1. Take the 3/4 example and convince yourself you fully understand the difference between 3/4 time and 6/8 time.
2. Let your ostensible understanding lead you to listen to a waltz.
3. Get familiar enough with the waltz that you can sing along with the melody.
4. Now ask yourself: does the melody sound like it divide up into groups of measures, or is the melody just freely moving around in no discernible pattern?
5. Realize very quickly that the melody divides up into groups of measures.
6. Realize that the melody very likely divides up into groups of two measures to build larger phrases.
7. Realize that many waltzes move at a rapid tempo so that each measure of 3/4 moves by quite quickly.
8. Realize that regularly recurring fast 3/4 measures which divide up perceptually into two-measure groups sounds exactly like... 6/8.
This bug affects all CPUs.
The only currently known workarounds are genre literacy and knowledge of notational convention.
ONE two three TWO two three ONE two three TWO two three
and that indeed sounds more similar to the article's 6/8 example than its 3/4 example.
I'm more familiar with 4/4 time due to the genres I know well, but it's a similar thing there. I used to think that the 1 and the 2 beats were indistinguishable - you can start off by one and it still repeats with period 4. But now I can reliably pick up the difference, generally by listening to where the bass drum lands versus the high hat. However I'm not as good at telling the 1 and 3 counts apart or the first measure in a phrase from the second. These are just more subtle conventions on longer scale.
6/8 and all time signatures are just notations, just ways to encode information about the song. There's a correct answer but yes, it depends upon conventions. You can call it 1/1 time if you want, but it's not going to help you play your part or dance along if the conductor tells you that.
Here's 6/8 beat hierarchy:
Beat 1: Strongest
Beat 2: Weak
Beat 3: Weak
Beat 4: Strong
Beat 5: Weak
Beat 6: Weak
The first beat of the measure is the strongest. Beat 4 is strong but typically not as strong as the first beat.
Now here is the 3/4 beat hierarchy for many types of pieces that are in 3/4 time:
Measure 1 Beat 1: Strongest
Measure 1 Beat 2: Weak
Measure 1 Beat 3: Weak
Measure 2 Beat 1: Strong
Measure 2 Beat 2: Weak
Measure 2 Beat 3: Weak
The first beat of the measure 1 is the strongest. Beat 1 of measure 2 is strong but typically not as strong as the first beat of measure 1. These two measure groups typically continue for the entire piece, as in a waltz.
The two are functionally equivalent in terms of rhythm.
It's confusing because there are three variables: the number of beats in a measure (top of the fraction), which duration gets the beat (bottom of the fraction), and the tempo (how long each beat lasts).
Instead, I find it useful to think about combinations and layers of twos and threes. So the different being talked about in this article is about whether the beat pattern is more of three groups of two, or two groups of three. Convention has mapped those, typically, to 3/4 and 6/8 respectively, but again that's entirely arbitrary.
Likewise 9/8 time is usually three groups of three. 4/4 is two groups of two (though the second two often have slightly less emphasis, whereas 2/4 time is just single groupings of two). 7/8 is a group of three and two groups of two (could be 2-2-3, or 3-2-2, or 2-3-2). 5/4 or 5/8 is a group of two and a group of three.
But ultimately time signatures are just a convenient way to hint at the beat pattern expected, and to give a framework in which to write the musical notation. The actual _music_ is not so easily transcribed.
It's not always easy to pick out what specific signature is being played at every point in the song, but the "suspended" feeling of hanging beats as the signature changes is very obvious.
For example, a 2/2 tempo with 100 BPM is easier to "manage" than a 4/4 tempo with 200 BPM, and they are the same as each 2/2 beat corresponds to two 4/4 beats. So a "Presto" or "Prestissimo" will often be written as 2/2, with half the BPM that it would have in 4/4. Likewise, a 6/4 is usually faster than a 6/8 or 12/8.
So: the time signature just describes how many times to count within a bar/measure, and what subdivision (that corresponds to a certain notation) you are counting. For communicating to another musician the rhythm of a song you'd just drop the subdivision part, because it's only relevant to notation.
You would lose something by doing so; when a song is written in 6 it's because (unless someone is playing silly buggers) it has some kind of 1-2 pattern. For a lot of songs in 6, if you want to count something smaller you're better off counting it in 2s (with some level of triplet-pervasiveness).
3/4 is ONE two three, with a foot stomp on the ONE. It's a dance beat - STOMP skip skip.
4/4 is so common it appears in a lot of variations, from the bass drum beat of EDM to all the different rock and pop variations. The usual - not infallible, but strongly suggestive - tell is how often the chords change. Failing which, there's often a unique rhythm marker at the starter of each bar.
6/8 is skiddledeediddledee - often used in folk and/or ethnic music. It's a much lighter, more skittery feel.
You can generalise the /8 time sigs to 9/8 and 12/8, although they're more rare. They're often used to signify something exotic, alien, ethnic, or maybe a bit spiritual.
Like this, which you've probably heard, and is in 12/8 when it eventually gets going. The clue is in the phrase length:
Exotic sigs like 5/4 and 7/4 are much less standardised, so they're open to interpretation. You can play 5/4 as 2+3 or 3+2 or 4+1. Or just as 5.
Likewise 7/4 (listen to the snare):
There are two common forms of 6/8 (jigs) at least in the kinds of traditional music I'm used to: single jigs and double jigs. A double jig is "skiddledeediddledee" as you said, like the song "99 bottles of beer on the wall", while a single jig is more like "humpty dumpty".
How can you talk about feet stomping when that's not part of the music? Two people could chose to stomp their feet on different beats or on more or fewer beats.
So 6/8 is a variant of 2/4, with 2 main beats in the bar. 3/4 has 3 beats to a bar.
Or in quavers, 6/8 is Da du du Da du du, whilst 3/4 is Da du Da du Da du.
Basically you try to hear what groups of notes are "played as one". You also hear how the accents are distributed among the notes. It's easier to get the hang of it if you have to actually adhere to it when playing an instrument.
numerator = beats per measure
denominator = which note "gets the beat"
3/4 time has 3 beats per measure, where quarter (1/4) notes get the beat.
6/8 time has 6 beats per measure, where eighth notes get the beat.
That gets to the concept of simple and compound meter. In simple meter the the beat gets divided in two and in compound the beat gets divided in three. (Complex is a mix, like 7/8 may be divided 1-and 2-and 3-tee-ta).
Ultimately, the beat can be more interpretive. The 2nd movement of Beethoven’s 9th symphony is in (mostly) 3/4 but it is so fast, no conductor beats it in three, they beat in in one.
I've never heard this. I've only ever heard it as "1 2 3 4 5 6"
One thing about 6/8 that is not literally communicated by the notation is the rhythm: the first and fourth beats of the bar are stressed. But not equally, because that would be indistinguishable from 3/8.
And 6/8 says nothing about the beat structure within the 6 beats. You're stating the most common occurrence, but that's not the definition of 6/8.
The point stands that time signatures are not rational numbers (as you acknowledge, the unit of the denumerator can be scaled) so 3/4 and 6/8 aren't part of some equivalence class. They have different meanings which are only sustained by the presence of a cyclical pattern of stressed notes. So if there's some music theory you can link to which elaborates on all the possible different rhythmic patterns of 6/8 vs 3/4, that would provide examples of the distinction we both agree exists.
I might almost call it 6/4, which wouldn't exactly be wrong (as long as you double all your note values when notating). But that's conventionally reserved for unusual beat groupings like 4/4 + 2/4.
6/4 is extremely common when notating Renaissance music, btw. Although the originals are often in 6/2. Or lack bar lines, so they're X/2.
You might argue that anything in "waltz time" is a waltz, but then your argument becomes circular. You would be saying it's a waltz because it's in 3/4 time and it's in 3/4 time because it's a waltz.
Possibly it makes more sense to musicians to notate it as 6/8 because the triples come in pairs. It's still a waltz though, and dancers' instinct will be to break it into triples. It's not hard to scramble a 6/8 signature to make it not a waltz (don't put downbeats every three, and it isn't a waltz) but that song definitely doesn't do that.
For this piece, I think it's a waltz because it's in 3/4, at a typical waltz tempo, and it "feels like" a waltz, which is to say that the emphasis on the beats and their precise timing feels like waltz music usually does.
So no, I would not argue that anything in "waltz time" is a waltz.
Just as a sanity check, I decided to look up some sheet music and see how others have interpreted the song. Every single one that I can find notates it in 6/8 (interestingly with some individual measures in 9/8).
If you write it in 6/8 instead, many musicians will emphasize 4 less than 1.
I think that dancers knowing music and musicians knowing dance is extremely useful. It changes your opinions about notation.
Whether it makes more sense to musicians write it 6/8 or not, I have no idea, but it's still a waltz.
(Source: I am a professional drummer)
While some inexperienced composers/arrangers/scorers may transcribe 3/4 pieces in 6/8 to make the score look better, it is a fundamentally incorrect thing to do.
3/4 has one significant beat per bar: ONE two three | ONE two three
- Think any waltz you've ever heard.
6/8 has two siginficant beats per bar: ONE two three Four five six | ONE to three Four five six
- Think Follow the Yellow Brick Road from the Wizard of Oz, or We Are the Champions by Queen.
The second down beat has less significance than the first. In this way 6/8 is like 2/4, except in triple form, not duple form. Pieces in 6/8 do not (and generally should not) feel the same as pieces written in 3/4.
The only thing 3/4 and 6/8 share is the number of note-lengths that fit into a bar, which has no bearing on the feel, sound or rhythm of a piece.
Sources: https://www.musictheory.net/lessons/15 , https://www.reddit.com/r/musictheory/comments/36fn1g/i_still... , and own experience
This phrase also has two significant beats. There's just a barline in the middle. See my point?
I would argue that We Are The Champions is actually a 12/8 groove (conceptually triplets in 4/4). And we would both be right!
The convention is that these two time signatures stand-in for two different actual perceptually different music feelings.
The "tactus" (the place we feel the beat) certainly can be subjectively moved to different levels in the hierarchy. Furthermore, you're right that the bottom number is basically just a notation preference (6/8 and 6/16 are effectively identical, though nobody uses the latter).
But the whole point of anyone describing the difference between 6/8 and 3/4 is that they are using the convention to describe the actual feel difference between dividing the same amount of time into 2 vs 3, the hemiola issue.
I basically was taking issue with seeing a reply to a post that was highlighting this difference that is a real perceptual one (not just a notational one, but described, unfortunately, with focus on notation) with the claim "there is no difference".
I apologize for the aspects of my reply that were ad hominem instead of just critiquing the post itself.
It is impossible to quantify or intellectually stratify feelings and perceptions. All I have to say is "I feel it differently" and now your stratification is incomplete.
But you can say without a doubt that 3÷4 === 6÷8.
Of course I am aware of the conventional approach to playing 6/8 that results in this perception that beats 1 and 4 are not of exactly equal weight, and of all the different ways you can play two against three, three against four and so on. Polyrhythm doesn't stop at hemiola by the way. Are you also feeling five against three, seven against five, etc.?
I can show you examples of music in 6 where you may be unable to find the downbeat at all. So you can't say for certain how I or anybody else is going to hear it in every case. These prejudicial approaches to music cause closed ears.
The whole point is that when we communicate, we use (often mediocre) conventions.
3/4 and 6/8 are notational things with nothing but convention determining their meaning. But same with the entire notation system, it's just shapes with no meaning until we assign meaning to it.
The only really valid theory of music is one that embraces the subjective psychology of it (music cognition etc).
To say that music where one can't find the beat is "in 6" is already weird. It's only "in 6" if there's something about a 6-beat meter in the mind of some person, listener or performer. We can listen to something together and you can experience it in 6 while I experience it in 7, if we're capable of those different subjective interpretations (and the sound content will affect whether that's easier or harder).
The whole point is that while the prejudicial approaches to music are wrong (music is 100% subjective), the purpose of the original article (by my charitable interpretation) is to describe two different subjective experiences that are possible, hemiola being about the most basic introduction to such concepts for beginners.
So, I took your original "no difference" comment to be a denial of the existence of two distinct subjective experiences just because the notation can be seen (ignoring convention) to have no indication of the difference.
You can see how I could take your post that way. I think it's really valuable for anyone learning about music to understand these subjective experiences and their differences. We agree that it's crappy to assert that these subjective experiences are in the notation, but I was willing to see "6/8 vs 3/4" as a communication stand-in for the subjective difference that is real.
Surely, some people say "6/8 vs 3/4" and mean to assert some difference that is just not really there. And others use it to refer to the hemiola distinction of subjectively parsing an accent in these two ways. The former is a delusion, the latter is a valid insight.
P.S. In case you haven't seen it, one of the neatest rhythm things out there is http://bouncemetronome.com/ — it goes intro demostrating beautifully any level of polyrhythms, including offset ones evolving ones, rhythms that phase over time because of differently changing tempos, and a ludicriously long list of other things… a fun crazy tool to get anyone into stuff way beyond whatever conventional music system they may have learned otherwise. I doubt much of it would be entirely novel to you, but you may still appreciate it. The options are enormous, hard to find the limits.
If your phrases really go ONE two three FOUR five six then notate your piece as 3/8. 6/8 is for ONE two three Four five six SEVEN eight nine Ten eleven twelve, where beat four is significant, but not as significant as beat one.
Of course you do have patterns of bar phrases, not all first-beats-of-the-bar are equal in a larger piece, and where you draw the line between a bar and a phrase is ultimately a matter of taste and judgement. But a player will absolutely understand 6/8 and 3/4 differently; a run of quavers in 6/8 is ONE two three Four five six, a run of quavers in 3/4 is ONE two Three four Five six.
Of course you can take 3/4 music that happens to use a lot of two-bar structures and play it with the same feel as the same thing notated as 6/8.
But the point of comparing the two is not to highlight that case where the same music could be written either way. The point is to describe how if you take the same 6 8th-notes and give them a 3×2 feel, it's musically different from a 2×3 feel.
The easiest way that happens is lcm(2,3).
I assume you meant to write 'compound meter', in which case yes, absolutely.
> If you see 6/8, it does not imply there are 2 significant beats
It should. If it does not, then you'll be notating a lot of accented notes explicitly in the music to convey to the player exactly what beat formation is.
If these accents are regular, this is a waste/clutter of notation because it's clear you're actually writing a piece in a time other than 6/8. If the accents are irregular, then they are likely either indicating syncopation, or they are completely irregular in which case you're deliberately writing music with a feel that cannot be accurately described by a single time signature, and you should be changing time signatures through the piece as necessary to describe the beat to the player. (Or it cannot be nicely described by the notation in use).
Jacob Collier is an example of a musician who enjoys exploring this kind of music. See for example: https://youtu.be/b78NoobJNEo?t=14m40s onwards. He invented a new terminology for time signatures to accommodate his style of writing.
Of course, this only works well if you have multiple players per part. This ain't really practical outside of marching or symphonic/orchestral contexts.
Rhythm is a cognitive/perceptual/psychological process whereby we relate events to one another. It is not mere timing. When you impose in your mind a structure on a timing by giving extra attention to certain events, then you are experiencing rhythm. taDA and TAda are different rhythms even if the timing is the same and the sounds even are the same but you treat them as having those accent patterns (either at-will or through other things that draw your attention such as a their timing in relation to a meter that has gotten set in your mind or even visual cues as to which should be accented).
The 3/4 vs 6/8 distinction is a historic convention, not something in the math. By convention, 6/8 is divided into 2 sets of 3. And yes, these get fuzzy in various real-world concepts like the whole idea of hemiola which is the overlaying of these two meters.
(1) 2 3 (4) 5 6
are rhythmically identical. You're only conceptualizing them differently.
Anyway, thank you for taking the time to write this myopic and extremely condescending explanation of my area of study. I will be sure to return the favor someday.
Same reason why we treat 2/4 and 4/4 differently.
Your decision to give certain beats more or less emphasis is a subjective one. You can glean absolutely no information about a piece from the way the rhythm is subdivided, except maybe the intended tempo.
So, for example, lots of pop/rock music gets notated rather arbitrarily in practice because it's mostly about the feel from recordings anyway. It's common in that world to see what classical convention would call incorrect notation. And since the core notes all work still and you can go by the feel from the sound you know, it doesn't really matter.
But the classical conventions include ideas that the subjective accents you describe are in fact implied by certain time-signatures.
Similar deal with 3/4 v. 6/8. In 3/4, you have 3 beats per measure, subdivided into halves (duplets). In 6/8, you have 2 beats per measure, subdivided into thirds (triplets).
The point was to compare (1) & (2) & (3) & to the different accent pattern of (1) 2 3 (4) 5 6.
Anyway, even in the case where you are instead counting the 8ths of 6/8 with the same timing as the quarters of 3/4, the 3/4 more readily allows the possibility of odd-numbers of measures in phrases.
That's like how 2/4 and 4/4 are truly identical if the notes are the same (the same son in either time signature is unchanged), but only in 2/4 can you readily have 5-measure sections (i.e. 10 quarter notes) as phrases.
Anyway, there's obviously some miscommunication between us. I assume you actually would agree with everything I'm saying if we were discussing in person. But your original post here will read to many people here as making the claim that there's no distinction between:
3/4 A E C E C E (all 8ths)
6/8 A E C E C E (all 8ths)
whereas the whole point of the original article was to describe that these identical timings have different feel because of the different accent structure.
Well, I did say I was a drummer!
I was replying to:
> There is no difference between 3/4 and 6/8
Which is simply wrong. There's no difference in the number of 8th notes. And the same music can be written and felt when written as two bars of 3/4 with quarter notes versus one half-speed bar of 6/8. But that's a much more qualified point.
There is a distinction, and it's not in the notation itself but in what the notation means.
To say there's no difference is like saying present tense and past tense of "read" has no difference in pronunciation. Of course, the plain letters fail to capture the difference, and the difference can be confused at times, and is just a matter of convention. In the case of 3/4 and 6/8, they have a different accent structure, and thus a different musical feeling by convention, and discussing that difference was the only point of the article that this comment was relating to.
Huh, maybe you are violently agreeing with @nerflad? I read the parent comment to mean that convention is the only thing that matters.
> You also certainly feel rhythm but do not intellectually understand it.
Why the snark and personal attack? You have no idea what @nerflad understands intellectually. I’m always surprised when someone with your level of HN karma hasn’t learned to avoid insults and condescension in comments like yours. Are you threatened by the idea that there’s more that one right way to write a tempo?
> Rhythm is a cognitive/perceptual/psychological process whereby we relate events to one another.
I think that definition of rhythm is very bad. Rhythm can exist without a human perceiving it. Google dictionary’s definition sounds better: “a strong, regular, repeated pattern of movement or sound”. So does Wikipedia’s: “Rhythm (from Greek ῥυθμός, rhythmos, "any regular recurring motion, symmetry") generally means a "movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions". This general meaning of regular recurrence or pattern in time can apply to a wide variety of cyclical natural phenomena having a periodicity or frequency of anything from microseconds to several seconds (as with the riff in a rock music song); to several minutes or hours, or, at the most extreme, even over many years.”
So, in summary, the meaning of the word pretty much is mere timing. Your treatise on perceptual psychology is talking about something else.
> The 3/4 vs 6/8 distinction is a historic convention, not something in the math.
Isn’t that exactly what @nerflad was saying??
Anyway, the post I was replying to didn't say that the difference is due to convention, it asserted the difference didn't exist.
And I stand by my points about rhythm (which I think @nerflad would agree with in the end incidentally).
The "strong and weak" part from Wikipedia only exists in music in the mind of a person. It's not musically strong or weak based on physics of sound waves. Whether something is loud or quiet can be relevant to describing rhythm generically, but music is 100% subjective.
Human beings predictably experience certain musical things in certain ways, especially those from the same music cultures. But a full 100% of everything in music is only music when there are listeners (or just imaginers) having a subjective experience. Otherwise, there is no music. Pressure waves in air or dots on paper are not music.
I don't care what Google's dictionary says. Describing a trite, pithy one-sentence thing for a complex concept is necessarily going to be simplistic.
But a minor nit... I wish the publisher had done a more apples-to-apples comparison between 6/8 and 6/4.
3/4 is universally accepted to be a Waltz by composers and performers.
However, there's not much consensus in the 6 and 7 beat signatures whether the notes should be quarter or eighth notes.
The audio policy in question:
HN discussion when the policy was instated/removed:
Just to pick two of my favorite songs: per my understanding, the opening theme to Vision of Escaflowne would be notated in 3/4, while "Flagpole Sitta" by Harvey Danger might be notated in 6/8.
That is: 6/8 is approximated not by 3/4, but rather by a very-triplet-heavy 2/4.
The article explains this somewhat ("one and two and three and" v. "one and ah two and ah"), but the comparisons/examples don't really do a good job of demonstrating it in practice.
6/8, in typical musical theory fashion, is an awful name for something like (3/4)/2
It is technically precise and in practice misses the point completely.
(And don't get me started on mode names. Just don't)
A time signature N/B is actually a tuple...:
(division-of-N, subdivision-of-N, B)
(beats/measure, base_notes/beat, base_notes/whole_note)
E.g. 3/4 is actually a tuple:
(3 beats/measure, 2 base_notes/beat, 4 base_notes/whole_note).
The × operator works like...:
A × (N/B) =
= A × (D, S, B) =
= (A * 1 division, D * 1 subdivision/division, B / 2)
= 2×([division-of-N-3, subdivision-of-N-3, 8 base_notes/whole_note]) =
= 2×([3 beats/measure, 2 base_notes/beat, 8 base_notes/whole_note]) =
= [2 beats/measure, 3 base_notes/beat, 8 base_notes/whole_note / 2] =
= [2 beats/measure, 3 base_notes/beat, 4 base_notes/whole_note]
= [division-of-N-6, subdivision-of-N-6, 4 base_notes/whole_note]
_UNINTENTIONALLY BURIED THE LEDE, IT'S HERE_
But honestly this just works only with traditional time signatures which follow this neat table-simple-compound-duple-triple-quadruple nonsense; for other compound N like 5/4, 7/4 etc. it won't work.
E.g. 5/4 is either (2/4 + 3/4) or (3/4 + 2/4) depending on the song (can't think any of the former off the top of my head, but Mission:Impossible's theme and Take Five are representatives of the latter). It can even be (1/4 + 3/4 + 1/4).
Or, like Gorillaz's 5/4 which sounds like (2.5/4 + 2.5/4) (which I'd argue is actually not 5/4 but 10/8 and the guitar definitely sounds like it). Also the lyrics+drums are actually in 4/4 so it's just a polyrhythm and both rhythms synchronize every LCM(5, 4) = 20 beats (4 guitar bars, 5 lyrics+drums bars) and in fact the macro song structure changes every 20 beats instead of 16 like in traditional 4/4 so maybe it is 5/4... or 10/8. Or 4/4 with 5 measures per hypermeasure? Or both? Or neither?
It's all just implicit. It's on your ears. Listen for the subdivisions.
This IMHO is the right way to look at time signatures.
- N=2 simple duple - 2 beats/measure * 2 base_notes/beat = 4 base_notes/measure
- N=3 simple triple - 3 beats/measure * 2 base_notes/beat = 6 base_notes/measure
- N=4 simple quadruple - 4 beats/measure * 2 base_notes/beat = 8 base_notes/measure
- N=6 compound duple - 2 beats/measure * 3 base_notes/beat = 6 base_notes/measure
- N=9 compound triple - 3 beats/measure * 3 base_notes/beat = 9 base_notes/measure
- N=12 compound quadruple - 4 beats/measure * 3 base_notes/beat = 12 base_notes/measure