What is the strict definition of any chord in the world?

Question

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 ? )

Answer 1

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.

Answer 2

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.

Answer 3

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".

Answer 4

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.

Answer 5

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.

Answer 6

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.

Answer 7

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.

Answer 8

Much has been said already, so I'll just add my thoughts on the matter. I'm one of those who do not hesitate to call two notes a chord.

Firstly, apart from if you're an academic on the subject, there's rarely a need to distinguish combinations of two notes from combinations of three or more. In most cases, the objection "2 notes are not strictly speaking a chord" does not add anything of value to the topic.

I would also argue that music terminology is widely used by people who don't care about theory at all. They just want to play music and be able to explain what they mean to other musicians. They don't care at all about academics.

IMHO, if academics feel a need to distinguish groups of three pitch classes from groups of two or less, it's up to them to invent a new word for that. Especially since the terms "2-note chords" and "power chords" are commonly used.

Octaves has been mentioned. I would not call two notes of the same pitch class but different octaves a chord. The reason is how overtones work. When you play two octaves together, the lower note will contain ALL the frequencies of the higher note. Adding a higher octave to a lower note does not produce ANY new frequencies. But at the same time, even if new frequencies are not introduced you can often still clearly hear that there are two distinct pitches, one octave apart. Personally, I would not make a thing of it as long as it does not cause any misunderstandings.