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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. —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"— 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. —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)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Harmonic


text:
Grisons

The Grisons or Graubünden, more formally the Canton of the Grisons or the Canton of Graubünden, is one of the twenty-six cantons of Switzerland. It has eleven districts, and its capital is Chur. The German name of the canton, Graubünden, translates as the "Grey Leagues", referring to the canton's origin in three local alliances, the Three Leagues. The other native names also refer to the Grey League: Grischùn in Sutsilvan, Grischun in the other forms of Romansh, and Grigioni in Italian. Rhaetia is the Latin name for the area. The Alpine ibex is the canton's heraldic symbol.

The largest and easternmost canton of Switzerland, it is also one of the three large southern Alpine cantons, along with Valais and Ticino. It is the most diverse canton in terms of natural and cultural geography, as it encompasses both sides of the Alps and several natural and cultural regions. The diversity of the canton is often compared to that of Switzerland as a whole and warrants it the name of "Little Switzerland". The Grisons is bordered by four cantons as well as Austria, Italy and Liechtenstein.

The state is the only trilingual canton of Switzerland. It is also the only one where Romansh, Switzerland's fourth national language, has official status. Romansh language and culture is an important part of local identity. In the canton had a population of. It is the least densely populated canton of Switzerland. The only sizable city in the canton is Chur, as the majority of the population lives in mountainous areas, including some of the most remote valleys of the country. One of the birthplaces of winter sports, the canton is a major tourist destination year-round, including a large number of Alpine resort towns, notably Davos and St. Moritz. The canton is also renowned for its extensive narrow-gauge railway network, operated by the Rhaetian Railway, and linking the capital with most valleys of the Grisons.

Formerly occupied by the Rhaeti, most of the lands of the canton became part of the Roman province called Raetia, which was established in 15 BC, with Curia, a settlement dating back to the Pfyn culture, as capital city. The area later became part of the lands of the diocese of Chur. The late middle ages saw the foundation of the League of God's House, the Grey League and the League of the Ten Jurisdictions. In 1471 an alliance gave birth to the Three Leagues, and before the end of the 15th century, the latter became an ally of the Old Swiss Confederacy. In 1803 the Three Leagues finally became one of the cantons of the Confederation.

Geography and climate

The Grisons is Switzerland's largest and at the same time easternmost canton. Its geography, essentially marked by the Alps, is complex and encompasses a wide range of climates and ecosystems. It is one of the three large southern Alpine cantons, along with Ticino and Valais, which include regions on the south side of the Alps. But in contrast to those (and all other cantons), it fully extends on both sides of the great Alpine barrier, from the northern plains at Maienfeld to the southern plains at Roveredo. However, a large portion of the canton is neither clearly north nor south of the Alps, it is the Engadin (the "garden of the Inn"), a large inner Alpine valley oriented towards eastern Europe. Therefore there are parts of this canton in four of the five drainage basins of the country. The north of the canton is drained by the Rhine (ending in the North Sea), the south by the Po and Adige through several affluents (Mediterranean Sea), and the Engadin by the Danube through the Inn (Black Sea).

The Grisons lies fully within the Alps, with elevations above sea-level ranging from 260 to 4049 m. It is both one of the highest and lowest cantons, and the second-highest when considering mean elevation. As a consequence, its topography is extremely rugged and many of the highest settlements in the country (and Europe) are found there, notably in the Upper Engadin. The mountains are numerous; well over 1,000 summits are in the canton. The highest is Piz Bernina, closely followed by numerous peaks in the homonymous range. Other prominent mountains are Piz Russein, Piz Kesch, Calanda, Aroser Rothorn and Rheinwaldhorn, see list of mountains of Graubünden for a more exhaustive list. The canton includes numerous subranges of the Alps other than the Bernina. These are the Albula, the Bregaglia, the Glarus, the Gotthard, the Lepontine, the Livigno, the Plessur, the Oberhalbstein, the Ortler, the Rätikon, the Samnaun, the Sesvenna and the Silvretta ranges.

The regions on the north side of the Alps are all drained by the Rhine and form an intricate network of valleys. The Rhine is both one of the longest rivers within the canton and the only one flowing directly into a sea. The sources of the Rhine are found in the west of the canton and form the Anterior Rhine and the Posterior Rhine. These two rivers converge at Reichenau to form the Rhine in the strict sense of the term. Just after the convergence, the valley opens and its floor constitutes the flattest plains of the canton, from Domat/Ems to Fläsch at the St. Gallen border. In the area around Chur, at the foot of the Calanda, the Rhine progressively changes its direction, from eastward to northward. The Anterior Rhine and Posterior Rhine include numerous tributaries as well before their own convergence. The former constitutes a long and straight valley, the Surselva, shut off from the lower plains by the Rhine Gorge. Its biggest tributaries are the rivers Glogn, Valser Rhine, Rabiusa, forming respectively the Val Lumnezia, the Vals Valley and the Safiental. The other one, the Posterior Rhine, notably collects the waters of the Avers Rhine and the Albula, which in turn collects the waters of the Gelgia and the Landwasser. Similarly to the Anterior Rhine, the upper portion of the Posterior Rhine is also shut off from the plains by the Viamala Gorge. After the convergence with the Albula, the Posterior Rhine forms a wide valley, the Domleschg, until it meets its anterior counterpart. After that, the Rhine collects the water of two important rivers: the Plessur at Chur, forming the valley of the Schanfigg, and the Landquart at the homonymous town, forming the Prätigau.

The Engadin is entirely drained by the Inn and is the only valley in Switzerland in the Danube basin. The Inn is one of the longest rivers in the canton and forms an almost straight valley, from the Maloja Pass to Martina, with a change of direction near Zernez. Despite its length and numerous tributaries, only a few long rivers converge with the Inn. These are the Flaz (forming the Val Bernina), the Spöl (forming the Val da Spöl) and the Clemgia (forming the Val S-charl). In the lower part of the Engadin is also the side valley of Samnaun. The main passes connecting the Engadin with the northern Grisons are (from west to east): the Julier Pass, the Albula Pass and the Flüela Pass.

The valleys on the south side of the Alps are not contiguous to each other and form four distinct regions. The Mesolcina, drained by the Moesa, the Val Bregaglia, drained by the Mera, the Val Poschiavo, drained by the Poschiavino, and the Val Müstair, drained by the Rom. The first three are in the Po basin and the last one is in the Adige basin. While the first two (Mesolcina and Bregaglia) are contiguous to the region north of the Alps, through the San Bernardino Pass, and the Septimer Pass respectively, the three last ones (Bregaglia, Poschiavo and Müstair) are contiguous to the Engadin, through the Maloja Pass, the Bernina Pass, and the Ofen Pass.

Although no large bodies of water are found in the canton, numerous mountain lakes (above 800 m elevation) dot the landscape, some of them being used as reservoirs for hydroelectricity production. The largest natural lakes are Lake Sils, Lake Silvaplana, Lago di Poschiavo and Lake St. Moritz (all in Upper Engadin except that of Poschiavo). Artificial lakes are more numerous, the largest (over 100 ha) being Lago di Livigno, Lago di Lei, Lai da Sontga Maria, Zervreilasee, Lago Bianco, Lai da Marmorera and Lägh da l'Albigna. The total number of lakes has been estimated to 600. See list of mountain lakes of Switzerland for a more exhaustive list.

Unlike other large cantons, the Grisons includes very few cities. The largest (and capital city) is Chur. It is followed by Davos, Landquart, Domat/Ems and St. Moritz, which are, however, far less populated. The canton is particularly renowned for its numerous Alpine resort towns, notably two of the aforementioned ones (Davos and St. Moritz), but also Klosters, Arosa, Lenzerheide, Disentis, Flims, Pontresina and Scuol.

The diversity of the climate of the Grisons is high and comparable to that of Switzerland. In the southernmost and lowest regions, vineyards and olives are grown, while on the highest summits, snow is found year-round. The inner valleys, particularly the Engadin, are significantly drier than the north and south side of the Alps, being sheltered by the high mountains of the range. On the south side of the Alps, Grono is one of the top warmest places in the country with an average of 12.4 C. The nationwide record temperature of 41.5 °C was registered there. The southern valleys are also significantly wetter than the rest of the canton (1,476 mm of rain in Grono, 849 mm in Chur, and 705 mm in Scuol). The coldest places are naturally at high elevations, such as on Piz Corvatsch. The localities of the Upper Engadin are amongst the coldest inhabited regions in the country, notably Samedan with an average temperature of 2.0 °C. The cantonwide record-low temperature of -37.9 °C was registered there. The low-elevation region of Chur, including the Bündner Herrschaft, experiences naturally less harsh temperatures with an average of 10.0 °C.

The area of the Grisons is 7105.2 km2, 19.2% larger than the canton of Bern, the second largest canton. Only about a third of this is commonly regarded as productive land of which forests cover about a fifth of the total area. The canton is almost entirely mountainous and it is the most sparsely populated region of the country. In its southeastern part lies the only official Swiss National Park. In its northern part, the mountains were formed as part of the thrust fault that was in 2008 declared a geologic UNESCO World Heritage Site, under the name Swiss Tectonic Arena Sardona. Another Biosphere Reserve is the Biosfera Val Müstair adjacent to the Swiss National Park, while Ela Nature Park is one of the regionally supported parks.

The Grisons is sometimes included in the larger region of Eastern Switzerland, together with six other cantons. The Grisons shares border with numerous regions of Europe, reflecting its cultural diversity, and is the only canton adjacent to three different countries. On the national level it shares borders with four other cantons: Uri, Glarus, St. Gallen to the northwest (essentially across the Glarus Alps) and Ticino to the west (essentially across the Gotthard Massif and the Lepontine Alps but also at the level of the plain at Roveredo). On the international level, the canton shares borders with three countries: Liechtenstein to the north, the Austrian regions of Vorarlberg and Tyrol to the northeast and the Italian regions of Trentino-South Tyrol and Lombardy to the east and south.

History
The deep Alpine valleys of the present-day Grisons were originally settled by the Raetians (Rhaeti). In Chur, archaeological evidence of settlement goes back as far as the Pfyn culture (3900–3500 BC), making the capital city of the Grisons one of the oldest settlements in Switzerland.

Most of the lands of the canton were once part of a Roman province called Raetia, which was established in 15 BC. The current capital of the Grisons, Chur, was known as Curia in Roman times. The area later was part of the lands of the diocese of Chur.

In 1367 the League of God's House (Cadi, Gottes Haus, Ca' di Dio) was founded to resist the rising power of the Bishop of Chur. This was followed by the establishment of the Grey League (Grauer Bund), sometimes called Oberbund, in 1395 in the Upper Rhine valley. The name Grey League is derived from the homespun grey clothes worn by the people and was used exclusively after 16 March 1424. The name of this league later gave its name to the canton of the Grisons. A third league was established in 1436 by the people of ten bailiwicks in the former Toggenburg countship, as the dynasty of Toggenburg had become extinct. The league was called League of the Ten Jurisdictions (Zehngerichtebund).

The first step towards the canton of the Grisons was when the league of the Ten Jurisdictions allied with the League of God's House in 1450. In 1471 the two leagues allied with the Grey League. In 1497 and 1498 the Leagues allied with the Old Swiss Confederacy after the Habsburgs acquired the possessions of the extinct Toggenburg dynasty in 1496, siding with the Confederacy in the Swabian War three years later. The Habsburgs were defeated at Calven Gorge and Dornach, helping the Swiss Confederation and the allied leagues of the canton of the Grisons to be recognised. However the Three Leagues remained a loose association until the Bundesbrief of 23 September 1524.

The last traces of the Bishop of Chur's jurisdiction were abolished in 1526. The Musso war of 1520 drove the Three Leagues closer to the Swiss Confederacy.

Between 1618 and 1639 it became a battleground between competing factions during the Bündner Wirren. The Protestant party was supported by France and Venice, while the Catholic party was supported by the Habsburgs in Spain and Austria. Each side sought to gain control of the Grisons to gain control over the important alpine passes. In 1618, the young radical Jörg Jenatsch became a member of the court of 'clerical overseers' and a leader of the anti-Habsburg faction. He supervised the torture to death of the arch-priest Nicolò Rusca of Sondrio. In response, Giacomo Robustelli of the pro-Catholic Planta family, raised an army of rebels in the Valtellina. On the evening of 18/19 July 1620, a force of Valtellina rebels supported by Austrian and Italian troops marched into Tirano and began killing Protestants. When they finished in Tirano, they marched to Teglio, Sondrio and further down the valley killing every Protestant that they found. Between 500 and 600 people were killed on that night and in the following four days. The attack drove nearly all the Protestants out of the valley, prevented further Protestant incursions and took the Valtellina out of the Three Leagues.

In response, in February 1621, Jenatsch led a force of anti-Habsburg troops to attack Rietberg Castle, the home of a leader of the pro-Catholic faction, Pompeius Planta. They surprised Planta and according to legend he was killed by Jörg Jenatsch with an axe. The murder of Planta encouraged the Protestant faction and they assembled a poorly led and disorganized army to retake the Valtellina and other subject lands. However, the army fell apart before they could attack a single Catholic town. This Protestant invasion provided the Spanish and Austrians with an excuse to invade the Leagues. By the end of October, Spain and Austria had occupied all of the Grisons. The resulting peace treaty of January 1622, forced Grisons to cede the Müstair, the Lower Engadine and Prättigau valleys. The treaty also forbade the Protestant religion in these valleys. In response, in 1622, the Prättigau valley rebelled against the Austrians and drove them out of the valley. The Austrians invaded the valley twice more, attempting to reimpose the Catholic faith, in 1623–1624 and 1629–1631.

In 1623 the Leagues entered into an alliance with France, Savoy and Venice. Jürg Jenatsch and Ulysses von Salis used French money to hire an 8,000-man mercenary army and drive out the Austrians. The peace treaty of Monzon (5 March 1626) between France and Spain, confirmed the political and religious independence of the Valtellina. In 1627 the French withdrew from the Valtellina valley, which was then occupied by Papal troops. Starting in 1631 the League, under the French Duke Henri de Rohan, started to expel the Spaniards. However, Richelieu still did not want to hand the valley over to its residents. When it became clear that the French intended to remain permanently in the Leagues, but would not force the Valtellina to convert to Protestantism, Jürg Jenatsch (now a mercenary leader) converted in 1635 to the Catholic faith. In 1637, he rebelled and allied with Austria and Spain. His rebellion along with the rebellion of 31 other League officers forced the French to withdraw without a fight. On 24 January 1639, Jürg Jenatsch was killed during Carnival by an unknown attacker who was dressed as a bear. The attacker may have been a son of Pompeius Planta or an assassin hired by the local aristocracy. According to legend he was killed by the same axe that he used on Pompeius Planta. On 3 September 1639 the Leagues agreed with Spain to bring the Valtellina back under League sovereignty, but with the promise to respect the free exercise of the Catholic faith. Treaties with Austria in 1649 and 1652, brought the Müstair and Lower Engadine valleys back under the authority of the Three Leagues.

In 1798, the lands of the canton of the Grisons became part of the Helvetic Republic as the canton of Raetia except Valtellina, which was separated in 1797 for joining the Cisalpine Republic. It was later part of the Empire of Austria in 1814 before joining the Kingdom of Italy in 1859. With the Act of Mediation the "perpetual ally" of Switzerland became a canton in 1803. The constitution of the canton dates from 1892. In the following century, there have been about 30 changes made to the constitution.

The arms of the three original leagues were combined into the modern cantonal coat of arms in 1933.

Government
The Grand Council (Grosser Rat; Gran Consiglio, Cussegl Grond), the legislature of the canton, sits in Chur, the cantonal capital. Its 120 members, elected in 39 districts using a majority system, are in office for four years. The last district elections were in 2014. The cantonal government, exercising executive authority, is made up of five members, elected by the people for a term of four years and limited to three terms using a majority system.

The constitution of the Grisons, last revised on 14 September 2003, states in its preamble that the canton's purpose is to "safeguard freedom, peace, and human dignity, ensure democracy and the Rechtsstaat, promote prosperity and social justice and preserving a sane environment for the future generations, with the intention of promoting trilingualism and cultural variety and conserving them as part of our historical heritage".

The constitution allows for the enfranchisement of foreign residents at a municipal level, at discretion of the local governments. In 2009, the municipality of Bregaglia became the first in the canton to make use of this provision, granting voting rights to foreigners.

Federal election results

 * FDP before 2009, FDP.The Liberals after 2009
 * "*" indicates that the party was not on the ballot in this canton.

Regions
as of January 2017

 * Albula with capital Tiefencastel
 * Bernina with capital Poschiavo
 * Engiadina Bassa/Val Müstair with capital Scuol
 * Imboden with capital Domat/Ems
 * Landquart with capital Igis
 * Maloja with capital Samedan
 * Moesa with capital Roveredo
 * Plessur with capital Chur
 * Prättigau/Davos with capital Davos
 * Surselva with capital Ilanz
 * Viamala Region with capital Thusis

Municipalities
There are 114 municipalities in the canton.

Demographics
The inhabitants of the Grisons are called Bündner or (rarely) Grisonians.

The population of the canton (as of ) is. , the population included 28,008 foreigners, or about 14.84% of the total population. The main religions are Catholicism and Protestantism. Both are well represented in the canton, with Roman Catholics forming a slight plurality (47% Catholic to 41% Protestant).

Languages
The Grisons is the only canton of Switzerland with three official languages: German (74.7%), Romansh (13.9%), and Italian (13.9%) with the remaining 13% speaking another language natively.

More speakers of the Romansh language live in the Grisons than in any other canton, although it has become a minority language there. Romansh consists of five dialect groups, each with its own written language: Sursilvan, Vallader, Puter, Surmiran and Sutsilvan. There also exists a common written language called Rumantsch Grischun. Romansh has been recognized as one of four "national languages" by the Swiss Federal Constitution since 1938. It was declared an "official language" of the Confederation in 1996, meaning that Romansh speakers may use Romansh for correspondence with the federal government and expect to receive a response in Rumantsch Grischun. Romansh has official language status at the canton level. Municipalities in turn are free to specify their own official languages.

Economy
Agriculture is still essential to keep remote valleys inhabited and cultivated, differing it from sheer wilderness. Agriculture is therefore supported by subsidies by the authorities both national and regional. Eight per cent of the population work in agriculture and forestry, where 50 per cent of the production is certified as organic. Agriculture includes forests and mountain pasturage in summer, particularly of cows, sheep and goats. Since wolf and bear have returned, the use of Maremma Sheepdogs is not unusual. Although mountain pastures are predominant, there is also wine production in the Rhine Valley, particularly in Fläsch, Maienfeld, Jenins and Malans. This area is referred to as the Bündner Herschaft. In the southern valleys of Mesolcina and Val Poschiavo there is corn (maize) and chestnut farming, allowed by the milder climate. In the Mesolcina, olive trees are also grown.

24 per cent of the workforce are employed in industry whereas 68 per cent work in the service industry. The most industrialized region is naturally that of Chur. Ems-Chemie is based in Domat/Ems and is a major employer in the area.

The tourism industry is a major player and reaches a remarkable 14 per cent of the GDP. Tourism is concentrated around the towns of Davos, Klosters, Lenzerheide, Arosa, Flims, St. Moritz and Pontresina, which have large ski areas. There are, however, a great number of other tourist resorts in the canton, divided by the official tourist board for winter sports for example into categories "Top - Large - Small and beautiful". St. Moritz is one of the oldest winter sport resorts, being popular in winter since 1864. The following year, Davos also saw its first tourists in winter. St. Moritz hosted the 1928 Winter Olympics and the 1948 Winter Olympics. Summer tourism is also an important source of revenue. Trekking, mountaineering, and mountain biking are some of the main activities. Business tourism is also a source of revenue, notably in Davos, where the World Economic Forum meetings are traditionally organised.

Transport

As the canton extends on both sides of the great Alpine barrier, many important mountain passes are found there, particularly on the north-south axis. Transport has always been an important issue in the area; cart tracks from the Roman era were found on Julier Pass and Septimer Pass was rebuilt for cart use in 1387 and, although it later became unimportant, it is still in its 1800 form (for hikers only). Corniche paths were necessary for long stretches, and gorges such as the Viamala gave construction problems for any kind of transport. The first real roads of 4 yd width were built across the Alps from around 1816, one of which is still in a very good historical condition as this connection across Splügen Pass lost its importance after the opening of rail tunnels crossing the alps. The last valley to be connected to the road system in the Grisons was Avers, whose remote hamlet of Juf was only reached in 1897. After the Swiss Post expanded their Postal Bus transport services, the region's inhabitants became more used to motorized traffic. In 1925, there were already 250 vehicles in service. Eventually, the inhabitants of the Grisons gave up their resistance against individual motor traffic in 1926, In 1967 opened San Bernardino road tunnel, built to host tourism traffic, is used also by heavy goods vehicles nowadays although not really suitable for them because of its ascent gradients. Most other passes have lost their importance for goods transport nowadays.

Unlike Valais and Ticino, the Grisons does not benefit from major railway axes across the Alps such as the Lötschberg and Gotthard. As a consequence, the only standard gauge railway in the canton is that of the Rhine Valley, ending at Chur station. Conversely, the latter has become a major railway station and a transport hub of the canton since the construction of the Rhaetian Railway, which links most regions of the canton from the Rhine Valley.

Huge efforts ensure public transport to (nearly) every settlement by an integrated timetable of different transport companies. Even Juf, inhabited by some 30 people only but holding a European record, is reached five times a day by public transport. The two main transport companies are PostBus, the national post bus company, and the Rhaetian Railway, essentially owned by the cantonal government. The latter uses the largest narrow-gauge railway network in Switzerland and serves most regions of the canton, with branches towards Central Switzerland and Italy. This network is notably travelled by two of the longest distance trains of Switzerland: the Glacier Express and the Bernina Express. The Swiss Federal Railways extend only a few kilometres into the canton, from Maienfeld, and serve essentially Landquart and Chur, where passengers transfer to the Rhaetian Railway and a large number of PostBus routes. The Albula Line became a UNESCO world heritage as did the Bernina Railway, the highest and only railway to cross the Alps without the use of a tunnel at the pass. In winter some of the road passes are closed whereas several high mountain passes such as the Julier, Bernina and Lukmanier are kept open all winter (subject to restrictions). Being the highest elevated state in Switzerland, the Grisons hosts huge alpine areas that are not accessible by any means of transport but have to be walked to. A large number of cable transport facilities provide easy access to some of the mountains of the Grisons, the highest being on Piz Corvatsch.

The Engadin valley has its own airport, Samedan Airport. It is the highest airport in Switzerland.

Culture
The Grisons is culturally the most diverse region of Switzerland. Its common denominator, however, is a strong mountain culture marked by life in isolated rural communities, notably depicted in Johanna Spyri's Heidi. Traditional customs include Alpine transhumance in spring and autumn, and the Chalandamarz at the end of winter.

The canton has a large concentration of medieval castles (and ruins). The most notable, in the Engadin, is that of Tarasp, guarding the Inn valley. Many ruins and castles are found in the Domleschg area. Close by lies the church of Zillis, where 1130/40 a famous romanesque illustrated ceiling was added which is now treated as national heritage. Three World Heritage Sites are located in the canton: the Benedictine Convent of Saint John, the Swiss Tectonic Arena Sardona and the Rhaetian Railway in the Albula and Bernina Landscapes.

The gastronomy of the Grisons is mostly known for a dried-beef delicacy called Bündnerfleisch, often simply referred to as Grisons Meat. Other meat specialities include dried sausages (especially Salsiz, made of various meats), speck and ham. Cheeses produced in the Grisons are also numerous. Among notable dishes are the Capuns, predominantly made in the western part of the Grisons. Capuns consist of hearty dumplings with pieces of meat wrapped in chard leaves, then gratinated in oven with cheese and cream. The Maluns are another well-known dish of the Grisons. They are made of boiled potatoes mixed with flour, then fried in butter. Maluns are typically served with a compote of apples and various other local products such as cheeses and meat specialities. The Pizzoccheri are another dish, essentially eaten in the valley of Poschiavo. They consist of buckwheat noodles, cooked with potatoes, vegetables and cheese. The emblematic dessert of the Grisons is the Bündner Nusstorte. It is essentially a shortcrust pastry filled with a mix of caramelized walnuts and honey. Another similar pastry, but containing chestnuts instead, the Torta di Castagne, is made in the southern valleys, especially in the Val Bregaglia.

Wines are essentially produced in the Bündner Herrschaft. In the vineyards between Fläsch and Malans, 42 types of vines are found, Pinot Noir being the most popular. Wines are also naturally produced in the southern valleys but in smaller quantities. The valley of the Mesolcina is contiguous with the Ticino wine region and that of Poschiavo is contiguous with the Valtellina wine region. Numerous breweries can be found in the canton as well. The largest, located at Chur, is Calanda Bräu.

Radiotelevisiun Svizra Rumantscha is the Romansh-speaking division of the Swiss Broadcasting Corporation and focuses on the Grisons. Die Südostschweiz (in German) and La Quotidiana (Romansh) are some of the most important written media of the region.

Nature
The Grisons successfully reintroduced ibex in the early 20th century after it had all but died out from the Alps, except for an area in the Aosta Valley in Italy, Parco Nazionale Gran Paradiso. Similarly, it reintroduced the bearded vulture and lynx in the 21st century, which had been extinguished, though the lynx remains rare.

title: Grisons


text:
Additional-member system

The additional-member system (AMS) is a mixed electoral system under which most representatives are elected in single-member districts (SMDs), and the other "additional members" are elected to make the seat distribution in the chamber more proportional to the way votes are cast for party lists. It is distinct from parallel voting (also known as the supplementary member system) in that the "additional member" seats are awarded to parties taking into account seats won in SMDs (referred to as compensation or "top-up"), which is not done under parallel voting (a non-compensatory method).

AMS is generally categorised as a semi-proportional electoral system, distinct from pure mixed-member proportional representation (MMP). In practice, the way that proportional additional-member systems work depends on the number of additional ("top-up") seats and the votes cast in a specific election.

This article focuses primarily on semi-proportional implementations of AMS, like the ones used in the UK. AMS is used to elect the Scottish Parliament, and the London Assembly. In Scotland list members ("top-up" seats) are elected by region; in London there is a single London-wide pooling of list votes.

AMS was previously used to elect the Senedd, but was replaced by a closed list system by the Senedd Cymru (Members and Elections) Act 2024.

How AMS works
In an election using the additional member system, each voter usually casts two votes: a vote for a candidate standing in their local constituency (with or without an affiliated party), and a vote for a party list standing in a wider region made up of multiple constituencies (or a single nationwide constituency).

Voters are not required to vote for the same party in the constituency and regional votes. If a voter votes for different parties at the constituency and regional levels this is referred to as split-ticket voting. In the regional vote, the voter votes for a specific party, but has no control over which candidates from the party are elected. On the other hand, in the constituency vote, the voter votes for a specific candidate rather than a party.

The main variation was the 1993 Italian electoral law for the Senate, later abolished in 2005. In that case, voters could cast only a single vote, while regional party lists were automatically created with the losers in the FPTP races. That system could be described as a mixed single vote.

Calculation of votes
The first vote is used to elect a member from their constituency under the first past the post (FPTP) system (i.e. in the constituency, the candidate with the most votes takes the seat).

The second vote is used to determine how many additional seats a party may get. Parties receive additional seats to match the voting percentages which they received, making the legislature more representative of voters' preferences.

In the model of AMS used in the United Kingdom, the regional seats are divided using a D'Hondt method. However, the number of seats already won in the local constituencies is taken into account in the calculations for the list seats, and the first average taken in account for each party follows the number of FPTP seats won. For example, if a party won 5 constituency seats, then the first D'Hondt divisor taken for that party would be 6 (5 seats + 1), not 1. In South Korea, which uses the largest remainder method, constituency seats are taken into account by subtracting the number of constituency seats that the party won from the number of seats initially won by the party proportionally, with the result then being divided by 2.

Example
In a 100 seat assembly 70 members are elected in single-member constituencies. Because the system generally favours the largest party and those parties/candidate that are strong in a particular region, the total result of the FPTP elections can be very disproportional. In this example, the party with a plurality in the popular vote (party A) won a majority of all seats (54), while the second largest party (B) only won 11 districts. One of the two smaller parties (party C) won no districts, despite having 13% support nationwide, but a smaller (regional) party with only 3% nationally did get 5 of their candidates elected, as their voters were concentrated in those constituencies. In the example, additional seats are assigned on a nationwide level. Parties A and D are already overrepresented, so they are not entitled to additional seats. Parties B and C receive top-up seats, as there are only 30, this is not enough to make the results proportional.

Compared to similar systems
If the 30 additional seats in the example were allocated independently by list-PR the system would be called parallel voting or a supplementary vote system. This would be a mixed-member majoritarian system, under which even party A received additional seats, even though it is overrepresented even without getting any.

Mixed-member proportional systems, like the ones used for electing the national parliaments of Germany and New Zealand, compensate for overhang seats as well, by adding seats to the assembly if needed. In the most basic implementation, like that used in New Zealand (and until 2013, also in Germany), only the parties with a seat deficit are given the additional seats, and only to compensate for their deficit, which is not a perfect correction for the disproportionality. An implementation with leveling seats, like the one used in Germany from 2013, adds even more additional seats (called leveling seats) to the assembly to ensure full proportionality.

In this example, the assembly size is increased by 13 to compensate for parties B and C's seat deficits under the basic implementation, and by 65 (which allows parties A, B and C to receive more seats) under the leveling seats implementation.

The additional member system sometimes provides proportional representation (when there are no overhang seats that would need to be compensated), in which case it the same as MMP, if the results of the FPTP elections were completely proportional (which is almost never the case in reality). If decoy-lists and tactical voting are used (see below) the results under AMS would be the same as under parallel voting.

In all other cases AMS is more proportional than parallel voting, but less proportional than MMP.

Threshold
As in many systems containing or based upon party-list representation, in order to be eligible for list seats in some AMS models, a party must earn at least a certain percentage of the total party vote, or no candidates will be elected from the party list. Candidates having won a constituency will still have won their seat. In almost all elections in the UK there are no thresholds except the "effective threshold" inherent in the regional structure. However the elections for the London Assembly have a threshold of 5% which has at times denied seats to the Christian Peoples Alliance (in the 2000 election), the British National Party, Respect – The Unity Coalition (both in the 2004 election), and the Women's Equality Party (in the 2016 election).

AMS vs. MMP
AMS is used by some as another term to mean mixed-member proportional representation (MMP), but as the term additional member system is used here, AMS is unlike some MMP systems because it does not compensate for the disproportionate results caused by a leading party taking so many district seats that the fixed number of top-up seats cannot compensate. Such is the case where the leading party takes overhang seats and the legislature has a fixed number of seats. In some MMP systems, leveling seats (extra additional members) are filled in such a way as to ensure parties have proportional representation, but not in AMS as the term is used here.

Due to the problem of district contests electing too many members for leading parties (overhang), the AMS systems discussed here, instead of producing fully proportional results, often produce only semi-proportional representation. However, even semi-proportional representation is a considered by some a great advance on a electoral system that uses only the first-past-the-post voting system, where the number of seats a party takes only vaguely reflects the number of votes that party receives.

The term additional member system, as introduced by the Hansard Society, has been confused in the literature with the term mixed member proportional representation (in the broader sense) coined by New Zealand's Royal Commission on the Electoral System (1984–1986).

Ways to make the UK elections using AMS more proportional are discussed below. Also discussed are ways for voters to cast votes for individual candidate and not just for parties. The MMP systems used in Bavaria and elsewhere in Germany are discussed below for comparison.

Variations of AMS
The Arbuthnott Commission recommended that Scotland change to a model where the voter can vote for a specific regional candidate as well (called an open list), but this has not been implemented. A similar system is used in Bavaria, where the second vote is not simply for the party but for one of the candidates on the party's regional list and both votes count for party and candidates so that every vote counts twice (Bavaria uses seven regions for this purpose). In Baden-Württemberg there are no lists; they use the "best near-winner" method (Zweitmandat) in a four-region model, where the regional members are the local candidates of the under-represented party in that region who received the most votes in their local constituency without being elected in it, but this model has not been copied in the United Kingdom.

To produce more proportional results without increasing the number of seats in the chamber, reforms might include changing the way district members are elected. If STV or SNTV is used, the district elections are likely to be more proportional than if districts seats are filled through First past the post, and thus the available top-up seats could be used to produce more proportional overall chamber composition.

Decoy lists
So-called "decoy lists" are a trick to unhinge the compensation mechanisms contained into the proportional part of the AMS, so to de facto establish a parallel voting system.

For instance in the 2001 Italian general election, where a system in many respects similar to AMS was used, one of the two main coalitions (the House of Freedoms coalition, which opposed the scorporo system) linked many of their constituency candidates to a decoy list (liste civetta) in the proportional parts, under the name Abolizione Scorporo. As a defensive move, the other coalition, Olive Tree, felt obliged to do the same, under the name Paese Nuovo. The constituency seats won by each coalition would not reduce the number of proportional seats they received. Between them, the two decoy lists won 360 of the 475 constituency seats, more than half of the total of 630 seats available, despite winning a combined total of less than 0.2% of the national proportional part of the vote. In the case of Forza Italia (part of the House of Freedoms), the tactic was so successful that it did not have enough candidates in the proportional part to receive as many seats as it in fact won, missing out on 12 seats.

Although a theoretical possibility, decoy lists are not used in Scotland, Wales, or most other places using AMS, where most voters vote for candidates from parties with long-standing names. In the run up to the 2007 Scottish election, the Labour party had considered not fielding list candidates in the Glasgow, West of Scotland, and Central Scotland regions, as their constituency strength in the previous two elections had resulted in no list MSPs; instead they proposed to support a list composed of Co-operative Party candidates. Before this the Co-operative party had chosen not to field candidates of its own but merely to endorse particular Labour candidates. However the Electoral Commission ruled that as membership of the Co-operative party is dependent on membership of the Labour party they could not be considered distinct legal entities.

In contrast, in the 2007 Welsh Assembly election, Forward Wales had its candidates (including sitting leader John Marek) stand as independents, to attempt to gain list seats they would not be entitled to if Forward Wales candidates were elected to constituencies in the given region. However the ruse failed: Marek lost his seat in Wrexham and Forward Wales failed to qualify for any top-up seats.

For the 2020 South Korean legislative election the electoral system was changed and a partial use of AMS was implemented. In response, there were two satellite parties that only ran in the proportional part, the Future Korea Party (controlled by the United Future Party) and the Platform Party (controlled by the Democratic Party of Korea). Both merged with the parent party after the election.

In the 2021 Scottish Parliament election, former SNP leader, Alex Salmond announced his leadership of the newly formed Alba Party, with the stated aim of winning list seats for pro-independence candidates. At the party's public launch, Salmond quoted polling suggesting the SNP would receive a million votes in the forthcoming election but win no regional seats. He said that having Alba candidates on the regional lists would end the "wasted votes", and the number of independence supporting MSPs could reach 90 or more.

Use
AMS is used in:

 * Unicameral nation/city elections in the United Kingdom:
 * Scotland: the Scottish Parliament
 * London: the London Assembly
 * Bicameral general elections in Bolivia:
 * the Chamber of Deputies (Lower house).
 * Unicameral general elections in South Korea (for some seats besides parallel voting):
 * the National Assembly, even if decoy lists largely change it into a de facto parallel voting system

It was used from 1953 to 2011 in Germany:

 * the Bundestag, if there are more overhang seats than proportional seats, these have been added to the legal size of the parliament

In 1976, the Hansard Society recommended that a mixed electoral system in a form different from the German be used for UK parliamentary elections, but instead of using closed party lists, it proposed that seats be filled by the "best runner-up" basis used by the German state of Baden-Württemberg, where the compensatory seats are filled by the party's defeated candidates who were the "best near-winner" in each of the state's four regions. It was the way that compensatory seats were allocated that made their report the origin of the additional member system, the term which the report also invented, which was then applied along with the much older "mixed system" by English-speaking writers on voting systems to West Germany's system and similar models until mixed member proportional (MMP) was invented for the adoption of the German system proposed for New Zealand in a royal commission report in 1986, which would explain why AMS and MMP have been used as synonyms. The system the Hansard Society proposed was eventually adopted but with closed lists instead of the "best runner-up" (popularly known in Britain as "best losers") provision for elections to the Scottish Parliament, Senedd and London Assembly, but not for that proposed for elections to the House of Commons.

This system was proposed by the Independent Commission in 1999, known as Alternative vote top-up (AV+). This would have involved the use of the Alternative Vote for electing members from single-member constituencies, and regional open party lists. However, contrary to the Labour Party's earlier manifesto promises, no referendum was held before the 2001 general election and the statement was not repeated.

The AMS system in use in the London Assembly would have been used for the other proposed regional assemblies of England, but after the overwhelming No vote in the 2004 North East England devolution referendum, the Government abolished all the regional assemblies in 2008-2010.

Scotland
The system implemented for the Scottish Parliament is known to make it more difficult for any one party to win an outright majority, compared to the first-past-the-post system used for general elections to the UK Parliament in Westminster. However, in 2011, the Scottish National Party won 69 seats, a majority of four.

In the first election for Scotland's new Parliament, the majority of voters surveyed misunderstood some key aspects of the difference there between the "first" (constituency) vote and the "second" (regional list) vote; indeed in some ways the understanding worsened in the second election.

The Arbuthnott Commission found references to first and second votes fuelled a misconception that the constituency vote should be a first preference and the regional vote a second one. That misconception was not helped by the Green Party's tactic of running only regional candidates and appealing for "second votes".

To deal with the misunderstanding between "first" and "second" votes, the ballot for the 2007 Scottish Parliament election was changed as recommended by the Arbuthnott Commission. The British government announced on 22 November 2006 that the two separate ballot papers used in the previous Scottish Parliament elections would be replaced for the elections in May 2007 by a single paper, with the left side listing the parties standing for election as regional MSPs and the right side the candidates standing as constituency MSPs.

title: Additional-member system