Talk:Harmonic series (music)

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Rather than saying

"the difference between consecutive harmonics is constant. But because our ears respond to sound logarithmically...,we perceive higher harmonics as 'closer together' than lower ones"....

would it not be more accurate to say that the distance between consecutive harmonics, as measured in semitones, decreases, but because of our ears respond to sound logarithmically, the frequency difference between consecutive harmonics is constant?

Kj4321 (talk) 17:19, 9 December 2008 (UTC)kj4321[reply]

Here's another try: "The difference in number of cycles per second between the frequencies of consecutive members of any harmonic series remains constant, but because the human ear and brain compare frequencies logarithmically (by division rather than by subtraction), higher harmonics sound closer together intervalically." -- Another Stickler (talk) 19:04, 9 December 2008 (UTC)[reply]

Thanks for the response. Considering first the sound source, before it reaches the listener, each standing wave in a vibrating object with harmonic overtones is larger than the succeeding standing wave (1/2, 1/3, 1/4, 1/5...). And this also conforms with tonal practice, with intervals of the harm series decreasing in size. So is it just the distance between them which is constant? Couldn't this 'constant frequency between harmonic numbers' be an "imprint" of the logarithmic human hearing system? Kj4321 (talk) 03:02, 10 December 2008 (UTC)kj4321[reply]

I don't know. -- Another Stickler (talk) 05:33, 10 December 2008 (UTC)[reply]

Not sure that assertion concerning combination tones contradicts overtone series as source of consonance and dissonance.

The discussion designed to rebut the concept of natural harmonic series as source of consonance and dissonance does not argue well. The writer is merely demonstrating that these sine wave frequencies are members of a natural harmonic series, but not the holders of the fundamental frequency. All lowest common denominator calculations are merely indicating the harmonic series to which both frequencies belong. The higher the partial numbers of the two frequencies, the more dissonant those frequencies will be perceived. This article needs cleanup. Davidbrucesmith 07:36, 21 February 2007 (UTC)[reply]

On the use of the term "overtone", this page says: "Barbershop uses overtone colloquially in reference to the psychoacoustic phenomenon of close harmony." But the Barbershop music page and other info I've seen emphasis the use of Just intonation and the resulting resonant "ringing" sound. Unless I'm mistaken (quite possible), I don't think "overtone" just means "close harmony" in barbershop.. ? Pfly 07:47, 9 March 2007 (UTC)[reply]

Concurred. There's no reason wide harmony can't ring too. I changed "close harmony" to "just intonation harmony". -- Another Stickler (talk) 22:19, 9 December 2008 (UTC)[reply]

If memory serves, bluegrass singers call this phenomenon "the bird," referring to a mixing tone heard "above" the actual notes being sung. Can't recall where I read that, but will keep looking. __Just plain Bill (talk) 19:40, 10 December 2008 (UTC)[reply]

This article is incorrect in:

Terminology...

Harmonic serie on the moodswinger...

From what I have experienced all overtones up to the 7th grade are clearly harmonic to the fundamental. If you go behind the 7th overtone, the string doesn't clearly resonate anymore, with the exception of the prime positions (8/1, 9/1, ->16/1). So the main dotted harmonic serie mentioned at moodswinger is the perfect consonant serie related to the fundamental tone. The 2nd smaller line serie (8/1 -> 16/1) mentioned at the instrument are less consonant, because the string only clearly resonates at the prime overtone. (14/1 is clear, 14/3 or 14/5 for example cannot be heard clearly). 8/3 and 8/5 are maybe also consonant, but that's shaky. I'm still considering to put those tones in the scales, because they are important tones for the minor scale. They are the Plutos of the consonant harmonic serie.YuriLandman 07:58, 18 August 2007 (UTC)[reply]

Nomenclature...

I'd like to point out two things: I think everything will be much clearer if the fundamental is numbered as O, the first harmonic as 1, so that the following order ensues: octaves 1,2,4,8,16 etc fifths 3,6,12,24 thirds 5,10,20 sevenths 7,14,28 etc. This order seems logical and certainly practical. Above is mentioned "the 7th degree or sixth overtone which is utterly confusing.

Secondly, nr 11 on the staff notation is given as a g-flat which is wrong as it is a raised f. Normally, special signs such as half flats and sharps come in handy here.Martinuddin (talk) 11:30, 20 July 2008 (UTC)[reply]

Please count again. In the current table Harmonic series (music)#Harmonics and tuning you can see that the order you claim is achieved by starting from the fundamental as 1. −Woodstone (talk) 15:05, 20 July 2008 (UTC)[reply]

Wow. I never noticed that pattern of multiples in the numbers.

talk) 19:18, 12 August 2008 (UTC)[reply

]

A while back the table of harmonic series was changed to a new format. I think the old version was easier for novices to understand. The current table has a two dimensional array in place of a table column, which could perplex readers.

I'm confused by this statement. A few lines above you expressed surprise that the table brings out the pattern so beautifully. In a single column table it is not visible that easily. −Woodstone (talk) 19:23, 12 August 2008 (UTC)[reply]

It's still harder to grasp. It was necessary for

talk) 19:53, 12 August 2008 (UTC)[reply

]

I see there's already a section above on some disputed stuff in this article, but those aren't what I consider to be the problems. Since it's all unsourced made-up stuff, of course it's largely free to say whatever came to someone's mind, like the nutty idea that an instrument is in some sense like a harmonic oscillator, or that a harmonic oscillator would have harmonics in its oscillation. Nonsense, all; hence, the disputed tag. With a merge, maybe it could be cleaned up, if there's anything here worth merging. Dicklyon (talk) 04:12, 5 September 2008 (UTC)[reply]

Please remember to make some effort at civility.

I agree that the factual accuracy needs to be reviewed and in several places edited a good bit. But any suggestion that the content of the Article is wholly or even largely contrived is quite wrong. If the implication of the posting of fictional content is meant as an exaggerated criticism of its lack of citation then I do acknowledge that point. But the notion that the physics concepts discussed in the Article were fabricated from the imagination of the author does not ring at all true to me. Personally, I have read a great deal about harmonics as they relate to music but my physics expertise is limited to a handful of honors Physics Dept. classes that I took while in college, largely because I liked the professor.

Given my relatively novice status I cannot defend or dispute many of the specific details. But I can offer reliable evidence that musical instruments are indeed significantly akin to harmonic oscillators and that the mathematics that describe them are in fact quite useful an Ideal model for the oscillation produced in making music.

To try to be a bit more succinct I am just going to provide the relevant links for citation and an explanation if necessary.

1. http://ccrma.stanford.edu/~jos/SimpleStrings/ a goldmine of information about modeling oscillating strings on musical instruments--discusses that "quai-harmonic" model in relation to the ideal oscillation model
   1. http://ccrma.stanford.edu/~jos/mus423h/Analysis_Resynthesis_Quasi_Harmonic_Sounds.html This specific page discusses the phrase "quasi-harmonic" to explain the jargon.
2. http://books.google.com/books?id=rVq8YiInxz0C&pg=PA106&lpg=PA106&dq=Harmonic+Oscillator+piano+string+dampened&source=web&ots=qojiULCXcx&sig=RL1DEK1ss_CBivSwBGzfm8wkG9I&hl=en&sa=X&oi=book_result&resnum=2&ct=result discusses how dampened harmonic oscillation may be effectively analyzed as ideal harmonic oscillation
3. http://hyperphysics.phy-astr.gsu.edu/hbase/waves/string.html#c1 discusses the harmonic nature of an oscillating stretched guitar string

There's obviously plenty of more sources out there. The main point that I mean to demonstrate in this is that, however much cleanup the Article may need, the content is relevant and there are no lack of sources for an ambitious editor. For these reasons I oppose the proposed merge with Harmonic. Korbnep (talk) 06:19, 13 September 2008 (UTC)[reply]

Well and good, but the sources about strings don't mention harmonic oscillators, and the one about harmonic oscillators doesn't mention harmonics. The confusion of these things should be removed. Dicklyon (talk) 22:29, 9 December 2008 (UTC)[reply]

Dicklyon, I undid your replacement of the Harmonic numbering paragraph with something true, because 1) the something true is true but redundant with the paragraphs above it, and 2) the point of the original paragraph is to expose two harmonic numbering systems (not to be confused with overtone numbering or partial numbering). I put the ^{[citation needed]} tag on it yesterday, hoping someone might defend it. We don't know for sure that it's not true, just that it's un-cited, and one of the wikipedia policies is to not destroy information, so let's leave it tagged for a while and see if someone champions it. If no one does, then eventually the Harmonic numbering subsection should be removed in whole. There's no need to replace it with anything. I personally suspect that the practice of numbering harmonics by excluding the fundamental is a terminological mistake by people who confused overtones with harmonics, and not worthy of encyclopedic note, but let's wait and see. -- Another Stickler (talk) 04:19, 10 December 2008 (UTC)[reply]

OK, we can wait on that. Dicklyon (talk) 18:49, 10 December 2008 (UTC)[reply]

Stickler, I don't like your statement about sine waves. The claim "Any complex tone or timbre is a sum of sine waves of different frequencies, amplitude envelopes, and phases" has two problems: first, the phrase "or timbre" is not needed, and is not using the word timbre in the way it's defined in its article; second the statement is defensible only for periodic tones. The way I had it was better: "A tonally complex waveform, such as a musical tone, can be approximated as a sum of sine waves of different frequencies, amplitudes, and phases," since any such decomposition of real sounds is necessarily approximate. Dicklyon (talk) 18:49, 10 December 2008 (UTC)[reply]

I just put the approximation back. Does the article need to expand on the fact that any musically interesting sound varies with time, and so is not strictly periodic, except when observed in a time window on the order of tens or dozens of milliseconds? I find that a lot of people automatically assume a steady mix of partials when talking about tone or timbre, when in fact the dynamic response of the instrument(s) to human input is what brings music to life, and allows it to be shaped by the player(s). __Just plain Bill (talk) 19:00, 10 December 2008 (UTC)[reply]

Probably this is not the article where we need to go into that issue, but we certainly don't want to state things that depend on the illusion that tones are periodic or even stationary. The "approximation" concept can cover a lot of sins. Dicklyon (talk) 22:30, 10 December 2008 (UTC)[reply]

The section is for defining terminology. The first term defined is partial, which I have defined as "any of the composite sine waves in a complex tone," and no one disagreed. Are either of you now saying there's something else beside sines in a complex tone? -- Another Stickler (talk) 03:01, 11 December 2008 (UTC)[reply]

Yes, of course. The breakdown of things into sines is almost arbitrary, and many ohter decompositions are known and used. However, sines are the things to which the concept of "frequency" applies, and so they are the things that harmonics, partials, overtones, etc. refer to. If you'd like to see a bit of what's wrong with thinking of our ears as Fourier analyzers (that is, of trying to break everything into sines), see my talk about modeling how hearing works, in which I make Ohm and Helmholtz and Fourier the "bad guys": http://www.archive.org/details/Helen_Wills_2007_10_01_Richard_Lyon Dicklyon (talk) 03:31, 11 December 2008 (UTC)[reply]

Unless the signal exactly repeats itself endlessly, it cannot be said to be a sum of sines. Better to say it may be approximated by a sum of sines. Real signals' harmonic composition varies with time, introducing complications. Fourier transforms of a time-limited signal segment have their own issues to do with the time window being sampled; shaping the edges of that window may be done various ways to serve various analytic needs. I am only vaguely familiar with that much of the iceberg's tip, and I agree with Dick (who knows a whole lot more about it) that the "approximation" concept covers as much as we need to go into in this article. __Just plain Bill (talk) 03:41, 11 December 2008 (UTC)[reply]

There's so much to respond to, this may be long. Sorry. My version of the old paragraph wasn't describing Fourier. The Fourier series is only a harmonic series, plus an out-of-phase clone of that series, plus amplitude information for both. I changed the original editor's "amplitudes" to "amplitude envelopes" to make it describe all tones including non-repeating tones. I don't mind dropping "or timbre" since it means tone color, which is implicit in tone, which is inherited by complex tone. Wave-form, sound, signal, and tone are equivalent, but we shouldn't complicate the article with needless synonyms. I don't like the addition of "such as a musical tone" because it opens the can of worms of judging what is musical vs. what is not, and it allows the reader to misinterpret that non-musical tones might not be included in the description. My last question above (is there anything else but sines) was rhetorical, but I guess it didn't make my point. The point is that the mainstream model for the composition of sound, modulation of the frequency spectrum, is sufficient for all sounds. Each point in the spectrum is a frequency, which is a sine. Any tone is therefore composed of sines just as the number line is composed of points. No mention needs to be made that there are an indefinite number of points. That's the model we can assume here. If there are alternative models, I'm not aware of them, but we can create new articles for them. "Unless the signal exactly repeats itself endlessly, it cannot be said to be a sum of sines." J.p.B., I have two answers to that. First, the simplest example that proves that your rule is not true is the non-repeating signal that is the sum of two sines at an irrational frequency relationship. Second, any signal, repeating or non-repeating, is the sum of sines if you include the whole spectrum, if you allow that they don't all have to be in phase, and allow for amplitude changes over time. D.l., I can't get your video links to work on my computer/browser combination. It looks interesting, but it's about models for hearing, which is outside the scope of this article. I would really like to learn more about it, but not here. Here's a reworked paragraph I would like to put back in: "Any tone is a sum of sine waves of different frequencies and phases, changing in volume over time." That describes the mainstream model in a simple sentence, it accounts for all sounds, repeating and non-repeating, musical and non-musical, and sets the foundation for the following paragraphs which define terms starting with partial. -- Another Stickler (talk) 05:18, 12 December 2008 (UTC)[reply]

Oops, I meant this one: "Any complex tone is composed of sine waves of different frequencies and phases, changing in volume over time." —Preceding unsigned comment added by Another Stickler (talk • contribs) 05:24, 12 December 2008 (UTC)[reply]

"Changing in volume over time" implies other spectral components (representable as phased sines again, but still a needless complication for this article.) I'd prefer to see "Any complex tone may be approximated as a sum of sine waves of different frequencies and phases." and leave it at that.

I suppose inharmonic partials do deserve passing mention, but the context of the article is, simply put, the harmonic series. __Just plain Bill (talk) 06:04, 12 December 2008 (UTC)[reply]

Originally Stickler wrote it with justification via the

Fourier theorem, which only applies to periodic functions, not real sounds. Obviously by allowing the amplitude coefficients to vary with time, any signal can be written as a sum of sinusoids, for example trivially as f(t)*cos(0*t). Getting into what it means to have slowly varying amplitudes is too complicated for here, and too ambiguous. Saying "Any tone is a sum of sine waves of different frequencies and phases, changing in volume over time" is a bit misleading in saying "is". It would be more OK as "can be decomposed into" or "can be described as" or "can be approximated as". Dicklyon (talk) 08:44, 12 December 2008 (UTC)[reply

]

I didn't write the Fourier paragraph. I just moved it to the top, which probably caused some confusion. D.L. was right to replace it with something less restrictive. Let's super refine it. I'm assuming we can ignore phase as harmlessly as we can ignore amplitude and time, because each can be brought in as needed in a more detailed description beyond this article without making this statement false. In other words, a sine, shifted in phase, and changing in amplitude over time, is still a sine. How about this: "A complex tone is composed of

sine waves of different frequencies." -- Another Stickler (talk) 21:13, 12 December 2008 (UTC)[reply

]

I object to "is composed of", which suggests something much too strong and real when it's in fact not true; I would be OK with "can be approximated as" or "can be analyzed as" or "can be modeled as" or "is conceptualized as" or something like that. Dicklyon (talk) 22:44, 12 December 2008 (UTC)[reply]

I see now that the Fourier thing came in in 2006 with this edit. Sorry for the confusion, and thanks for helping. Dicklyon (talk) 22:49, 12 December 2008 (UTC)[reply]

Thank all of us. I wonder if readers appreciate how much work can go into building one correct sentence. I based "is composed of" on your "can be decomposed into", reversed into the non-passive voice. It also works with the next sentence that uses the adjective "composite". I think "is composed of" is at least as "true" as any other geometric or mathematical statement describing the situation can be, as well as being mainstream, and therefore defensible for the article text. Why do you say it's "in fact not true"? -- Another Stickler (talk) 01:12, 13 December 2008 (UTC)[reply]

Not sure what "mainstream" has to do with it... Those sinusoid decomposition products are useful for some analytical purposes, but it's just as valid to call them "artifacts of one of many possible ways to describe the signal." They aren't inherent in the signal, but appear when someone goes looking for them with certain tools.

The active voice is a fine thing to use in descriptive writing, but I'm not sure that means we need to get rid of the passive voice altogether. Here especially, I believe the specialized use of "decompose" in an analytic context is not reciprocal with "compose" as it is commonly used.

Of the choices offered a few paragraphs earlier, I favor "can be modeled as" over the others. I hope most readers will understand that the modeling may more or less accurate, but still understand that "the map is not the territory." __Just plain Bill (talk) 04:32, 13 December 2008 (UTC)[reply]

The excellent new book Music, Thought, and Feeling: The Psychology of Music, by William Forde Thompson, uses "can be described as", that is, "Any naturally occurring sound, ..., can be described as a combination of many simple periodic waves (i.e., sine waves) or partials, each with its own frequency of vibration, amplitude, and phase." That's a "mainstream" view, and is not really true, but it's a language that I wouldn't object much to. Of course, "naturally occurring" is irrelevant, and doesn't make it more true or less true. Dicklyon (talk) 16:21, 13 December 2008 (UTC)[reply]

I think both of you are still stuck on approximation. An approximation is not true in that it leaves parts out. When you accept the whole continuous unbroken frequency spectrum, and not a subset like a Fourier series, it is a complete and sufficient description to say every signal is composed of sines; it doesn't leave any parts out, it's not an approximation, and therefore as "really true" as any statement can be. J.p.B., I said composed not compose, as a whole is composed of parts. The map is not the territory, but all perception and all language is mapping, including science, music theory, and wikipedia articles, so that is not a reason not to rely on our best maps and even call them "true". As far as mainstream, that's a combination of the wiki-tenets of neutrality, verifiability, and no-original-research-ity. Thinking of a wave as a spectrum of frequencies is the first tool of analysis. Graphs of time vs frequency are common in the literature. The model is definitely mainstream. I know no other model. Do you? D.L., thanks for the research; the Thompson sentence exactly parallels the sentence in question, and it's verifiable. I've put it in. Please check that I did the citation right. It kind of screws up the flow a little, in that it defines partial too early and as a secondary subject in the sentence, it says partials in plural, and italicizes it, so it makes the next sentence look redundant, but the next sentence should not be removed because it's important to define "partial" in it's own sentence. I'm satisfied. Are we all? -- Another Stickler (talk) 18:30, 13 December 2008 (UTC)[reply]

Darn it. I just realized the Thompson quote uses "amplitude" instead of "amplitudes", which makes it not apply to some evolving complex tones. -- Another Stickler (talk) 19:11, 13 December 2008 (UTC)[reply]

The notion of partials is inherently discrete, and the conditions needed to make Fourier analysis work exactly leave out all sounds that have a discrete spectrum, so it's hard to see what kind of Fourier theorem you believe in to justify your outlook. Of course, as I said already, if you let amplitudes change in time it's trivial, but no longer are the partials sinusoids. You can't have it both ways, mathematically, so it's best to just stick to admitting an approximation, or a "description". The previous statement relying on the

Fourier theorem was at least true for periodic sounds, but making something periodic out of a bit of music is itself a way to approximate that piece of music, no? The "mainstream" view in the not-quite-technical music literature is actually just wrong; even Thompson is wrong in places. I'm OK leaving it not mathematically rigorous, but we ought to not pretend that it rigorous, either. I toned down a few things that I felt were stated too strongly, including the bit about "harmonics" being "technically incorrect" when the partials are not perfect. That would need a source. And I took out timbre since it hadn't been explained how it stood for a sound and I don't like the implicit assumption that it corresponds to spectrum; looks like I still have some work to do on that... Dicklyon (talk) 00:31, 14 December 2008 (UTC)[reply

]

OK, I did some more work, broke up the long lead into what looked like intended paragraphs (had single returns in places instead of double), and then broke off a long example section and put it after the terminology, and some more edits. I apologize that I did more at once than you can easily follow by looking at the diff, but I hope you will all find it OK, or work to improve it further. There is still a lot of redundancy, like about the musical intervals at the end of the new section and the start of the next section. Dicklyon (talk) 01:01, 14 December 2008 (UTC)[reply]

I also took out the bit about our ears responding logarithmically, since I'm an ear guy and it's not really true, and has little to do with why musical intervals are consonant or dissonant or sound alike when transposed. Dicklyon (talk) 01:06, 14 December 2008 (UTC)[reply]

I'll be letting this particular point sit for a while, and taking some time to look over the whole article's big picture. I don't see the original issue of this section as too badly broken at the moment, so no rush to fix it. Stickler, I understand how you meant composed (of parts) but I still don't think of that and decomposed (into analytical elements) as exactly reciprocal cognitive items. __Just plain Bill (talk) 06:39, 14 December 2008 (UTC)[reply]

D.L., if you think I'm proposing Fourier it in any way, let alone defending it, you haven't understood what I've written. I'll say it once again: I'm talking about the whole, complete, unbroken, continuous, frequency spectrum. Here's an analogy: if the frequency spectrum is like the positive domain of the real number line, then a Fourier series is like a series of equidistant points on that line. The problem with Fourier is the gaps between its points. It's an incomplete model. -- Another Stickler (talk) 17:19, 14 December 2008 (UTC)[reply]

But the whole complete spectrum is also not a useful concept. I presume you mean the Fourier transform, or maybe the power spectral density. But neither of these is applicable to all sounds (Fourier transform applies to finite-energy sounds, but not sounds that last forever, such as periodic ones; power spectral density applies only to stationary processes), and neither leads to a decomposition that can be called partials, so it's really unclear what you have in mind in terms of connecting spectrum to partials. Dicklyon (talk) 06:11, 15 December 2008 (UTC)[reply]

D.L., you said "if you let amplitudes change in time it's trivial, but no longer are the partials sinusoids." I don't see a mathematical problem with calling them sines with changing amplitude. That explains that the shape will change slightly as the amplitude changes. It shows that two signals are present, the sine and the amplitude/time curve. It doesn't confuse things in any way because the sine is still present in the mix. -- Another Stickler (talk) 17:29, 14 December 2008 (UTC)[reply]

The trivial example Dick gave was a time-varying amplitude function applied to a sinusoid of frequency zero, or cos(0), which amounts to DC. Then the frequency components of the modulating signal become an issue... __Just plain Bill (talk) 19:42, 14 December 2008 (UTC)[reply]

It actually does makes some sense to think of sounds as being decomposed into modulated sinusoids, but you also need frequency modulation to get a sensible decomposition, for cases such as vibrato. It's considerably more complicated though to put constraints on the modulating functions, since there are trivial solutions and an infinity of alternative decompositions. So as a way to define partials it's not altogether helpful. Dicklyon (talk) 06:03, 15 December 2008 (UTC)[reply]

Do the frequency relationships between fundamental and partials change during vibrato? I suppose they might, depending on the instrument. Of course, in the case that they don't, there's no need to redefine the partials, as they track the fundamental. In the case that they do, then there are two ways to think of it, either as the partials retaining their identity while being modified, or as different partials. I think the latter is consistent with the definitions we already have, where each partial's identity is precisely its relation to the fundamental, but I don't remember this question even coming up, let alone being written about to cite. -- Another Stickler (talk) 07:49, 15 December 2008 (UTC)[reply]

The whole complete frequency spectrum is not only useful, it's essential in that it holds all possible partials. No Fourier series can do that. -- Another Stickler (talk) 07:59, 15 December 2008 (UTC)[reply]

I'm a stickler myself on statements like "although the partials are not harmonics by the strict meaning of the word if they have any inharmonicity at all." This is an inference from a strict interpretation, and unless it is sourced it is either an editor's opinion or original research. I don't see how it adds anything to the statement before, which is that partials are commonly called harmonics even there's a bit of inharmonicity. The reader can be left to deal with the implied bending of the definitions, or to do further research on how strictly the terms are used in various communities; if we want to tell him, we better find out, verifiably, before doing so. Dicklyon (talk) 01:18, 14 December 2008 (UTC)[reply]

It's the "Terminology" section. That's why it's important to make extra sure the meanings are not accidentally blurred. I'll tone it down, but the point still must be made, harmonics are a special case of partials. -- Another Stickler (talk) 01:50, 14 December 2008 (UTC)[reply]

But you linked a dictionary that says in music a harmonic is any overtone. We need better sources if we want to make stricter statements. Dicklyon (talk) 02:19, 14 December 2008 (UTC)[reply]

D.L., why did you remove the harmonic citation [1]? The majority of dictionaries listed there have at least one sense of the word that exactly corresponds to the sense in the sentence I placed the citation after, the sense that harmonics are integer multiples of the fundamental, which is why we need to be sure to distinguish from partials, of which they are a subset. -- Another Stickler (talk) 02:08, 14 December 2008 (UTC)[reply]

I removed as I said in the edit summary because the definition that it list in the music field does not agree with what is stated in the article. Also, it was not a reference, but an in-line external link. If you want to put it back as a citation, it would be good to quote both the physics and music definitions and maybe modify the text to suit. Even better, seek a music book to cite, since dictionaries are actually pretty poor sources. GBS finds no sources that mention the notion of an "ideal partial", so that should probably be reworded. Dicklyon (talk) 02:15, 14 December 2008 (UTC)[reply]

Here's a book in which harmonics follow from the approximation of a sound as "essentially periodic". This seems appropriate, and is quite distinct from what you seem to have in mind, which is the notion that partials can be found rather exactly, and then compared with an ideal to see if they are harmonics. There's no theory I know of by which the latter makes much sense, though one can estimate inharmonicity of a partial in some cases. Dicklyon (talk) 02:27, 14 December 2008 (UTC)[reply]

You didn't read all the dictionaries did you? You stopped at Random House Unabridged Dictionary that says in music harmonics are a synonym with overtones, which is clearly wrong. You have to read all of them, then you'll see that the majority do define it as we understand it, as an integer multiple of the fundamental. That's not saying actual instruments are capable of producing exact integer multiples. Partials can be harmonic or inharmonic. There's nothing wrong with an in-line link. If you want to improve it into a citation, do so, but don't remove the inline link until you do. Don't destroy information. -- Another Stickler (talk) 16:42, 14 December 2008 (UTC)[reply]

The only dictionary entry I read was the one you cited. Dicklyon (talk) 06:07, 15 December 2008 (UTC)[reply]

I thought so. Wait for it to load and use the scroll bar. There are six dictionaries if I remember right. No wonder you thought it was a bad citation. Try again, then put the citation back in. -- Another Stickler (talk) 07:08, 15 December 2008 (UTC)[reply]

Looking for a source, I found this one that makes it clear that inharmonicity is a property of an individual partial, not of a tone. There may be other definitions, so need to look more before changing this in the article. Dicklyon (talk) 02:13, 14 December 2008 (UTC)[reply]

That's my understanding too. Inharmonicity refers to individual partials, not tones. -- Another Stickler (talk) 16:56, 14 December 2008 (UTC)[reply]

Bill, it seems counterproductive to link pitch to

• "The musical pitch of a note is usually perceived as the lowest partial present, which may be the one created by vibration over the full length of the string or air column, or a higher harmonic chosen by the player" makes me question whether "usually" is what we want here. It's probably true, but also tends to point away from the possibility of a missing fundamental, which may not be usual at the instrument, but would be usual if listing over a telephone, for example. Maybe "often" would leave it more open. Also, in brasses and woodwinds, it would seem important to note that the excitation rate from the lips or the reed is what directly determines the pitch; it does certainly tend to sync up pretty nearly with one of the harmonic resonances, as "chosen by the player". What might we say here that would make this stuff more clear? Or is it good enough? Consult some sources?

• Inharmonicity; most books I've looked at in GBS talk about it per partial, but at least one talked about inharmonicity of a complex tone; I guess we better mention both. Thompson, which I have with me and was quoting in the middle of the jet-lagged night, doesn't have "inharmonicity" in the index, but has "inharmonic", and says "naturally produced sounds typically include inharmonic components" (p.47); I'm not sure what he has in mind there, in the middle of his discussion of periodic tones. And (p.59), section on Timbre, "In naturally occurring sounds, inharmonic partials (i.e., partials with frequency equal to a non-integer multiple of the fundamental) also affect timbre. When inharmonic partial are removed from a piano note, for example, the note sounds artificial and unfamiliar." So I guess a piano is "natural".

• The idea that what's important about a harmonic series is that all the frequencies are integer multiples of a fundamental is hard to connect with hearing, especially with the notion that frequencies are measured on a log scale, which would make the integer relationship completely non-obvious. It would be more sensible, but pretty much mathematically equivalent, to say that a harmonic series is a set of frequencies that share a common period (that is, all partials being periodic at the period corresponding to the pitch). Thinking about it this way helps to clear up a lot of mysteries about consonance, harmonic intervals, etc. The repetition interval is something that's easy to extract and represent in neural circuits, as J. C. R. Licklider showed in 1951, and these representations explain essentially all pitch phenomena, consonance and dissonance, harmony, etc. It takes the musical harmonic series out of the realm of numerology and puts it into the realm of neuroscience. Why don't we mention something about that? Probably because musicians don't. Malcolm Slaney and I wrote a chapter back in '93, "On the Importance of Time – A Temporal Representation of Sound," which covered some of this stuff, like illustrating the pitch of the strike note of an inharmonic chime. Others, like Roy D. Patterson, and Alain de Cheveigne, and John R. Pierce, and Egbert de Boer, have written about aspects of this approach. But these works have mostly not been music focused, and have not focused on the "harmonic series", so may be hard to pull relevant nuggets from for this article. It strikes me in reading Thompson that several of things he sees as quite mysterious are so easy to understand in this temporal domain. When I get back to my office, I'll have to check Perry Cook's 2001 book Music, Cognition, and Computerized Sound: An Introduction to Psychoacoustics, which has relevant chapters by John Pierce and Max Mathews, and see if it has some nuggets we can use.

Anyway, I'm back now but pooped. Maybe more later. Dicklyon (talk) 06:06, 15 December 2008 (UTC)[reply]

Be cautious about putting in original research. The article isn't about hearing or neuroscience. I'm sure there are perfectly good places to put that in other articles. Let's stick to the harmonic definition as integer multiples of the fundamental, as in my citation you deleted without reading. I don't see anything wrong with adding that they share a period. It is equivalent and may give some readers a quicker grasp. -- Another Stickler (talk) 07:25, 15 December 2008 (UTC)[reply]

I've adjusted the language about standing waves; the previous "to and fro" was not clear to me whether it meant longitudinal travel or transverse motion (in the case of a string.) For now, I'd like to leave the links to

Definite pitch since they are more relevant to the context where they stand. The first sentence of the second lead paragraph has a link to Pitch (music)

where it applies, so that info is only a click away for the reader.

Not sure yet how to word the stuff around missing fundamental etc. I have read that low notes on a violin do indeed have an attenuated fundamental at the instrument... I was more concerned with the "lowest possible" seeming to exclude the possibility of overblown notes, or string flageolets, or higher-frequency excitation of brasses. __Just plain Bill (talk) 15:27, 15 December 2008 (UTC)[reply]

Excuse me if I'm not filling this form with correct standards, but I'm new to this. My understanding of the harmonic series is that the pattern 1/2, 1/3, and 1/4 makes a statement regarding fourths and fifths relationship with octaves. That being said I didn't understand how a fifth that was only 2 cents off could translate into a fourth that was 29 cents off. So I did the math and personally found the equal temperament fourth to in fact be 2 cents sharp. Am I simply misunderstanding the table? 24.21.9.176 (talk) 22:03, 23 May 2009 (UTC)[reply]

According to the table, the 21st harmonic is a fourth (in some octave). Within the same octave the ratio comes to 21/16. In equal temperament 12*log(21/16)/log(2)= 4.71 or 29 cents flat of 5 semitones. The table seems correct. −Woodstone (talk) 22:57, 23 May 2009 (UTC)[reply]

fast response, I'll remember to check back more consistently in the future! I've always understood the fourth and fifth as summing to an octave. I've read in numerous places that the ratio 3:2 is equivalent to the perfect fifth. Since the 1/3 that makes the 3:2 splits an octave, I was explained that you could conclude that 4:3 was a fourth since it and a perfect fifth make the octave. If you plug that into the equation you showed you get 4.98, or 2 cents flat of 5 ET semitones. The chart doesn't list that as one of the ratios however...I guess I'll reread the article, but in case you answer swiftly again where's the source for those specific intervals?24.21.9.176 (talk) 21:40, 30 May 2009 (UTC)[reply]

Your reasoning is correct, but this article does not talk about compounding intervals. It just shows the interval between a tone and its multiples (reduced to within an octave). Since you see in the table that the fifth is 2 cents sharp, you could have concluded immediately that the fourth that completes the octave must be 2 cents flat. For more on compound intervals you might look at just intonation. −Woodstone (talk) 22:52, 30 May 2009 (UTC)[reply]

I think this points at a general problem with this section. It seems to imply that, for example, the occurrence of the fourth in Western music has something to do with its relationship to the 21st harmonic, and that it is only the use of equal temperament that makes this inexact (The Western chromatic scale has been modified into twelve equal semitones, which is slightly out of tune with many of the harmonics). In fact the fourth corresponds to 4:3 in just intonation, and has nothing to do with the 21st harmonic. The same is true of most of the other intervals. 68.239.116.212 (talk) 02:27, 1 December 2009 (UTC)[reply]

For example, a perfect fifth, say 200 and 300 Hz (cycles per second), produces a combination tone of 100 Hz (the difference between 300 Hz and 200 Hz); that is, an octave below the lower (actual sounding) note. This 100 Hz first order combination tone then interacts with both notes of the interval to produce second order combination tones of 200 (300-100) and 100 (200-100) Hz and, of course, all further nth order combination tones are all the same, being formed from various subtraction of 100, 200, and 300.

I'm not sure what this is intended to mean. Is it supposed to describe some psychoacoustic effect? Certainly no such tones are actually produced (unless the sound is passed through some sort of nonlinearity). 68.239.116.212 (talk) 02:33, 1 December 2009 (UTC)[reply]

I have no idea what that paragraph is trying to say, either. But there really are physical combination tones produced by nonlinearities in the normally functioning

Tartini noticed that you could use these to tune a fifth to an appropriate temperament, since you can hear beats between the f2-f1 and the 2f1-f2 combination tones. For example, with 200 Hz and 301 Hz, the f2-f1 is 101 Hz and the 2f1-f2 is 99 Hz, so you hear a 2 Hz beat. The beat is slow enough that you can rely on it to get a particular tuning of the fifthen when tuning a piano or organ (see this page for example. Dicklyon (talk) 07:10, 1 December 2009 (UTC)[reply

]

Why, what, where, and how does this article need additional citations for verification? Hyacinth (talk) 03:29, 18 October 2010 (UTC)[reply]

Tag removed. Hyacinth (talk) 17:17, 15 July 2011 (UTC)[reply]

Timbre of musical instruments

Why and where does this section need additional citations for verification? What references does it need and how should they be added? Hyacinth (talk) 00:22, 30 January 2012 (UTC)[reply]

the A-natural above C is a Major Sixth not a Minor Sixth. I don't know how to edit this table but it seems inaccurate. — Preceding unsigned comment added by Shastymax (talk • contribs) 02:30, 23 July 2016 (UTC)[reply]

The 13th harmonic is close to a neutral sixth, half way between minor and major sixths, but closer to minor (41 cents off). Is the note name wrong in the table? No, it says A flat. Dicklyon (talk) 02:49, 23 July 2016 (UTC)[reply]

Yes, in the table is a wrong note name. The mathematically reliable name must be A-natural with a flattering by tridecimal comma. Shastymax is right, because the talking is about the tridecimal version of Major Sixth and the table requires correction. --93.76.26.31 (talk) 19:26, 3 August 2016 (UTC)[reply]

The above section has been added, reverted, and re-added several times. (See

No guests and hosts in the article. There is equality for all. The section has been removed contrary to the mandatory rule for all

WP: NOTCENSORED and therefore unreservedly restored. Now is possible to discuss its shortcomings and make improvements. --93.76.26.88 (talk) 16:18, 19 August 2016 (UTC)[reply

]

"Be my guest" is an English idiom for "feel free" [to fix the text in question, in this case.] Removing this kind of content is not censorship, but is normal editing. This text needs some serious sandbox work before it will be suitable for inclusion in the article. Just plain Bill (talk) 00:12, 20 August 2016 (UTC)[reply]

Discussion of potentially objectionable content should usually focus not on its potential offensiveness but on whether it is an appropriate image, text, or link. Beyond that, "being objectionable" is generally not sufficient grounds for the removal. Unreservedly restored. Which namely image, text, or link is not appropriate and why? --93.76.28.131 (talk) 20:47, 21 August 2016 (UTC)[reply]

"WP is not censored" is irrelevant here. I don't see anybody saying there are offensive images or text. Have a look at

WP:NOTTEXTBOOK

instead.

Most importantly, this article is not the place to explain at great length, with illustrations in set notation, how Pythagorean tuning fits (or does not fit) with scales written in Western notation. The section on "Harmonics and tuning" already explains the relation between the harmonic series and equal-tempered notes.

The issues of iffy translation, use of unencyclopedic first- and second-person language, and clumsy formatting (e.g. the mix of unreadably small superscripts and overly large low-resolution images) are all secondary to the question of whether this material belongs in an article on the harmonic series in music, or whether it is excessive detail explaining a tangential topic. Just plain Bill (talk) 13:32, 22 August 2016 (UTC)[reply]

The section "Harmonics and tuning" is written without the support of a sufficient number of different sources, what led it to the spread of goofy table with a lot of errors even in the names of basic intervals. Therefore, the section giving a rigorous and highly visual (for familiar with arithmetic and pre-algebra schoolchildren) evidence of the necessity to rely on primary Schlesinger notation for error-free preparation so simple tables, is restored. If you and Woodstone do not like it, then vs. those whom it is not offended is only 0.(571,428)% of you together with him. So stop your censor habits with demands to beg your permission for the restoration of a good cognitive material. --93.76.28.238 (talk) 23:53, 7 September 2016 (UTC)[reply]

It has never been clarified what the relevance of the section "Musical notation" is for the subject of this article. The section talks mostly about sequences of pythgorean fifths, not about harmonics. That alone—aside from doubts about quality of writing and sourcing—should be enough grounds to eliminate it from the article. It does not make sense to start making small adjustments. The whole is irrelevant. −Woodstone (talk) 15:18, 25 August 2016 (UTC)[reply]

I agree that attempts to polish this section are pointless, since its relevance to the article's subject is scant to nil. I've removed it again. Just plain Bill (talk) 20:32, 30 August 2016 (UTC)[reply]

This is not really getting anywhere. The section is clearly unreadable at this point, and likely not relevant anyway, yet what seems to be the same person on 93.76.0.0/20 keeps restoring it without any explanation of its relevance, without sandboxed revisions, and in violation of

You did not say in addition that different IPs is always one person, the verifiable information and for you hardly understandable characters like ${\displaystyle 2\times 2=4}$ are original researches. Labels {off topic} and {original research} are removed. --93.76.18.18 (talk) 08:09, 15 September 2016 (UTC)[reply]

Please stop removing these templates. Clearly both the relevancy and the unoriginality of the sections contents is disputed; just take a look at this talk page. You saying that these issues do not exist does not make it so. In stead, the section should be edited as to resolve the issues, or it should be removed altogether. SBareSSomErMig (talk) 21:02, 15 September 2016 (UTC)[reply]

"Psychophysical properties" section

This section may require copy editing for grammar, style, cohesion, tone, or spelling. You can assist by editing it. (October 2016) (Learn how and when to remove this message) Simultaneous sounding of all overtones of harmonic series forms the so-called klang [1] [2] usually audible as one pitch[3] at the level of fundamental ie the lowest, first partial.[4] The timbre of klang depends on the loudness distribution on the set of all partials and can move sensation of klang pitch on the level of second or third or some other partial in selected cases of close to zero loudness of some partial subsets. Vertical harmonic series or klang as a kind of complex sound,[5] makes active some group of nerve fibers separated by groups of inactive fibres and the active fibers correspond to partials. The properties of of nerve fibers to conduct separately an appropriate for each partial sensation develop, probably before the birth of organism under the influence of tireless sound of mother's heart. The interaction of nerve fibers in the perception partials of several complex sounds have a significant impact on the overall assessment of pleasantness/unpleasantness of the received sensations. The interaction of nerve fibers in the perception partials of several complex sounds have a significant impact on the overall assessment of pleasantness / unpleasantness of the received sensations. In case perception of several klangs no doubt a dependence of feeling the consonance / dissonance from the expressed by rational numbers frequency relations of fundamentals.[6] Important role in perception of klang playing ability of its partials collectively reproduce the sensation of pitch of missing fundamental, or some other partial from such most notable, ie low frequency partial in a given klang.[7] Therefore, the sensation of klang pitch in general is a sensation of exact unison between pitch of taken separately fundamental and collectively expressed pitch of its residue, as the set of all partials of given klang without the fundamental, ie the lowest from partials. Overtone as partial tone, in opposed to partial, is not the single pure tone,[8] but a complex sound, which formed by specific subset of partials of any klang, ie klang in klang, as stated in a detailed description[9] with musical example: The score clearly show an essence that with involvement of alphabetic notation of Helmholtz looks more clear perhaps as math expression: ${\displaystyle \left\{{\begin{matrix}:\\~~~c^{3}{:}[16]\\~~~b^{2}{:}[15]\\bes^{2}{:}[14]\\~~~a^{2}{:}[13]\\~~~g^{2}{:}[12]\\~~~f^{2}{:}[11]\\~~~e^{2}{:}[10]\\~~~d^{2}{:}[9]\\~~~c^{2}{:}[8]\\bes^{1}{:}[7]\\~~~g^{1}{:}[6]\\~~~e^{1}{:}[5]\\~~~c^{1}{:}[4]\\~~~~g{:}[3]\\~~~~c{:}[2]\\~~~~C{:}[1]\\\end{matrix}}\right\}\supseteq \left\{{\begin{matrix}:\\~~~c^{3}{:}[16]\\~~~b^{2}{:}[15]\\bes^{2}{:}[14]\\~~~a^{2}{:}[13]\\~~~g^{2}{:}[12]\\~~~f^{2}{:}[11]\\~~~e^{2}{:}[10]\\~~~d^{2}{:}[9]\\~~~c^{2}{:}[8]\\bes^{1}{:}[7]\\~~~g^{1}{:}[6]\\~~~e^{1}{:}[5]\\~~~c^{1}{:}[4]\\~~~~g{:}[3]\\~~~~c{:}[2]\\~~~~C{:}[1]\\\end{matrix}}\right\}\cup \left\{{\begin{matrix}:\\~~~e^{3}{:}[20]\\~~~d^{3}{:}[18]\\~~~c^{3}{:}[16]\\bes^{2}{:}[14]\\~~~g^{2}{:}[12]\\~~~e^{2}{:}[10]\\~~~c^{2}{:}[8]\\~~~g^{1}{:}[6]\\~~~c^{1}{:}[4]\\~~~~c{:}[2]\\\end{matrix}}\right\}\cup \left\{{\begin{matrix}:\\~~~b^{3}{:}[30]\\~~~a^{3}{:}[27]\\~~~g^{3}{:}[24]\\~~~f^{3}{:}[21]\\~~~d^{3}{:}[18]\\~~~b^{2}{:}[15]\\~~~g^{2}{:}[12]\\~~~d^{2}{:}[9]\\~~~g^{1}{:}[6]\\~~~~g{:}[3]\\\end{matrix}}\right\}\cup \left\{{\begin{matrix}:\\~~~c^{4}{:}[32]\\bes^{3}{:}[28]\\~~~g^{3}{:}[24]\\~~~e^{3}{:}[20]\\~~~c^{3}{:}[16]\\~~~g^{2}{:}[12]\\~~~c^{2}{:}[8]\\~~~c^{1}{:}[4]\\\end{matrix}}\right\}\cup \left\{{\begin{matrix}:\\~~~e^{4}{:}[40]\\~~~d^{4}{:}[35]\\~~~b^{3}{:}[30]\\gis^{3}{:}[25]\\~~~e^{3}{:}[20]\\~~~b^{2}{:}[15]\\~~~e^{2}{:}[10]\\~~~e^{1}{:}[5]\\\end{matrix}}\right\}\cup \left\{{\begin{matrix}:\\~~~f^{4}{:}[42]\\~~~d^{4}{:}[36]\\~~~b^{3}{:}[30]\\~~~g^{3}{:}[24]\\~~~d^{3}{:}[18]\\~~~g^{2}{:}[12]\\~~~g^{1}{:}[6]\\\end{matrix}}\right\}\cup }$ ${\displaystyle \cup \left\{{\begin{matrix}:\\~~~f^{4}{:}[42]\\~~~d^{4}{:}[35]\\bes^{3}{:}[28]\\~~~f^{3}{:}[21]\\bes^{2}{:}[14]\\bes^{1}{:}[7]\\\end{matrix}}\right\}\cup \left\{{\begin{matrix}:\\~~~g^{4}{:}[48]\\~~~e^{4}{:}[40]\\~~~c^{4}{:}[32]\\~~~g^{3}{:}[24]\\~~~c^{3}{:}[16]\\~~~c^{2}{:}[8]\\\end{matrix}}\right\}\cup \left\{{\begin{matrix}:\\~~~a^{4}{:}[54]\\fis^{4}{:}[45]\\~~~d^{4}{:}[36]\\~~~a^{3}{:}[27]\\~~~d^{3}{:}[18]\\~~~d^{2}{:}[9]\\\end{matrix}}\right\}\cup \left\{{\begin{matrix}:\\~~~b^{4}{:}[60]\\gis^{4}{:}[50]\\~~~e^{4}{:}[40]\\~~~b^{3}{:}[30]\\~~~e^{3}{:}[20]\\~~~e^{2}{:}[10]\\\end{matrix}}\right\}\cup \cdots }$ Since any given klang always contains other klangs, it definitely exists as klang in the own compound and can be klang in compound of other klang with pitch always perceived as lower and always corresponds to the frequency of the stimulus that Integer multiple of stimulus frequency with sensation of given klang pitch. In other words every klang is an overtone of some undertone,[10] including case when klang is the first overtone of its first undertone, ie of itself. ^ Riemann by Shedlock 1876, p. 143: «Since it has been known that the sounds of our musical instruments are not simple tones, but compounded of a series of simple tones which can be distinguished by a most attentive listener (but commonly are not thus distinguished), the term S., in scientific works, has been replaced by the more general, comprehensive one, C, whilst sound is applied to the simple sounds as part of the C. The height of the C[lang] is determined by the pitch of the lowest, and, as a rule, the strongest of its compound tones» ^ Partch 1974, p. 70: «Harmonic Content: practically synonymous with quality of tone; the term used to indicate that characteristic of a musical tone which is determined by the distribution and comparative energy of its partials, or harmonics; the klang» ^ IEV 1994, 801-29-01: «pitch that attribute of auditory sensation in terms of which sounds may be ordered on a scale extending from low to high Note 1 — The pitch of a complex wave depends primarily upon the frequency content of the stimulus, but it also depends upon the sound pressure and the waveform. Note 2 — The pitch of a sound may be described by the frequency of that pure tone having a specified sound pressure level that is judged by subjects to produce the same pitch» http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=801-29-01 ^ IEV 1994, 801-30-02: «partial sinusoidal component of a complex sound wave» http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=801-30-02 ^ IEV 1994, 801-21-06: «complex sound sound that is not a simple oscillation» http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=801-21-06 ^ Datta, Sengupta, Dey and Nag 2006, p. 21: «Іt is suggested that the perception of complex tones begins at a later stage of development of the foetus. The fluid in which a foetus is immersed transmits the throbbing of the mother's heart, activating continuously the auditory processes. The concept of partials is developed at that stage. It is an experimental fact that when musical notes, which are in simple, integral ratios, are sounded together they sound pleasant. This does not always hold true for pure tones [15]. One theory is that when some upper partials of the two tones match consonance results. In fact, Helmholtz [16] in 1862 explained the dimension of consonance in terms of the coincidence and proximity of the overtones and difference tones. These tones arise when simultaneously sounded complex tones excite real non-linear physical resonators, e.g. the human ear. To the extent that an interval's most powerful secondary tones exactly coincide, it is consonant or sweet sounding. To the extent that any of its secondary tones are separated in frequency by a small enough difference to "beat" at a rate, which he puts at around 33 c/s, it is dissonant, or harsh. Same effects are observed even when these two sounds are not simultaneous but in succession. A complex wave would give rise to a series of active groups of nerve fibres separated by groups of inactive fibres. The active fibres correspond to partials [12], Recent studies revealed prints of harmonic structures in the auditory cortex A1 [17]. The other theory of preference of pair of tones relies on the similarity of the temporal patterns of neural discharge for tones having simple frequency ratios [18]» ^ Schouten 1940, pp. 356-61: «It is a fact that a pitch equal to that of the fundamental tone is ascribed even to those sounds in which the fundamental tone is not present <...> one or more components may be perceived which do not correspond with any individual sinusoidal oscillation, but which are a collective manifestation of some of those oscillations which are not or scarcely individually perceptible. These components (residues) have an impure, sharp tone-quality <...> the harmonics highest in frequency are perceived as a subjective component almost lowest in pitch» ^ IEV 1994, 801-21-05: «pure sound pure tone sinusoidal acoustic oscillation» http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=801-21-05 ^ Тюлин 1966, pp. 41-3: «each overtone <...> has its own natural skala in the number of overtones [of klang with pitch] of fundamental tone (Russian: каждый из обертонов <…> имеет свою собственную натуральную ска́лу в числе обертонов [со́звука с высотой] основного тона)» ^ Helmholtz 1865, p. 76: «It's easy to make sure using the tests in these properties resonators. You hold the such to ear and let play a polyphonic piece of music any instrumentswhere often occurs the natural tone of the resonator. So often as this tone is given, armed resonator ear hears its penetration through all other sounds of the chord. Weaker, but often heard such marked in lower klangs, namely as showing the first detailed study of this when klang given with one of harmonic overtones at own tone of your resonator. These lower klangs are called harmonic undertones of resonator tone. These are klangs, whose period of oscillations in 2, 3, 4, 5 etc. times more than the resonator tone. If such is, for example, ${\displaystyle c''}$, you can hear its sound when a musical instrument playing: ${\displaystyle c',F,C,As,F,D,C~~etc.}$ In these cases resonator sounds from one of overtones in external airspace of the specified klang. But it should be noted that klangs of certain instruments do not always contain all harmonic overtones, and that they have a different power. In the sound of the violin, piano and harmonium first 5 or 6 most clearly present. On overtones of strings followed a more detailed description in the next chapter (German: Man kann sich durch Versuche von den angegebenen Eigenschaften der Resonatoren leicht überzeugen. Man setze einensolchen an das Ohr und lasse irgend ein mehrstimmiges Musikstück von beliebigen Instrumenten ausführen, in dem öfters der Eigen ton des Resonators vorkommt. So oft dieser Ton angegeben wird, wird das mit dem Resonator bewaffnete Ohr ihn gellend durch alle anderen. Töne des Accords hindurchdringen hören. Schwächer wird es ihn aber oft auch hören, wenn tiefere Klänge angegeben werden, und zwar zeigt die nähere Untersuchung zunächst, dass dies geschieht, wenn Klänge angegeben werden, zu deren harmonischen Obertönen der Eigenton des Resonators gehört. Man nennt dergleichen tiefere Klänge auch wohl die harmonischen Untertöne des Resonator tones. Es sind die Klänge, deren Schwingungsperiode gerade 2, 3, 4, 5 u. s. w. Mal grösser ist, als die des Resonator tones. Ist dieser also z. B. ${\displaystyle c''}$, so hört man ihn tönen, wenn ein musikalisches Instrument angiebt: ${\displaystyle c',f,c,As,F,D,C~~u.s.w.}$ In diesen Fällen tönt der Resonator durch einen der harmonischen Obertöne des im äusseren Luftraume angegebenen Klanges. Doch ist zu bemerken, dass nichtimmer alle harmonischen Obertöne in den Klängen der einzelnen Instrumente vorkommen, und dass sie bei verschiedenen auch sehr verschiedene Stärke haben. Bei den Tönen der Geigen, des Ciaviers, der Physharmonica sind die ersten 5 oder 6 meist deutlich vorhanden. Ueber die Obertöne der Saiten folgt Genaueres im nächsten Capitel)»

The same ip range as before has now created this piece of gibberish. Although it is marginally better sourced than the previous "Musical Notation" section, it is still of very poor quality. The English is near-incomprehensible and the "mathematical" notation is highly non-standard. I have thus taken the liberty of removing it. SBareSSomErMig (talk) 11:48, 12 October 2016 (UTC)[reply]

Elementary operations of set theory can not be "mathematical" notation is highly non-standard. This is a weak excuse to remove the entire section. Another excuse (The English is near-incomprehensible) is also far-fetched. In the section there is a tag for the language experts calling to take part in improving the text. The section has a right to exist in the article and thus was restored. --46.201.181.89 (talk) 12:58, 12 October 2016 (UTC)[reply]

Qouting from the section: "The score clearly show an essence that with involvement of alphabetic notation of Helmholtz looks more clear perhaps as math expression". I don't know what that is supposed to mean, and I don't think a "language expert" would either. The first, and maybe even the second paragraph might be relevant to the article after some some considerable sandbox work (at present it is barely readable and reads like a

textbook). The rest of the section is plain nonsense and looks like the same original research that we previously reached consensus for removing. The set expression is a very poor communication of the idea that it tries to convey (indeed, as written, it is completely vacuous). SBareSSomErMig (talk) 13:20, 12 October 2016 (UTC)[reply

]

Leave alone the material, for you personally (well and else for such within half percent out of daily readers) not understandable, as it turns out. The harmonic series is a natural system, and the systems are described by language of set theory, which has long and successfully implemented in general educational process. If it frightens you personally, it does not mean that out of 400 readers per day it frightens everyone. Frightening only you signs are recovered with small addition. Let at least 40 different readers will explain here why these inscriptions are so offensive that must be removed. May be then will happens consensus... --93.76.25.155 (talk) 23:36, 12 October 2016 (UTC)[reply]

original research, which does not belong on Wikipedia. Just plain Bill (talk) 00:00, 13 October 2016 (UTC)[reply

]

I have removed the section as uninterpretable. Someone who understands the intent can perhaps work with us here to recreate something better. Dicklyon (talk) 02:39, 13 October 2016 (UTC)[reply]

Several of these harmonics do not match their counterparts an octave lower. How can this be correct? For the octaves to match each other:

• 26 should be A♭, same as 13
• 28 should be B♭, same as 14
• 30 should be B♮, same as 15

Burninthruthesky (talk) 09:34, 21 March 2017 (UTC)[reply]

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The article's "Terminology" section states that "An overtone is any partial above the lowest partial" This is technically incorrect -- it implies that the lowest overtone is the fundamental, which is untrue. According to this definition, ANY partial (other than the lowest one) is an overtone. I believe it should read, "An overtone is any partial above the FUNDAMENTAL." — Preceding unsigned comment added by 98.109.98.74 (talk) 03:27, 5 July 2018 (UTC)[reply]

what is harmonic singing 102.89.3.217 (talk) 18:20, 18 January 2022 (UTC)[reply]

The section "Harmonics and tuning" currently says, "...small whole-numbered ratios are likely the basis of the consonance of musical intervals." The closest thing it has to a supporting citation is a reference to Hindemith's The Craft of Musical Composition, Book 1, pg. 15. I have that book on hand and I can't find a statement quite like that; the closest he comes that I've found is his statement that "[the ear] hears simple ratios as beautiful and correct sounds" in Ch. 2, Sec. 4, "The Triad." That's not nearly as strong a statement as "basis of consonance," and considering that he basis the whole discssion in that section first and foremost on the actual overtone series I don't think he means to imply that either.

Even if he had said that, though, it would just be his opinion (he doesn't offer any further evidence even for "simple ratios" being "beautiful" except to suggest that the reader go listen for themselves). Research on human subjects has been done which shows that the perception of dissonance between two pure tones is typically greatest when their interval is 25% of the critical band in that area of the spectrum, and the perception of consonance is greatest when their interval is 100% of the critical band. Perceptions of dissonance and consonance between complex pitched sounds is the result of the ratios and loudnesses of their partials on that basis. (See Plomp and Levelt's Tonal Consonance and Critical Bandwidth.) Models for predicting and quantifying the consonance of a set of notes together have been developed from this that work quite well; William Sethares provides such a model (with source code for a computer program) based on Plomp and Levelt in Tuning, Timbre, Spectrum, Scale.

If this kind of material was accounted for in that section it would change the presentation considerably. It's worth remembering that some quite-dissonant intervals correspond to small whole-number ratios (7/4, 9/8) and some intervals that are widely considered more consonant correspond to ratios with larger whole numbers (19/16, 21/16, 25/16, 27/16). However, evaluating their consonance based on critical bands and acoustic beating as described above accounts for this. It's true that many consononant intervals do correspond to small whole-number ratios, and it's not a coincidence, but it doesn't tell the whole story just to say that.

Of course, an in-depth exploration of this topic probably belongs better in Consonance and dissonance, so to some extent there's not much reason to go into it very far here. Given all this, I sort of think that if we're going to talk about tuning in this article, it might make more sense to discuss things like spectralism than just comparing the "harmonic intervals" to 12-TET and briefly mentioning just intonation. Most popular forms of just intonation (e.g. 5-limit) aren't perfectly in-tune with the harmonic series any more than 12-TET is, but there are composers out there who write music explicitly based on the harmonic series, or on one instrument's overtones or the like. I don't think it would hurt to mention the bugle on that basis, speaking of, and it would probably also make sense to take about things like choirs and string ensembles instinctively tuning their chords harmonically. I do find the chart there really useful, but not so much the parts relating to 12-TET; I like the column giving the best-fit diatonic interval, because it helps you get an idea of the sound if you have that background, but those interval names are not specific to 12-TET (they're just diatonic). Mesocarp (talk) 07:34, 29 November 2022 (UTC)[reply]