Interpreting Irrational Rhythms

I never learned or figured out how to do it.

As here:

Is anybody really good at it and can teach mi

You just gotta feel it man.

Not good enough

I'm not entirely sure about this but if I had to tackle that first tuplet, I'd probably do something like this:

As far as I understand, a 7:5 would be a septuplet within a quintuplet so you would work out the lowest common multiple of 7 and 5 which is 35. Now, imagine the tuplet is split into 35 equal parts. Every 7 parts=1 quaver of the quintuplet. Every 5 parts=1 quaver of the septuplet that is contained within the quintuplet (the actual quaver that is notated on the page.) If you look at my drawing, you can see the 35 divisions in the middle with the quintuplet quavers underneath and the septuplet quavers above. Above the septuplet quavers, I've written out the first tuplet from your example.

Obviously this would be very time consuming and impractical and you would have to learn the tuplet very slowly as if it had 35 "beats", though I can imagine that over time you'd get an intuitive feel for the rhythm of a 7:5 or 5:4 or whatever and be able to get through it relatively quickly.

Like I said, I'm not 100% on this; that's just how I'd go about it. Common sense tells me there is a simpler way but I don't know what it is.

Not good enough

It is what it is.

Just approxifake it like everybody else.

Try some Ferneyhough

Mnemonics can be useful. Pass the goddamn butter for 3:4, cold cup o' tea for 2:3. I'm sure there are other ones out there, those are just the ones I've heard.

Polyrythmic subdivision is difficult, but you can do it if you multiply both tuplet numbers by each other and then dubdivide according to the number you got, in this case 35. Then you can see exactly where the beats line up. Gosh, I don't think I explained that well.

Really though, the composer doesn't expect you to play that exactly as it's written. It's pretty much just a written out rubato.

Really though, the composer doesn't expect you to play that exactly as it's written.

I hate you.

I hate you.

Come on, If the composer wants you to play that precisely as it's notated, I'll just go ahead and add him to my list of most nefarious villains along with Darth Vader and Sauron.

Vader is so misunderstood :(

Come on, If the composer wants you to play that precisely as it's notated, I'll just go ahead and add him to my list of most nefarious villains along with Darth Vader and Sauron.

Perhaps if you don't respect the composer enough to play his music as he wrote it you shouldn't be playing it in the first place.

Try some Ferneyhough

Opposite of helpful. I'm well aware of Ferneyhough's existence, also. Thanks

I listened to Ferndog's 6th String Quartet. All of a sudden, I am able to interpret 31:29. 

Lately, I've been approaching 'basic' irrational beat divisions in a certain way which has been of some help. What I do is subtract the 2nd number from the first and then put the remainder in a fraction as the numerator and the 2nd number in the original ratio as the denominator. For example: 4:3 would be 4-3=1 and then 1/3. I then add this fraction to every original division of the beat. This shows me how the original division fits into the irrational one (in this example, the old division is equivalent to 1 and 1/3 of the new beat division). Of course, something like 4:3 can be more easily 'felt', but this approach could be extended to more complex irrational divisions. The obvious weakness to this approach is that it's a bit imprecise: you would need to have a feeling for how much time the beat occupies since the new division would be more important for calculating specific durations. 

After working out rhythms in this way, it has made me wonder if using 'wrong' ratios (smaller #: larger #) would be more effective, since the original division would be remain prominent when calculating durations. For example: if we were working with 3 8th notes in the time of 5, each of the 3 8th notes would be equivalent to 1 and 2/3rds the length of the old 8th note value.