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If compound time signatures are the result of the following operation

comp. ts = simple ts x 3/2 (for ex. 6/8 = 2/4 x 3/2)

why 3/8 , that can be the result of 1/4 x 3/2 , is said to be simple rather than compound?

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    You seem to think time signatures are fractions. To an extent, they are, but they cannot be simply manipulated like a maths problem.
    – Tim
    May 20 '20 at 13:03
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The bottom number in time signatures refers to the kind of notes involved - 4 is equivalent to crotchets, 8 to quavers.

The top number refers to how many of those are contained within one bar.

So 3/4 means there are three crotchets per bar, and 3/8 means there are there quavers to a bar. Simple - it's simple time.

Compound times are so called because they can be, and often are, counted in two distinct ways. 6/8, for example, is, from the numbers, 6 quavers, but they're not counted in the same way as 6 quavers in 3/4 time.

6/8 can be thought of as two counts worth 3 quavers each. So instead of counting 123 456, it is often counted 1--2--. This makes it countable in two ways - compound.

6/4, 9/8, 12/8 are other similarly compound time signatures.

Back to 3/8. How could that be counted in more than one way? Only by counting one bar as just 1--. It could work if the piece was very quick, but generally, 3/8 is considered as simple time.

Warning - there are websites that state 3/8 is compound - on the premise that there's an 8 at the bottom! I think they are confusing. 6/8, 9/8 and 12/8 are, but 3/8 just happens to have the same '8' on the bottom. Not a lot to do with compound!

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  • To my mind, the difference between 3/4 and 3/8 is that the former is conducted in three and the latter is conducted in one. If a piece isn't fast enough to justify conducting one dotted-quarter-note beat per measure, why would it be written in 3/8?
    – supercat
    May 20 '20 at 19:38
  • @supercat - who knows? Whims of the composer? B.p.m. may help solve this. 3/4 works for me!
    – Tim
    May 20 '20 at 19:47
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Time signatures are not fractions nor can the be multiplied like fractions. They indicate two things: the number of beats per measure and what size note gets a single beat. Thus 3/8 indicates that measures are three beats long with an eighth note getting one beat. Historically, time signatures also carried some tempo and style information but that convention is not used nowdays.

A top number of 6 or 12 or 9 (or 16 or 24) and a few others indicates a compound signature. For example, a signature of 6/8 represents a measure with 6 eighth notes conventionally grouped in threes. It's almost like two measures of 3/8; in 6/8, there is a secondary accent on the 4th eighth note; in 3/8, the beginnings are accented equally (except for the tendency to group measures in to chunks but that's another story.)

Musical notation has developed historically (rather than being recreated every few years like programming languages). There are conventions. A waltz is commonly written in 3/4 time but could be written in 3/8 (or 3/2). Rags and tangos were often written in 2/4 but with a eighth note pulse (though some composers preferred to write in 4/4 which I find easier to read.)

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The term "compound time signature" typically refers to a time signature which has some number of dotted quarter notes per measure; the duration of each dotted quarter beat three eighth-note beats. So a 6/8 time signature would be two dotted quarter beats, each consisting of three eighth-note beats.

In 3/8 time, the act of multiplying the three eighth notes per beat by one beat per measure might not be seen as a real "multiplication", and thus some would argue that 3/8 isn't a compound time signature. I would argue the opposite: the notion of a time signature where the dotted quarter is a beat is more useful than the notion of a time signature which has two arbitrary nested subdivisions. If a piece of music that's in 6/8 has an occasional 3/8 measure or run thereof, the 3/8 measure should be only be conducted as three discrete beats if the 6/8 measures were conducted as six discrete beats. If the 6/8 bars were conducted in two (as is more common) the 3/8 bars should be conducted in one.

Note that there is nothing "weird" about the notion of conducting a 3/8 piece in one. The conductor simply flicks the baton once per measure. The pieces where that wouldn't make sense would typically be those which are slow enough that they may as well be written in 3/4, or those where a 3/8 measure serves to fill in an odd-length gap (e.g. if a piece of music is in 2/4, but one measure is an eighth-note shorter than usual, it may make more sense to regard that measure as having a full-length quarter note beat and a half-length eighth-note beat than to conduct in in three or one). In that situation, though, I wouldn't really say that the piece is ever really "in" 3/8 time. Instead, it's in 2/4 time but has an oddball-length measure.

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