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Hm, it's possible I'm misremembering something, but the thing I think of when I see the word "hemiola" is that thing you get at the end of courantes where two bars in 3/2 are phrased as if they are three bars of 2/2. I don't know if this is the correct meaning, an alternative meaning, or completely the wrong meaning, and the only music dictionary I've got to hand doesn't have the word in. Anybody know? --Camembert

My Oxford companion says: Hemiol aor hemiolia: superimposing two notes in the time of three -- Tarquin 12:51 24 May 2003 (UTC)

I just signed up for the free trial at to check up on this, and the Grove Concise Dictionary came back with "In early music theory, the ratio 3:2. In the modern metrical system it denotes the articulation of two bars in triple metre as if they were three bars in duple. It is often used in Baroque dances such as the courante and the sarabande, generally just before a cadence; it also appears in the Viennese waltz." It seems in any case that it's limited to the ratio 3:2 - would it be fair to say that the business about 5 against 4 doesn't belong here? --Camembert

Yup. But where does it go? And how do you feel about making PNG files hsowing how "cold cup of tea" works? -- Tarquin 13:03 24 May 2003 (UTC)

I suppose I'd call 5 against 4 a "cross rhythm", although whether anybody else would, I admit I don't know. Perhaps it would fit in polyrhythm? I'm not sure - I think I know what "polyrhythm" means when applied to African music and that sort of thing, but whether it can be extended to Liszt or whoever, I'm not sure. As for the other: I'd love to make a PNG to show how "cold cup of tea" works, but I must admit I'm at a bit of a loss as to how it does work! It's a new one on me (my teacher always thumped rhythmic patterns into us by repetition, we couldn't afford mnemonics, we were down the pit until nine oclock, slept on a cold concrete floor etc). If you can explain what "cold cup of tea" is about, I'd be happy to make a PNG for it. --Camembert

Actually, I think you were maybe right first time. I was thinking about the example in my Oxford Companion. It shows music in 6/8, with two dotted crotchets vs 3 crotchets. ie, no triplets involved. Does this mean triplet-against-quavers is NOT a hemiola (because it breaks the metre), or maybe they gave this example because it's simple to write? Confused, anyway. What software package do you use for music PNGs? I have an ancient Finale and Cakewalk, but neither anti-aliases so they both looks REALLY ugly. But I could send you a cakewalk file or a PNG of it to show you how it works. -- Tarquin 14:46 24 May 2003 (UTC)

The way I'm understanding from the term now, I think triplet quavers versus straight quavers would still count because they're still in the ratio 3:2 - however, this seems to be a fairly rare (but not non-existent) usage. I'm really not sure though - before today I'd only known it as specifically relating to two bars in triple time phrased as three bars in duple, which is completely different because they happen at different points in time, if you see what I mean. I'll see what Grove has to say on the matter the next time I get the chance, if I remember. For PNGs, I use Sibelius - there's a free version at which doesn't let you save anything, but which is probably good enough if you're prepared to take a screen grab and export it to a graphics programme. If you want to dump your png in my sandbox then I'll see what can be done with it. --Camembert

I have here the piano album of Dave Brubeck's Miro Reflections. In the notes, he explains the timing in "It's a Raggy Waltz". The actual lenghts of the quavers does not change, but their melodic grouping puts them in threes. This is in 3/4, so the groups end up crossing bar lines. He says this shifting of accents is "hemiola" (and above, I was thinking of this, but remembering it incorrectly -- sorry), and refers to the Harvard Dict. of Music. -- Tarquin 16:21 24 May 2003 (UTC)

I guess that would work because the groups of 3 quavers are working against the basic beat of 2 quavers. I think my local library has the Harvard Dictionary, so I'll see what it has to say on Monday. I'm going to leave the article until then though, because I've got pretty confused about it all, and want to check some more sources. --Camembert

Ok. I'll make the "cold cup of tea" stuff anyway, whever it ends up being :-) -- Tarquin 16:48 24 May 2003 (UTC) PS: you're in the UK, right? Bank holiday...

Another one? We've only just had Easter and May Day.... (not that I'm complaining, mind) --Camembert

Cold cup of tea:

Music cross-rhythm, cold cup of tea.PNG

Weather, though this is crummy because I made it with Finale. Sibelius refused to write the 4 as quavers, insisting on semiquavers. Grumble.... -- Tarquin 22:21 24 May 2003 (UTC)

Music cross-rhythm, what atrocious weather.PNG

Ah! I get it now! Now we just have to work out where to put them... (I just spent half an hour trying to get Sibelius to write quavers, because I was convinced there was a way, but I shouldn't have doubted you - I'm now convinced there isn't a way. However, I did make a version with quavers by erasing the second beam in graphics software. I'll upload it eventually (29th June, 2003 - finally uploaded it) --Camembert

The more I ponder this, the more I'm convince cross-rhythms (or whatever they're called) havie nothing to do with hemiola. Here's a snip from Mozzy's K332, with hemiola in the second two bars:

Mozart piano sonata K332 hemiola excerpt.PNG

That's just the sort of thing I was thinking of. I'm pretty convinced this is where the article's going as well, but I'll still check in Grove tomorrow before editing it just to be absolutely sure.
By the way, the Grove Concise Dictionary reckons "cross-rhythms" have more to do with syncopation than anything else - shifting the stress to off the beat (which, now I come to think of it, seems right to me as well). So I guess that's not what we're looking for with your cold cups of tea. Do you happen to know if there's a generic name for triplets, quadruplets, quintuplets and so on? That'd be a good place to put them (I can't think of such a name myself, tho). --Camembert

Well in maths they're n-tuples. Finale calls one of its tools the "Tuple" tool, though Finale is the worst piece of software ever written by monkeys. But the cold cup of tea is combined cross-rhythms that don't match. The plot thickens.... Still, at least we have a pic for this hemiola article now. I might try recording an OGG of me playing that bit -- what do you think? -- Tarquin 21:20 26 May 2003 (UTC)

Sounds great - go for it (you might perhaps continue a bar or two beyond the .png to show the return to 3/4 - then again, that might confuse things). I think I've heard references to tuples in music, but can't seem to find any evidence of this usage on the web (where I admit I've not looked very hard) or in any dictionaries, so maybe I dreamt it (I didn't pick it up from Finale, I've never used Finale (thank god, by the sound of it)). --Camembert

On second thoughts, MIDI might be simpler, since I downloaded one to make that PNG. I don't have a decent microphone, and those bass notes will probably overload and sound dreadful. -- Tarquin

Well, I got to Grove, and the page as it stands reflects what Grove says - hope it all makes sense. That just leaves the cold cups of tea: Grove says that "cross-rhythms" are where accents are shifted to the wrong place in the bar - it gives the example of breaking a bar in 4/4 down into groups of 3, 3 and 2 quavers (like those things in "Bulgarian rhythm" that Bartók wrote). I think that polyrhythm is probably the best place for the cold tea and bad weather - I wasn't sure if the word was properly applied to things on such a small scale (I was thinking polyrhythm would be, for example, parts in 3/4 time and 5/4 time going on at the same time) but Grove says it is "the superposition of different rhythms or metres..." (it goes on to to say that "cross-rhythm" is sometimes used as a synonym for polyrhythm, but that this isn't strictly speaking correct). So that looks like it - I certainly couldn't come up with a better name (there was no article on "tuple"). --Camembert

Great work on the article! I'll read through the notes in my Chopin and Schubert to see if the editors refer to tuples by name -- Tarquin 19:45 27 May 2003 (UTC)

According to the definition given above,

"In the modern metrical system it denotes the articulation of two bars in triple metre as if they were three bars in duple."

any example needs to have TWO bars in triple metre that sounds as if they are THREE bars in duple. The simplest way to do that is to connect the last beat of a 3/4 measure to the first beat of the next 3/4 measure. While I do not have verifiable sources for this, it seems to me that there are at least two ways to do this.

The first way would be the simple use of a tie between the two measures. The second way would be to have the secondary dominant on beats one and two of the first 3/4 measure, the dominant on beat three of the first 3/4 measure, the dominant seventh on beat one of the second 3/4 measure and the tonic on beats two and three of the second 3/4 measure.

However, that having been written, the only use of the term that I have heard in the past 40 years has been to describe alternating measures of 6/8 and 3/4.

JimCubb 04:59, 5 October 2007 (UTC)

West Side Story's "America"[edit]

Now, I'm not completely sure if this is relevent since I'm not completely sure that I understand the concept of the hemiola, but America has a dual time signature, every other measure is 6/8. There is a pattern- 6/8, 3/4, 6/8, 3/4, 6/8, 3/4, etc. So based on that, I don't think it classifies.

Please, Wikipedia:Sign your posts on talk pages. Thanks.
It is the classic example, as "Maria" is for the tritone. Hyacinth 21:11, 17 Mar 2005 (UTC)
Seems to me simply like a more detailed way of notating what for all intents and purposes is still a hemiola. 17th century courantes might have been written like that, if people then were as pedantic about notation as we are today. EldKatt (Talk) 16:37, 12 April 2006 (UTC)

"Hemiola and mixed metres should not be confused", eh? I think that clarity and pedantry should not be confused. It seems to me that the comments about West Side Story NOT being a hemiola were written by somebody with their knickers in a knot about a particular issue, and are hence not great encyclopaedic writing. NcLean

There's only a very small difference between America's mixed meter and a true instance of hemiola. True, it is a mixed meter, because it alternates in time signature between 6/8 and 3/4, but that's purely a notation issue*. If it had been written in 3/8, then it would indeed be a hemiola: (here, I'll just put the words, use | as a barline, and - as a note lengthifier (for crotchets))

I want to | be in a | me - ri | - ca - |

So the difference is trivial.

  • It is more than an arbitrary decision, though. It wouldn't really be appropriate to write is as a hemiola, because in the context of classical music, hemiolas were used rarely, ie only at cadence points, whereas America uses swaps every bar. 00:51, 14 July 2006 (UTC)
    • I wouldn't agree with this generalization. I've seen courants where hemiolas almost outnumber the "regular" bars. We're not talking about a regularized mixed meter with hemiolas precisely every other bar, but it is in some cases used to a great extent in classical music as well. Still, I wouldn't mind dropping America from this page altogether, only because it would be so easy to find lots and lots of examples of hemiolas in cases where everyone would agree on what to call them. EldKatt (Talk) 09:55, 15 July 2006 (UTC)

I agree with NcLean. Written time signatures should not be the definitive answer as to whether something is a hemiola or not. Especially considering that the accented notes in the left hand of the example spells out the exact same rhythm (albeit much more slowly). I might also add that common usage among professional classical musicians today is to refer ro any regrouping of 6 notes as a hemiola. AndrewT 01:16, 14 July 2006 (UTC)

The Grove Online "hemiola" article specifically cites Bernstein's (and Sondheim's) "America" as an example of hemiola. Paul Creston in his Principles of Rhythm says that a piece with alternate measures in 6/8 and 3/4 is not a multimeter (his term for what I think we've been calling "mixed meter" here) piece and shouldn't be notated as what someone above called a "dual meter". TheScotch (talk) 08:36, 21 December 2007 (UTC)
Well, since we have a citation saying it is a hemiola, and none saying it is not, I think the article needs to be changed. I'll try to be a bit generous. — trlkly 03:27, 20 April 2010 (UTC) [Modified. See next section]

Removal of counter-sourced section[edit]

Actually, I just went ahead and nuked the whole section. The pedantry is not only not sourced, but it takes the POV that the other definition is merely an amateur affectation. Both the definition and assertion need to be cited to warrant inclusion.

Here's the section I removed, after trying to rewrite as NPOV and failing:

Musicians' common speech has extended the definition of "hemiola" to include any occasion of a "three-against-two" metrical feel[citation needed] — including some mixed meters and polyrhythms — contrary to the word's original meaning. For example, "America" from Leonard Bernstein's West Side Story is often said to contain good examples of hemiola. However, many [who?] argue that, while "America" does alternate between 6/8 time and 3/4 time, this is not strictly hemiola. They [who?] define hemiola specifically as the regrouping of notes in simple triple meter into groups of two beats rather than three.
[[Image:Polyrhythm.png|thumb|350px|center|Polyrhythm: Triplets over duplets in all four beats<ref name="Fingertips">Slenczynska (1976). ''Music At Your Fingertips: Advice For The Artist And Amateur On Playing The Piano'', p.43. ISBN 0-306-80034-9.</ref> ({{audio|Polyrhythm.mid|Play}})]]
Likewise, three-against-two polyrhythms are not hemiola[citation needed], since 1) they may or may not occur over two bars of triple meter, and 2) in hemiola, the triple-meter feel is altogether absent from the two bars in 2010

Also, the reference in the unlinked image needs to either be in the work if that's where it's copied from (and thus may not be CCA as claimed) or moved to the article. I don't think it says anything about hemiolas, however.

trlkly 03:59, 20 April 2010 (UTC)

Composer examples[edit]

I feel somewhat uncomfortable with this sentence from the article:

Composers of classical music who have used the device particularly extensively include Arcangelo Corelli, George Frideric Handel and Johannes Brahms.

Hemiolas are so frequent (at least during some periods) that it feels rather misleading to point out individual composers. Sure, Corelli used it a lot, but so did a vast amount of his contemporaries. (For starters, just about everybody who has written a courant, and that's a lot of people.) And just about all of those guys probably used it more than Händel and Brahms (I don't really associate their respective styles with hemiolas). I decided to suppress my urge to delete it until I get at least one second opinion. EldKatt (Talk) 16:41, 12 April 2006 (UTC)

In fact, Brahms used hemiolas a lot (3 against 2 is not necessary for a hemiola which mostly refers to something suggesting a 3/4 rhythm within a 6/8 context, as I understand it. Handel used the device mostly in cadences as I recall but Brahms used it in many other instances.) and one of our old music school jokes was that "Brahms died of hemiola!" (I guess this is neither here nor there but thought I'd put my 4 tildas in.)Ed (talk) 14:21, 15 June 2016 (UTC)

Bad examples? Maybe not[edit]

Neither of the two excerpts here appears to me to be true hemiola at all, much less a good, clear example of it.

In the Mozart, only bar 64 looks like even a candidate, and it'd be a stretch to call it hemiola when it's so similar to the rhythm in the first two bars. [EDIT: I see it now that I actually read the accompanying text. My bad. SFT | Talk] And I don't know what in the world someone was thinking with the Des Prez. Yes, it has a couple of places where one voice holds while the other moves, then the other holds while the one moves, but um, that's not three-against-two.

I'll try to come up with some better examples when I'm back in front of my computer that has Finale.

(Oh, and incidentally -- if Finale is so Godforsaken, why could you get it to notate your example correctly but not Sibelius? 8) ) SFT | Talk 19:41, 28 May 2006 (UTC)

Seeing the Desprez example makes me think I'm missing something, and this alone makes me hesitate about removing it right away. It's beyond me how hemiolas can exist at all in duple metre, but perhaps there's something I don't understand. EldKatt (Talk) 09:35, 29 May 2006 (UTC)
I almost think the same, and am tempted to give it benefit of the doubt. But as the example is unmistakeably weird and unclear --- regardless of its correctness --- I think the burden of proof is on the folks who want the example included. So I'm nuking it for now. SFT | Talk 05:05, 1 June 2006 (UTC)

Eroica Symphony[edit]

Perhaps a good example of Hemiola is the Eroica symphony. I'll get a file. --Stratford15 00:21, 14 January 2007 (UTC) It seems to me that I can't upload in bitmap, TIFF or EPS.--Stratford15 00:37, 14 January 2007 (UTC)

I just heard Professor Greenberg in The Teaching Company lecture on Beethoven's Third (1st movement) do an excellent analysis of it. Which is why I landed here.

The last sentence on this article seems to contradict the information above it. Does it belong there?

-- (talk) 13:31, 7 November 2008 (UTC)

"Shine On You Crazy Diamond"?[edit]

Is there a hemiola effect in Pink Floyd's "Shine On You Crazy Diamond"? I'm thinking of Part VI, the first part of the second half. One bass guitar plays a high part in a 6/8 rhythm (ONE-and-two-AND-three-and), while a second bass guitar plays the same note two octaves lower like so: ONE TWO (rest). In fact, this second bass actually comes in first (the only instrument, amidst wind effects), so the listener is tricked into thinking a 4/4 beat will emerge. I'm not describing it well, and I sure don't know how to make an image of the sheet music, but hopefully somebody else knows what I'm talking about. -- 17:10, 19 April 2007 (UTC)

References and Citations[edit]

Were I more adept at editing this article would be filled with "citation needed" tags and tagged for its complete lack of references. The Talk Page has incomplete references and a mention of a source but they need to be put in the article.

JimCubb 04:25, 5 October 2007 (UTC)

What needs to be cited and why? Hyacinth (talk) 03:02, 5 March 2010 (UTC)

Since I wrote that some references have been added and, since you put in a citation needed tag, I copied it and put in a few places I feel need citations such as the basic definition and the expansion of the definition. JimCubb (talk) 01:58, 9 March 2010 (UTC)

List page?[edit]

I for one would love to see a "list of" page for this page.

That is, a "List of works using hemiola" page. Or at least a "List of works significantly using hemiola" page

Similar to the page List of musical works in unusual time signatures.

If such a page is made, you can include as one entry the song "I'll Believe in Anything" by Wolf Parade which you can listen to at . That song uses hemiola throughout. —Preceding unsigned comment added by (talk) 13:21, 22 September 2009

As with "List of works in unusual time signatures" criteria would have to be created or selected. For example, how would one verify hemiola use in a work? Would one one need to cite a written source describing its use, as many listings on the "unusual time signatures" list do? Would one be able to cite a passage in a score, as some listings on the "unusual time signatures" list do, and if so how would one settle disputes such as "Is this a true hemiola (3X2 feeling) or just a triplet (3 in isolation)"? See the discussion and archived discussion at Talk:List of musical works in unusual time signatures and also see Wikipedia:Verifiability. Hyacinth (talk) 07:54, 1 April 2010 (UTC)

the use of hemiola in European and African musics[edit]

HEMIOLA "This rhythmic devise consists of superimposing two notes in the time of three or three notes in the time of two."-Oxford Dictionary of Music (1994: 398).

The example shows two quarter-notes over three quarter-notes in 3/4 time. In European art music this tends to be a momentary devise used to contrast the prevailing meter. In traditional African music it is regular and systemic, in other words, the basis for the entire rhythmic matrix. The page on "African Hemiola Style" is therefore incorrect. The page on "Polyrhythm" is pretty sloppy too. I would like to correct these pages. --Dr clave (talk) 02:22, 1 April 2010 (UTC)

See Wikipedia:Stub and Wikipedia:Manual of Style (music). Hyacinth (talk) 07:40, 1 April 2010 (UTC)

Merger proposal[edit]

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section.

It has been proposed that African hemiola style be merged into this article. Hyacinth (talk) 07:46, 1 April 2010 (UTC)

  • Merge tag has been there since 2008. Time to just do it. Mostly duplication. -- P 1 9 9 • TALK 16:21, 15 March 2011 (UTC)

The above discussion is closed. Please do not modify it. Subsequent comments should be made in a new section.

Additional citations[edit]

Why, what, where, and how does this article need additional citations for verification? Hyacinth (talk) 20:21, 27 August 2011 (UTC)

Tag removed. Hyacinth (talk) 04:47, 4 February 2012 (UTC)

Harmony section[edit]

I believe this section goes into more detail than necessary for this article. Kepler's and Helmholtz's "imperfect fifths" will be better presented at Perfect fifth. Extended discussion of just intonation vs. equal temperament is more than this article needs. I believe a brief mention, with hyperlinks, will be enough.

There seems to be some confusion about the meaning of "perfect" in this context. My understanding is that it has nothing to do with temperament or intonation, but simply means that the musical interval of a fifth is neither major nor minor.

While I am somewhat familiar with the use of "hemiola" to describe rhythmic patterns, this is the first time I have seen it used to refer to a pitch ratio. How common is that usage, compared to the rhythmic sense of the word? __ Just plain Bill (talk) 18:29, 3 February 2012 (UTC)

I just finished adding a fairly lengthy discussion about this, over on Talk:Perfect_fifth#hemiola.—Jerome Kohl (talk) 20:27, 3 February 2012 (UTC)

hi Just plain Bill, The New Harvard Dictionary of Music (1986: 376) states first that hemiola is: "The ratio 3:2." The second thing it states is: "In terms of pitch, it is the ratio of the lengths of two strings, three-to-two (3:2), that together sound a perfect fifth." Thirdly, the dictionary defines the meaning of the term in regards to rhythm. I think in common usage, hemiola is used mainly as a rhythmic term, but the fact that The New Harvard Dictionary of Music first defines it in regards to pitch is significant. It is also noteworthy that the New Harvard Dictionary of Music defines hemiola as a perfect fifth.

Concerning rhythm, there is disagreement about the terms hemiola and sequialtera among the various dictionaries and other scholarly sources. I addressed this rather clumsily in the article, but will attempt to straighten that issue out today.

hi Jerome Kohl, I'm going to go over to the perfect fifth page and read the discussion. Thanks.Dr clave (talk) 22:25, 3 February 2012 (UTC)

Citation needed?[edit]

  • Many people can hear the slight deviation from the just perfect fifth when they play the equal-tempered interval on a piano.

The above statement was tagged with "{{Citation needed|date=February 2012}}<!--Perfectly true, but the threshold for inclusion on Wikipedia is verifiability, not truth.-->". If true, why would it specifically need a citation? Hyacinth (talk) 02:02, 4 February 2012 (UTC)

OK if I just edit it slightly, to read "No one can hear the slight deviation from …"?—Jerome Kohl (talk) 02:07, 4 February 2012 (UTC)
We could edit the introduction to read:
    • In music, hemiola is the ratio 3:2.{{fact}} The word hemiola derives from the Greek adjective ἡμιόλιος - hemiolios,{{fact}} meaning "one and a half".{{fact}} This term was used in a music-theoretic context by Aristoxenus.[1] (The noun ἡμιολία - hemiolia "one and a half (fem.)" was also used by the Greeks to refer to a galley powered by one and a half banks of oars.{{fact}}) The equivalent Latin term is sesquialtera.{{fact}}
and edit the rest of the article similarly. (I would prefer we didn't.) My question is why you chose this one sentence. Hyacinth (talk) 04:44, 4 February 2012 (UTC)
First of all, the article lede should only summarise what exists in the article. Inline citations (and calls for them) are therefore inappropriate in that section. In spite of this, one inline citation (to the Thesaurus Musicae Grecae) already establishes two of the hypothetical points you offer as candidates for {{fact}} tags. As to your question: I tagged it because (1) the inexpert reader cannot be expected to take your word or mine that anyone or everyone can hear the difference, (2) "many people" and the nature of "hearing the difference" is vague beyond belief (is this a rare capability, or a common one?), but I thought adding a {{vague}} tag in addition would be overkill, and the {{Citation needed}} tag and editorial comment would be sufficient. My remark "Perfectly true" is my opinion. I did not say "everyone knows this is perfectly true, just as everyone knows the sky is blue, not pink". It is in fact a very small deviation, and most people cannot hear the difference, even under the most favourable circumstances, for example, direct succession of simultaneously played just and equal-tempered fifths on the same base pitch. Play a clipped staccato melodic succession in the piano's low register: B descending to E, then ascending to A and ascending again to E, where one of the fifths is equal tempered and the other is justly intoned, and I doubt whether even a highly trained musician with absolute pitch could tell the difference. Or does this mean what it says: play first B, and then F a fifth higher, and "many people" can "hear the deviation from a just fifth", even if they have never heard a just fifth before? This is insupportable, and the reader deserves better guidance, such as a citation to a good textbook where a thorough discussion of these matters can be found. I'm sorry to say I do not have such a source to offer at the moment, but I will certainly try to find one.—Jerome Kohl (talk) 07:46, 4 February 2012 (UTC)
Elegant solution to this situation, Hyacinth. Thank you.—Jerome Kohl (talk) 04:09, 5 February 2012 (UTC)

Three dictionaries[edit]

Assumption is being made, based on comparing three dictionaries. Drawing a conclusion from this data is improper synthesis and original research. If the misspelled word "sequialtera" was actually sought, it is no wonder it was not found.--Thanks for your assist. I will removed the improper synthesis and original researchDr clave (talk) 05:10, 4 February 2012 (UTC)


  • The term "hemiola" could also be applied to patterns that are repeated, outside of the agogic stress of the written meter, creating either a temporary feeling of a meter change or one meter over another. This could be a 5-quarter-note ostinato, in a common-time piece, or any compound meter superimposed over a even one.[citation needed] See: Meter (music)#Polymeter.

The above was removed as uncited for quite a while. Hyacinth (talk) 00:45, 5 February 2012 (UTC)