I've always wondered how time signatures were thought of- I got the question because I noticed that well in terms of 'fractions', 3/4 is just half of 6/8. Does that apply to music when counting beats as well?
Actually, in terms of fractions, 3/4 is the same as 6/8. But time signatures are not fractions.
3/4 means each bar has 3 notes of 1/4 each. 6/8 means each bar has 6 notes of 1/8 each. And yes, the difference is in the way you count it: In 3/4 you count 1,2,3 and in 6/8 you count up to 6 and the notes are shorter.
The accents change as well; 6/8 is an even signature while 3/4 is odd; you usually emphasize the first beat of each measure in 3/4 while in 6/8 you could emphasize beats 1-3-5, or just 1 and 4 (which ends up feeling like triplets), or 2-4-6...
Time signatures look like fractions, but are not really. I grew up on crotchets and quavers, so I'll use those words, but the American/German number-names drop naturally out of the time signatures.
3/4 does not mean "3 divided by 4", it means 3 times 1/4, or 3 beats of a crotchet. So the piece is "in 3".
In all traditional notation (Beethoven, Mozart, et al) 6/8 is called compound time, and it means not "6 times 1/8", but 2 times 3/8, or 2 beats of a dotted crotchet (3/8 isn't quite the American name, but close enough). So the piece is "in 2", but with each beat ready divided into triplets, giving it a lilting quality.
Generally "compound time" means 3n/8, so 3/8, 6/8, 9/8, and 12/8 are the time signatures for 1, 2, 3, and 4 beats per bar. In principle 15/8 might occurs as compound time for a piece "in 5", though you have to be careful: the only piece I recall immediately in 15/8 is Scriabin's prelude op. 11 no. 14, but it is very clear from the note stems that this is not 5 times 3/8, but 3 times 5/8; the piece is marked Presto and each of the three beats is very fast duh-duh-duh-duh-duh.
They are very different.
In 3/4 you are playing in threes: [ONE two three] [ONE two three] [ONE two three].
In 6/8 you are playing twos [[ONE two three] [Four five six]] [[ONE two three] [Four five six]]
Hard to illustrate but in 6/8 the underlying pattern is 1-2-1-2-1-2 where the 1 occurs on the first quaver and the 2 on the fourth. If you were playing a big hand drum you could play 6/8 by just going
doom boom doom boom 1-2-3 4-5-6 1-2-3 4-5-6
When the music is a long string of eighth notes, 3/4 is 3 groups of 2; 6/8 is two groups of 3:
- 3/4: [e e] [e e] [e e]
- 6/8: [e e e] [e e e]
and the first note in each group is (usually) slightly accented relative to the others, and of course ,the first note of the measure is (usually) more strongly accented.
late to the party: Let me elaborate on my humorous comment, which was "I like to be in America; OK by me in America; everything free in America; for a small fee in America! (If that makes no sense, go look up the sheet music for West Side Story)"
This song maintains a steady eighth-note speed, but switches often between a 6/8 rhythm ("I like to be in A-") and 3/4 ("me-ri-ca") <- I boldfaced the lead beats there.
[3:21] You may have noticed that we have two meter signatures that seem to add up to the same thing math wise. 3-4 and 6-8 both dictate six eighth notes in a measure. 3-4 means three quarter notes in a measure, so six eighth notes. And 6-8 means six eighth notes in a measure. So why have two different meter signatures for the same number of notes in a measure?
It's because the implied different beats and different eighth note grouping.
By our definition of meter signatures, we know that one of these meter signatures suggest grouping eighth notes by three, namely 6-8. The measure with eighth notes group by twos is best shown with a meter signature of 3-4.
We feel different meter beats in 6-8 and 3-4. In 6-8 we're likely to feel one, two, three, four, five, six. In other words each beat contains three eighth notes, which equals a dotted quarter note.
So to complete our definition, 6-8 means there are six eighth notes in every measure. The eighth notes are grouped by threes, and the meter beat, the beat we tap along with, is likely to be the dotted quarter note. The traditional definition of 6-8, six beats in a measure and the eighth note gets the beat, is mostly not correct. It's not impossible, but it would mean that 6-8 was being played unnaturally slowly. In 6-8, the beat we’re most likely to move to is usually the dotted quarter note. [Bold mine]
@Joshua Siktar you are correct about 6/8 in its meaning that there are six 8th notes per measure, but I am going to attempt to explain why that alone is not nearly enough to describe what makes it different from 3/4.
If they were the same then it would just be a matter of preference for the writer but it's obviously a bit more than that. The timing of music is what creates a lot of the feel. Generally, in 4/4 time for instance: a steady string of 8th notes would be written out in four sets of two notes, and that is because the quarter note is the defining time keeper, representing one beat within the measure. Therefore, it takes the same amount of time to play two 8th notes as it does to play one quarter note. That's all looking at the notes on a more individual basis.
There are more to the notes that are played than just how long they carry out: sometimes they are accented, sometimes they're barely heard at all, there's staccato and everything else that adds character to the individual notes in relation to the other notes that are being played around it or along with it or whatever. Those are the characteristics that create the audible distinction between 4/4 and 3/4. So now for the 6/8: same concept really except the 8th notes are not being written out in pairs but rather as triplets. This means, roughly, that you should be playing three 8th notes in the same amount of time as it takes to play one quarter note instead of just two.
It may even help to visualize (haha with your ears though, not your eyes) a 4/4 signature with two regular 8th notes followed by a triplet of 8th notes:
BUM--buh Buh-buh-buh BUM--buh Buh-buh-buh...
(hyphens connect sounds within a single beat; spaces between the individual beats).
That would be a 4 beat count per measure...6/8 is based on the feel of the triplets vs. the feel of the doublet making it feel more like a 2 beat count per measure, but with more of a sense of movement or urgency...kind of higher energy. 3/4 uses the doublets with lead notes and accents, etc. distinguishing it from 4/4 and differing from 6/8 in that it lacks that extra note per beat making it more steady and relaxed in its rhythm (steady is probably not a good word to use for that description but hopefully you are understanding the difference now). It may sound more urgent than 4/4 because it's missing a beat (not literally, I say missing a beat because 4/4, I'm pretty sure, is the most common time signature).
It is hard to put all this in words really but I hope this helps to get an idea in your mind. I ought to shoot a video demonstrating the different signatures and post it on Youtube...
The fractional music notation is a bit misleading. In terms of what they actually mean, musically, 3/4 means each measure has three beats of one quarter note each. We could write it like this:
We may count it like "1 and 2 and 3 and", where the "and"s are the eighth notes in between.
6/8, on the other hand, means each measure has two beats of a dotted quarter note each (i.e. three 1/8 notes). We could write it like this:
We may count it like "1 la li 2 la li", where the "la"s and the "li"s are the eighth notes in between.
Seeing them written like this, you may instead wonder why anybody may think they're the same in the first place!
In a way six eighth beats equals three quarter beats (at the same tempo one measure in each time signature would take the same amount of time to play), but you must ask why a composer would choose one time signature over the other. It really depends on the composition of the measures. 6/8 literally means "six eighth notes" while 3/4 literally means "three quarter notes." Usually a score in 6/8 will be full of eighth notes and dotted quarter notes, while a score in 3/4 will primarily contain quarter notes, half notes, and dotted half notes. It really depends. For a score that uses a wide range of all the note types I listed, usually 3/4 will be chosen for simplicity, but conductors can certainly opt to conduct select measures in 6/8 if it helps their musicians follow the music more effectively--that is a judgment call on part of the conductor.
This same logic can be applied to other groups of time signatures with mathematically equivalent beats, namely:
2/2 and 4/4
3/2 and 6/4 and 12/8
2 measures of 3/8 vs. 1 measure of 6/8
There really isn't a difference. Its just notational protocol that make the music easier for the reader to interpret and conceptualize.
3/4 time designates that each measure gets 3 quarter note beats.
6/8 time designates that each measure gets 6 eighth note beats.
4/4 time designates that each measure gets 4 quarter note beats.
8/8 time designates that each measure gets 8 eighth note beats.
You can write a 4/4 time song in any other time signature so long as you pad the ending with rest notes. Its awkward as hell to do this in practice, but nothing stops you from writing a 3/4 time song in 4/4 time.
3/4: Do Re Mi | Do Re Mi | Do Re Mi | Fa Re Do
4/4: Do Re Mi Do(>)|Re Mi Do(>) Re| Mi Fa(>) Re Do
6/8: (1)Do- (3)Re- (5)Mi-| (1)Do- (3)Re- (5)Mi| ,,, etc
Time signatures are fractions. Its just the denominator isn't reducible.
If you want 8 apples, and you have 6, thats not the same as having 3 apples and wanting 4. The ratio of apples you have compared to your goal is the same, but that doesn't mean the fractions themselves are the same quantity. (the only reason why we think they are is because 5/6 of 1 and 10/12 of 1 both resolve to 1/1. In music 3/4 resolves to 4/4 and 6/8 revolves to 8/8 because we change the definition of a measure (in other words the definition of 1).
Time signatures changes the base of a measure (4/4 time is quadral based, 6/8 is octal base, 1/2 is binary base, 7/10 is decimal based, etc)