first beats.

Sometimes other musicians will ask me what my chord progression is for a particular tune and I'll have to admit I don't know, intellectually. But I can play it. :-)

Taking your example:

     C C E | E E D | C C A | G G G |
     C C E | E E D | G G G | G G E |

I see that all the notes of the melody fit into the C scale and the time signature is 3/4 which means just the first beat is accented.

So a first pass at harmony would be with the C harmonized scale on just the first beat of each bar:

      C     | Em    | C     | G7     |
      C     | Em    | G7    | G7     |

Putting some more chord motion into the progression I might try something like this on each beat:

     C  Bm Am | G Em F  | C  Bm Am | G G  Em |
     C  Dm Em | G Em Dm | Em F  G  | C G  Em |

but it would depend on the voicings I used and I would usually avoid seconds (notes next to each other in the scale) on accented notes. I also would only play a selection of these chords, not all of them.

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I think I've answered a similar question a long time ago.You've got the basics correct, in that most melody lines reflect the underlying harmony - generally speaking, if they didn't, either the tune or the chords are in the wrong place !

Not being interested in the theory makes it a difficult question to answer, as the theory is there to explain it. I can't see another way, except giving thousands of examples in all the keys.

As you are aware, in any given key, there are 6 common harmonies, as in 3 major and 3 minor triads. Don't want to dig deeper yet.From a major standpoint, they are I, IV and V. The minors are ii, iii and vi. The 7th chord, as m7b5 is useful in limited situations, so not addressed here.

If you study loads of popular songs,you'll see that most will have 3 or 4 chords. Obviously, as you already know, most 'journeys' start on I and end back at I. Check the penultimate chord, and in lots, it'll be V.That's the trick that dominant harmonies play, the move the music on to a place one fourth up (as in G-C).Look further into songs, and you'll see this trick many times - there's a Bb bar. Followed by an Eb bar. Being maj. or min. doesn't necessarily matter - F# can be followed with B or Bm.So - plan A.Try to guess if the 'cycle of fourths' is there - it may be for a couple of bars, or several. Plan B. Often, with some experience, you can guess that the next bar is either maj. or min. If you think it's maj. and you're already on a maj. chord, there's a 50/50 chance you'll guess right. Not bad odds.If you're on maj. and you guess min. there's still a 33% chance.

Moving on to notes contained in the underlying harmony.Yes, that 4th bar of yours could be any chord containing a G. So - G, C, Em, Am7, Eb, Go, the list is not endless, but there are choices, fair enough. That bar is at the end of the first line. Clue ! Lots of songs go on that journey, and stop for a moment as far from home as possible. Thus V is probably the best, certainly the most expected.

Plan C. There doesn't HAVE to be a change in the next bar in a song - often, a chord will last 2 or 3 bars. Look at 12 bar songs! But the converse also applies - chords can come 2 (or more) in a bar.It may be that ,say, there's a bar of Am, followed by what can only be a G bar, so sometimes, you can slip a D or Dm into the end of that 1st bar. Consecutive 4ths !

Most of this diatribe has covered triads, but using extra notes gives more scope. Consider sus2, sus4, 6th, dom7, maj7, min7. Then get into 9th, 13th, B5#9th and all sorts of sometimes weird sounding harmonies.Now, that G note in the bar above will have lots of chords which MAY fit under it...

Long question - long answer. I hope it's helped, and do look at the theory behind it - that'll help too.

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Thanks a lot for your answer. I think I made confusion by saying "not actually interested in theory itself". I mentioned it to express I want to know the theory for the practical purpose. I wouldn't ask a paper or a book or a theory if I were not interested in theory. I'd like to know the theory behind our judge by our ear and our mind. Please understand that English is not my mother tongue. –  Chanwoo Apr 29 at 8:38
    
You're doing a damned sight better than I would !! –  Tim Apr 29 at 8:40

While melodies usually emphasize chord tones of the harmony, the relationship varies greatly between styles and even from one song to another. For example, some blues solos strictly follow the chord tones of the underlying 12-bar progression, but others stick closer to the tonic center while the harmony changes around it. You could even play a legitimate blues solo on just one or two notes, using rhythm for expressiveness instead of pitch. There’s no way you could infer a harmonic progression from that; you need to know the harmonic conventions of the style to get it right.

In short, no algorithm is possible because there is no fixed relationship between melody and harmony. Indeed, you can create tension and release by bending the usual “rules” of harmony like that, playing with the listeners’ expectations.

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Chanwoo:

1) divide the tune into section(s) where each has its own tonal center or temporary tonal center. Then for each section, use any chord or chord progression that establishes/reinforces that particular tonality. You may use any chord(s) that do this, but usually you want to keep an eye to make sure the melody does not clash (ie. not an avoid note for that chord.)

2) pay attention to the bass line you create. Bass line comes first. Choice of chords reflects your choice of bass line.

For help/details/inspiration, two books:

a) Understanding and Implementing Harmony

b) Counterpoint. This book gives you an algorithm for constructing a counterpoint (harmony) against a melody. The algorithm basically reflects (fits into) the diatonic/secondary-dominant way of analyzing tonal music.

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Thank you for your suggestions. Do you have any plan to publish your books as Kindle by any chance? Kindle is more accessible to people outside of the USA. –  Chanwoo Apr 30 at 6:17
    
No Kindle, but I can give you PDFs of my books. –  Michael Martinez Apr 30 at 17:09

I think a simple theoretical concept that might help bridge the gap here is the notion that a chunk of the melody ITSELF can often be reduced to the arpeggiation of one of the basic chords of the key. If you can spot an arpeggiation of this type, you can harmonize a bunch of melodic notes at once, rather than running the "what chords fit under this note" algorithm for every pitch in a tune. (This allows you to think "faster" when you need to harmonize in real time!)

Let's consider the first line of the melody you gave us:

C C E | E E D | C C A | G G G |

  1. There is an arpeggiation of the F-chord in bar three, followed by the note G repeated in bar four: this would imply to me using the chord of F for all of bar three, followed by the chord of G for bar four, which would give a strong IV-V progression for the first half of the tune.

  2. The opening six notes are all from C major, the I chord. I would harmonize all of these notes with C.

  3. The one note not dealt with is the D at the end of bar two. You have two choices here: a) treat this like a passing note, and IGNORE IT. Simply play two bars of C; b) treat it as belonging to the G chord, and use a G chord on the last beat of bar two.

Once this basic framework is set, a more sophisticated harmonization would begin to transform the chords to create interesting bass lines, or add secondary chords to support the basic ones. But rather than trying to find "cool" chords for each note right away, it is better to get the basic outline of the progression correct, then smooth things out and add flavor.

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