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I was recently looking at the the definition of a chord and got me thinking about the max size of a chord.

A chord, in music, is any harmonic set of three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may, for many practical and theoretical purposes, constitute chords.

Typically, chords are built in 3rds and the biggest chord I know is a 13th chord which can have seven notes in it, but usually have some note omitted because of it's size (the 9th and the 11th are optional). The 13th chord uses every scale degree in its construction, but there are 12 named notes and there are also quarter tones not to mention all the frequencies in between each note.

Because of this, I have two questions:

  • What is the theoretical max chord size?
  • What is the practical max chord size? (A chord that a musician or a group of musicians could play)
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Can you tell us exactly what you mean by "note" and "as if sounding simultaneously"? This is important for both of your questions, as the definitions are extremely fluid. Also, the answer might depend on whether you have a specific instrument or ensemble in mind, since in some situations you can hear overtones or sympathetic resonances, which could count as additional "notes". –  ninemileskid Jun 24 at 20:12
    
@ninemileskid I mean unique notes. I.E. not including octaves or overtones. –  Dom Jun 24 at 20:14
    
Do 440.00 Hz and 440.01 Hz count as unique notes? Can we consider electronic instruments with arbitrarily large number of "unique" oscillators? Do you want to restrict the amount time over which the notes can be arpeggiated? –  ninemileskid Jun 24 at 20:43
    
@ninemileskid That is the heart of the question. What is theoretically a unique note and practically a unique. –  Dom Jun 24 at 20:51
    
@Dom, this is really interesting. Are you asking about limits to which the octave can be divided before notes are either: not discernibly different in pitch; not discernibly different in function (i.e. they just sound "out-of-tune")? If so, might it be worth making some mention of microtonality in the question (and maybe title)? –  Bob Broadley Aug 4 at 22:38

2 Answers 2

Falling back on the limiting definition of a "note" as any discrete frequency that can be detected, then the largest theoretical chord is a computer synthesizing noise. (The phase relationships between frequencies must change with time for as long as the "chord" is sounding; fixed phase relations create wave interference, reducing the volume of some specific frequencies below the detection threshold.)

The computer with the fastest processor (capable of synthesizing the finest grid of discrete frequencies) will win, in that it will generate the "chord of the maximum size".

(Between two very fast computers, it may be that the one with the better random-number generator may sometimes win even if it has a slightly slower processor, as it is capable of inserting the highest degree of randomness into phase relations.)

The largest practical chord is the result of the same computer, but where we turn up the volume in order to exploit the nonlinear elasticity of the playback mechanism (e.g. the speaker cone), the medium (e.g. air), or the detector. In this way, nearby frequencies will become mixed and the spectrum will literally become continuous, creating a "chord with infinite size".

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I'd love to see a couple of super-computers slugging it out to see who can be the "noisiest"! –  Bob Broadley Jun 24 at 23:45
    
What about white noise? That's a sound produced by playing every single frequency at once (more or less). –  Kevin Aug 4 at 16:49
    
"White" noise simply means the intensity spectrum is flat. As long as the whole spectrum is above the detector threshold, I don't think its exact shape is important. –  ninemileskid Aug 4 at 22:34

I suppose you're asking about what the largest named chord is. You can have a chord with as many pitches as you like, across the whole range of the instruments playing that chord, and of course even more if you are using quarter-tones and micro-tones (as you say in your question). However, as you also say, the largest number of different pitches you could have with the "normal" chromatic system is 12.

You are right that chords being described with common naming conventions (built in thirds for instance) usually have no more than 7 distinct pitches, and so the 13th chord is the limit. Interestingly, one feature of this way of describing chords is that these chords usually have no semitone clusters (i.e. three adjacent semitones).

Beyond this, and for chords with semitone clusters, I would use PC Set analysis to describe sets of pitches.

There is one exception. Chords based upon a full Octatonic (diminished) scale, have no semitone clusters, but do have eight distinct pitches. These can be described using conventional naming, too, and are used in, for instance, Jazz.

To give an example, two Octatonic scales (and so also Octatonic chords) have roots on C: one with a semitone as the lowest interval; one with a whole-tone as the lowest interval:

  • C Db D# E F# G A Bb can be described as C13#9b9 - yes it's a bit of a mouthful, but it is completely legitimate, and certainly used. (You always have to decide which letter name is used twice in an octatonic chord; here it seems sensible to use D twice, as we describe it with #9 and b9.)
  • C D Eb F Gb Ab A B I'm not sure how you'd describe this… (without forcing it to fit a description; any ideas anyone…?)

So, the first of these two Octatonic chords would be my candidate for largest chord, using the conventional system of building and describing chords.

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TBH, I really am more interested in the theory behind chords then the largest named chord. –  Dom Jun 23 at 13:50
    
PC Set analysis of groups of pitches is definitely the way to go then. +1 for the question, BTW! –  Bob Broadley Jun 23 at 13:51
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@BobBroadley - if the first scale - half/whole diminished, is C13#9b9, the other - whole/half dim., could be B13#9b9,could it? –  Tim Jun 23 at 16:17
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As for the second 8-note chord, since the whole-half scale is the basic scale for a diminished chord, I would interpret the chord as a Cdim chord with tensions maj7 (yes, this is a tension for a dim chord), 9, 11, and b13: Cdim (maj7,9,11,b13). These are in fact all 'allowed' tensions for a diminished chord. –  Matt L. Jun 23 at 17:11
    
I think the OP is more thinking along the lines of "what is the line between how many notes can I put together before something sounds like a chord and is just a bunch of noise". Like if you took all notes from two octaves of a scale and played them all at once would that be a chord? How would it be named? –  user1886419 Jun 23 at 19:21

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