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This seems to be the implication from what I have seen posted on here. If this is so then it is quite profound, because then even in any complex sound wave without a clear pitch and with many partials that are not whole number integers, in amongst that 'noise' you will find harmonics and therefore tonality.

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  • Hi, welcome to this site! This question seems very broad, at least to me, maybe you could try to precise it a bit! For instance there is a big difference between sounds which are periodic or not in terms of partials! – Tom Apr 22 at 15:28
  • Hit any random piece of copper or iron pipe & you can probably discern a fundamental note. Trying to figure out a chord within the harmonics isn't really going to be all that easy. – Tetsujin Apr 22 at 15:37
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No. A trivial counterexample for periodic sounds would be a sine wave, which has only one tone and therefore cannot contain a major chord. Now, many (most?) naturally created periodic sounds will have the harmonics that form a major chord, but it's not a requirement.

As far as unpitched sounds, proper noise may technically have some energy at the frequencies corresponding to a major chord, but if it also contains energy at all the frequencies in between, it doesn't mean much to say it "contains a major chord". I could just as well say it contains Beethoven's 5th symphony.

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    Many (most?) naturally created sounds aren't that periodic, either. :) Even musical instruments, which are created for the express purpose of generating periodic sounds, have frequency shifts throughout. (Just watch a guitar tuner needle twitch more or less chaotically...) – João Mendes Apr 23 at 9:04
  • I would read their question about "periodic or natural" sounds to mean sounds that are both natural and periodic. They seem to be asking if all natural sounds we consider pitched contain a major chord. in its harmonics. – trlkly Apr 23 at 23:04
  • @trlkly They did mention unpitched sounds specifically in the body of their question. Though if we reduced the question to "natural sounds that are periodic (or nearly periodic) and pitched" then the answer would still be "many (most?) naturally created [pitched] sounds will have the harmonics that form a major chord, but it's not a requirement." – Edward Apr 24 at 0:00
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"any complex sound wave without a clear pitch and with many partials that are not whole number integers"

The major chord is the frequency ratio 4:5:6, so if the partials are inharmonic and don't include the 4th, 5th, and 6th harmonics, or their octave equivalents, then you wouldn't find the major chord in the partials.

Stringed instruments and wind instruments have harmonic partials, while percussion instruments have inharmonic partials. Though instrument makers like to shape percussion instruments like the marimba and bells so that the partials line up with the harmonic series or with 12EDO.

I'm not familiar with the term periodic sound, but inharmonic partials would make a waveform not periodic.

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  • Re. 2nd para, the harmonic series is infinite and does not converge on any finite value, so assuming inharmonicity in the starting conditions, how can we be so sure that the ratio of 4:5:6 never appears among any three notes of that series? P.S. I know it would be completely ridiculous to ascribe meaning to the conclusion that a rock thrown against my car door creates an entirely imperceptible major chord between the 457th, 673rd, and 921st overtones or what have you. But it's an interesting maths question! – user45266 Apr 23 at 9:40
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    @user45266 In that case they're not the 4th, 5th and 6th harmonics. If you only want to find three frequencies with those relationships, and you don't particularly care if they're peaks (or prominent peaks), and you don't care how long they last for, then for sure you can find them. That's the "p-value fallacy", where you decide ahead of time what you're going to find, and keep looking until you find it. But unless those frequencies are sustained and audible, then you won't find "harmonics and tonality". – Graham Apr 23 at 13:33
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I think the thing you are talking about, the overtone series where the first bunch of overtones outline a major chord, is about a vibrating string. It's not about "all natural sounds." At least that is the historic origin as I understand from my reading. Chord of Nature and Klang are topic to look up regarding the music theory history.

...This seems to be the implication from what I have seen posted on here.

I'm not sure if scientific rigor is the main concern in your question, but I'll share a little personal anecdote. I took some music appreciation courses in college, and in one of those courses the teacher demonstrated the overtone series on a piano by holding his finger on the various nodes of a string to show the relative strength of the first overtones outlining a major chord. The rest of the talk was basically, every note contains a major chord, this is the work of nature, it sets the major triad as humanity's basis for consonance and dissonance.

There is a kind of dogmatic thinking about it. No proof is given for why the presence of those overtones, on some instruments, should then determine the sense of dissonance. By the same reasoning you might as well say everyone's favorite color is blue, because that's the color of the sky! If you want to have some pseudo-scientific, non-cultural explanation of consonance, then it's easy to accept the idea. It's been repeated many times on this forum.

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    I guess it's about any instrument that produces something close to a harmonic series, rather than just a vibrating string. Arguablly closed pipes are even more "major chordish" than strings, as their first 3 harmonics are H1, H3, H5 . – topo Reinstate Monica Apr 22 at 16:30
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    Yes, but my point is about how it got into music theory originally. I think those early descriptions about about strings. – Michael Curtis Apr 22 at 16:32
  • Sure.... it's one of those parts of music theory that's a fundamental reality of physics, rather than a stylistic choice or an accident of history, so someone was going to spot it at one time or another! – topo Reinstate Monica Apr 22 at 16:41
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    I definitely agree that "every note contains a major chord...[which] sets the major triad as humanity's basis for consonance and dissonance" is bogus. – topo Reinstate Monica Apr 23 at 9:18
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    The rationale would be a claim about consonance being due to harmonics of one note not creating beating pattern with the other notes. I wouldn't argue such a claim must be true, but It should be a testable claim. Do other cultures with vertical harmony tend to also favor notes that are in tune with the harmonics? What about melodic harmony? I do know that there is a claim that the reason the neutral 7th is considered consonant in the Blues and its ancestral African traditions are that it is in tune with the seventh harmonic. – trlkly Apr 23 at 23:16
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Do all periodic or “natural” sounds contain major chords?

Just to be a bit nitpicky, 'periodic' and 'natural' aren't necessarily the same thing. In fact I will go as far as to say that no 'natural' sounds, by what I think would be a reasonable person's definition of 'natural', are entirely periodic - you can usually only create something close to genuinely periodic with electronics.

Anyway, back to your question. Certainly not all periodic sounds 'contain major chords', for the reasons given in Edward's answer. However, there are a bunch of sounds that tend to contain most energy at the frequencies of the harmonic series, and which tend to have most energy at the lower harmonics. They will therefore tend to have prominent first, third, and fifth harmonics, which do correspond to the root, fifth, and third of a major chord. If you try sweeping a resonant filter on an analogue synth, you can quite easily pick these frequencies out.

Of course these sounds usually contain energy at a bunch of other frequencies as well, but you could still reasonably say that there are some sounds that do 'contain' major chords. Importantly, these are often the kinds of sounds that man-made instruments produce.

So while it's not true to say that all periodic or “natural” sounds contain major chords, we can observe that many instrumental sounds do, in a way. Of course they also 'contain' other chords, so there's nothing super special about the fact they 'contain' major chords.

If this is so then it is quite profound, because then even in any complex sound wave without a clear pitch and with many partials that are not whole number integers, in amongst that 'noise' you will find harmonics and therefore tonality.

Yes, it is quite profound! It means that the perception of timbre and the perception of harmony are highly-related... in fact you could argue that they are simply different ways to think about the same phenomena.

A simple example - if you play three sine waves at 100Hz, 300Hz and 500Hz, you could think of that as a single note with 3 harmonics, or a particular voicing of a major chord (with the 'timbre' of each note being a sine wave).

You can try to make this - and other 'chords' - from the harmonic series at https://meettechniek.info/additional/additive-synthesis.html.

Here's quite a nice little 'is it a chord, is it a note?' set of sine waves:

Series

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  • Even with electronics, strictly periodic signals are a modeling abstraction. The inherent non-linearities of the physical components of sound generation, propagation and perception (i.e. speakers, air, eardrums, etc...) will introduce minute distortions. Naturally, for most practical applications, those can be ignored, but they're there nonetheless. – João Mendes Apr 23 at 9:13
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    @JoãoMendes I agree - even with electronics you can only get close. I suspect you can often get as close as makes no difference given the limits of human perception though, while things like a typical string pluck or horn blow produce sounds that are perceptibly very different to entirely periodic sounds. – topo Reinstate Monica Apr 23 at 9:21
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The question is a little bit ill-posed, as the term natural is not well defined. I'll try to clarify from my point of view which is that of a physicist and musician.

  1. Define "Major chord" as the sound of 3 sine waves in the frequency relations 4:5:6

In physics, the simplest equation to describe wave propagation is the d'Alembert equation. In one spatial dimension confined to a certain length (eg a string, or a column of air, but not bell or a plate (those are 2d)) yields the constraints that all sine waves with frequency a multiple of a base frequency are a solution to this equation. Moreover all superpositions (additions) of a solution are again a solution. This is where the overtone series originates from.

If such a system (a string, etc) is brought into oscillation, this is usually done with stimulus that contains all (or at least a lot of) frequencies, such as noise or a hit. The system then picks out the frequencies it "likes" which are all integer multiples of the base frequency. And thus the sound will likely contain a major triad.

This is only the most simple case of the description of what happens in nature/reality.

  • The d'Alembert equation is a simplification, e.g. real strings or the air column of our voice only follow it approximatively (but to a good approximation usually).
  • Not all systems are 1d, bells, plates, .. are 2d and the frequencies that solve their wave equation are NOT distributed that simply. It depends a lot on the form
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  • Off topic, but do spherical harmonics and even higher dimensional harmonics have real number frequences? – awe lotta Apr 24 at 0:01
  • Not as far as I know. – Thomas Apr 29 at 13:33
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Not in the sense that we usually take a "chord" to mean. A single C note played doesn't have a harmonic the next E up or the next G up in it. It may have one at the G an octave up from the next G up, though (third harmonic) and there may be one much higher up that happens to be an E but if it had both, that series of notes is not what we typically think of as a chord (maybe a C12+23??). So the short answer is no.

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    This answer relies on an assumption that most would consider to be a false statement: what you point out above is all true, except that chords are defined under the principle of octave equivalence. Thus, intervals P12th and M23rd up from a root would still be considered a major triad - the order of the notes cannot disqualify its status as a voicing of that chord. Oh, also: the harmonic series' intervals get closer together as one continues upwards, so showing that it can't exist in the first few partials isn't sufficient to rule out a close-position major triad among higher harmonics.. – user45266 Apr 23 at 9:48
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    @user45266 Wouldn't that basically render this whole answer completely useless? – Divide1918 Apr 23 at 11:09
  • As @user45266 pointed out, the intervals get closer together. When people say that a (close and root position) major chord has the ratio 4:5:6, that's the ratio between the 4th, 5th, and 6th (e.g. C1:C2:G2:*C3:E3:G3*). So this answer is wrong, except insofar as the harmonic series is indeed not 1:5/4:3/2:... – awe lotta Apr 24 at 0:04

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