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Using John Varney's rhythm wheel to differentiate 3/4 and 6/8 time signatures (megan-vo.github.io)
95 points by mathisonian 7 months ago | hide | past | web | favorite | 89 comments

Bug: rapid calls to 3/4 get parsed as 6/8

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.

My understanding is rudimentary compared to yours, but I learned (perhaps incorrectly) long ago that for 3/4 time (waltz time) you can count:

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.

That’s a common thing to hear when trying to follow the steps for a waltz (counting out RIGHT left right LEFT right left can only be correct for one partner at a time).

I don't think genre literacy counts as a workaround: I think it's really the definition of what is or is not 6/8. The 6/8 time wheel gives a heavy bass drum on the four count. I don't notice such a thing in the waltz every other measure.

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.

> The 6/8 time wheel gives a heavy bass drum on the four count. I don't notice such a thing in the waltz every other measure.

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).

I just stick with 4/4 and do two lines of melody every three measures.

While being a marching band nerd, we always thought of 3/8 as 6/8 for the simple fact that one is always the left foot. Counting in 3/8 would alternate one to be on the right every other measure. It's hard enough to get new members to march to the right beat, but having 3/8 time was just never going to work even for experienced members

I'm a pretty non-musical person, and time signatures have always confused me. Unfortunately, this explanation left me just as confused. I can hear the difference between the two sample beats but I cannot figure out how to generalize this to other time signatures beyond the 3/4 and 6/8 described here.

The full time signature is arbitrary, and partially related to how the notes are written. It's wrong to put too much weight on "6/8" vs "3/4" per se. There are conventions that have developed in western music as to which time signature matches which natural beat pattern, but there's nothing _inherent_ in the time signatures that's important.

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.

One of my favorite songs for helping to explain the importance and differences between time signatures is "Question!" by System of a Down (https://www.youtube.com/watch?v=ENBv2i88g6Y). The intro is 9/8 (as a 3-2-2-2 grouping), followed by a section in 5/4. The verses are the same 9/8, except for regular jumps to 6/8 (during the phrase "Are you dreaming?"). The chorus is 6/4, with repeats of the same 5/4 section from the intro. The bridge is a mash-up of the 5/4 again with jumps between 9/8 and 3/4 and the outro is 4/4 back to a final 9/8 section.

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.

Can you explain what the difference between /4 and /8 are? like for example, what is the difference between 9/8 and 9/4? I've made something up that has an 11 time signature, 2-3-3-3(or 3-3-2-3), but how do I know if it's 11/8 or 11/4?

It only indicates which note symbol is the beat unit. /4 means that each quarter note gets the beat, while /8 means that each eighth note gets the beat. 3/4 means there are 3 quarter notes of time, while 6/8 means there are 6 eighth notes of time. This might help: https://en.wikipedia.org/wiki/Note_value

You don't. However, in general faster tempo has a lower denominator (in classical music at least, and more rarely in jazz).

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.

Time signatures are about writing and reading music. A beat being in 3 or 6 is independent from the time signature, which is whatever the transcriber thought best (you can always count a song in 6 in 3.) A piece in 4 might have pervasive use of triplets, so it would make it more readable to notate in 12/8 rather than 4/4, but there is no triplet-pervasiveness threshold for when to prefer one over the other. Likewise, it would be foolish to have the stress in a waltz occur on the 1st and 4th, then 3rd, then 2nd beat of the bar (this happens if you notate one in 4), but any enterprising composer would be able to thwart any rules you cared to come up with to codify that without much effort.

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 can always count a song in 6 in 3.

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).

As someone who casually plays the guitar and piano and understands the basics of time signatures, your explanation left me more confused and almost forgot what I already know. You seem like a very knowledgeable person, but don't seem to realize that what is common knowledge to you is meaningless technical jargon to everyone else.

That’s fair, but my assumption was that someone reading my reply would also have read the others, and I didn’t want to repeat what has already been said.

It's not a math thing. It's more about feel than counting.

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):


> 6/8 is skiddledeediddledee - often used in folk and/or ethnic music. It's a much lighter, more skittery feel.

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".

> with a foot stomp on the ONE

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.

The term "foot stomp" is just referring to what's actually called a downbeat: https://en.wikipedia.org/wiki/Beat_(music)#Downbeat_and_upbe...

It's a bit strange, but here's the rule: if you can divide the time signature by 3/2 (and not get 1 anywhere), it's the same as the result, but in triplets.

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.

You may be confused. I've spent 9 years in a music school, and whenever there was an exercise to tell the measure by listening to the music I've always been confused how others manage to discern 3/4 from 6/8. Or 2/2 vs 4/4 for that matter. However, I've got the hang of it in the latter years. Point being, this is something that just requires some bigger time commitment to learn.

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.

Beyond the basic principle of noting "beats per measure" and "note size of a beat", it's really just convention when it comes to the meter (the accent pattern). You learn the common mapping, but there are definitely exceptions.

May or may not be helpful, but the way I learned it:

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.


Not quite. It is correct to say that the numerator is the count and the denominator is what is counted. So 3/4 is 3 quarter notes, and 6/8 is 6 eighth notes. However which notes get the beat is a bit more fuzzy. 6/8 is usually but not always two beats per measure, with three eighths per beat (counted 1-tee-ta 2-tee-ta)

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.

"... two beats per measure, with three eighths per beat (counted 1-tee-ta 2-tee-ta)"

I've never heard this. I've only ever heard it as "1 2 3 4 5 6"

or 1 and a 2 and a..

The denominator is not as important as the numerator. (The Wikipedia page on time signatures makes that clear)

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.

The denominator is not important at all, though there seems to be a convention of keeping the rhythm fraction around 1, so 6/8 instead of 6/4, but say, 5/4 instead of 5/8.

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.

You're not the only one in the comments on this article who has asserted that some pieces in 6/8 have a different pattern of stresses. So I'm totally prepared to hear about it, even if basic music theory doesn't cover those cases.

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.

Additionally, when you are listening to music the denominator has no meaning. You can hear how many beats to the bar (the numerator) but the way that it is notated (quarter note gets the beat or eighth note) is just a matter of how it is written.

If you really want to confuse yourself, try figuring out the time signature for Kiss By A Rose by Seal.


I'm would call that 6/8, no question. It's slow enough that the accompaniment often subdivides into 16ths, giving the immediate impression of each measure divided into two 3/4 bars. But listen to underlying drum beat, and it clearly repeats every 6 beats, so I'm comfortable calling it 6/8.

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.

Waltzes are usually notated in 3/4, and the measures usually come in pairs, which fits nicely with a rotary waltz doing a complete turn in 2 measures.

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.

It's a waltz. Normally waltzes are notated in 3/4.

Why do you say it's a waltz? The intended audience is clearly not ballroom dancers.

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.

For what it's worth, it's quite easy to dance a waltz to the song. It's got enough of an oom pa pa that a waltz is very natural.

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.

I have no idea what the intent of the artist is, but it's worth noting that the overwhelming majority of rock music is in ballad meter, not 3. So this is extremely unusual music for the audience this artist usually plays for.

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.

Well, my whole argument was that while it superficially "feels like" a waltz in some ways, it's clearly in 6/8 because of how the underlying beat is grouped. That's what matters.

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).







The overwhelming majority of waltzes are notated in 3/4 with the measures in pairs, because it takes 2 measures (6 dance steps) to do one rotation of a rotary waltz. The two downbeats are equal. The music video on YouTube of Seal performing this song has equal downbeats.

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.

It certainly has the feel of a waltz. It's not that hard to make a 6/8 time signature not sound like a waltz (as you say, just hide the second down beat, or move it). But it's very very easy to waltz to the song.

Whether it makes more sense to musicians write it 6/8 or not, I have no idea, but it's still a waltz.

There is no difference between 3/4 and 6/8 unless you are trying to decide on which one makes your score easier to read. It's just different ways of conceptualizing the phrase. Mathematically (and therefore rhythmically) they are the same, of course. Maybe the site is trying to make some other differentiation but it didn't work at all in Firefox.

(Source: I am a professional drummer)

This is not the case.

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

> ONE two three | ONE two three

This phrase also has two significant beats. There's just a barline in the middle. See my point?

In an effort not to be snarky, my point is that rhythm is fractal and these are essentially just two different levels of magnification. You're absolutely right that there are conventions and implications in how they are written, but the thing about conventions (let's use a software term: "best practices") is that people's opinions on what they are tend to be heterogeneous. As a jazz musician, to me the denominator is not important, as it only represents the level of magnification. The important part is that the piece is in (some multiple of) 3.

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!

I agree with you, probably 100% at the end of the day. But I don't agree with your first post that seemed to tell readers that there was no distinction.

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.

> 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".

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.

So we do agree. You're saying nothing new to me, but you're showing that we share understanding in the end.

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.

That's an argument that 3/4 is the same as 6/4, not an argument that 3/4 is the same as 6/8.

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.

The point is that when someone directly compares 6/8 and 3/4, the implication is that the tactus (the place you feel the primary beat) is supposed to be different.

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.

6/8 doesn't need 2 (or any static number of) significant beats. As long as there are really 6 rhythmic atoms before the pattern repeats, it deserves a 6/x.

The easiest way that happens is lcm(2,3).

It's called convention. By convention (not by anything about the notation itself), 6/8 is used for compound time with 2 significant beats.

You're confusing cause and effect. If you have compound time with 2 significant beats, you should see 6/8. If you see 6/8, it does not imply there are 2 significant beats.

> If you have compound time with 2 significant beats, you should see 6/8.

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.

6/8 does imply 2 strong beats (at least in western classical music tradition).

As a musician, the reactions to almost every post on hacker news involving music ends up both cracking me up and serving as a healthy reminder of the arrogance and hubris around here. In all my time I've never met another musician/composer who tried to convince me that there is some kind of fundamental rythmic difference between 2/3 and 6/8 time, yet here we have scores of people who are fighting for the idea as if it were part of their identity or something... At least it's a healthy reminder that the eloquence and apparent confidence with which a statement is delivered really isn't indicative of it's truthfulness at all haha...

thank you from the depths of my musician heart.

In a non-Archer sense of the word, how do percussionists think of phrasing? As a non-percussionist/string player, a phrase was a great place to take a breath for us regular humans that can't circular breath. The basic definition I was always given was 8 bars. That was always worked well for me. As a DJ, the 8 bars would tell me the percussionist is due for a cymbal crash ;-). I always got a chuckle when I'd get a piece of music where the composer would add a breath mark for the woods/brass players. Funny thing that breathing concept.

Depending on the context, you might actually want to "stagger-breathe" to avoid breathing right on the phrase boundary. You generally don't want the breaths to be noticeable, especially if it's in the middle of a long sustained note. Instead, you'd take a breath on one measure mid-phrase, another player would take a breath in the next measure or so, etc. to keep the note going. When I marched in a drum and bugle corps, we'd actually all have individually preassigned breath marks.

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.

Well this gets subjective almost immediately, but in a general sense, not closely related to one instrument, I think of phrases as the music within the length of time (la dee da dee dum), as opposed to the length of time itself (1234, 1234). I wouldn't play a cymbal crash at the end of 8 bars if the musical climax didn't happen until the end of bar 9. The barlines aren't as important as the music sitting around them.

You may be a professional drummer, but you are of some sort of mindset that has you in denial of the concept of convention. You also certainly feel rhythm but do not intellectually understand it.

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 | (1) 2 3


(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.

They have different hierarchies. In typical 3/4, the first beat of each measure is given equal weight. In typical 6/8, the first beat is given a bit more weight than the fourth beat.

Same reason why we treat 2/4 and 4/4 differently.

Who's we?

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.

Perhaps you work in an idiom that has no connection to the conventions of the notation system…?

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.

2/4 v. 4/4 is more about the number of quarter notes (beats) per measure (2 v. 4, respectively).

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 whole point of the original post and of the lesson describing 3/4 vs 6/8 was not to compare those two notations that indeed are effectively interchangeable.

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.

You write, I'm not sure why, as if you are an imposing genius addressing someone with grave intellectual disabilities. It's unfathomable to me by what process you decided our drummer friend is in denial of, has no intellectual understanding of, the bleeding obvious. What you say is mostly the exceedingly basic needlessly expressed in a long-winded way. But perhaps I don't 'intellectually understand' it either.

> addressing someone with grave intellectual disabilities.

Well, I did say I was a drummer!

Haha! I originally in fact had the sentence "Drummer jokes are just jokes!" but edited it out. (disclosure: musician/composer)

I was not intending to come across condescendingly, but I'll totally accept guilt for being not careful enough in that regard.

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.

> You may be a professional drummer, but you are of some sort of mindset that has you in denial of the concept of convention.

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??

Apparently, there was mostly miscommunication and the two of us probably agree entirely at the end of the day. The ad hominem aspects of my post weren't warranted really, and I don't care to explain why I fell into it in this case. I didn't mean to be snarky or violent or anything.

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.

Hm, not sure I like the example for 6/8 time. It's so much slower tempo than 3/4 time example that it's very hard to compare the two for me.

Agreed. The differences are much clearer at equal BPM (or even equal measures per minute).

It would have been nice with a negative example, e.g being able to play the 6/8th on top of the 3/4th piece, in a suitable tempo.

A lot of work into visualization and media on that page. Impressive.

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.

Site doesn’t work for shit on mobile.

Works fine for me on Firefox for Android (surprisingly, since a lot of these sorts of things tend to only work on Chrome). You just have to tap the things instead of hovering over them.

Side note: If you're on Chrome and you check the JS console, you'll see that the audio for this page will stop working in October when Chrome reinstates the ill-considered audio policy they rolled out in May and then removed because it broke a bunch of sites.

The audio policy in question:


HN discussion when the policy was instated/removed:


The way I understood it was that 3/4 is used to notate waltzes and other music where you are supposed to "feel" all three beats per bar, and 6/8 is used to notate music where you only "feel" the downbeats. Things like swung rhythms. Though (again as I understand it) actual swing music is often notated in common or cut time, but played as though the first eighth note of each beat is about twice as long as the second.

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.

I think a lot of the confusion/misunderstanding around here has to do with how folks are defining "beat"; seems like folks are defining the "beat" to be each eighth-note, when (in my experience) it's actually each quarter note, whether plain (for 3/4) or dotted (for 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.

Site's trying to imply that any slower 2/4 rhythm subdivided into triplets can be re-written as 6/8, whereas 3/4 does not have more rhythmic subdivisions in the three beats.

When I think of 6/8 time, I think of triplets as well. Not saying triplets don't play out in standard 4/4, but I remember thinking about how many triplets were going to be in the music whenever we were handed new music in 6/8 time. I just assumed it was me making that assumption rather than it being an actual thing.

I wish I could use that to better understand the beat of Pink Floyd hit "Money" that was composed in 7 / 8 ...

If that hurts your brain, try counting https://www.youtube.com/watch?v=tKDXe0FP2wc.

Oh now I see.

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)

More like 6/4 = 2×(3/8) but 3/8 is not a scalar because it also carries division and subdivision information, and × is a new operator that is barely similar to multiplication.


A time signature N/B is actually a tuple...:

    (division-of-N, subdivision-of-N, B)
...with units:

    (beats/measure, base_notes/beat, base_notes/whole_note)
...where division-of-N and subdivision-of-N are inferred from N (see explanation at [0] and table at [1]).

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)
...where X is a unitless scalar.


      2×(3/8) =
    = 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]
    = 6/4


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.

[0] https://www.musictheory.net/lessons/15


    - 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
Notice how N=3 and N=6 share the same base_notes/measure hence the confusion.

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