Why are waltz time and 6/8 time different, although they have the same beat values? Why is one a compound time signature, and the other is not? We'll try the answer these questions, as elementary as possible, with this article.
First of all, waltz time have the same meaning with 3/4 time, three quintets used per every bar. The reason why it's called a waltz time is that all waltz pieces and waltz dance style is set upon a certain time signature, 3/4. But when used as a jazz term, a jazz artist using waltz time generally have no intentions to make the piece sound more "waltzy".
On the other hand -by solid definition- 6/8 is a compound time signature which six quaver/eighth notes are used per every bar.
So far, in theory, 6/8 and waltz time seems to be the same, as one is another fancy way of writing the other. However, this is not true. Even though they have the same number of beats, the accented beats are quite different, and we'll see why! (This is why there are two such different time signatures, otherwise why would we bother writing more fancier!).
Imagine or search for a waltz dance, if you carefully look at the artists, you'll see that a waltz box is contained of three main movements, after three accents artists came back to the point where they started and they continue performing the 3-step movement again and again. So going back to theory, where we know waltz time uses 3/4 time the rhythm must have 3 three subdivisions every bar, so that a waltz movement can be completed properly. With this deduction, we've know reached the conclusion that 3/4 beat is composed of 3 subdivisions.
However, for our purposes, comparing two time signatures, what those subdivisions contain is not important. They may contain 1 quartet (DUN DUN DUN) or 2 quavers (DUN-da DUN-da DUN-da) or any other combination which each subdivisions adding up to 1 beat.
Consequently, when we look at a 6/8 time signature, it's called a compound time, where compound meter means each subdivision is divided into three equal beats. Having six quavers in our hand, only way to have three equal beats in a subdivision is to have only two subdivisions. So there it is! We only have 2 subdivision in 6/8 time signature, whereas we have three subdivisions in 3/4 time. Again, how subdivision are arranged is not important in our context, it might contain 3 quavers (DUN-da-da DUN-da-da), or any other combination adding up to a dotted quartet, one and a half beat.
Okay, number of subdivisions are different between to time signatures, so what?! Again, mathematically the analysis we made about both time signatures are completely gibberish, at the end of the day, they both add up to three complete beats, not less not more. However, subdivisions mean accents, and accents means rhythm, melody, basically lots of things in a single piece. Basically in music and especially jazz, which are more about feeling, emotion and "the swing" than any other thing, gives much value to rhythm, melody.
At the end of the day, we understand that there is a huge difference between a 3/4 and 6/8 time!
Here are two pieces one waltz time using and the other using 6/8 time. Have fun figuring out which one is which!
Three to Get Ready - The Dave Brubeck Quartet
All Blues - Miles Davis