# What does "three on four, five on seven, etc" mean?

I kinda know they have something to do with polyrhythms, but most search results on google tell me the time signature 3/4 instead of more detail on what that phrase translates to in music..

Is 3 on 4 like playing 3 notes in a 4/4 piece? And does 4 on 3 mean you play 4 notes in for example 3/4? Forgive me for my lack of certainty, I just would appreciate some clarification if it's given to me :)

There seem to be two separate concepts being conflated in the question: "time signature" and "polyrhythm".

Time signature

In a time signature, the upper number denotes how beats are grouped. An upper number of 4 indicates a cycle of four beats; an upper number of 3 indicates a cycle of 3 beats.

The lower number designates the musical notation corresponding to a single beat. A lower note of 4 means the "quarter note" represents one beat; a lower note of 8 means the "eighth note" represents one beat.

So a time signature of 3/4 means that the musical will be made up of three-beat cycles, with the quarter-note representing a single beat. A time signature of 3/8 also indicates three-beat cycles, but with the eighth-note representing a single beat.

Polyrhythm

Polyrhythm is different. It means that there are two different beat groupings happening simultaneously but in the same amount of total time. A 3:4 polyrhythm would mean that three pulses and four pulses are happening simultaneously within the same total duration. A 5:7 polyrhythm would mean that simultaneous groupings of 5 and 7 beats occur within the same overall amount of time. That is, one grouping divides the total time equally into fifths while the second grouping divides the total time equally into sevenths.

I'm going to use the British note-duration names, because I think (certainly at times like this) they are less confusing. In 3 4 time the beat isn't a 'quarter' of anything; it's far easier to say "3 4 time is 3 crotchets per bar"

Here are some normal bars in 4 4 time:

``````X:1
M:4/4
L:1/4
K:C
C C C C | D D  D D | E E E  E ||
``````

Is 3 on 4 like playing 3 notes in a 4/4 piece?

Yes, it's exactly that:

``````X:1
K:C
M:4/4
L:1/4
%%staves {(RH) (LH)}
V:RH clef=treble
(3:2:3 C2 C2 C2 | (3:2:3 D2 D2 D2  | (3:2:3 E2E2E2 ||
V:LH clef=bass
C, C, C, C, | D, D,  D, D, | E, E, E,  E, ||
``````

Those treble clef notes are written as minims, but the `3` above is an instruction that they are 'out of time', and you have to look at the context to understand the total time they occupy. By convention, with triplets, the understood total duration is of two of the note-type contained.

And does 4 on 3 mean you play 4 notes in for example 3/4?

You've got it. Here are some normal bars in 3 4 time:

``````X:1
K:C
M:3/4
L:1/4
C C C | D D D | E E E ||
``````

And here is some "4 on 3" :

``````X:1
K:C
M:3/4
L:1/4
%%staves {(RH) (LH)}
V:RH clef=treble
(4:3:4CCCC | (4:3:4DDDD | (4:3:4EEEE  ||
V:LH clef=bass
C, C, C,  | D, D,  D,  | E, E, E,   ||
``````

Typically all such constructs are found only briefly in the middle of otherwise 'in time' music:

``````X:1
K:C
M:3/4
L:1/4
%%staves {(RH) (LH)}
V:RH clef=treble
CCC | (4:3:4DDDD | EEE  ||
V:LH clef=bass
C, C, C,  | D, D,  D,  | E, E, E,   ||
``````

but there's nothing to stop someone writing an entire piece like this:

``````X:1
K:C
M:4/4
L:1/4
%%staves {(RH) (LH)}
V:RH clef=treble
(5:4 CCCCC | (5:4 DDDDD | (5:4 EEEEE ||
V:LH clef=bass
C, C,C,C,   | D, D, D,D,   | E, E, E, E,  ||
``````