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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.
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
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<<
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. [email protected]
-- Yes, this is a good way of thinking about it. The table itself could use some cleaning.
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)
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)
[ [1]] Notation und MIDI-Sound -- 88.73.222.2 08:21, 4 December 2006 (UTC)
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)
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)
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)
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)
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)
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.
Pitch Name |
String |
Frequency |
Frequency-multiple |
HARMONICS |
PARTIALS |
OVERTONES |
|
C2 |
1:1 |
64Hz. |
f0 |
Fundamental |
First partial |
Fundamental |
|
C3 |
1:2 |
129Hz. |
2 f0 |
Second harmonic |
Second partial |
First overtone |
|
G3 |
1:3 |
192Hz. |
3 f0 |
Third harmonic |
Third partial |
Second overtone |
|
C4 |
1:4 |
256Hz. |
4 f0 |
Fourth harmonic |
Fourth partial |
Third overtone |
|
E4 |
1:5 |
320Hz. |
5 f0 |
Fifth harmonic |
Fifth partial |
Fourth overtone |
|
G4 |
1:6 |
384Hz. |
6 f0 |
Sixth harmonic |
Sixth partial |
Fifth overtone |
|
|
etc. |
||||||
A comparison of harmonic, partial andovertone naming conventions. |
--
Dirk (
talk) 19:51, 24 October 2009 (UTC) —Preceding
unsigned comment added by
87.160.255.117 (
talk)
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)
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)
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:
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 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)
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)
"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)
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)
The numbering scheme used here is inconsistent with the description of square wave in Waveform.
Learjeff ( talk) 15:07, 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)
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)
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)
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)
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
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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)
The molecular representation GIFs are probably confusing without an intermediary graph showing pressure. Bright☀ 08:00, 1 July 2019 (UTC)
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)
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:
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)
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)