Talk:Harmonic

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Integral multiple
It might be helpful to define integral multiple. I think I know what the authors mean, and would be happy to edit the page, but I don't want to jump to any incorrect conclusions. I'm not entirely sure.


 * I've put an example in. Hope that clears it up. -- Tarquin 20:31 Jan 16, 2003 (UTC)

Thanks, it clears things up perfectly. I'm a beginning graduate student in mathematics, and I use Wikipedia often because my background is in computer science, so thanks so much! -- Brittany

Like above, would anyone be willing to explain why we have an "itegral multiple" instead of just an "integer multiple." I guess I just don't really understand.

"Integral" is an adjective, while "integer" is a noun. Of course, in English, we can use nouns and adjectives but why bother when have the right kind of word already. ---Ben


 * It's just confusing because of the other uses of the word integral. - Omegatron


 * I can't find any instance of "integral" in the article today. Can we close this topic as resolved? I forget how to fold a topic so its body text is hidden and only its title shows on the Talk page unless clicked. Does anyone else remember? 108.60.216.202 (talk) 11:13, 31 May 2015 (UTC)

subharmonics
I don't understand how subharmonics can be generated from a wave. How are they numbered? - Omegatron 17:23, Feb 18, 2005 (UTC)

>> Think of the opposite function, mutiplication instead of division. Wonders of acoustics allow us to hear lower octaves of fundamentals, as if the string would be twice as long<<


 * Subharmonics are numbered in the same order except going down. If the first harmonic is 1/1 f (f = frequency of the fundamental) and the second harmonic is 2/1 f, then the first subharmonic is 1/1 f and the second subharmonic is 1/2 f. Subharmonics don't actually exist in nature. They're a mathematical construct. The only way you'll ever perceive lower frequencies than the fundamental is from "difference tones" when two periodic signals are combined and some sort of distortion exists in the measuring apparatus. For example, if you stand really close to two flute players playing different pitches, the notes will be so loud that your own ears will distort and you'll get intermodulation that adds in the sum and difference tones like a ring modulator would. You'll think you "hear" other pitches in addition to the two they're actually playing. 108.60.216.202 (talk) 19:20, 25 May 2015 (UTC)

Harmonic series
In the article, what is presented as the harmonic series is the series of successive diminishing intervals between increasing numbers of harmonics. I think it makes much more sense to present them as a matrix of sub-tones in their relation to the fundamental! in which 1,2,4,8,16,32 are octaves of the Fundamental; 3,6,12,24 pure fifths; 5,10,20 natural major thirds; 7,14,28 natural minor sevenths; 9,18 major second, 11,22 natural augmented fourth; 13,26 flattened sixth; 15,30 major seventh. In every successive higher octave twice the amount of harmonics are found appearing as neighbouring tones between the octaves of previous numbers. If nr. 13 is a flattened sixth, double the number minus one gives 25, which is an even flatter sixth, just as 23 is an even sharper augmented fourth. martinspaink@yahoo.com

-- Yes, this is a good way of thinking about it. The table itself could use some cleaning.

Article split
This article talks about two different concepts: I suggest we merge the former with Overtone and move the remainder to "Harmonic mode" or "Flageolet tone" to make the distinction clearer. Comments? Peter S. 16:05, 23 August 2006 (UTC)
 * the technical/telecommunication side, which is basically the same thing as the article on Overtone
 * the musical term "Harmonic mode" / "Flageolet tone"
 * I don't know if this has been done, or what, but I am pretty certain that, because Flageolet tone redirects to this article, the term should at least be mentioned at some point within the article. Ari (talk) 01:17, 4 June 2008 (UTC)

I suggest that this article be removed entirely. There are many fundamental errors, much confusion, much incomplete / misleading information, and is written, largely incorrectly, apparently by a grade 10 student who does not understand the subject. But that's just my opinion, based upon teaching this material for 40 years. — Preceding unsigned comment added by Kaustin6969 (talk • contribs) 04:49, 15 January 2014 (UTC)

My anonymous, unweighted vote would be to keep this article but allow it to continue to migrate towards a musical perspective, and let harmonic resonance specific to electronic telecommunication (which means radio signals, heterodyning, ring modulation, side channels, and such) split away. Pythagoras was a universal philosoper possibly capable of fusing all human-understandable facts into a single topic, and his harmonics could probably be an umbrella for all related topics musical and other. However, our Wikipedia crowd-effort seems to prefer topics that are fractally and infinitely bifurcated and are therefore increased in local focus and detail--meaning that musical harmonics and telecommunicational harmonics can be split with acceptable, and potentially beneficial, consequence. Anonymous 108.60.216.202 (talk) 11:57, 31 May 2015 (UTC)

Notation + MIDI-Sound
[] Notation und MIDI-Sound --88.73.222.2 08:21, 4 December 2006 (UTC)

Fourier
I removed the passage that said "Harmonics come from the fact that any periodic signal of frequency f is mathematically equivalent to the sum of harmonic signals (sine-like or cosine-like signals) of integer frequencies (f, 2f, 3f...) — see Fourier decomposition." This is misleading, and doesn't actually help in understanding how harmonics arise. Not all periodic signals contain harmonics (Fourier notwithstanding). The significance is more the other way around: because of this property of Fourier series, the sum of a signal and its harmonics is always periodic at the signal frequency. Whether all of the harmonics are resonant in the resonator producing the signal depends on the design of the resonator (damping as a function of frequency, etc.) --Srleffler 02:50, 10 March 2007 (UTC)

Partials
One question from a German native speaker: in german, "partials" is the same as "harmonics", i.e. integer multiples of the base frequency. In this article here partials are regarded the "non-harmonics". Is that so, or is it just an asumption? In the Harmonic series (music) partials are used just as harmonics.

The terms are used to mean different things. Keep in mind that there are complex sounds, such as the ringing of bells, where there are non-harmonic components (component frequencies that are not whole number multiples of the lowest or fundamental frequency). One possible consistent usage would be to define a partial as any component of a complex sound and a harmonic as a partial that is a whole number multiple of a fundamental frequency.

I've always heard "partials" and "harmonics" to be almost synonymous, except that the first partial of a sound is the fundamental frequency, and the first harmonic is double that - i.e. the 2nd partial. This is in a musical context, most often regarding wind instruments, though not exclusively. In my experience, "partial" certainly doesn't just refer to extremely inharmonic components to the sound, as this article currently states, though maybe that's a more technically accurate definition. Either way, the article should be updated to explain the terminology.Jaddle 05:27, 12 May 2007 (UTC)


 * According to the Harvard Dictionary of Music, in the article "Acoustics":
 * Although the terms harmonics and partials are frequently used as if interchangeable, the latter term has, in scientific studies, a wider significance, since it also includes nonharmonic overtones like those that occur in bells and in the complex sounds called noises.
 * So I'd say that harmonics are a subset of partials. It's therefore not wrong to refer to a harmonic as a partial, but we should be aware of this technical distinction. &mdash;Wahoofive (talk) 17:15, 12 May 2007 (UTC)

Confusing opening paragraphs
The following section is a little confusing:

Many oscillators, including the human voice, a bowed violin string, or a Cepheid variable star, are more or less periodic, and thus can be decomposed into harmonics.

Most passive oscillators, such as a plucked guitar string or a struck drum head or struck bell, naturally oscillate at several frequencies known as overtones. When the oscillator is long and thin, such as a guitar string, a trumpet, or a chime, the overtones are still integer multiples of the fundamental frequency. Hence, these devices can mimic the sound of singing and are often incorporated into music. Overtones whose frequency is not an integer multiple of the fundamental are called inharmonic and are sometimes perceived as unpleasant.

The untrained human ear typically does not perceive harmonics as separate notes. Instead, they are perceived as the timbre of the tone. In a musical context, overtones that are not exactly integer multiples of the fundamental are known as inharmonics. Inharmonics that are not close to harmonics are known as partials. Bells have more clearly perceptible partials than most instruments. Antique singing bowls are well known for their unique quality of producing multiple harmonic overtones or multiphonics.

Here are some things I feel need clearing up in the above paragraphs:

1) what is the relationship between overtones and harmonics? What exactly the difference between an overtone and a harmonic?  You mention overtones suddenly, as if drawing a rabbit from a hat, without any explanation why they might be mentioned in an article on harmonics.  Please remember that people visiting this page will normally have very little prior knowledge, so don't assume they know the difference.  If you are going to introduce a subject related to the harmonics, try and explain why you are introducing it beforehand.  For example: 'harmonics are intrinsically related to overtones,' or 'certain harmonics are also called overtones,' and then go on to explain what an overtone is and why it is significant.  The fact is, I always get confused about harmonics and overtones, so I won't try rewriting it myself.  But you are not doing much to dispel my confusion!

2) The second paragraph seems to start repeating the first paragraph when talking about inharmonic overtones. The whole thing seems thrown together and unplanned.  Try rewriting both paragraphs from scratch, combining them into a simple, clear statement.  It looks like people have stepped in and tried to rewrite things willy-nilly, with the result being messy and confusing.

To reiterate, the paragraph beginning 'most passive oscillators' makes perfect sense in isolation, but it does not make sense in the context of the article. It seems to appear from nowhere. Then the paragraph that follows it starts repeating some of the stuff from the previous paragraph. Basically, I'm not sure why you are talking about overtones in a subject on harmonics. There may be a good reason, but you have not explained what that reason is.

Basically the section is okay, but it needs putting in context and cleaning up a little.

--Dpolwarth (talk) 07:31, 3 August 2008 (UTC)


 * "Many oscillators, including...a Cepheid variable star, are more or less periodic, and thus composed of harmonics, also known as harmonic partials." Do Cepheid variable stars have harmonics? I don't think so. From what I've been able to search, they don't. First, simply being periodic doesn't mean something has harmonics. A sine wave is periodic but has no harmonics (other than the fundamental which is not useful as a harmonic of itself), so any Cepheid variable star with only one period doesn't count. Second, those Cepheid variable stars that have been observed to exhibit more than one period simultaneously do not have those periods in a harmonic relationship. In other words, the frequencies of the shorter periods are not integer multiples of the frequencies of the longest period, or even at a simple ratio (which would be the case if they were both harmonics of a much longer invisible period). While it's nice to try to insert a cosmic perspective, it's inaccurate to say that Cepheid variable stars exhibit harmonic behavior. One might consider Orbital_resonance as an alternative (for example, the orbital periods of Pluto and Neptune are very close to a 3:2 relationship). If no one defends Cepheid variable stars, I'm going to remove them. I also have a problem with using "a struck drum head" and "a chime" as examples, since both of those contain inharmonic partials, not harmonics! I'll remove them at the same time if nobody defends them. 108.60.216.202 (talk) 03:26, 27 May 2015 (UTC)


 * I know nothing about the periodicity of Cepheid stars. Drum heads and chimes, though, are given as examples of vibrating objects with inharmonic partial components, as contrasted with "long and thin" oscillating systems. If that is unclear, then some copyediting is in order, but I would favor keeping them.


 * I do not think a trumpet is a good example in that section, since tubes with one closed end show only odd harmonics; the partials of a brass instrument are made to resemble the complete harmonic series by the shape of the flared bell and the cup/throat arrangement of the mouthpiece. The degree of success of that realignment is one of the differences between a prized instrument and a so-so horn. I'm not sure if a flute or an organ pipe makes a better example there. Perhaps a panflute pipe would offer fewer theoretical complications, being cylindrical and without side openings. Their timbre, or balance of partials, is affected by the ratio of length to diameter, or so I'm told. Just plain Bill (talk) 14:20, 27 May 2015 (UTC)


 * I've cleaned up the Characteristics section, mostly rewriting it but keeping the citations. I better sorted the instruments into separate paragraphs by type so there's no confusion by proximity between dissimilar instruments such as flutes and cymbals. I also explained about trumpets and clarinets having only odd harmonics. I also removed Cepheid stars because it turns out even the ones with complex light curves are not behaving harmonically. Here's my justification for that: On Google books, in the book "The Life of Stars: The Controversial Inception and Emergence of the Theory of Stellar Structure", on page 137, under an illustration of idealized first and second harmonics of a violin string, it says "Eddinton's explanation for the non-symmetric light curve of the Cepheids. The sum of two harmonics leads to a non-symmetric light curve. ... As soon as more accurate observations had been made, it became clear that this explanation by Eddington for the shape of the light curve was not correct. The Cepheids oscillate in the fundamental mode and the shape is determined by the properties of the 'heat engine', the absorption coefficient. Once these had been properly taken into account (after extensive calculations), the predicted and the observed light curves agreed very well. But it took several decades to reach this agreement." 38.86.48.38 (talk) 10:08, 7 June 2015 (UTC)

Merge proposal
I propose that Harmonic series (music) be merged with this article. Are the articles different enough in scope that they deserve to remain separate? They seem very similar to me. SharkD (talk) 10:28, 16 August 2008 (UTC)


 * Summary would eventually require "Harmonic series (music)]] to be split off anyways, though merging tends to provide better context at both locations. Hyacinth (talk) 10:48, 16 August 2008 (UTC)


 * Maybe I went about the merge in the wrong direction. Rather than merging material from "Harmonic series" to here, some of the information in this article could be merged to there. Particularly, the "Harmonics on stringed instruments" section could be reduced to a stub and a "Main article" link [edit: i.e., to "Harmonic series"]. The guitar harmonics table could be moved to Pinch harmonic. SharkD (talk) 11:08, 16 August 2008 (UTC)

I agree that some info from this site should be transferred to the 'Harmonic series' page, and make it a page more oriented towards musicians. Thanks! These pages are proving very useful. —Preceding unsigned comment added by Mary Edward (talk • contribs) 04:29, 17 August 2008 (UTC)

It is not a good idea to merge, I guess, because a harmonic is something like a flageolet or an overtone and the harmonic series is a serie which has a relation with musical scales. When you merch the two articles this will be difficult to express. The harmonic series expres a tonal structure (1,2,3,4,5,6,7,8,9,10,etc = E-E-B-E-G#-B-D-E-F#-G#-etc. if the fundamental is an E). Outdepth (talk) 15:56, 4 December 2008 (UTC)


 * Oppose, and since it seems there isn't a consensus to merge, I'll take the tag off the article now. Hope I'm not being too hasty... better context at both locations, and cross-linking as SharkD suggested, always help, in my view. __Just plain Bill (talk) 16:31, 4 December 2008 (UTC)

Harmonics are not overtones, when counting
Musicians freely use the terms overtones, harmonics and partials interchangably. That is not correct. Even overtones are odd harmonics and even harmonics are odd overtones. That seems not to be obvious, because they say overtones are the same as harmonics.

-- Dirk (talk) 19:51, 24 October 2009 (UTC) —Preceding unsigned comment added by 87.160.255.117 (talk)

Context in the lede
I removed "In acoustics and telecommunication..." from the first line of the article, because it is unnecessarily restrictive. Any physical wave can have harmonics. We could start "In physics..." but that also misses a large group. Discussion of harmonics are not restricted to telecommunications or acoustics. Any electronic amplifier will introduce some harmonics into the signal. And what about power engineering? Or lasers? Maybe we could say "In physics and engineering...", or even "In science and engineering..."? But that still misses mathematics (Fourier is all about harmonics). Signal analysis is a vast area, touching all science and technology. Harmonics are a very general concept. This article should reflect that. GyroMagician (talk) 13:40, 2 April 2010 (UTC)
 * I am the one who put those back, along with "and other areas of signal analysis," since I agree that harmonics are relevant in other areas, but I believe the top paragraph should provide not only context, but focused context. The way it now stands does not seem overly restrictive to me. Got any ideas about further change, or shift of emphasis? All ears here... __ Just plain Bill (talk) 17:27, 2 April 2010 (UTC)
 * Hi JpB, having thought about it for a while, I actually quite like "In science and engineering...". Would you find that acceptable? The way the article currently stands, it sounds as if harmonics are mainly relevant to telecomms and acoustics, and are maybe used in some other areas too. I don't think this is accurate - harmonics are relevant to just about all areas of physics, analogue electronics from instrumentation amplifiers to power generation, and potentially many other areas in engineering (mechanical? civil?). I agree that it is useful to give some context, but the context should reflect the breadth of the topic. I could say "In Argentina, gravity pulls things towards the ground". While the statement is true, it's misleading, suggesting there is something special about gravity in Argentina. I think we have something similar here. I'm finding lots of articles on WP that state "In telecommunications..." in the first line, when the article topic applies to many areas of science and engineering - I'm trying to broaden them as I find them. GyroMagician (talk) 18:12, 2 April 2010 (UTC)
 * "In science and engineering" seems overly broad to me. For example, harmonics are not central to the study of archaeology, gene splicing, or metallurgy, along with many others. Although those areas may make use of signal-processing instrumentation, wherever harmonics are mentioned there is usually some idea of signal analysis implied. (As of now, that redirects to signal processing, which seems like a fair fit, and may change some day.) How about declaring the context baldly, with something like "In the context of signal analysis, a harmonic of a wave is a component..."?
 * Somewhere else in the article there should be a place to mention those areas of science, engineering, music, and so on, where harmonics play a key role. __ Just plain Bill (talk) 19:17, 2 April 2010 (UTC)
 * I've looked around a little. Velocity and wavelength both start "In physics...". Frequency and Phase (waves) don't give a context. Wavenumber is qualified "...in the physical sciences...". Based on these, I would suggest "In physics...". I know this misses out engineering, but harmonics are really about waves, not about how they are analysed or used. I don't like "In the context of signal analysis..." because harmonics are more fundamental (excuse the pun!) than their analysis. Think, for example, of a laser frequency doubler. It generates harmonics whether you analyse them or not. GyroMagician (talk) 10:40, 3 April 2010 (UTC)
 * "In physics..." seems to me like a fair interim solution (nothing so permanent as a temporary arrangement.) It is not inaccurate, but de-emphasises mathematics, and misses music entirely. Musicians playing string, brass, and wind instruments are quite familiar with how a harmonic series feels and sounds, although they may not think of it in mathematical terms. There is also the matter of musical timbre being tightly coupled to harmonic content.
 * I will quibble with your "generates harmonics whether you analyse them or not" by saying that an encyclopedia is a vehicle of human discourse. They may well "exist" whether we discuss them or not, but here we are writing about the human endeavour of understanding the world. Tertiary source, and all that.
 * With all that said, I'll go change it and continue pondering, trying to find a more tightly focussed and informative way to put it. __ Just plain Bill (talk) 16:17, 3 April 2010 (UTC)
 * I think it looks better now. Harmonics mean several different, albeit related, things in mathematics, as described at Harmonic (mathematics), so I'm not too upset to miss them on this page. I agree that we clearly need to discuss harmonics in music - and I have never seen a physics lesson about harmonics that didn't use music as an explanation. I almost wonder about splitting the page into Harmonic (physics) and Harmonic (music), but I'm not sure that is necessary. Alternatively, maybe we could use level 1 sections on this page to discuss physics, music, electronics, etc, (maybe merging in Harmonics (electrical power) at the same time). What do you think?
 * When I say "generates harmonics whether you analyse them or not" I do not mean the analysis is unimportant - I just want to emphasise that the harmonics are not a property of the analysis, but have a strong physical basis. We should certainly discuss their analysis, but I don't think that belongs in the first sentence. I'm always open to persuasion though ;-) GyroMagician (talk) 17:28, 3 April 2010 (UTC)

The body of this article is a patchwork, Harmonic (disambiguation) needs work, and the whole set of articles clustering around "harmonic" could use some rational organisation. It's now on my to-do list... Bit of trivia for your amusement: The wing-mounted guns of a pursuit aircraft such as a P-51 Mustang were said to be "harmonized" when their fire converged at something like 600 yards, if memory serves. __ Just plain Bill (talk) 18:22, 3 April 2010 (UTC)

Second thoughts
If you read the content of this article, it relates entirely to acoustics, more particularly music. I'm strongly tempted to recast the first sentence as:
 * A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency ...

That first wikilink to wave sends the reader to a member of Category:Fundamental physics concepts. In my view, that gives plenty of context, while allowing the focus here to remain on the topic of this article.

When I went over to Harmonic (disambiguation) to rectify some of its issues, I found it explicitly assigns the primary topic as "components of sound." I left that standing, since it seems consistent with the Principle of least astonishment as broadly applied to a general reader (i.e. not necessarily a scientifically oriented one) searching in an encyclopedia for "harmonic(s)."

There is more to be done on that disambiguation page, as well as several "See also" sections, to bring in spectral issues of radio bandwidth management such as key clicks and other spurious emissions. I intend to save that work for another day though. Best, __ Just plain Bill (talk) 02:58, 6 April 2010 (UTC)


 * I made the change - glad you came around ;-) I agree that the context should be obvious from the explanation. It's true, this page deals almost entirely with music - maybe it would make sense to rename it Harmonic (music) after all. I could imagine something like the noise page, where one master page, with a medium amount of detail, points the reader to several sub-pages. If we follow this route, I think we would need Harmonic (music), Harmonic (electrical power) and Harmonic (signal processing) for starters. I don't think there is a whole lot to say for Harmonic (physics), so I imagine that could be covered on the master page. Do you think that would be a reasonable approach? GyroMagician (talk) 08:40, 7 April 2010 (UTC)
 * Cheers, I aim to please ;-) no small feat for an awkward old sort such as yours truly. Something like Harmonic (signal processing) might be useful. Rooting around in harmonic-related articles, I haven't noticed anything exactly or even fuzzily congruent with that. We have Harmonic analysis as well as another disambiguation page at Harmonic (mathematics); What topics do you think the signal processing page ought to cover? Do we need a page for Harmonic (mechanics)?
 * Not sure about calling anything a "master page"&mdash; I think this article could stand to be kept as the primary topic dealing with musical and acoustic matters. The encyclopedia article seems to have grown that way, reflecting the way human understanding of harmonics came about. Taking the historical view, Joseph Fourier is a relative newcomer. Again, the audience here is diverse; while I don't have survey results in hand, I'm pretty sure a fair number of users will come looking for the acoustic part of it, and the scientifically oriented readers will be able to sort through the disambiguation without losing their stride. __ Just plain Bill (talk) 14:23, 7 April 2010 (UTC)

Not Just for Acoustics
I have the unenviable distinction of being a French Horn player, an acoustic engineer, and an rf engineer. This same principal applies to deeper understanding in all 3 areas of expertise. It is selling the subject of harmonics short to imply, as this article does, that harmonics are strictly a musical phenomenon. For example: Propagated RF waves from things like cell phones, computers, or just about anything electronic that uses an oscillator are required by the FCC and other similar authorities in other countries to be measured out to their 10th harmonic to insure they are adequately suppressed so as to not cause interference. Just because the waves are not audible doesn't mean they are not present. —Preceding unsigned comment added by 66.150.46.254 (talk) 13:21, 2 September 2010 (UTC)
 * There are several pages devoted to these topics, including: Harmonics (electrical power), Harmonic oscillator, Harmonic (mathematics), Simple harmonic motion. You're correct, that there doesn't seem to be mention of harmonics as they relate to RF, and as both an EE and musician myself, that bother me as well.  Not sure which would be better: to expand this article with sections of harmonics in general, in music in particular, and in RF/elsewhere; create a new article for EM harmonics; or create a new article for EM, rename this one as Harmonic (sound), and redirect Harmonic to either this article or the disambiguation page.  Good catch! Bakkster Man (talk) 14:04, 2 September 2010 (UTC)


 * As a physicist I find it incredible that this page assumes harmonics relate to sound alone. It's an important concept, fundamental (ahem!) to any wave - be it mechanical, electro-magnetic, or I assume gravitational (I've never thought about gravitational harmonics before, but I guess they could exist). Harmonics certainly have an important and particular place in music and acoustics, but I think the beauty of the universe is in similarities across different fields. The page named 'harmonic' should reflect that, without getting stuck in the minutia of any particular specialisation. See the discussion above - I'd favour moving this page to Harmonic (music), and starting a new page to cover Harmonic more generally. GyroMagician (talk) 23:15, 2 September 2010 (UTC)


 * I just changed the wording of the hatnote, as anyone else here could have done. I also changed the first line of Harmonic (disambiguation) similarly. Where else do you see that "this page assumes harmonics relate to sound alone" ? The lead section does not impose any such limit.


 * I suggest adding sections on EM or mechanical harmonics. For now, gravitational harmonics may be difficult to source reliably. There is a stub at Spurious tone that needs work. __ Just plain Bill (talk) 00:44, 3 September 2010 (UTC)


 * That was a well deserved poke in the ribs ;-) But I think the problem is deeper - we need to substantially rewrite this page. Or probably better, keep this page (I rather like it) and write another, more general, harmonics page. I don't have the time to do it now, but I'll try to chip-in if anyone else does. I've just been over to Harmonic (disambiguation) and tried to sort things out there a bit. I now remember why I didn't do more before - it's complicated. I'm not sure I really understand how mathematicians use the work harmonic, but it is different to it's usage in physics. I think engineering (esp. electrical) usage is the same as physics. I could imagine having Harmonic (mathematics), Harmonic (physics) and Harmonic (music). I prefer (music) to (sound) - while technically all music is sound, I think the sound part should be covered under physics. This page would work well for Harmonic (music). I may have invented gravitational harmonics, but if anyone finds them, remember it was my idea! GyroMagician (talk) 14:46, 3 September 2010 (UTC)
 * Absolutely, credit must be given where due ;-) This page counts still under ten thousand bytes; wiki-sense says that at around forty thousand bytes it's time to think about splitting the page up for readability and browser-friendliness. Why not include and expand sections on physics, mechanics if you must separate that from physics, electromagnetic signals, and bandwidth regulatory issues? There is a useful established format for an umbrella article whose sections summarise further, more specialised articles using the template. I am most familiar with the Violin article in this regard, having given it such a breakup some years ago. __ Just plain Bill (talk) 16:44, 3 September 2010 (UTC)

Planck's Postulate, nhf, is precisely a harmonic expression quantizing energy in physical systems. I thought it should be somewhere in here. KickAssClown (talk) 11:28, 19 May 2011 (UTC)

I come from a musical background, but I see reason for not adding any of the non-acoustics topics mentioned above. So add all that stuff, complainers. What's holding you back? Just change the intro to be more high-level and inclusive, such as "harmonic means any member of the harmonic series" and segregate the various topics by sections. I recently saw a video that explained harmonics also arise in alternating current (AC) as unwanted, heat-causing distortion caused by non-linear loads, though, interestingly, only the odd harmonics appear (kind of like wind instruments that are pipes closed at one end, such as reeds, which I guess means there's a node at the electrical-generator end?), and, more interestingly, in a balanced 3-phase system, only those odd harmonics that are not also multiples of 3. (I wonder what that would sound like, and I guess it would be easy to synthesize it to find out). Why don't one of you electronics guys who can explain AC well add that too? 38.86.48.38 (talk) 05:39, 15 June 2015 (UTC)

Fundamental frequency on musical instruments
"In many musical instruments, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g., recorder)..."

A question: To my knowledge, in the example cited, the recorder, there are not prominent even harmonics (when played smoothly), and, as I understand it, jumping the octave is more a matter of exciting the next set of harmonics (starting at the second). The wording might be confusing as it seems to imply that it is simply a matter of removing the fundamental. Is that truly the case? If so, I'm surprised that the second octave is so loud and clear on the recorder.

Also: Does "fundamental note" mean "fundamental frequency"? Nielsed (talk) 03:46, 22 April 2011 (UTC)

Harmonic = frequency?
Is a harmonic a frequency or is it a signal with a certain frequency? The first sentences are ambiguous at the moment: "A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc." From my understanding (neither musician nor native speaker), the second is correct and suggest changing the first sentence to "A harmonic of a wave is a wave with a frequency that is an integer multiple ..." or something similar. MatteX (talk) 13:13, 20 November 2012 (UTC)


 * To my eyes, the sentence appears to be compact correct unambiguous English. Since a harmonic is a theoretical abstraction, it makes sense to omit the understood "sinusoidal waveform | [a]", leaving "A harmonic of a wave is a frequency that is an integer multiple ..."


 * The physical phenomenon corresponding to a theoretical harmonic is better called an overtone, in my favored usage. (Musical strings are said to have gone false when their overtones deviate too much from a harmonic series.) __ Just plain Bill (talk) 18:58, 20 November 2012 (UTC)


 * The sentence doesn't appear to claim both that a harmonic is a frequency, and that it is a signal. Could you elaborate by explaining what is ambiguous about the sentence, rather than simply quoting it? Hyacinth (talk) 20:34, 20 November 2012 (UTC)


 * I quoted the sentence because in the beginning, a harmonic is said to be a frequency and later it is said to have a frequency. "A frequency having a frequency of X" is at least bad English I would say. In the current version, another sentence follows the one quoted above: "The harmonics have the property that they are all periodic at the fundamental frequency, therefore the sum of harmonics is also periodic at that frequency." If the harmonics were frequencies (say 10 Hz, 20 Hz, 30 Hz, etc.) and not signals, they could - to my understanding - neither be periodic, nor could their sum (i. e. 10 Hz + 20 Hz + 30 Hz + ...) be periodic. I still think that the first sentences are ambiguous and that compactness should not come at the price of ambiguity. MatteX (talk) 07:19, 12 April 2013 (UTC)


 * You know what? Reading closer, I agree with MatteX. The opening has some mistakes and ambiguities, and it's sloppy with the terms.
 * 1) "a wave" could mean any signal, even noise, because an old trunk full of junk falling down a flight of stairs still produces "sound waves" no matter that they are periodic, aperiodic, harmonic, inharmonic, or some combination.
 * 2) The fundamental must be a sine, not "a wave" and not a "signal" because wave and signal are a higher logical level than sine, being combinations of components.
 * 3) Harmonics are precisely sines whose frequencies are positive integer multiples of the fundamental, including the fundamental.
 * 4) It fails to assert an important detail that a harmonic doesn't have to be found in the signal for it to be considered a harmonic. In other words, it's appropriate to say "the even harmonics are missing from a square wave" because those harmonics are still those harmonics, whether they exist in the signal or not.
 * 5) A harmonic can't "be" a frequency. A harmonic has a frequency. When people use the phrase "harmonic frequencies", harmonic is meant as an adjective, not a noun, and that does not change the strict definition of the noun "harmonic".
 * 6) It fails to assert an important detail that harmonics also have wavelengths but frequencies are preferred in discussion by convention because it takes fewer characters to write f1, f2, f3 than it would to write w1, w1/2, w1/3 and other conveniences.
 * 7) In "a sum of harmonics", "sum" is ambiguous, because if you already know that it means wave summation, and not summing like arithmetic adding (where 1+2+3+4+5=15 or whatever), then you already know what it means, and you don't need to read it, but if you don't already know what it means, and you came to the article to learn something, it doesn't explain itself. Unambiguous writing doesn't just allow correct interpretation, it eliminates incorrect interpretations.
 * 8) Responding to Just plain Bill, not to the opening: If I understood his book correctly, overtones, taking Helmholtz's original meaning, and not later misinterpretations, as cleared up by Ellis, are upper partials, not upper harmonics. Overtones can have any relationship to the fundamental including inharmonic, just like partials can, and overtones are numbered like partials (except one off of course), not numbered like harmonics. Overtones, like partials, must be present in the signal to be considered. Harmonics don't have to be present (see 4 above). That's why it's proper to say that a string's "overtones deviate too much from a harmonic series", just as it would be proper to say a string's partials do so, but it's not proper to call a missing harmonic an overtone. However, I would know exactly what you meant in casual conversation and wouldn't even notice it and would no doubt blur terms myself for convenience, except that we're talking here about encyclopedic accuracy. 108.60.216.202 (talk) 06:52, 30 May 2015 (UTC)
 * Thanks, 108.60.216.202. I reworked the stanza now, it is now also in agreement with the (newer) first introduction stanza. I feel those two should be merged, there is some repetition. I may to do that later. MatteX (talk) 10:40, 30 January 2016 (UTC)
 * I have merged them now. MatteX (talk) 14:31, 31 January 2016 (UTC)

Inconsistency with Waveform
The numbering scheme used here is inconsistent with the description of square wave in Waveform.

Learjeff (talk) 15:07, 27 June 2013 (UTC)
 * How so? The fundamental is the first harmonic, as far as I can tell, in both articles. &mdash;Wahoofive (talk) 15:30, 27 June 2013 (UTC)

The fundamental is the first partial. The question would be, how many harmonics in a sine tone? 2014 - I - 14  [kaustin6969]  — Preceding unsigned comment added by Kaustin6969 (talk • contribs) 04:59, 15 January 2014 (UTC)


 * Harmonics are partials. So same number.  In a sine wave, just one; but zero overtones.  Dicklyon (talk) 05:41, 15 January 2014 (UTC)


 * (More than a year later, but who cares, because idea-space is timeless.) Hm. Harmonics are not partials. Harmonics are ideal sinusoidal components that might or might no be present in an actual sonic signal. Partials are the real thing. Harmonics only exist at prescribed frequency relationships to the fundamental. Partials can have any relationship to the fundamental. The number of partials therefore has no connection at all with the number of harmonics. Even the fundamental harmonic is not guaranteed to be present because of the "missing fundamental" affect. However, there will always be a first partial--else there will be no sound! 108.60.216.202 (talk) 11:05, 31 May 2015 (UTC)

incoherent
I find the article to be incoherent, and in many places simply incorrect. I would suggest deleting the whole thing, and use the term "partial" instead of 'harmonic', to avoid such quaint terms as 'inharmonic harmonic'. I think it needs to be written by someone who has a broader understanding of the fundamentals, acoustics, and the physics of instruments. For example, brass instruments do not produce the harmonic series, as they are pipes closed at one end, and as such generate only odd partials.

The use of the plucked string as the 'example' is probably among the worst possible choices. A plucked string is stretched, and is placed under greater tension, thus the harmonicity of the partials is constantly changing. And there are more such fundamental errors.

Kevin 2014 – I – 14  — Preceding unsigned comment added by Kaustin6969 (talk • contribs) 04:55, 15 January 2014 (UTC)


 * 1) "Harmonic" and "partial" aren't synonyms. 2) I moved pizzicato strings into the paragraph of examples with "a mix of harmonic and inharmonic partials". 3) Help fix the article instead of complaining. 38.86.48.38 (talk) 20:37, 9 June 2015 (UTC)

We need better animations
I figured it out. The animations unrealistically model a closed pipe. Wind instruments are open at one or both ends. If one end, the harmonics are odd. The string-like animations confusingly model a closed pipe too. We need real animations for strings, pipes open at one end, and pipes open at both ends. Any volunteers? 38.86.48.38 (talk) 20:23, 9 June 2015 (UTC)

The animations are still all wrong. Does no one have the tools to correct them? They don't even match each other on the same row. For example, in the first row, showing the first partial, the first animation shows the air pressure changing in the middle while the pressure remains the same at the ends, but the second animation on the same row shows the pressure changing at the ends instead of the middle. It makes no sense to model a wind instrument constructed of a pipe with no openings. Such an instrument would be silent! The existing animations probably do more harm than good. 104.236.225.168 (talk) 19:52, 7 February 2016 (UTC)

A different issue
The wave representation column actually shows the same frequency four times. The top one being half a wavelength, then 1 wavelength, 1·5 wavelengths and then finally 2 wavelengths. I'd suggest all should be of one wavelength but with each moving red line increasing in speed by 2,3 & 4 times the first. pmailkeey 15:34, 4 June 2017 (UTC)

Counting harmonics
The word 'harmonics' comes from 'harmony'. Which means 'together' 'in unision' etc. It does not applie to music, frequency or acustics only. One can live in harmony with nature; colours and patterns can be in harmony or not - for example. In all cases there needs to be at least TWO something. One 'thing' can not be in harmony because there is no 'togetherness' or 'unision'. Therefore a single sinusoidal signal can not be a harmonic. There MUST BE another signal to be able to compare the two. The lowest frequency is chosen to be the base to what the other frequencies are compared to. Thus the first higher frequency is the first harmonic. (If it is indeed a harmonic) People instinctively know this. The confusion comes from that some 'experts' try twisting the natural meaning. The included table trying to explain the relationships between naming the same is the perfect example for the distortion-efforts. As there is only a need for this table if the meaning of the word is not clear. In other words, it is clear to all but to those who want to re-define the meaning. Anybody saying otherwise reveals, s/he doesn't understand what the word means. — Preceding unsigned comment added by 202.8.39.83 (talk) 07:27, 8 April 2016 (UTC)

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Confusion with the harmonic series in mathematics
The first paragraph of the article seems to be taken verbatim from Harmonic series (mathematics) despite the article supposedly being about components of waveforms.

I think the paragraph should be removed to avoid confusion, since it explains the wrong sense of the word 'harmonic', but I'm not sure how to tweak the following paragraph to adequately introduce what a harmonic is.

117.60.176.103 (talk) 08:06, 23 August 2018 (UTC)


 * I also think that some extra information needs to be given about the definition of a harmonic. One important piece of information will be timing. For example, if we have a fundamental waveform - sinusoidal. And then we have a sinusoidal waveform having a frequency that is three times the fundamental frequency, then will that higher frequency sinusoid be considered a 'harmonic' regardless of timing? That is - will a time-shifted version of a 'third harmonic' waveform still be considered as a 'third harmonic' waveform? KorgBoy (talk) 01:45, 17 July 2021 (UTC)

Molecular representation
The molecular representation GIFs are probably confusing without an intermediary graph showing pressure. Bright☀ 08:00, 1 July 2019 (UTC)

Define "periodic"
The intro is confusing for several reasons. For example, there is no definition of "periodic" harmonics. What differentiates periodic harmonics from others? There should at least be a link. Better yet, let's try to explain it, from the get-go, for someone who doesn't have a background in physics or the science of sound. Even the first sentence is confusing; it defines "harmonic" as a member of something else ("the harmonic series") whose definition is equally confusing. Why not start with something like: A harmonic is one part of a set of tones, waves, or sounds that make up a "harmonic series." Keithscoot (talk) 15:59, 1 January 2021 (UTC)
 * All harmonics are periodic, as plainly stated in the first paragraph. (Treating "harmonic" content of a transient signal such as an impulse function, or single click, may be beyond the scope of this article.) I've added a link to Periodic function which may help readers understand the definition of it. Just plain Bill (talk) 18:36, 1 January 2021 (UTC)

Errors in "Terminology" section
I've tried twice to update (fix) the Terminology section with the content below. Both times my changes were reverted automatically. If anyone is able, please replace the content in that section (which is largely incorrect) with this:

Terminology
Although you might hear "harmonic" and "overtone" used synonymously, they're not the same. To explain, we need to talk about pure tones, complex tones, and partials.

A pure tone is a sine wave, and it has just one frequency. But most sounds we hear are not pure tones; they're complex tones. A complex tone is made up of multiple pure tone components all superimposed. And all of those pure tone components of a complex tone are known as "partials". The main partial is known as the "fundamental frequency"; that's the loudest. The other, quieter, partials are known as the "upper partials", or "overtones".

When you knock on a door, or pluck a guitar string, you hear partials. You hear the fundamental plus overtones. But a door knock doesn't sound musical; whereas a guitar does. Why is that? The reason is that the overtones of a guitar tone are positive integer multiples of the fundamental frequency. But the overtones of the door knock are not related to the fundamental frequency in such a regular, simple, and predictable way. What we think of as a musical tone is all about the simple mathematical relation between fundamental and overtones. For a musical tone, we call the partials "harmonic partials". And that's where the terms "harmonic" and "harmonic series" come from. In a musical tone, the fundamental is the first harmonic (partial), and the upper harmonics are the second, third, and so on, harmonic (partials) or overtones. Although, one might say "harmonic overtones" to differentiate them from the inharmonic overtones in a door knock.

So there are two reasons why "harmonic" and "overtone" are not the same. First, because there are plenty of overtones that are not harmonic (because they're not positive integer multiples of the fundamental). And second, because the fundamental of a musical tone is counted as a "harmonic" (partial). It's the first harmonic (partial) just like the fundamental of any complex tone (harmonic or not) is counted as the first partial. Whereas overtones (or upper partials) do not include the fundamental. 2601:600:A480:4C20:5CDD:8591:49C8:C73F (talk) 21:59, 18 January 2024 (UTC)


 * You're getting reverted because this is all unsourced. See WP:V and WP:NOR, which are core policies. It is also not written in encyclopedic style - it addresses the reader, uses rhetorical questions, etc. - MrOllie (talk) 22:10, 18 January 2024 (UTC)

Longitudinal wave Represention
The table in the Partials, overtones, and harmonics section with images in it has a column: “Longitudinal wave Represention” included. This representation is confusing and the link doesn’t seem helpful. A short explanation of what it means and how to interpret it would be helpful. The previous column has the helpful “Standing Wave Representation” which has a brief explanation earlier on. CuriousMarkE (talk) 03:26, 26 April 2024 (UTC)