Question about cross-rhythm 3:4, 4:5, 4:7

[Juan Expósito]

Hello,
I´m trying to make a list of basic phrases for playing with snare, bass drum or whatever...against an ostinato or beat played with the other elements.
The list is done and used for many years but I have a question about the way they are named.

In this case, about these (Polyrhythm) cross-rhythmes examples. I understand them and can play them...
It´s about their names (3:4, 4:7 and 4:5)

What indicates exactly the numerator and the denomitator?
My doubt is created by this:
Why the first cross-rhythm is named 3:4, (denominator indicates the beats and the numerator indicates the number of notes played against it? (so the pulse is in the numerator)
and the other examples are the other way arround (4:5 means 5 notes (or groupings of them) played while 4 beats) (so the pulse is in the denominator, idem with 4:7)

Why is not 4:3, 5:4 and 7:4?
Which are the rules for that?
Or it doesn´t matter ?

I hope you understand my question.
This pictures are from Kenny Aronoff Power Workout 2, with that type of naming:

[Paul Marangoni]

I wouldn't call those polyrhythms in the truest sense. Those exercises are all in 4/4 with simple rhythmic figures (albeit, broken up and syncopated), and the rhythms are implying a polyrhythmic pulse. The first example is the equivalent of consecutive dotted eighth notes played over the bar line, and they "resolve" every three quarter notes, thus implying a four against three (or three bass drum quarter notes against four snare drum dotted eighths). It's the same idea for the following exercises.

To better understand and familiarize yourself with polyrhythms, I suggest picking up Gary Chaffee's book Rhythm and Meter Patterns.

[Rene]

Chaffee defines your first example as 4 over 3 .... not 3 :4

3 against 4 would mean a half note triplet played against 4 quarter notes.

The relative space between the notes is exactly the same... of course

My 2ct

[Juan Expósito]

I wouldn't call those polyrhythms in the truest sense. Those exercises are all in 4/4 with simple rhythmic figures (albeit, broken up and syncopated), and the rhythms are implying a polyrhythmic pulse. The first example is the equivalent of consecutive dotted eighth notes played over the bar line, and they "resolve" every three quarter notes, thus implying a four against three (or three bass drum quarter notes against four snare drum dotted eighths). It's the same idea for the following exercises.

To better understand and familiarize yourself with polyrhythms, I suggest picking up Gary Chaffee's book Rhythm and Meter Patterns.

Thanks folks, I understand the relationships of the two lines of every example showed (the two pulses beeing played of every example)
My question is the way of naming ... why 3:4 and not 4:3 in the first example?
Is it there a rule about what goes in the numerator an what goes in the denominator? (the pulse of the "song" or the figure beeing played against it)

When we say the signature is 12/8, 7/8, 4/4, 3/4... it´s plain clear about what the numerator and denominator means. The writting rules are clear.
I´m asking about those cross-rhythmes nomenclature.

Chaffee defines your first example as 4 over 3 .... not 3 :4
3 against 4 would mean a half note triplet played against 4 quarter notes.
The relative space between the notes is exactly the same... of course
My 2ct

The 4:3 way is more logical (as Chaffee´s book: the main pulse in the denominator and the "figure pattern" played in the numerator, as the 4:5 and 4:7)

[Paul Marangoni]

The ratio is usually placed immediately above the notes it applies to, and the first (leftmost) number merely indicates how many notes of that value are to be played in the space of the second (rightmost) number.

In the case of a simple triplet, we usually just write the number three over the three notes, but to be more explicit, it could be written as 3:2, to make it clear that you are to play 3 notes in the space of 2.

The examples you have attached are showing the relationship between TWO simultaneous rhythms on two sound sources. Those examples are to help people hear the relationship between two rhythms, and where they resolve. You would never use a ratio in the music notation to aid in reading that sort of thing.

[Juan Expósito]

So, in the first example I showed...Would it be ok to name it both ways. 4:3 or 3:4 ?

[Paul Marangoni]

None of those examples have any cases where you would notate a polyrhythmic ratio. They are just comparing two rhythms. When you write a ratio to indicate a polyrhythmic relationship, you would say "three OVER four" or "four OVER three".

The first example has the snare playing a beat every three sixteenth notes and the bass drum playing a beat every four sixteenth notes. It's just math, so the snare will end up matching the bass drum every four snare beats (or every three bass drum beats). What you decide to call it would depend on your point of view, but I wouldn't use a ratio. Three against four or four against three makes sense, but those exercises were created merely to help someone understand the relationship between different static pulses. This can help feel things like superimposed metric modulation.