
Using John Varney's rhythm wheel to differentiate 3/4 and 6/8 time signatures - mathisonian
https://megan-vo.github.io/basic-beats/
======
jancsika
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.

~~~
rhapsodic
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.

~~~
bdhess
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).

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dylan604
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

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aftbit
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.

~~~
glitcher
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.

etc...

~~~
abruzzi
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.

~~~
delinka
"... 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"

~~~
yesenadam
or _1 and a 2 and a.._

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nerflad
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)

~~~
quadrangle
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.

~~~
nerflad
(1) 2 3 | (1) 2 3

and

(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.

~~~
UncleMeat
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.

~~~
nerflad
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.

~~~
quadrangle
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.

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tgb
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.

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

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wodenokoto
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.

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matchagaucho
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.

------
monochromatic
Site doesn’t work for shit on mobile.

~~~
yellowapple
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.

------
fenomas
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:

[https://developers.google.com/web/updates/2017/09/autoplay-p...](https://developers.google.com/web/updates/2017/09/autoplay-
policy-changes#webaudio)

HN discussion when the policy was instated/removed:

[https://news.ycombinator.com/item?id=17079724](https://news.ycombinator.com/item?id=17079724)

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bitwize
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.

------
yellowapple
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.

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pishpash
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.

~~~
dylan604
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.

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

~~~
jlebar
If that hurts your brain, try counting
[https://www.youtube.com/watch?v=tKDXe0FP2wc](https://www.youtube.com/watch?v=tKDXe0FP2wc).

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raverbashing
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)

~~~
kaoD
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.

E.g.

    
    
          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

________

_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.

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

[1]

    
    
        - 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.

