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I tried to look for something clear and unambiguous but I can't find it, or I'm missing something simple. The questions is: What do all chords have in common, and is there a set of rules allowing to say that these 2...N pitches are for sure a chord?

I know that most of chords contain at least 3 pitches, a Root , third and fifth, but as far as I understood this is not essential for every chord.

The other definition I read that a chord is a harmonic composition of at least 3 pitches which belong to the same scale, but it would mean that any 3 pitches from the for instance Chromatic Scale form a chord, which I guess is not true?

So - is there any rule which would allow me to form any possible chord (not just some subset of them) on guitar?

Or in the end it turns out that the list of chords comes rather from history/tradition and cannot be exactly described by a strict mathematical rule (like it is possible for instance with semitones in octave which can be mathematically described and mapped to frequencies of the sounds ? )

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    An interesting question, maybe with no absolute answer. Even the minimum number of notes contained therein is still being debated ! – Tim Nov 17 '17 at 16:30
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    Why on earth do you need a "strict mathematical rule" to describe chords? And there is absolutely no rule that would allow you "to form any possible chord ... on the guitar," because many chords (or at least many voicings) can't be played on the guitar. – David Bowling Nov 17 '17 at 16:35
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    I thought a chord was simply defined as two or more notes, played at the same time or in arpeggios? That's what I learnt in music class anyways... – Unknown Nov 18 '17 at 1:13
  • Here is a list that might interest you, OP. – John Wu Nov 18 '17 at 2:35
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    What is the strict definition of any chord in the world? - And what is the meaning of life! :) – Stinkfoot Nov 18 '17 at 19:47
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There are many good answers. I will hopefully add something new by (1) identifying an issue with the question, and (2) distinguishing two types of chords, and (3) explain why context matters.

A Slight Issue

Chords exist in a stunning variety. This is problematic for your question. There is only way to create a single definition of the word "chord" that adequately captures every empirical instantiation of a chord: to encompass them all, we must define the word "chord" incredibly broadly. This has, in fact, been done. The broadest definition that exists of a chord is: "any two notes that appear to sound simultaneously." As you read this definition, you can probably tell that, the broader a definition becomes, the less useful it becomes for your purposes. If you want to use the definition as a road map--a guide--for creating new chords, you'll be frustrated by a broad definition. Perhaps it would be more useful to choose a specific genre and narrow in on the concept of a chord within that genre.

Two Concepts of Chord

There are at last two major ways the term "chord" could be used:

  • chord in general: any two notes that appear to sound simultaneously
  • a definite chord: any three notes appearing to sound simultaneously, which have a defined chord quality

    (some would say that a definite chord is the same as a common chord)

A definite chord contains enough information to identify whether the chord is major, minor, suspended, etc. By contrast, a chord in general may not contain this information.

Context

Do you agree that the combination of notes C-C#-D form a chord? What about the notes C-C#? The answers to these questions depend on your perspective and on the genre of music you're working in. I would think folks who write atonal music would say "yes" to both questions. But someone who only writes pop songs might be more likely to answer, "no; they're not chords." If you're looking for a functional definition, it's fine to limit the definition to the examples of chords you actually encounter/want to study.

  • How much of a fundamental psychoacoustic truth do you think it is that three notes are said to define a chord quality, and how much is it an accident of terminology? In jazz, 3 notes often seem to be seen as not quite enough... While other genres manage to make themselves understood well with 2. (this was my last question on the site: music.stackexchange.com/questions/52294/…) – topo morto Nov 19 '17 at 9:35
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    @topomorto, I think that's a fascinating question. I'm extremely limited and can only speak to Western music. I think we can answer the question "what's that chord?" or "what's that harmony?" with varying degrees of specificity. The difference between Cmaj and Cmaj6 is much less than the difference between Cmaj and Cmin. This suggests layers of distinction, with some "most fundamental" distinction between different chords. In many cases, the most fundamental differences lie in the 3rd and 5th (for Western). Why are a Cmaj and Cmaj9 so similar? I think it's because of harmonic function. – jdjazz Nov 19 '17 at 14:46
  • Also a good answer here, which I hadn't yet seen. – David Bowling Nov 19 '17 at 15:33
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Unfortunately, many words in the English language aren't really defined very rigorously. That's as true of music theory terminology as many other fields (some would say more so!), and 'chord' is one of those words that's not very well-defined. See e.g. A chord is three notes? What do you call just two notes?

Even if we assume that most people agree that a chord is at least two notes, we might still find disagreement on whether 2 notes precisely an octave apart constituted a 'chord'.

We might think that in a 'chord', the notes have to be played at the same time. But human players don't play notes at exactly the same time, even if they're notated together, and it might not always be possible to distinguish a 'chord' from a fast melodic run or arpeggio. (This aspect might be slightly tangential to your question).

If looking to play all possible chords on the guitar, be aware that:

  • There are many different voicings of chords that have the same name (e.g. there are lots of ways to play 'C major' on the guitar)
  • Different instrumental timbres will make the same chord sound different, and may even cause it to work differently as part of the harmony in a piece of music.
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Try this for size: Pyscho-acoustically speaking, a chord is a tone perceived by the listener as more than one pitch played simultaneously. In this sense, a guitarist could produce a chord by strumming multiple strings simultaneously, or by playing a single string through an effects box that would add harmonies (some sort of "auto-chord" box) or even by playing through certain fuzz pedals, if the listener hears the added overtones as extra pitches. (which, if you listen for it, is not hard to do) Examples abound - some listeners might hear ambient tones as part of the music, and find that an air conditioner or an electrical hum alters the chords that they're hearing. Monk famously taught John Coltrane to play "two notes at once" on the sax - obviously, the saxophone is only emitting one wave at a time, but you hear it as two notes. To the brain, it's a chord if you hear it as a chord.

Since you talk about pitches, I think that definition goes towards what you're looking for.

If you want to stay in the realm of theory (and think of notes rather than pitches), the term is a bit more ambiguous. For a classical theoretician, a chord might be defined in terms of > 3 notes including root, third, and fifth. For a jazz player, a chord might just mean a frame of mind, or a tone cluster suggesting a scale (see Mark Levine's books on jazz piano for this perspective). For a guitarist, "chord" often is conflated with "voicing". To encompass this ambiguity, I expect you'd have to say "more than one note sounded simultaneously comprise a chord".

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    Flexibility in the way you think about music is important, so it seems silly to look for "strict definitions" of concepts which are fluid (not a pointless exercise to entertain potential definitions, though). +1 for mentioning ambiguity and that chords and harmony mean different things to different musicians. WRT "For a guitarist": this seems to be a trait of inexperienced guitarists, probably a result of learning from chord diagrams. One descriptive term I have always liked for guitar: grips. A grip is not a chord, and not a voicing, but a way of fingering a voicing on the neck. – David Bowling Nov 18 '17 at 1:18
  • @DavidBowling I find that most guitarists I meet think like inexperienced guitarists, which is why I say "often conflated". I like the term "grip", I'm probably going to be making use of that. Thanks! – Jon Kiparsky Nov 18 '17 at 21:23
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This doesn't have the mathematical certainty you're probably looking for. You can get close, but it first depends on your definition of chord, and there's no official definition.

If you define a chord as any group of notes, then you don't really need a rule... just choose two or more notes and you have a chord. Of course you'll end up with a lot of weird sounding chords, but there is in fact a whole field of theory about this, called musical set theory. It's not for the faint of heart!

What you're probably looking for is a rule to create good-sounding chords, and that again is pretty subjective. But you can come close by realizing that many chords in western music are constructed by stacking notes in major and minor thirds. That will cover quite a few of them, even up into extended harmonies, but it's important to note that there are quite a few exceptions to this rule, such as sus2 chords, 6/9 chords, or even complicated things like augmented sixth chords.

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The questions is: What do all chords have in common, and is there a set of rules allowing to say that these 2...N pitches are for sure a chord?

The answers is: They are a group of three or more notes (some say two are sufficient to be classed as a chord) of different pitch classes - i.e. octave displacement doesn't change a chord's harmonic identity.

And already I'm seeing loopholes...

OK, let's try another definition. 'Chords are the result of several melodic lines played together.' No, not much use. That may be how chords STARTED, but they self-evidently AREN'T the result of several contrapuntal lines to a guitarist, or to a keyboardist playing block chords.

So, as we can't even decide on the definition of a chord, I guess there's no point in looking for a test.

Are you falling into the common trap of trying to use Theory to create music rather than to describe it? Theory can come up with a list of 'things that have been found to work'. It can label and catalogue them. It can even (sometimes) come up with a plausible explanation of WHY they work - though this ground can get very rocky :-) But (some of you must be getting really tired of me saying this) Theory Describes, It Does Not Command.

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A chord is pretty much any combination of notes. If you are playing around with chords, just take the root, the third, or the 5th and substitute it with any other note in that scale and see what it sounds like. Ask yourself what does it feel like when you hear each one of those combinations. With enough ear training and practice, you should be able to play any combination of notes and make them sounds good. If you end up with a weird sounding chord, see if you can change a note or 2 and make it not weird again.

You can use combinations/permutations in statistic to analyze it but I would not spend too much time on it. I would not try to make any mathematical formula for them either. The key is to play around with different combinations as much as possible until you get the sound and the expression that you want.

  • @BichPham, I think this is an interesting take. You've emphasized how the purpose of a chord is simply to achieve a particular sound, and hence there is no single formula for producing pleasing/effective chords--only our ears can be the judge. I like the practicality of this functional approach to defining a chord. In the end, music theory is meant to be descriptive of what sounds we like. – jdjazz Nov 19 '17 at 15:17
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    @jdjazz -- initially I hesitated to upvote as this answer seemed to advocate aimlessness with "see if you can change a note or 2 and make it not weird again." But your comments have won me over, and the answer does mention "ear training and practice." And after all, it seems that in the moment it often happens that fingers find a group of notes to play without mind consciously thinking of a "chord", but rather based on a desired sound. +1 – David Bowling Nov 19 '17 at 15:30
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I have a lot of comments/summarization here so I'm posting it as an answer, but I don't know if it should be an edit of my question, if it's so, mods please edit.

Ok. It shed some more light, or in fact revealed that this is all not really well defined.

  1. So it looks like the most broad definition I was looking for is a bit useless in creating music (not painful for the listener) Did I understand correctly that in this broadest definition the sounds don't have to even belong to the same octave, or even 12-tones? I mean in this broadest definition the C1, C#1, and C#1+15 cents would form a chord? :O

  2. And if I understand correctly all tutorials saying that any combination of sounds on piano is not a chord, in fact all refer to COMMON CHORD term?

  3. So maybe trying to narrow it down, but not to narrow : what is then 'a definite chord' and 'a defined chord quality'? Is it broader or narrower term than common chord?

  4. Is there a set of rules which would encompass all common, jazz, 6/9 chords? Allowing to say that certain 'chord formula' is compliant with it?

  5. Someone said why I am looking for a rule - I think deep understanding and figuring things out can help with creating own music, more than just learning list of chords treated like an axiom. (Or it turns out I have to? ) And was born with being an engineer so it helps me to learn.. ;)

  6. Referring to guitar, and all possible chords on guitar, I meant 'all chords which are possible to build on guitar' not all chords in the universe ;) I didn't mean grips, or voicing - conversely, I thought that knowing these 'strict rules', I will be for instance able to find grips and voicing myself, as a mind and musical imagination expanding exercise.

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    1) yes 2) yes, probably 3) 'definite chord' isn't a commonly-understood term 4) there are certainly guidelines that have been made / could be made when it comes to certain styles of music 5) A lot of people have been bitten by the way music theory presents itself as 'rules', but in many ways it isn't. They're just trying to warn you! 6) probably a personal question and a personal answer! – topo morto Nov 19 '17 at 14:52
  • BTW this definitely shouldn't be an answer and it doesn't really lend itself to being an edit either... chat would be the best place but unfortunately it's rarely-used. – topo morto Nov 19 '17 at 14:53
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    There are so many ways to approach this topic, and it seems that your question is really very broad and manifold. When confronted with chord names such as C+maj7#11, you can learn how the nomenclature works to find the constituent notes, and you can (and should) learn the name of every note at every location on the fretboard, so you can find fingerings for yourself. A good thing to work on is learning, and using, simple triad (maj, min, aug, dim) voicings on each of the 4 groups of 3 strings, in all 3 inversions. This can carry you a long way. – David Bowling Nov 19 '17 at 15:47
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    And if you don't yet know what "simple triad (maj, min, aug, dim) voicings on each of the 4 groups of 3 strings, in all 3 inversions" means, then you have something new to learn about, and something new to work on for a while.... – David Bowling Nov 19 '17 at 15:48
  • @EricDuminil helped make the point that, for #2, the term "common chord" may be too limiting. A better term might be "definite chord," which refers to a chord with a defined chord quality (e.g., major, minor, diminished, sus4, etc.). – jdjazz Nov 19 '17 at 18:13

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